diff --git a/.buildinfo b/.buildinfo
new file mode 100644
index 00000000000..178bcbce24a
--- /dev/null
+++ b/.buildinfo
@@ -0,0 +1,4 @@
+# Sphinx build info version 1
+# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
+config: 7fa7496cedd22a33b10cd91d84b7920f
+tags: 645f666f9bcd5a90fca523b33c5a78b7
diff --git a/.circleci/config.yml b/.circleci/config.yml
index 9f803ece4ac..075a613be0d 100644
--- a/.circleci/config.yml
+++ b/.circleci/config.yml
@@ -6,7 +6,7 @@ orbs:
jobs:
build_doc:
docker:
- - image: cimg/python:3.12
+ - image: cimg/python:3.10
steps:
- checkout
- run:
diff --git a/.github/FUNDING.yml b/.github/FUNDING.yml
index 0d943696cce..24f09262998 100644
--- a/.github/FUNDING.yml
+++ b/.github/FUNDING.yml
@@ -1,4 +1,4 @@
# These are supported funding model platforms
github: AtsushiSakai
patreon: myenigma
-custom: https://www.paypal.com/paypalme/myenigmapay/
+custom: https://www.paypal.me/myenigmapay/
diff --git a/.github/dependabot.yml b/.github/dependabot.yml
index 6ffedf6f3b7..07f1bc80e06 100644
--- a/.github/dependabot.yml
+++ b/.github/dependabot.yml
@@ -6,8 +6,3 @@ updates:
interval: weekly
time: "20:00"
open-pull-requests-limit: 10
-
-- package-ecosystem: github-actions
- directory: "/"
- schedule:
- interval: weekly
diff --git a/.github/pull_request_template.md b/.github/pull_request_template.md
index b6ac52efa24..c5410631563 100644
--- a/.github/pull_request_template.md
+++ b/.github/pull_request_template.md
@@ -1,7 +1,7 @@
<!--
Thanks for contributing a pull request!
Please check this document before submitting:
-- [How to contribute](https://atsushisakai.github.io/PythonRobotics/how_to_contribute.html#adding-a-new-algorithm-example)
+- [How to contribute](https://pythonrobotics.readthedocs.io/en/latest/how_to_contribute.html#adding-a-new-algorithm-example)
Note that this is my hobby project; I appreciate your
patience during the review process.
@@ -19,6 +19,6 @@ Again, thanks for contributing!
<!--Any additional information you think is important.-->
#### CheckList
-- [ ] Did you add an unittest for your new example or defect fix?
-- [ ] Did you add documents for your new example?
-- [ ] All CIs are green? (You can check it after submitting)
+-[] Did you add an unittest for your new example or defect fix?
+-[] Did you add documents for your new example?
+-[] All CIs are green? (You can check it after submitting)
diff --git a/.github/workflows/Linux_CI.yml b/.github/workflows/Linux_CI.yml
index 7b3dc14751a..73f8aa5c0d0 100644
--- a/.github/workflows/Linux_CI.yml
+++ b/.github/workflows/Linux_CI.yml
@@ -12,16 +12,16 @@ jobs:
runs-on: ubuntu-latest
strategy:
matrix:
- python-version: [ '3.12' ]
+ python-version: ['3.10']
name: Python ${{ matrix.python-version }} CI
steps:
- - uses: actions/checkout@v4
+ - uses: actions/checkout@v2
- run: git fetch --prune --unshallow
- name: Setup python
- uses: actions/setup-python@v5
+ uses: actions/setup-python@v2
with:
python-version: ${{ matrix.python-version }}
- name: Install dependencies
diff --git a/.github/workflows/MacOS_CI.yml b/.github/workflows/MacOS_CI.yml
index 5ea15ac72e3..5c796120a51 100644
--- a/.github/workflows/MacOS_CI.yml
+++ b/.github/workflows/MacOS_CI.yml
@@ -16,17 +16,17 @@ jobs:
runs-on: macos-latest
strategy:
matrix:
- python-version: [ '3.12' ]
+ python-version: [ '3.10' ]
name: Python ${{ matrix.python-version }} CI
steps:
- - uses: actions/checkout@v4
+ - uses: actions/checkout@v2
- run: git fetch --prune --unshallow
- name: Update bash
run: brew install bash
- name: Setup python
- uses: actions/setup-python@v5
+ uses: actions/setup-python@v2
with:
python-version: ${{ matrix.python-version }}
@@ -36,4 +36,4 @@ jobs:
python -m pip install --upgrade pip
pip install -r requirements/requirements.txt
- name: do all unit tests
- run: bash runtests.sh
+ run: bash runtests.sh
\ No newline at end of file
diff --git a/.github/workflows/Windows_CI.yml b/.github/workflows/Windows_CI.yml
deleted file mode 100644
index b9c8dea649c..00000000000
--- a/.github/workflows/Windows_CI.yml
+++ /dev/null
@@ -1,36 +0,0 @@
-# This is a basic workflow to help you get started with Actions
-
-name: Windows_CI
-
-# Controls when the action will run. Triggers the workflow on push or pull request
-# events but only for the master branch
-on:
- push:
- branches:
- - master
- pull_request:
-
-
-jobs:
- build:
- runs-on: windows-latest
- strategy:
- matrix:
- python-version: [ '3.12' ]
- name: Python ${{ matrix.python-version }} CI
- steps:
- - uses: actions/checkout@v4
- - run: git fetch --prune --unshallow
-
- - name: Setup python
- uses: actions/setup-python@v5
- with:
- python-version: ${{ matrix.python-version }}
-
- - name: Install dependencies
- run: |
- python --version
- python -m pip install --upgrade pip
- pip install -r requirements/requirements.txt
- - name: do all unit tests
- run: bash runtests.sh
diff --git a/.github/workflows/circle_artifacts.yml b/.github/workflows/circle_artifacts.yml
new file mode 100644
index 00000000000..56ac78ed152
--- /dev/null
+++ b/.github/workflows/circle_artifacts.yml
@@ -0,0 +1,13 @@
+on: [status]
+jobs:
+ circleci_artifacts_redirector_job:
+ runs-on: ubuntu-20.04
+ name: Run CircleCI artifacts redirector
+ steps:
+ - name: GitHub Action step
+ uses: larsoner/circleci-artifacts-redirector-action@master
+ with:
+ repo-token: ${{ secrets.GITHUB_TOKEN }}
+ artifact-path: 0/html-scipyorg/index.html
+ circleci-jobs: build_docs
+ job-title: build_doc artifact
\ No newline at end of file
diff --git a/.github/workflows/circleci-artifacts-redirector.yml b/.github/workflows/circleci-artifacts-redirector.yml
index 78eb479aa16..d988d2c38ef 100644
--- a/.github/workflows/circleci-artifacts-redirector.yml
+++ b/.github/workflows/circleci-artifacts-redirector.yml
@@ -3,12 +3,11 @@ on: [status]
jobs:
circleci_artifacts_redirector_job:
runs-on: ubuntu-latest
- name: Run CircleCI artifacts redirector!!
+ name: Run CircleCI artifacts redirector
steps:
- name: run-circleci-artifacts-redirector
- uses: larsoner/circleci-artifacts-redirector-action@v1.0.0
+ uses: larsoner/circleci-artifacts-redirector-action@0.3.1
with:
repo-token: ${{ secrets.GITHUB_TOKEN }}
- api-token: ${{ secrets.CIRCLECI_TOKEN }}
artifact-path: 0/html/index.html
circleci-jobs: build_doc
diff --git a/.github/workflows/codeql.yml b/.github/workflows/codeql.yml
index 878a4a44359..148260a835b 100644
--- a/.github/workflows/codeql.yml
+++ b/.github/workflows/codeql.yml
@@ -16,7 +16,7 @@ jobs:
steps:
- name: Checkout repository
- uses: actions/checkout@v4
+ uses: actions/checkout@v2
with:
# We must fetch at least the immediate parents so that if this is
# a pull request then we can checkout the head.
@@ -24,7 +24,7 @@ jobs:
# Initializes the CodeQL tools for scanning.
- name: Initialize CodeQL
- uses: github/codeql-action/init@v3
+ uses: github/codeql-action/init@v1
with:
config-file: ./.github/codeql/codeql-config.yml
# Override language selection by uncommenting this and choosing your languages
@@ -34,7 +34,7 @@ jobs:
# Autobuild attempts to build any compiled languages (C/C++, C#, or Java).
# If this step fails, then you should remove it and run the build manually (see below)
- name: Autobuild
- uses: github/codeql-action/autobuild@v3
+ uses: github/codeql-action/autobuild@v1
# ℹ️ Command-line programs to run using the OS shell.
# 📚 https://git.io/JvXDl
@@ -48,4 +48,4 @@ jobs:
# make release
- name: Perform CodeQL Analysis
- uses: github/codeql-action/analyze@v3
+ uses: github/codeql-action/analyze@v1
diff --git a/.github/workflows/gh-pages.yml b/.github/workflows/gh-pages.yml
index e08c6106c08..e51197cb37c 100644
--- a/.github/workflows/gh-pages.yml
+++ b/.github/workflows/gh-pages.yml
@@ -1,4 +1,4 @@
-name: GitHub Pages site update
+name: Pages
on:
push:
branches:
@@ -6,15 +6,9 @@ on:
jobs:
build:
runs-on: ubuntu-latest
- environment:
- name: github-pages
- url: ${{ steps.deployment.outputs.page_url }}
- permissions:
- id-token: write
- pages: write
steps:
- name: Setup python
- uses: actions/setup-python@v5
+ uses: actions/setup-python@v2
- name: Checkout
uses: actions/checkout@master
with:
@@ -24,7 +18,12 @@ jobs:
python --version
python -m pip install --upgrade pip
python -m pip install -r requirements/requirements.txt
- - name: Build and Deploy
- uses: sphinx-notes/pages@v3
+ - name: Build and Commit
+ uses: sphinx-notes/pages@v2
with:
- requirements_path: ./docs/doc_requirements.txt
+ requirements_path: ./docs/doc_requirements.txt
+ - name: Push changes
+ uses: ad-m/github-push-action@master
+ with:
+ github_token: ${{ secrets.GITHUB_TOKEN }}
+ branch: gh-pages
\ No newline at end of file
diff --git a/.lgtm.yml b/.lgtm.yml
new file mode 100644
index 00000000000..b06edf35106
--- /dev/null
+++ b/.lgtm.yml
@@ -0,0 +1,4 @@
+extraction:
+ python:
+ python_setup:
+ version: 3
diff --git a/AerialNavigation/__init__.py b/.nojekyll
similarity index 100%
rename from AerialNavigation/__init__.py
rename to .nojekyll
diff --git a/AerialNavigation/drone_3d_trajectory_following/Quadrotor.py b/AerialNavigation/drone_3d_trajectory_following/Quadrotor.py
deleted file mode 100644
index c379e5eda0e..00000000000
--- a/AerialNavigation/drone_3d_trajectory_following/Quadrotor.py
+++ /dev/null
@@ -1,87 +0,0 @@
-"""
-Class for plotting a quadrotor
-
-Author: Daniel Ingram (daniel-s-ingram)
-"""
-
-from math import cos, sin
-import numpy as np
-import matplotlib.pyplot as plt
-
-class Quadrotor():
- def __init__(self, x=0, y=0, z=0, roll=0, pitch=0, yaw=0, size=0.25, show_animation=True):
- self.p1 = np.array([size / 2, 0, 0, 1]).T
- self.p2 = np.array([-size / 2, 0, 0, 1]).T
- self.p3 = np.array([0, size / 2, 0, 1]).T
- self.p4 = np.array([0, -size / 2, 0, 1]).T
-
- self.x_data = []
- self.y_data = []
- self.z_data = []
- self.show_animation = show_animation
-
- if self.show_animation:
- plt.ion()
- fig = plt.figure()
- # for stopping simulation with the esc key.
- fig.canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
-
- self.ax = fig.add_subplot(111, projection='3d')
-
- self.update_pose(x, y, z, roll, pitch, yaw)
-
- def update_pose(self, x, y, z, roll, pitch, yaw):
- self.x = x
- self.y = y
- self.z = z
- self.roll = roll
- self.pitch = pitch
- self.yaw = yaw
- self.x_data.append(x)
- self.y_data.append(y)
- self.z_data.append(z)
-
- if self.show_animation:
- self.plot()
-
- def transformation_matrix(self):
- x = self.x
- y = self.y
- z = self.z
- roll = self.roll
- pitch = self.pitch
- yaw = self.yaw
- return np.array(
- [[cos(yaw) * cos(pitch), -sin(yaw) * cos(roll) + cos(yaw) * sin(pitch) * sin(roll), sin(yaw) * sin(roll) + cos(yaw) * sin(pitch) * cos(roll), x],
- [sin(yaw) * cos(pitch), cos(yaw) * cos(roll) + sin(yaw) * sin(pitch)
- * sin(roll), -cos(yaw) * sin(roll) + sin(yaw) * sin(pitch) * cos(roll), y],
- [-sin(pitch), cos(pitch) * sin(roll), cos(pitch) * cos(roll), z]
- ])
-
- def plot(self): # pragma: no cover
- T = self.transformation_matrix()
-
- p1_t = np.matmul(T, self.p1)
- p2_t = np.matmul(T, self.p2)
- p3_t = np.matmul(T, self.p3)
- p4_t = np.matmul(T, self.p4)
-
- plt.cla()
-
- self.ax.plot([p1_t[0], p2_t[0], p3_t[0], p4_t[0]],
- [p1_t[1], p2_t[1], p3_t[1], p4_t[1]],
- [p1_t[2], p2_t[2], p3_t[2], p4_t[2]], 'k.')
-
- self.ax.plot([p1_t[0], p2_t[0]], [p1_t[1], p2_t[1]],
- [p1_t[2], p2_t[2]], 'r-')
- self.ax.plot([p3_t[0], p4_t[0]], [p3_t[1], p4_t[1]],
- [p3_t[2], p4_t[2]], 'r-')
-
- self.ax.plot(self.x_data, self.y_data, self.z_data, 'b:')
-
- plt.xlim(-5, 5)
- plt.ylim(-5, 5)
- self.ax.set_zlim(0, 10)
-
- plt.pause(0.001)
diff --git a/AerialNavigation/drone_3d_trajectory_following/TrajectoryGenerator.py b/AerialNavigation/drone_3d_trajectory_following/TrajectoryGenerator.py
deleted file mode 100644
index 0b99af885c4..00000000000
--- a/AerialNavigation/drone_3d_trajectory_following/TrajectoryGenerator.py
+++ /dev/null
@@ -1,76 +0,0 @@
-"""
-Generates a quintic polynomial trajectory.
-
-Author: Daniel Ingram (daniel-s-ingram)
-"""
-
-import numpy as np
-
-class TrajectoryGenerator():
- def __init__(self, start_pos, des_pos, T, start_vel=[0,0,0], des_vel=[0,0,0], start_acc=[0,0,0], des_acc=[0,0,0]):
- self.start_x = start_pos[0]
- self.start_y = start_pos[1]
- self.start_z = start_pos[2]
-
- self.des_x = des_pos[0]
- self.des_y = des_pos[1]
- self.des_z = des_pos[2]
-
- self.start_x_vel = start_vel[0]
- self.start_y_vel = start_vel[1]
- self.start_z_vel = start_vel[2]
-
- self.des_x_vel = des_vel[0]
- self.des_y_vel = des_vel[1]
- self.des_z_vel = des_vel[2]
-
- self.start_x_acc = start_acc[0]
- self.start_y_acc = start_acc[1]
- self.start_z_acc = start_acc[2]
-
- self.des_x_acc = des_acc[0]
- self.des_y_acc = des_acc[1]
- self.des_z_acc = des_acc[2]
-
- self.T = T
-
- def solve(self):
- A = np.array(
- [[0, 0, 0, 0, 0, 1],
- [self.T**5, self.T**4, self.T**3, self.T**2, self.T, 1],
- [0, 0, 0, 0, 1, 0],
- [5*self.T**4, 4*self.T**3, 3*self.T**2, 2*self.T, 1, 0],
- [0, 0, 0, 2, 0, 0],
- [20*self.T**3, 12*self.T**2, 6*self.T, 2, 0, 0]
- ])
-
- b_x = np.array(
- [[self.start_x],
- [self.des_x],
- [self.start_x_vel],
- [self.des_x_vel],
- [self.start_x_acc],
- [self.des_x_acc]
- ])
-
- b_y = np.array(
- [[self.start_y],
- [self.des_y],
- [self.start_y_vel],
- [self.des_y_vel],
- [self.start_y_acc],
- [self.des_y_acc]
- ])
-
- b_z = np.array(
- [[self.start_z],
- [self.des_z],
- [self.start_z_vel],
- [self.des_z_vel],
- [self.start_z_acc],
- [self.des_z_acc]
- ])
-
- self.x_c = np.linalg.solve(A, b_x)
- self.y_c = np.linalg.solve(A, b_y)
- self.z_c = np.linalg.solve(A, b_z)
\ No newline at end of file
diff --git a/AerialNavigation/drone_3d_trajectory_following/__init__.py b/AerialNavigation/drone_3d_trajectory_following/__init__.py
deleted file mode 100644
index 2194d4c3033..00000000000
--- a/AerialNavigation/drone_3d_trajectory_following/__init__.py
+++ /dev/null
@@ -1,3 +0,0 @@
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent))
diff --git a/AerialNavigation/drone_3d_trajectory_following/drone_3d_trajectory_following.py b/AerialNavigation/drone_3d_trajectory_following/drone_3d_trajectory_following.py
deleted file mode 100644
index 029e82be62d..00000000000
--- a/AerialNavigation/drone_3d_trajectory_following/drone_3d_trajectory_following.py
+++ /dev/null
@@ -1,213 +0,0 @@
-"""
-Simulate a quadrotor following a 3D trajectory
-
-Author: Daniel Ingram (daniel-s-ingram)
-"""
-
-from math import cos, sin
-import numpy as np
-from Quadrotor import Quadrotor
-from TrajectoryGenerator import TrajectoryGenerator
-
-show_animation = True
-
-# Simulation parameters
-g = 9.81
-m = 0.2
-Ixx = 1
-Iyy = 1
-Izz = 1
-T = 5
-
-# Proportional coefficients
-Kp_x = 1
-Kp_y = 1
-Kp_z = 1
-Kp_roll = 25
-Kp_pitch = 25
-Kp_yaw = 25
-
-# Derivative coefficients
-Kd_x = 10
-Kd_y = 10
-Kd_z = 1
-
-
-def quad_sim(x_c, y_c, z_c):
- """
- Calculates the necessary thrust and torques for the quadrotor to
- follow the trajectory described by the sets of coefficients
- x_c, y_c, and z_c.
- """
- x_pos = -5
- y_pos = -5
- z_pos = 5
- x_vel = 0
- y_vel = 0
- z_vel = 0
- x_acc = 0
- y_acc = 0
- z_acc = 0
- roll = 0
- pitch = 0
- yaw = 0
- roll_vel = 0
- pitch_vel = 0
- yaw_vel = 0
-
- des_yaw = 0
-
- dt = 0.1
- t = 0
-
- q = Quadrotor(x=x_pos, y=y_pos, z=z_pos, roll=roll,
- pitch=pitch, yaw=yaw, size=1, show_animation=show_animation)
-
- i = 0
- n_run = 8
- irun = 0
-
- while True:
- while t <= T:
- # des_x_pos = calculate_position(x_c[i], t)
- # des_y_pos = calculate_position(y_c[i], t)
- des_z_pos = calculate_position(z_c[i], t)
- # des_x_vel = calculate_velocity(x_c[i], t)
- # des_y_vel = calculate_velocity(y_c[i], t)
- des_z_vel = calculate_velocity(z_c[i], t)
- des_x_acc = calculate_acceleration(x_c[i], t)
- des_y_acc = calculate_acceleration(y_c[i], t)
- des_z_acc = calculate_acceleration(z_c[i], t)
-
- thrust = m * (g + des_z_acc + Kp_z * (des_z_pos -
- z_pos) + Kd_z * (des_z_vel - z_vel))
-
- roll_torque = Kp_roll * \
- (((des_x_acc * sin(des_yaw) - des_y_acc * cos(des_yaw)) / g) - roll)
- pitch_torque = Kp_pitch * \
- (((des_x_acc * cos(des_yaw) - des_y_acc * sin(des_yaw)) / g) - pitch)
- yaw_torque = Kp_yaw * (des_yaw - yaw)
-
- roll_vel += roll_torque * dt / Ixx
- pitch_vel += pitch_torque * dt / Iyy
- yaw_vel += yaw_torque * dt / Izz
-
- roll += roll_vel * dt
- pitch += pitch_vel * dt
- yaw += yaw_vel * dt
-
- R = rotation_matrix(roll, pitch, yaw)
- acc = (np.matmul(R, np.array(
- [0, 0, thrust.item()]).T) - np.array([0, 0, m * g]).T) / m
- x_acc = acc[0]
- y_acc = acc[1]
- z_acc = acc[2]
- x_vel += x_acc * dt
- y_vel += y_acc * dt
- z_vel += z_acc * dt
- x_pos += x_vel * dt
- y_pos += y_vel * dt
- z_pos += z_vel * dt
-
- q.update_pose(x_pos, y_pos, z_pos, roll, pitch, yaw)
-
- t += dt
-
- t = 0
- i = (i + 1) % 4
- irun += 1
- if irun >= n_run:
- break
-
- print("Done")
-
-
-def calculate_position(c, t):
- """
- Calculates a position given a set of quintic coefficients and a time.
-
- Args
- c: List of coefficients generated by a quintic polynomial
- trajectory generator.
- t: Time at which to calculate the position
-
- Returns
- Position
- """
- return c[0] * t**5 + c[1] * t**4 + c[2] * t**3 + c[3] * t**2 + c[4] * t + c[5]
-
-
-def calculate_velocity(c, t):
- """
- Calculates a velocity given a set of quintic coefficients and a time.
-
- Args
- c: List of coefficients generated by a quintic polynomial
- trajectory generator.
- t: Time at which to calculate the velocity
-
- Returns
- Velocity
- """
- return 5 * c[0] * t**4 + 4 * c[1] * t**3 + 3 * c[2] * t**2 + 2 * c[3] * t + c[4]
-
-
-def calculate_acceleration(c, t):
- """
- Calculates an acceleration given a set of quintic coefficients and a time.
-
- Args
- c: List of coefficients generated by a quintic polynomial
- trajectory generator.
- t: Time at which to calculate the acceleration
-
- Returns
- Acceleration
- """
- return 20 * c[0] * t**3 + 12 * c[1] * t**2 + 6 * c[2] * t + 2 * c[3]
-
-
-def rotation_matrix(roll_array, pitch_array, yaw):
- """
- Calculates the ZYX rotation matrix.
-
- Args
- Roll: Angular position about the x-axis in radians.
- Pitch: Angular position about the y-axis in radians.
- Yaw: Angular position about the z-axis in radians.
-
- Returns
- 3x3 rotation matrix as NumPy array
- """
- roll = roll_array[0]
- pitch = pitch_array[0]
- return np.array(
- [[cos(yaw) * cos(pitch), -sin(yaw) * cos(roll) + cos(yaw) * sin(pitch) * sin(roll), sin(yaw) * sin(roll) + cos(yaw) * sin(pitch) * cos(roll)],
- [sin(yaw) * cos(pitch), cos(yaw) * cos(roll) + sin(yaw) * sin(pitch) *
- sin(roll), -cos(yaw) * sin(roll) + sin(yaw) * sin(pitch) * cos(roll)],
- [-sin(pitch), cos(pitch) * sin(roll), cos(pitch) * cos(yaw)]
- ])
-
-
-def main():
- """
- Calculates the x, y, z coefficients for the four segments
- of the trajectory
- """
- x_coeffs = [[], [], [], []]
- y_coeffs = [[], [], [], []]
- z_coeffs = [[], [], [], []]
- waypoints = [[-5, -5, 5], [5, -5, 5], [5, 5, 5], [-5, 5, 5]]
-
- for i in range(4):
- traj = TrajectoryGenerator(waypoints[i], waypoints[(i + 1) % 4], T)
- traj.solve()
- x_coeffs[i] = traj.x_c
- y_coeffs[i] = traj.y_c
- z_coeffs[i] = traj.z_c
-
- quad_sim(x_coeffs, y_coeffs, z_coeffs)
-
-
-if __name__ == "__main__":
- main()
diff --git a/AerialNavigation/rocket_powered_landing/rocket_powered_landing.py b/AerialNavigation/rocket_powered_landing/rocket_powered_landing.py
deleted file mode 100644
index 239f3629c1b..00000000000
--- a/AerialNavigation/rocket_powered_landing/rocket_powered_landing.py
+++ /dev/null
@@ -1,673 +0,0 @@
-"""
-
-A rocket powered landing with successive convexification
-
-author: Sven Niederberger
- Atsushi Sakai
-
-Ref:
-- Python implementation of 'Successive Convexification for 6-DoF Mars Rocket Powered Landing with Free-Final-Time' paper
-by Michael Szmuk and Behcet Acıkmese.
-
-- EmbersArc/SuccessiveConvexificationFreeFinalTime: Implementation of "Successive Convexification for 6-DoF Mars Rocket Powered Landing with Free-Final-Time" https://github.com/EmbersArc/SuccessiveConvexificationFreeFinalTime
-
-"""
-import warnings
-from time import time
-import numpy as np
-from scipy.integrate import odeint
-import cvxpy
-import matplotlib.pyplot as plt
-
-# Trajectory points
-K = 50
-
-# Max solver iterations
-iterations = 30
-
-# Weight constants
-W_SIGMA = 1 # flight time
-W_DELTA = 1e-3 # difference in state/input
-W_DELTA_SIGMA = 1e-1 # difference in flight time
-W_NU = 1e5 # virtual control
-
-solver = 'ECOS'
-verbose_solver = False
-
-show_animation = True
-
-
-class Rocket_Model_6DoF:
- """
- A 6 degree of freedom rocket landing problem.
- """
-
- def __init__(self, rng):
- """
- A large r_scale for a small scale problem will
- ead to numerical problems as parameters become excessively small
- and (it seems) precision is lost in the dynamics.
- """
- self.n_x = 14
- self.n_u = 3
-
- # Mass
- self.m_wet = 3.0 # 30000 kg
- self.m_dry = 2.2 # 22000 kg
-
- # Flight time guess
- self.t_f_guess = 10.0 # 10 s
-
- # State constraints
- self.r_I_final = np.array((0., 0., 0.))
- self.v_I_final = np.array((-1e-1, 0., 0.))
- self.q_B_I_final = self.euler_to_quat((0, 0, 0))
- self.w_B_final = np.deg2rad(np.array((0., 0., 0.)))
-
- self.w_B_max = np.deg2rad(60)
-
- # Angles
- max_gimbal = 20
- max_angle = 90
- glidelslope_angle = 20
-
- self.tan_delta_max = np.tan(np.deg2rad(max_gimbal))
- self.cos_theta_max = np.cos(np.deg2rad(max_angle))
- self.tan_gamma_gs = np.tan(np.deg2rad(glidelslope_angle))
-
- # Thrust limits
- self.T_max = 5.0
- self.T_min = 0.3
-
- # Angular moment of inertia
- self.J_B = 1e-2 * np.diag([1., 1., 1.])
-
- # Gravity
- self.g_I = np.array((-1, 0., 0.))
-
- # Fuel consumption
- self.alpha_m = 0.01
-
- # Vector from thrust point to CoM
- self.r_T_B = np.array([-1e-2, 0., 0.])
-
- self.set_random_initial_state(rng)
-
- self.x_init = np.concatenate(
- ((self.m_wet,), self.r_I_init, self.v_I_init, self.q_B_I_init, self.w_B_init))
- self.x_final = np.concatenate(
- ((self.m_dry,), self.r_I_final, self.v_I_final, self.q_B_I_final, self.w_B_final))
-
- self.r_scale = np.linalg.norm(self.r_I_init)
- self.m_scale = self.m_wet
-
- def set_random_initial_state(self, rng):
- if rng is None:
- rng = np.random.default_rng()
-
- self.r_I_init = np.array((0., 0., 0.))
- self.r_I_init[0] = rng.uniform(3, 4)
- self.r_I_init[1:3] = rng.uniform(-2, 2, size=2)
-
- self.v_I_init = np.array((0., 0., 0.))
- self.v_I_init[0] = rng.uniform(-1, -0.5)
- self.v_I_init[1:3] = rng.uniform(-0.5, -0.2,
- size=2) * self.r_I_init[1:3]
-
- self.q_B_I_init = self.euler_to_quat((0,
- rng.uniform(-30, 30),
- rng.uniform(-30, 30)))
- self.w_B_init = np.deg2rad((0,
- rng.uniform(-20, 20),
- rng.uniform(-20, 20)))
-
- def f_func(self, x, u):
- m, _, _, _, vx, vy, vz, q0, q1, q2, q3, wx, wy, wz = x[0], x[1], x[
- 2], x[3], x[4], x[5], x[6], x[7], x[8], x[9], x[10], x[11], x[12], x[13]
- ux, uy, uz = u[0], u[1], u[2]
-
- return np.array([
- [-0.01 * np.sqrt(ux**2 + uy**2 + uz**2)],
- [vx],
- [vy],
- [vz],
- [(-1.0 * m - ux * (2 * q2**2 + 2 * q3**2 - 1) - 2 * uy
- * (q0 * q3 - q1 * q2) + 2 * uz * (q0 * q2 + q1 * q3)) / m],
- [(2 * ux * (q0 * q3 + q1 * q2) - uy * (2 * q1**2
- + 2 * q3**2 - 1) - 2 * uz * (q0 * q1 - q2 * q3)) / m],
- [(-2 * ux * (q0 * q2 - q1 * q3) + 2 * uy
- * (q0 * q1 + q2 * q3) - uz * (2 * q1**2 + 2 * q2**2 - 1)) / m],
- [-0.5 * q1 * wx - 0.5 * q2 * wy - 0.5 * q3 * wz],
- [0.5 * q0 * wx + 0.5 * q2 * wz - 0.5 * q3 * wy],
- [0.5 * q0 * wy - 0.5 * q1 * wz + 0.5 * q3 * wx],
- [0.5 * q0 * wz + 0.5 * q1 * wy - 0.5 * q2 * wx],
- [0],
- [1.0 * uz],
- [-1.0 * uy]
- ])
-
- def A_func(self, x, u):
- m, _, _, _, _, _, _, q0, q1, q2, q3, wx, wy, wz = x[0], x[1], x[
- 2], x[3], x[4], x[5], x[6], x[7], x[8], x[9], x[10], x[11], x[12], x[13]
- ux, uy, uz = u[0], u[1], u[2]
-
- return np.array([
- [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
- [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0],
- [0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0],
- [0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0],
- [(ux * (2 * q2**2 + 2 * q3**2 - 1) + 2 * uy * (q0 * q3 - q1 * q2) - 2 * uz * (q0 * q2 + q1 * q3)) / m**2, 0, 0, 0, 0, 0, 0, 2 * (q2 * uz
- - q3 * uy) / m, 2 * (q2 * uy + q3 * uz) / m, 2 * (q0 * uz + q1 * uy - 2 * q2 * ux) / m, 2 * (-q0 * uy + q1 * uz - 2 * q3 * ux) / m, 0, 0, 0],
- [(-2 * ux * (q0 * q3 + q1 * q2) + uy * (2 * q1**2 + 2 * q3**2 - 1) + 2 * uz * (q0 * q1 - q2 * q3)) / m**2, 0, 0, 0, 0, 0, 0, 2 * (-q1 * uz
- + q3 * ux) / m, 2 * (-q0 * uz - 2 * q1 * uy + q2 * ux) / m, 2 * (q1 * ux + q3 * uz) / m, 2 * (q0 * ux + q2 * uz - 2 * q3 * uy) / m, 0, 0, 0],
- [(2 * ux * (q0 * q2 - q1 * q3) - 2 * uy * (q0 * q1 + q2 * q3) + uz * (2 * q1**2 + 2 * q2**2 - 1)) / m**2, 0, 0, 0, 0, 0, 0, 2 * (q1 * uy
- - q2 * ux) / m, 2 * (q0 * uy - 2 * q1 * uz + q3 * ux) / m, 2 * (-q0 * ux - 2 * q2 * uz + q3 * uy) / m, 2 * (q1 * ux + q2 * uy) / m, 0, 0, 0],
- [0, 0, 0, 0, 0, 0, 0, 0, -0.5 * wx, -0.5 * wy,
- - 0.5 * wz, -0.5 * q1, -0.5 * q2, -0.5 * q3],
- [0, 0, 0, 0, 0, 0, 0, 0.5 * wx, 0, 0.5 * wz,
- - 0.5 * wy, 0.5 * q0, -0.5 * q3, 0.5 * q2],
- [0, 0, 0, 0, 0, 0, 0, 0.5 * wy, -0.5 * wz, 0,
- 0.5 * wx, 0.5 * q3, 0.5 * q0, -0.5 * q1],
- [0, 0, 0, 0, 0, 0, 0, 0.5 * wz, 0.5 * wy,
- - 0.5 * wx, 0, -0.5 * q2, 0.5 * q1, 0.5 * q0],
- [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
- [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0],
- [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]])
-
- def B_func(self, x, u):
- m, _, _, _, _, _, _, q0, q1, q2, q3, _, _, _ = x[0], x[1], x[
- 2], x[3], x[4], x[5], x[6], x[7], x[8], x[9], x[10], x[11], x[12], x[13]
- ux, uy, uz = u[0], u[1], u[2]
-
- return np.array([
- [-0.01 * ux / np.sqrt(ux**2 + uy**2 + uz**2),
- -0.01 * uy / np.sqrt(ux ** 2 + uy**2 + uz**2),
- -0.01 * uz / np.sqrt(ux**2 + uy**2 + uz**2)],
- [0, 0, 0],
- [0, 0, 0],
- [0, 0, 0],
- [(-2 * q2**2 - 2 * q3**2 + 1) / m, 2
- * (-q0 * q3 + q1 * q2) / m, 2 * (q0 * q2 + q1 * q3) / m],
- [2 * (q0 * q3 + q1 * q2) / m, (-2 * q1**2 - 2
- * q3**2 + 1) / m, 2 * (-q0 * q1 + q2 * q3) / m],
- [2 * (-q0 * q2 + q1 * q3) / m, 2 * (q0 * q1 + q2 * q3)
- / m, (-2 * q1**2 - 2 * q2**2 + 1) / m],
- [0, 0, 0],
- [0, 0, 0],
- [0, 0, 0],
- [0, 0, 0],
- [0, 0, 0],
- [0, 0, 1.0],
- [0, -1.0, 0]
- ])
-
- def euler_to_quat(self, a):
- a = np.deg2rad(a)
-
- cy = np.cos(a[1] * 0.5)
- sy = np.sin(a[1] * 0.5)
- cr = np.cos(a[0] * 0.5)
- sr = np.sin(a[0] * 0.5)
- cp = np.cos(a[2] * 0.5)
- sp = np.sin(a[2] * 0.5)
-
- q = np.zeros(4)
-
- q[0] = cy * cr * cp + sy * sr * sp
- q[1] = cy * sr * cp - sy * cr * sp
- q[3] = cy * cr * sp + sy * sr * cp
- q[2] = sy * cr * cp - cy * sr * sp
-
- return q
-
- def skew(self, v):
- return np.array([
- [0, -v[2], v[1]],
- [v[2], 0, -v[0]],
- [-v[1], v[0], 0]
- ])
-
- def dir_cosine(self, q):
- return np.array([
- [1 - 2 * (q[2] ** 2 + q[3] ** 2), 2 * (q[1] * q[2]
- + q[0] * q[3]), 2 * (q[1] * q[3] - q[0] * q[2])],
- [2 * (q[1] * q[2] - q[0] * q[3]), 1 - 2
- * (q[1] ** 2 + q[3] ** 2), 2 * (q[2] * q[3] + q[0] * q[1])],
- [2 * (q[1] * q[3] + q[0] * q[2]), 2 * (q[2] * q[3]
- - q[0] * q[1]), 1 - 2 * (q[1] ** 2 + q[2] ** 2)]
- ])
-
- def omega(self, w):
- return np.array([
- [0, -w[0], -w[1], -w[2]],
- [w[0], 0, w[2], -w[1]],
- [w[1], -w[2], 0, w[0]],
- [w[2], w[1], -w[0], 0],
- ])
-
- def initialize_trajectory(self, X, U):
- """
- Initialize the trajectory with linear approximation.
- """
- K = X.shape[1]
-
- for k in range(K):
- alpha1 = (K - k) / K
- alpha2 = k / K
-
- m_k = (alpha1 * self.x_init[0] + alpha2 * self.x_final[0],)
- r_I_k = alpha1 * self.x_init[1:4] + alpha2 * self.x_final[1:4]
- v_I_k = alpha1 * self.x_init[4:7] + alpha2 * self.x_final[4:7]
- q_B_I_k = np.array([1, 0, 0, 0])
- w_B_k = alpha1 * self.x_init[11:14] + alpha2 * self.x_final[11:14]
-
- X[:, k] = np.concatenate((m_k, r_I_k, v_I_k, q_B_I_k, w_B_k))
- U[:, k] = m_k * -self.g_I
-
- return X, U
-
- def get_constraints(self, X_v, U_v, X_last_p, U_last_p):
- """
- Get model specific constraints.
-
- :param X_v: cvx variable for current states
- :param U_v: cvx variable for current inputs
- :param X_last_p: cvx parameter for last states
- :param U_last_p: cvx parameter for last inputs
- :return: A list of cvx constraints
- """
- # Boundary conditions:
- constraints = [
- X_v[0, 0] == self.x_init[0],
- X_v[1:4, 0] == self.x_init[1:4],
- X_v[4:7, 0] == self.x_init[4:7],
- # X_v[7:11, 0] == self.x_init[7:11], # initial orientation is free
- X_v[11:14, 0] == self.x_init[11:14],
-
- # X_[0, -1] final mass is free
- X_v[1:, -1] == self.x_final[1:],
- U_v[1:3, -1] == 0,
- ]
-
- constraints += [
- # State constraints:
- X_v[0, :] >= self.m_dry, # minimum mass
- cvxpy.norm(X_v[2: 4, :], axis=0) <= X_v[1, :] / \
- self.tan_gamma_gs, # glideslope
- cvxpy.norm(X_v[9:11, :], axis=0) <= np.sqrt(
- (1 - self.cos_theta_max) / 2), # maximum angle
- # maximum angular velocity
- cvxpy.norm(X_v[11: 14, :], axis=0) <= self.w_B_max,
-
- # Control constraints:
- cvxpy.norm(U_v[1:3, :], axis=0) <= self.tan_delta_max * \
- U_v[0, :], # gimbal angle constraint
- cvxpy.norm(U_v, axis=0) <= self.T_max, # upper thrust constraint
- ]
-
- # linearized lower thrust constraint
- rhs = [U_last_p[:, k] / cvxpy.norm(U_last_p[:, k]) @ U_v[:, k]
- for k in range(X_v.shape[1])]
- constraints += [
- self.T_min <= cvxpy.vstack(rhs)
- ]
-
- return constraints
-
-
-class Integrator:
- def __init__(self, m, K):
- self.K = K
- self.m = m
- self.n_x = m.n_x
- self.n_u = m.n_u
-
- self.A_bar = np.zeros([m.n_x * m.n_x, K - 1])
- self.B_bar = np.zeros([m.n_x * m.n_u, K - 1])
- self.C_bar = np.zeros([m.n_x * m.n_u, K - 1])
- self.S_bar = np.zeros([m.n_x, K - 1])
- self.z_bar = np.zeros([m.n_x, K - 1])
-
- # vector indices for flat matrices
- x_end = m.n_x
- A_bar_end = m.n_x * (1 + m.n_x)
- B_bar_end = m.n_x * (1 + m.n_x + m.n_u)
- C_bar_end = m.n_x * (1 + m.n_x + m.n_u + m.n_u)
- S_bar_end = m.n_x * (1 + m.n_x + m.n_u + m.n_u + 1)
- z_bar_end = m.n_x * (1 + m.n_x + m.n_u + m.n_u + 2)
- self.x_ind = slice(0, x_end)
- self.A_bar_ind = slice(x_end, A_bar_end)
- self.B_bar_ind = slice(A_bar_end, B_bar_end)
- self.C_bar_ind = slice(B_bar_end, C_bar_end)
- self.S_bar_ind = slice(C_bar_end, S_bar_end)
- self.z_bar_ind = slice(S_bar_end, z_bar_end)
-
- self.f, self.A, self.B = m.f_func, m.A_func, m.B_func
-
- # integration initial condition
- self.V0 = np.zeros((m.n_x * (1 + m.n_x + m.n_u + m.n_u + 2),))
- self.V0[self.A_bar_ind] = np.eye(m.n_x).reshape(-1)
-
- self.dt = 1. / (K - 1)
-
- def calculate_discretization(self, X, U, sigma):
- """
- Calculate discretization for given states, inputs and total time.
-
- :param X: Matrix of states for all time points
- :param U: Matrix of inputs for all time points
- :param sigma: Total time
- :return: The discretization matrices
- """
- for k in range(self.K - 1):
- self.V0[self.x_ind] = X[:, k]
- V = np.array(odeint(self._ode_dVdt, self.V0, (0, self.dt),
- args=(U[:, k], U[:, k + 1], sigma))[1, :])
-
- # using \Phi_A(\tau_{k+1},\xi) = \Phi_A(\tau_{k+1},\tau_k)\Phi_A(\xi,\tau_k)^{-1}
- # flatten matrices in column-major (Fortran) order for CVXPY
- Phi = V[self.A_bar_ind].reshape((self.n_x, self.n_x))
- self.A_bar[:, k] = Phi.flatten(order='F')
- self.B_bar[:, k] = np.matmul(Phi, V[self.B_bar_ind].reshape(
- (self.n_x, self.n_u))).flatten(order='F')
- self.C_bar[:, k] = np.matmul(Phi, V[self.C_bar_ind].reshape(
- (self.n_x, self.n_u))).flatten(order='F')
- self.S_bar[:, k] = np.matmul(Phi, V[self.S_bar_ind])
- self.z_bar[:, k] = np.matmul(Phi, V[self.z_bar_ind])
-
- return self.A_bar, self.B_bar, self.C_bar, self.S_bar, self.z_bar
-
- def _ode_dVdt(self, V, t, u_t0, u_t1, sigma):
- """
- ODE function to compute dVdt.
-
- :param V: Evaluation state V = [x, Phi_A, B_bar, C_bar, S_bar, z_bar]
- :param t: Evaluation time
- :param u_t0: Input at start of interval
- :param u_t1: Input at end of interval
- :param sigma: Total time
- :return: Derivative at current time and state dVdt
- """
- alpha = (self.dt - t) / self.dt
- beta = t / self.dt
- x = V[self.x_ind]
- u = u_t0 + beta * (u_t1 - u_t0)
-
- # using \Phi_A(\tau_{k+1},\xi) = \Phi_A(\tau_{k+1},\tau_k)\Phi_A(\xi,\tau_k)^{-1}
- # and pre-multiplying with \Phi_A(\tau_{k+1},\tau_k) after integration
- Phi_A_xi = np.linalg.inv(
- V[self.A_bar_ind].reshape((self.n_x, self.n_x)))
-
- A_subs = sigma * self.A(x, u)
- B_subs = sigma * self.B(x, u)
- f_subs = self.f(x, u)
-
- dVdt = np.zeros_like(V)
- dVdt[self.x_ind] = sigma * f_subs.transpose()
- dVdt[self.A_bar_ind] = np.matmul(
- A_subs, V[self.A_bar_ind].reshape((self.n_x, self.n_x))).reshape(-1)
- dVdt[self.B_bar_ind] = np.matmul(Phi_A_xi, B_subs).reshape(-1) * alpha
- dVdt[self.C_bar_ind] = np.matmul(Phi_A_xi, B_subs).reshape(-1) * beta
- dVdt[self.S_bar_ind] = np.matmul(Phi_A_xi, f_subs).transpose()
- z_t = -np.matmul(A_subs, x) - np.matmul(B_subs, u)
- dVdt[self.z_bar_ind] = np.dot(Phi_A_xi, z_t.T).flatten()
-
- return dVdt
-
-
-class SCProblem:
- """
- Defines a standard Successive Convexification problem and
- adds the model specific constraints and objectives.
-
- :param m: The model object
- :param K: Number of discretization points
- """
-
- def __init__(self, m, K):
- # Variables:
- self.var = dict()
- self.var['X'] = cvxpy.Variable((m.n_x, K))
- self.var['U'] = cvxpy.Variable((m.n_u, K))
- self.var['sigma'] = cvxpy.Variable(nonneg=True)
- self.var['nu'] = cvxpy.Variable((m.n_x, K - 1))
- self.var['delta_norm'] = cvxpy.Variable(nonneg=True)
- self.var['sigma_norm'] = cvxpy.Variable(nonneg=True)
-
- # Parameters:
- self.par = dict()
- self.par['A_bar'] = cvxpy.Parameter((m.n_x * m.n_x, K - 1))
- self.par['B_bar'] = cvxpy.Parameter((m.n_x * m.n_u, K - 1))
- self.par['C_bar'] = cvxpy.Parameter((m.n_x * m.n_u, K - 1))
- self.par['S_bar'] = cvxpy.Parameter((m.n_x, K - 1))
- self.par['z_bar'] = cvxpy.Parameter((m.n_x, K - 1))
-
- self.par['X_last'] = cvxpy.Parameter((m.n_x, K))
- self.par['U_last'] = cvxpy.Parameter((m.n_u, K))
- self.par['sigma_last'] = cvxpy.Parameter(nonneg=True)
-
- self.par['weight_sigma'] = cvxpy.Parameter(nonneg=True)
- self.par['weight_delta'] = cvxpy.Parameter(nonneg=True)
- self.par['weight_delta_sigma'] = cvxpy.Parameter(nonneg=True)
- self.par['weight_nu'] = cvxpy.Parameter(nonneg=True)
-
- # Constraints:
- constraints = []
-
- # Model:
- constraints += m.get_constraints(
- self.var['X'], self.var['U'], self.par['X_last'], self.par['U_last'])
-
- # Dynamics:
- # x_t+1 = A_*x_t+B_*U_t+C_*U_T+1*S_*sigma+zbar+nu
- constraints += [
- self.var['X'][:, k + 1] ==
- cvxpy.reshape(self.par['A_bar'][:, k], (m.n_x, m.n_x)) @
- self.var['X'][:, k] +
- cvxpy.reshape(self.par['B_bar'][:, k], (m.n_x, m.n_u)) @
- self.var['U'][:, k] +
- cvxpy.reshape(self.par['C_bar'][:, k], (m.n_x, m.n_u)) @
- self.var['U'][:, k + 1] +
- self.par['S_bar'][:, k] * self.var['sigma'] +
- self.par['z_bar'][:, k] +
- self.var['nu'][:, k]
- for k in range(K - 1)
- ]
-
- # Trust regions:
- dx = cvxpy.sum(cvxpy.square(
- self.var['X'] - self.par['X_last']), axis=0)
- du = cvxpy.sum(cvxpy.square(
- self.var['U'] - self.par['U_last']), axis=0)
- ds = self.var['sigma'] - self.par['sigma_last']
- constraints += [cvxpy.norm(dx + du, 1) <= self.var['delta_norm']]
- constraints += [cvxpy.norm(ds, 'inf') <= self.var['sigma_norm']]
-
- # Flight time positive:
- constraints += [self.var['sigma'] >= 0.1]
-
- # Objective:
- sc_objective = cvxpy.Minimize(
- self.par['weight_sigma'] * self.var['sigma'] +
- self.par['weight_nu'] * cvxpy.norm(self.var['nu'], 'inf') +
- self.par['weight_delta'] * self.var['delta_norm'] +
- self.par['weight_delta_sigma'] * self.var['sigma_norm']
- )
-
- objective = sc_objective
-
- self.prob = cvxpy.Problem(objective, constraints)
-
- def set_parameters(self, **kwargs):
- """
- All parameters have to be filled before calling solve().
- Takes the following arguments as keywords:
-
- A_bar
- B_bar
- C_bar
- S_bar
- z_bar
- X_last
- U_last
- sigma_last
- E
- weight_sigma
- weight_nu
- radius_trust_region
- """
-
- for key in kwargs:
- if key in self.par:
- self.par[key].value = kwargs[key]
- else:
- print(f'Parameter \'{key}\' does not exist.')
-
- def get_variable(self, name):
- if name in self.var:
- return self.var[name].value
- else:
- print(f'Variable \'{name}\' does not exist.')
- return None
-
- def solve(self, **kwargs):
- error = False
- try:
- with warnings.catch_warnings(): # For User warning from solver
- warnings.simplefilter('ignore')
- self.prob.solve(verbose=verbose_solver,
- solver=solver)
- except cvxpy.SolverError:
- error = True
-
- stats = self.prob.solver_stats
-
- info = {
- 'setup_time': stats.setup_time,
- 'solver_time': stats.solve_time,
- 'iterations': stats.num_iters,
- 'solver_error': error
- }
-
- return info
-
-
-def axis3d_equal(X, Y, Z, ax):
-
- max_range = np.array([X.max() - X.min(), Y.max()
- - Y.min(), Z.max() - Z.min()]).max()
- Xb = 0.5 * max_range * np.mgrid[-1:2:2, -1:2:2,
- - 1:2:2][0].flatten() + 0.5 * (X.max() + X.min())
- Yb = 0.5 * max_range * np.mgrid[-1:2:2, -1:2:2,
- - 1:2:2][1].flatten() + 0.5 * (Y.max() + Y.min())
- Zb = 0.5 * max_range * np.mgrid[-1:2:2, -1:2:2,
- - 1:2:2][2].flatten() + 0.5 * (Z.max() + Z.min())
- # Comment or uncomment following both lines to test the fake bounding box:
- for xb, yb, zb in zip(Xb, Yb, Zb):
- ax.plot([xb], [yb], [zb], 'w')
-
-
-def plot_animation(X, U): # pragma: no cover
-
- fig = plt.figure()
- ax = fig.add_subplot(projection='3d')
- # for stopping simulation with the esc key.
- fig.canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
-
- for k in range(K):
- plt.cla()
- ax.plot(X[2, :], X[3, :], X[1, :]) # trajectory
- ax.scatter3D([0.0], [0.0], [0.0], c="r",
- marker="x") # target landing point
- axis3d_equal(X[2, :], X[3, :], X[1, :], ax)
-
- rx, ry, rz = X[1:4, k]
- # vx, vy, vz = X[4:7, k]
- qw, qx, qy, qz = X[7:11, k]
-
- CBI = np.array([
- [1 - 2 * (qy ** 2 + qz ** 2), 2 * (qx * qy + qw * qz),
- 2 * (qx * qz - qw * qy)],
- [2 * (qx * qy - qw * qz), 1 - 2
- * (qx ** 2 + qz ** 2), 2 * (qy * qz + qw * qx)],
- [2 * (qx * qz + qw * qy), 2 * (qy * qz - qw * qx),
- 1 - 2 * (qx ** 2 + qy ** 2)]
- ])
-
- Fx, Fy, Fz = np.dot(np.transpose(CBI), U[:, k])
- dx, dy, dz = np.dot(np.transpose(CBI), np.array([1., 0., 0.]))
-
- # attitude vector
- ax.quiver(ry, rz, rx, dy, dz, dx, length=0.5, linewidth=3.0,
- arrow_length_ratio=0.0, color='black')
-
- # thrust vector
- ax.quiver(ry, rz, rx, -Fy, -Fz, -Fx, length=0.1,
- arrow_length_ratio=0.0, color='red')
-
- ax.set_title("Rocket powered landing")
- plt.pause(0.5)
-
-
-def main(rng=None):
- print("start!!")
- m = Rocket_Model_6DoF(rng)
-
- # state and input list
- X = np.empty(shape=[m.n_x, K])
- U = np.empty(shape=[m.n_u, K])
-
- # INITIALIZATION
- sigma = m.t_f_guess
- X, U = m.initialize_trajectory(X, U)
-
- integrator = Integrator(m, K)
- problem = SCProblem(m, K)
-
- converged = False
- w_delta = W_DELTA
- for it in range(iterations):
- t0_it = time()
- print('-' * 18 + f' Iteration {str(it + 1).zfill(2)} ' + '-' * 18)
-
- A_bar, B_bar, C_bar, S_bar, z_bar = integrator.calculate_discretization(
- X, U, sigma)
-
- problem.set_parameters(A_bar=A_bar, B_bar=B_bar, C_bar=C_bar, S_bar=S_bar, z_bar=z_bar,
- X_last=X, U_last=U, sigma_last=sigma,
- weight_sigma=W_SIGMA, weight_nu=W_NU,
- weight_delta=w_delta, weight_delta_sigma=W_DELTA_SIGMA)
- problem.solve()
-
- X = problem.get_variable('X')
- U = problem.get_variable('U')
- sigma = problem.get_variable('sigma')
-
- delta_norm = problem.get_variable('delta_norm')
- sigma_norm = problem.get_variable('sigma_norm')
- nu_norm = np.linalg.norm(problem.get_variable('nu'), np.inf)
-
- print('delta_norm', delta_norm)
- print('sigma_norm', sigma_norm)
- print('nu_norm', nu_norm)
-
- if delta_norm < 1e-3 and sigma_norm < 1e-3 and nu_norm < 1e-7:
- converged = True
-
- w_delta *= 1.5
-
- print('Time for iteration', time() - t0_it, 's')
-
- if converged:
- print(f'Converged after {it + 1} iterations.')
- break
-
- if show_animation: # pragma: no cover
- plot_animation(X, U)
-
- print("done!!")
-
-
-if __name__ == '__main__':
- main()
diff --git a/ArmNavigation/__init__.py b/ArmNavigation/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/ArmNavigation/arm_obstacle_navigation/arm_obstacle_navigation.py b/ArmNavigation/arm_obstacle_navigation/arm_obstacle_navigation.py
deleted file mode 100644
index 9047c138514..00000000000
--- a/ArmNavigation/arm_obstacle_navigation/arm_obstacle_navigation.py
+++ /dev/null
@@ -1,268 +0,0 @@
-"""
-Obstacle navigation using A* on a toroidal grid
-
-Author: Daniel Ingram (daniel-s-ingram)
-"""
-from math import pi
-import numpy as np
-import matplotlib.pyplot as plt
-from matplotlib.colors import from_levels_and_colors
-
-plt.ion()
-
-# Simulation parameters
-M = 100
-obstacles = [[1.75, 0.75, 0.6], [0.55, 1.5, 0.5], [0, -1, 0.25]]
-
-
-def main():
- arm = NLinkArm([1, 1], [0, 0])
- start = (10, 50)
- goal = (58, 56)
- grid = get_occupancy_grid(arm, obstacles)
- plt.imshow(grid)
- plt.show()
- route = astar_torus(grid, start, goal)
- for node in route:
- theta1 = 2 * pi * node[0] / M - pi
- theta2 = 2 * pi * node[1] / M - pi
- arm.update_joints([theta1, theta2])
- arm.plot(obstacles=obstacles)
-
-
-def detect_collision(line_seg, circle):
- """
- Determines whether a line segment (arm link) is in contact
- with a circle (obstacle).
- Credit to: https://web.archive.org/web/20200130224918/http://doswa.com/2009/07/13/circle-segment-intersectioncollision.html
- Args:
- line_seg: List of coordinates of line segment endpoints e.g. [[1, 1], [2, 2]]
- circle: List of circle coordinates and radius e.g. [0, 0, 0.5] is a circle centered
- at the origin with radius 0.5
-
- Returns:
- True if the line segment is in contact with the circle
- False otherwise
- """
- a_vec = np.array([line_seg[0][0], line_seg[0][1]])
- b_vec = np.array([line_seg[1][0], line_seg[1][1]])
- c_vec = np.array([circle[0], circle[1]])
- radius = circle[2]
- line_vec = b_vec - a_vec
- line_mag = np.linalg.norm(line_vec)
- circle_vec = c_vec - a_vec
- proj = circle_vec.dot(line_vec / line_mag)
- if proj <= 0:
- closest_point = a_vec
- elif proj >= line_mag:
- closest_point = b_vec
- else:
- closest_point = a_vec + line_vec * proj / line_mag
- if np.linalg.norm(closest_point - c_vec) > radius:
- return False
-
- return True
-
-
-def get_occupancy_grid(arm, obstacles):
- """
- Discretizes joint space into M values from -pi to +pi
- and determines whether a given coordinate in joint space
- would result in a collision between a robot arm and obstacles
- in its environment.
-
- Args:
- arm: An instance of NLinkArm
- obstacles: A list of obstacles, with each obstacle defined as a list
- of xy coordinates and a radius.
-
- Returns:
- Occupancy grid in joint space
- """
- grid = [[0 for _ in range(M)] for _ in range(M)]
- theta_list = [2 * i * pi / M for i in range(-M // 2, M // 2 + 1)]
- for i in range(M):
- for j in range(M):
- arm.update_joints([theta_list[i], theta_list[j]])
- points = arm.points
- collision_detected = False
- for k in range(len(points) - 1):
- for obstacle in obstacles:
- line_seg = [points[k], points[k + 1]]
- collision_detected = detect_collision(line_seg, obstacle)
- if collision_detected:
- break
- if collision_detected:
- break
- grid[i][j] = int(collision_detected)
- return np.array(grid)
-
-
-def astar_torus(grid, start_node, goal_node):
- """
- Finds a path between an initial and goal joint configuration using
- the A* Algorithm on a tororiadal grid.
-
- Args:
- grid: An occupancy grid (ndarray)
- start_node: Initial joint configuration (tuple)
- goal_node: Goal joint configuration (tuple)
-
- Returns:
- Obstacle-free route in joint space from start_node to goal_node
- """
- colors = ['white', 'black', 'red', 'pink', 'yellow', 'green', 'orange']
- levels = [0, 1, 2, 3, 4, 5, 6, 7]
- cmap, norm = from_levels_and_colors(levels, colors)
-
- grid[start_node] = 4
- grid[goal_node] = 5
-
- parent_map = [[() for _ in range(M)] for _ in range(M)]
-
- heuristic_map = calc_heuristic_map(M, goal_node)
-
- explored_heuristic_map = np.full((M, M), np.inf)
- distance_map = np.full((M, M), np.inf)
- explored_heuristic_map[start_node] = heuristic_map[start_node]
- distance_map[start_node] = 0
- while True:
- grid[start_node] = 4
- grid[goal_node] = 5
-
- current_node = np.unravel_index(
- np.argmin(explored_heuristic_map, axis=None), explored_heuristic_map.shape)
- min_distance = np.min(explored_heuristic_map)
- if (current_node == goal_node) or np.isinf(min_distance):
- break
-
- grid[current_node] = 2
- explored_heuristic_map[current_node] = np.inf
-
- i, j = current_node[0], current_node[1]
-
- neighbors = find_neighbors(i, j)
-
- for neighbor in neighbors:
- if grid[neighbor] == 0 or grid[neighbor] == 5:
- distance_map[neighbor] = distance_map[current_node] + 1
- explored_heuristic_map[neighbor] = heuristic_map[neighbor]
- parent_map[neighbor[0]][neighbor[1]] = current_node
- grid[neighbor] = 3
-
- if np.isinf(explored_heuristic_map[goal_node]):
- route = []
- print("No route found.")
- else:
- route = [goal_node]
- while parent_map[route[0][0]][route[0][1]] != ():
- route.insert(0, parent_map[route[0][0]][route[0][1]])
-
- print(f"The route found covers {len(route)} grid cells.")
- for i in range(1, len(route)):
- grid[route[i]] = 6
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.imshow(grid, cmap=cmap, norm=norm, interpolation=None)
- plt.show()
- plt.pause(1e-2)
-
- return route
-
-
-def find_neighbors(i, j):
- neighbors = []
- if i - 1 >= 0:
- neighbors.append((i - 1, j))
- else:
- neighbors.append((M - 1, j))
-
- if i + 1 < M:
- neighbors.append((i + 1, j))
- else:
- neighbors.append((0, j))
-
- if j - 1 >= 0:
- neighbors.append((i, j - 1))
- else:
- neighbors.append((i, M - 1))
-
- if j + 1 < M:
- neighbors.append((i, j + 1))
- else:
- neighbors.append((i, 0))
-
- return neighbors
-
-
-def calc_heuristic_map(M, goal_node):
- X, Y = np.meshgrid([i for i in range(M)], [i for i in range(M)])
- heuristic_map = np.abs(X - goal_node[1]) + np.abs(Y - goal_node[0])
- for i in range(heuristic_map.shape[0]):
- for j in range(heuristic_map.shape[1]):
- heuristic_map[i, j] = min(heuristic_map[i, j],
- M - i - 1 + heuristic_map[M - 1, j],
- i + heuristic_map[0, j],
- M - j - 1 + heuristic_map[i, M - 1],
- j + heuristic_map[i, 0]
- )
-
- return heuristic_map
-
-
-class NLinkArm:
- """
- Class for controlling and plotting a planar arm with an arbitrary number of links.
- """
-
- def __init__(self, link_lengths, joint_angles):
- self.n_links = len(link_lengths)
- if self.n_links != len(joint_angles):
- raise ValueError()
-
- self.link_lengths = np.array(link_lengths)
- self.joint_angles = np.array(joint_angles)
- self.points = [[0, 0] for _ in range(self.n_links + 1)]
-
- self.lim = sum(link_lengths)
- self.update_points()
-
- def update_joints(self, joint_angles):
- self.joint_angles = joint_angles
- self.update_points()
-
- def update_points(self):
- for i in range(1, self.n_links + 1):
- self.points[i][0] = self.points[i - 1][0] + \
- self.link_lengths[i - 1] * \
- np.cos(np.sum(self.joint_angles[:i]))
- self.points[i][1] = self.points[i - 1][1] + \
- self.link_lengths[i - 1] * \
- np.sin(np.sum(self.joint_angles[:i]))
-
- self.end_effector = np.array(self.points[self.n_links]).T
-
- def plot(self, obstacles=[]): # pragma: no cover
- plt.cla()
-
- for obstacle in obstacles:
- circle = plt.Circle(
- (obstacle[0], obstacle[1]), radius=0.5 * obstacle[2], fc='k')
- plt.gca().add_patch(circle)
-
- for i in range(self.n_links + 1):
- if i is not self.n_links:
- plt.plot([self.points[i][0], self.points[i + 1][0]],
- [self.points[i][1], self.points[i + 1][1]], 'r-')
- plt.plot(self.points[i][0], self.points[i][1], 'k.')
-
- plt.xlim([-self.lim, self.lim])
- plt.ylim([-self.lim, self.lim])
- plt.draw()
- plt.pause(1e-5)
-
-
-if __name__ == '__main__':
- main()
diff --git a/ArmNavigation/arm_obstacle_navigation/arm_obstacle_navigation_2.py b/ArmNavigation/arm_obstacle_navigation/arm_obstacle_navigation_2.py
deleted file mode 100644
index f5d435082a5..00000000000
--- a/ArmNavigation/arm_obstacle_navigation/arm_obstacle_navigation_2.py
+++ /dev/null
@@ -1,299 +0,0 @@
-"""
-Obstacle navigation using A* on a toroidal grid
-
-Author: Daniel Ingram (daniel-s-ingram)
- Tullio Facchinetti (tullio.facchinetti@unipv.it)
-"""
-from math import pi
-import numpy as np
-import matplotlib.pyplot as plt
-from matplotlib.colors import from_levels_and_colors
-import sys
-
-plt.ion()
-
-# Simulation parameters
-M = 100
-obstacles = [[1.75, 0.75, 0.6], [0.55, 1.5, 0.5], [0, -1, 0.7]]
-
-
-def press(event):
- """Exit from the simulation."""
- if event.key == 'q' or event.key == 'Q':
- print('Quitting upon request.')
- sys.exit(0)
-
-
-def main():
- # Arm geometry in the working space
- link_length = [0.5, 1.5]
- initial_link_angle = [0, 0]
- arm = NLinkArm(link_length, initial_link_angle)
- # (x, y) co-ordinates in the joint space [cell]
- start = (10, 50)
- goal = (58, 56)
- grid = get_occupancy_grid(arm, obstacles)
- route = astar_torus(grid, start, goal)
- if route:
- animate(grid, arm, route)
-
-
-def animate(grid, arm, route):
- fig, axs = plt.subplots(1, 2)
- fig.canvas.mpl_connect('key_press_event', press)
- colors = ['white', 'black', 'red', 'pink', 'yellow', 'green', 'orange']
- levels = [0, 1, 2, 3, 4, 5, 6, 7]
- cmap, norm = from_levels_and_colors(levels, colors)
- for i, node in enumerate(route):
- plt.subplot(1, 2, 1)
- grid[node] = 6
- plt.cla()
- plt.imshow(grid, cmap=cmap, norm=norm, interpolation=None)
- theta1 = 2 * pi * node[0] / M - pi
- theta2 = 2 * pi * node[1] / M - pi
- arm.update_joints([theta1, theta2])
- plt.subplot(1, 2, 2)
- arm.plot_arm(plt, obstacles=obstacles)
- plt.xlim(-2.0, 2.0)
- plt.ylim(-3.0, 3.0)
- plt.show()
- # Uncomment here to save the sequence of frames
- # plt.savefig('frame{:04d}.png'.format(i))
- plt.pause(0.1)
-
-
-def detect_collision(line_seg, circle):
- """
- Determines whether a line segment (arm link) is in contact
- with a circle (obstacle).
- Credit to: https://web.archive.org/web/20200130224918/http://doswa.com/2009/07/13/circle-segment-intersectioncollision.html
- Args:
- line_seg: List of coordinates of line segment endpoints e.g. [[1, 1], [2, 2]]
- circle: List of circle coordinates and radius e.g. [0, 0, 0.5] is a circle centered
- at the origin with radius 0.5
-
- Returns:
- True if the line segment is in contact with the circle
- False otherwise
- """
- a_vec = np.array([line_seg[0][0], line_seg[0][1]])
- b_vec = np.array([line_seg[1][0], line_seg[1][1]])
- c_vec = np.array([circle[0], circle[1]])
- radius = circle[2]
- line_vec = b_vec - a_vec
- line_mag = np.linalg.norm(line_vec)
- circle_vec = c_vec - a_vec
- proj = circle_vec.dot(line_vec / line_mag)
- if proj <= 0:
- closest_point = a_vec
- elif proj >= line_mag:
- closest_point = b_vec
- else:
- closest_point = a_vec + line_vec * proj / line_mag
- if np.linalg.norm(closest_point - c_vec) > radius:
- return False
- return True
-
-
-def get_occupancy_grid(arm, obstacles):
- """
- Discretizes joint space into M values from -pi to +pi
- and determines whether a given coordinate in joint space
- would result in a collision between a robot arm and obstacles
- in its environment.
-
- Args:
- arm: An instance of NLinkArm
- obstacles: A list of obstacles, with each obstacle defined as a list
- of xy coordinates and a radius.
-
- Returns:
- Occupancy grid in joint space
- """
- grid = [[0 for _ in range(M)] for _ in range(M)]
- theta_list = [2 * i * pi / M for i in range(-M // 2, M // 2 + 1)]
- for i in range(M):
- for j in range(M):
- arm.update_joints([theta_list[i], theta_list[j]])
- points = arm.points
- collision_detected = False
- for k in range(len(points) - 1):
- for obstacle in obstacles:
- line_seg = [points[k], points[k + 1]]
- collision_detected = detect_collision(line_seg, obstacle)
- if collision_detected:
- break
- if collision_detected:
- break
- grid[i][j] = int(collision_detected)
- return np.array(grid)
-
-
-def astar_torus(grid, start_node, goal_node):
- """
- Finds a path between an initial and goal joint configuration using
- the A* Algorithm on a tororiadal grid.
-
- Args:
- grid: An occupancy grid (ndarray)
- start_node: Initial joint configuration (tuple)
- goal_node: Goal joint configuration (tuple)
-
- Returns:
- Obstacle-free route in joint space from start_node to goal_node
- """
- colors = ['white', 'black', 'red', 'pink', 'yellow', 'green', 'orange']
- levels = [0, 1, 2, 3, 4, 5, 6, 7]
- cmap, norm = from_levels_and_colors(levels, colors)
-
- grid[start_node] = 4
- grid[goal_node] = 5
-
- parent_map = [[() for _ in range(M)] for _ in range(M)]
-
- heuristic_map = calc_heuristic_map(M, goal_node)
-
- explored_heuristic_map = np.full((M, M), np.inf)
- distance_map = np.full((M, M), np.inf)
- explored_heuristic_map[start_node] = heuristic_map[start_node]
- distance_map[start_node] = 0
- while True:
- grid[start_node] = 4
- grid[goal_node] = 5
-
- current_node = np.unravel_index(
- np.argmin(explored_heuristic_map, axis=None), explored_heuristic_map.shape)
- min_distance = np.min(explored_heuristic_map)
- if (current_node == goal_node) or np.isinf(min_distance):
- break
-
- grid[current_node] = 2
- explored_heuristic_map[current_node] = np.inf
-
- i, j = current_node[0], current_node[1]
-
- neighbors = find_neighbors(i, j)
-
- for neighbor in neighbors:
- if grid[neighbor] == 0 or grid[neighbor] == 5:
- distance_map[neighbor] = distance_map[current_node] + 1
- explored_heuristic_map[neighbor] = heuristic_map[neighbor]
- parent_map[neighbor[0]][neighbor[1]] = current_node
- grid[neighbor] = 3
-
- if np.isinf(explored_heuristic_map[goal_node]):
- route = []
- print("No route found.")
- else:
- route = [goal_node]
- while parent_map[route[0][0]][route[0][1]] != ():
- route.insert(0, parent_map[route[0][0]][route[0][1]])
-
- print(f"The route found covers {len(route)} grid cells.")
- for i in range(1, len(route)):
- grid[route[i]] = 6
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.imshow(grid, cmap=cmap, norm=norm, interpolation=None)
- plt.show()
- plt.pause(1e-2)
-
- return route
-
-
-def find_neighbors(i, j):
- neighbors = []
- if i - 1 >= 0:
- neighbors.append((i - 1, j))
- else:
- neighbors.append((M - 1, j))
-
- if i + 1 < M:
- neighbors.append((i + 1, j))
- else:
- neighbors.append((0, j))
-
- if j - 1 >= 0:
- neighbors.append((i, j - 1))
- else:
- neighbors.append((i, M - 1))
-
- if j + 1 < M:
- neighbors.append((i, j + 1))
- else:
- neighbors.append((i, 0))
-
- return neighbors
-
-
-def calc_heuristic_map(M, goal_node):
- X, Y = np.meshgrid([i for i in range(M)], [i for i in range(M)])
- heuristic_map = np.abs(X - goal_node[1]) + np.abs(Y - goal_node[0])
- for i in range(heuristic_map.shape[0]):
- for j in range(heuristic_map.shape[1]):
- heuristic_map[i, j] = min(heuristic_map[i, j],
- M - i - 1 + heuristic_map[M - 1, j],
- i + heuristic_map[0, j],
- M - j - 1 + heuristic_map[i, M - 1],
- j + heuristic_map[i, 0]
- )
-
- return heuristic_map
-
-
-class NLinkArm:
- """
- Class for controlling and plotting a planar arm with an arbitrary number of links.
- """
-
- def __init__(self, link_lengths, joint_angles):
- self.n_links = len(link_lengths)
- if self.n_links != len(joint_angles):
- raise ValueError()
-
- self.link_lengths = np.array(link_lengths)
- self.joint_angles = np.array(joint_angles)
- self.points = [[0, 0] for _ in range(self.n_links + 1)]
-
- self.lim = sum(link_lengths)
- self.update_points()
-
- def update_joints(self, joint_angles):
- self.joint_angles = joint_angles
- self.update_points()
-
- def update_points(self):
- for i in range(1, self.n_links + 1):
- self.points[i][0] = self.points[i - 1][0] + \
- self.link_lengths[i - 1] * \
- np.cos(np.sum(self.joint_angles[:i]))
- self.points[i][1] = self.points[i - 1][1] + \
- self.link_lengths[i - 1] * \
- np.sin(np.sum(self.joint_angles[:i]))
-
- self.end_effector = np.array(self.points[self.n_links]).T
-
- def plot_arm(self, myplt, obstacles=[]): # pragma: no cover
- myplt.cla()
-
- for obstacle in obstacles:
- circle = myplt.Circle(
- (obstacle[0], obstacle[1]), radius=0.5 * obstacle[2], fc='k')
- myplt.gca().add_patch(circle)
-
- for i in range(self.n_links + 1):
- if i is not self.n_links:
- myplt.plot([self.points[i][0], self.points[i + 1][0]],
- [self.points[i][1], self.points[i + 1][1]], 'r-')
- myplt.plot(self.points[i][0], self.points[i][1], 'k.')
-
- myplt.xlim([-self.lim, self.lim])
- myplt.ylim([-self.lim, self.lim])
- myplt.draw()
- # myplt.pause(1e-5)
-
-
-if __name__ == '__main__':
- main()
diff --git a/ArmNavigation/n_joint_arm_3d/NLinkArm3d.py b/ArmNavigation/n_joint_arm_3d/NLinkArm3d.py
deleted file mode 100644
index 0459e234b20..00000000000
--- a/ArmNavigation/n_joint_arm_3d/NLinkArm3d.py
+++ /dev/null
@@ -1,215 +0,0 @@
-"""
-Class of n-link arm in 3D
-Author: Takayuki Murooka (takayuki5168)
-"""
-import numpy as np
-import math
-from mpl_toolkits.mplot3d import Axes3D
-import matplotlib.pyplot as plt
-
-
-class Link:
- def __init__(self, dh_params):
- self.dh_params_ = dh_params
-
- def transformation_matrix(self):
- theta = self.dh_params_[0]
- alpha = self.dh_params_[1]
- a = self.dh_params_[2]
- d = self.dh_params_[3]
-
- st = math.sin(theta)
- ct = math.cos(theta)
- sa = math.sin(alpha)
- ca = math.cos(alpha)
- trans = np.array([[ct, -st * ca, st * sa, a * ct],
- [st, ct * ca, -ct * sa, a * st],
- [0, sa, ca, d],
- [0, 0, 0, 1]])
-
- return trans
-
- @staticmethod
- def basic_jacobian(trans_prev, ee_pos):
- pos_prev = np.array(
- [trans_prev[0, 3], trans_prev[1, 3], trans_prev[2, 3]])
- z_axis_prev = np.array(
- [trans_prev[0, 2], trans_prev[1, 2], trans_prev[2, 2]])
-
- basic_jacobian = np.hstack(
- (np.cross(z_axis_prev, ee_pos - pos_prev), z_axis_prev))
- return basic_jacobian
-
-
-class NLinkArm:
- def __init__(self, dh_params_list):
- self.link_list = []
- for i in range(len(dh_params_list)):
- self.link_list.append(Link(dh_params_list[i]))
-
- def transformation_matrix(self):
- trans = np.identity(4)
- for i in range(len(self.link_list)):
- trans = np.dot(trans, self.link_list[i].transformation_matrix())
- return trans
-
- def forward_kinematics(self, plot=False):
- trans = self.transformation_matrix()
-
- x = trans[0, 3]
- y = trans[1, 3]
- z = trans[2, 3]
- alpha, beta, gamma = self.euler_angle()
-
- if plot:
- self.fig = plt.figure()
- self.ax = Axes3D(self.fig, auto_add_to_figure=False)
- self.fig.add_axes(self.ax)
-
- x_list = []
- y_list = []
- z_list = []
-
- trans = np.identity(4)
-
- x_list.append(trans[0, 3])
- y_list.append(trans[1, 3])
- z_list.append(trans[2, 3])
- for i in range(len(self.link_list)):
- trans = np.dot(trans, self.link_list[i].transformation_matrix())
- x_list.append(trans[0, 3])
- y_list.append(trans[1, 3])
- z_list.append(trans[2, 3])
-
- self.ax.plot(x_list, y_list, z_list, "o-", color="#00aa00", ms=4,
- mew=0.5)
- self.ax.plot([0], [0], [0], "o")
-
- self.ax.set_xlim(-1, 1)
- self.ax.set_ylim(-1, 1)
- self.ax.set_zlim(-1, 1)
-
- plt.show()
-
- return [x, y, z, alpha, beta, gamma]
-
- def basic_jacobian(self):
- ee_pos = self.forward_kinematics()[0:3]
- basic_jacobian_mat = []
-
- trans = np.identity(4)
- for i in range(len(self.link_list)):
- basic_jacobian_mat.append(
- self.link_list[i].basic_jacobian(trans, ee_pos))
- trans = np.dot(trans, self.link_list[i].transformation_matrix())
-
- return np.array(basic_jacobian_mat).T
-
- def inverse_kinematics(self, ref_ee_pose, plot=False):
- for cnt in range(500):
- ee_pose = self.forward_kinematics()
- diff_pose = np.array(ref_ee_pose) - ee_pose
-
- basic_jacobian_mat = self.basic_jacobian()
- alpha, beta, gamma = self.euler_angle()
-
- K_zyz = np.array(
- [[0, -math.sin(alpha), math.cos(alpha) * math.sin(beta)],
- [0, math.cos(alpha), math.sin(alpha) * math.sin(beta)],
- [1, 0, math.cos(beta)]])
- K_alpha = np.identity(6)
- K_alpha[3:, 3:] = K_zyz
-
- theta_dot = np.dot(
- np.dot(np.linalg.pinv(basic_jacobian_mat), K_alpha),
- np.array(diff_pose))
- self.update_joint_angles(theta_dot / 100.)
-
- if plot:
- self.fig = plt.figure()
- self.ax = Axes3D(self.fig, auto_add_to_figure=False)
- self.fig.add_axes(self.ax)
-
- x_list = []
- y_list = []
- z_list = []
-
- trans = np.identity(4)
-
- x_list.append(trans[0, 3])
- y_list.append(trans[1, 3])
- z_list.append(trans[2, 3])
- for i in range(len(self.link_list)):
- trans = np.dot(trans, self.link_list[i].transformation_matrix())
- x_list.append(trans[0, 3])
- y_list.append(trans[1, 3])
- z_list.append(trans[2, 3])
-
- self.ax.plot(x_list, y_list, z_list, "o-", color="#00aa00", ms=4,
- mew=0.5)
- self.ax.plot([0], [0], [0], "o")
-
- self.ax.set_xlim(-1, 1)
- self.ax.set_ylim(-1, 1)
- self.ax.set_zlim(-1, 1)
-
- self.ax.plot([ref_ee_pose[0]], [ref_ee_pose[1]], [ref_ee_pose[2]],
- "o")
- plt.show()
-
- def euler_angle(self):
- trans = self.transformation_matrix()
-
- alpha = math.atan2(trans[1][2], trans[0][2])
- if not (-math.pi / 2 <= alpha <= math.pi / 2):
- alpha = math.atan2(trans[1][2], trans[0][2]) + math.pi
- if not (-math.pi / 2 <= alpha <= math.pi / 2):
- alpha = math.atan2(trans[1][2], trans[0][2]) - math.pi
- beta = math.atan2(
- trans[0][2] * math.cos(alpha) + trans[1][2] * math.sin(alpha),
- trans[2][2])
- gamma = math.atan2(
- -trans[0][0] * math.sin(alpha) + trans[1][0] * math.cos(alpha),
- -trans[0][1] * math.sin(alpha) + trans[1][1] * math.cos(alpha))
-
- return alpha, beta, gamma
-
- def set_joint_angles(self, joint_angle_list):
- for i in range(len(self.link_list)):
- self.link_list[i].dh_params_[0] = joint_angle_list[i]
-
- def update_joint_angles(self, diff_joint_angle_list):
- for i in range(len(self.link_list)):
- self.link_list[i].dh_params_[0] += diff_joint_angle_list[i]
-
- def plot(self):
- self.fig = plt.figure()
- self.ax = Axes3D(self.fig)
-
- x_list = []
- y_list = []
- z_list = []
-
- trans = np.identity(4)
-
- x_list.append(trans[0, 3])
- y_list.append(trans[1, 3])
- z_list.append(trans[2, 3])
- for i in range(len(self.link_list)):
- trans = np.dot(trans, self.link_list[i].transformation_matrix())
- x_list.append(trans[0, 3])
- y_list.append(trans[1, 3])
- z_list.append(trans[2, 3])
-
- self.ax.plot(x_list, y_list, z_list, "o-", color="#00aa00", ms=4,
- mew=0.5)
- self.ax.plot([0], [0], [0], "o")
-
- self.ax.set_xlabel("x")
- self.ax.set_ylabel("y")
- self.ax.set_zlabel("z")
-
- self.ax.set_xlim(-1, 1)
- self.ax.set_ylim(-1, 1)
- self.ax.set_zlim(-1, 1)
- plt.show()
diff --git a/ArmNavigation/n_joint_arm_3d/__init__.py b/ArmNavigation/n_joint_arm_3d/__init__.py
deleted file mode 100644
index 2194d4c3033..00000000000
--- a/ArmNavigation/n_joint_arm_3d/__init__.py
+++ /dev/null
@@ -1,3 +0,0 @@
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent))
diff --git a/ArmNavigation/n_joint_arm_3d/random_forward_kinematics.py b/ArmNavigation/n_joint_arm_3d/random_forward_kinematics.py
deleted file mode 100644
index f9caace3006..00000000000
--- a/ArmNavigation/n_joint_arm_3d/random_forward_kinematics.py
+++ /dev/null
@@ -1,33 +0,0 @@
-"""
-Forward Kinematics for an n-link arm in 3D
-Author: Takayuki Murooka (takayuki5168)
-"""
-import math
-from NLinkArm3d import NLinkArm
-import random
-
-
-def random_val(min_val, max_val):
- return min_val + random.random() * (max_val - min_val)
-
-
-def main():
- print("Start solving Forward Kinematics 10 times")
- # init NLinkArm with Denavit-Hartenberg parameters of PR2
- n_link_arm = NLinkArm([[0., -math.pi / 2, .1, 0.],
- [math.pi / 2, math.pi / 2, 0., 0.],
- [0., -math.pi / 2, 0., .4],
- [0., math.pi / 2, 0., 0.],
- [0., -math.pi / 2, 0., .321],
- [0., math.pi / 2, 0., 0.],
- [0., 0., 0., 0.]])
- # execute FK 10 times
- for _ in range(10):
- n_link_arm.set_joint_angles(
- [random_val(-1, 1) for _ in range(len(n_link_arm.link_list))])
-
- n_link_arm.forward_kinematics(plot=True)
-
-
-if __name__ == "__main__":
- main()
diff --git a/ArmNavigation/n_joint_arm_3d/random_inverse_kinematics.py b/ArmNavigation/n_joint_arm_3d/random_inverse_kinematics.py
deleted file mode 100644
index 91f6f1bba0f..00000000000
--- a/ArmNavigation/n_joint_arm_3d/random_inverse_kinematics.py
+++ /dev/null
@@ -1,35 +0,0 @@
-"""
-Inverse Kinematics for an n-link arm in 3D
-Author: Takayuki Murooka (takayuki5168)
-"""
-import math
-from NLinkArm3d import NLinkArm
-import random
-
-
-def random_val(min_val, max_val):
- return min_val + random.random() * (max_val - min_val)
-
-
-def main():
- print("Start solving Inverse Kinematics 10 times")
- # init NLinkArm with Denavit-Hartenberg parameters of PR2
- n_link_arm = NLinkArm([[0., -math.pi / 2, .1, 0.],
- [math.pi / 2, math.pi / 2, 0., 0.],
- [0., -math.pi / 2, 0., .4],
- [0., math.pi / 2, 0., 0.],
- [0., -math.pi / 2, 0., .321],
- [0., math.pi / 2, 0., 0.],
- [0., 0., 0., 0.]])
- # execute IK 10 times
- for _ in range(10):
- n_link_arm.inverse_kinematics([random_val(-0.5, 0.5),
- random_val(-0.5, 0.5),
- random_val(-0.5, 0.5),
- random_val(-0.5, 0.5),
- random_val(-0.5, 0.5),
- random_val(-0.5, 0.5)], plot=True)
-
-
-if __name__ == "__main__":
- main()
diff --git a/ArmNavigation/n_joint_arm_to_point_control/NLinkArm.py b/ArmNavigation/n_joint_arm_to_point_control/NLinkArm.py
deleted file mode 100644
index 854ade90383..00000000000
--- a/ArmNavigation/n_joint_arm_to_point_control/NLinkArm.py
+++ /dev/null
@@ -1,76 +0,0 @@
-"""
-Class for controlling and plotting an arm with an arbitrary number of links.
-
-Author: Daniel Ingram
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-
-class NLinkArm(object):
- def __init__(self, link_lengths, joint_angles, goal, show_animation):
- self.show_animation = show_animation
- self.n_links = len(link_lengths)
- if self.n_links != len(joint_angles):
- raise ValueError()
-
- self.link_lengths = np.array(link_lengths)
- self.joint_angles = np.array(joint_angles)
- self.points = [[0, 0] for _ in range(self.n_links + 1)]
-
- self.lim = sum(link_lengths)
- self.goal = np.array(goal).T
-
- if show_animation: # pragma: no cover
- self.fig = plt.figure()
- self.fig.canvas.mpl_connect('button_press_event', self.click)
-
- plt.ion()
- plt.show()
-
- self.update_points()
-
- def update_joints(self, joint_angles):
- self.joint_angles = joint_angles
-
- self.update_points()
-
- def update_points(self):
- for i in range(1, self.n_links + 1):
- self.points[i][0] = self.points[i - 1][0] + \
- self.link_lengths[i - 1] * \
- np.cos(np.sum(self.joint_angles[:i]))
- self.points[i][1] = self.points[i - 1][1] + \
- self.link_lengths[i - 1] * \
- np.sin(np.sum(self.joint_angles[:i]))
-
- self.end_effector = np.array(self.points[self.n_links]).T
- if self.show_animation: # pragma: no cover
- self.plot()
-
- def plot(self): # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
-
- for i in range(self.n_links + 1):
- if i is not self.n_links:
- plt.plot([self.points[i][0], self.points[i + 1][0]],
- [self.points[i][1], self.points[i + 1][1]], 'r-')
- plt.plot(self.points[i][0], self.points[i][1], 'ko')
-
- plt.plot(self.goal[0], self.goal[1], 'gx')
-
- plt.plot([self.end_effector[0], self.goal[0]], [
- self.end_effector[1], self.goal[1]], 'g--')
-
- plt.xlim([-self.lim, self.lim])
- plt.ylim([-self.lim, self.lim])
- plt.draw()
- plt.pause(0.0001)
-
- def click(self, event):
- self.goal = np.array([event.xdata, event.ydata]).T
- self.plot()
diff --git a/ArmNavigation/n_joint_arm_to_point_control/__init__.py b/ArmNavigation/n_joint_arm_to_point_control/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/ArmNavigation/n_joint_arm_to_point_control/n_joint_arm_to_point_control.py b/ArmNavigation/n_joint_arm_to_point_control/n_joint_arm_to_point_control.py
deleted file mode 100644
index a2375233367..00000000000
--- a/ArmNavigation/n_joint_arm_to_point_control/n_joint_arm_to_point_control.py
+++ /dev/null
@@ -1,168 +0,0 @@
-"""
-Inverse kinematics for an n-link arm using the Jacobian inverse method
-
-Author: Daniel Ingram (daniel-s-ingram)
- Atsushi Sakai (@Atsushi_twi)
-"""
-
-import sys
-from pathlib import Path
-sys.path.append(str(Path(__file__).parent.parent.parent))
-
-import numpy as np
-from ArmNavigation.n_joint_arm_to_point_control.NLinkArm import NLinkArm
-from utils.angle import angle_mod
-
-# Simulation parameters
-Kp = 2
-dt = 0.1
-N_LINKS = 10
-N_ITERATIONS = 10000
-
-# States
-WAIT_FOR_NEW_GOAL = 1
-MOVING_TO_GOAL = 2
-
-show_animation = True
-
-
-def main(): # pragma: no cover
- """
- Creates an arm using the NLinkArm class and uses its inverse kinematics
- to move it to the desired position.
- """
- link_lengths = [1] * N_LINKS
- joint_angles = np.array([0] * N_LINKS)
- goal_pos = [N_LINKS, 0]
- arm = NLinkArm(link_lengths, joint_angles, goal_pos, show_animation)
- state = WAIT_FOR_NEW_GOAL
- solution_found = False
- while True:
- old_goal = np.array(goal_pos)
- goal_pos = np.array(arm.goal)
- end_effector = arm.end_effector
- errors, distance = distance_to_goal(end_effector, goal_pos)
-
- # State machine to allow changing of goal before current goal has been reached
- if state is WAIT_FOR_NEW_GOAL:
- if distance > 0.1 and not solution_found:
- joint_goal_angles, solution_found = inverse_kinematics(
- link_lengths, joint_angles, goal_pos)
- if not solution_found:
- print("Solution could not be found.")
- state = WAIT_FOR_NEW_GOAL
- arm.goal = end_effector
- elif solution_found:
- state = MOVING_TO_GOAL
- elif state is MOVING_TO_GOAL:
- if distance > 0.1 and all(old_goal == goal_pos):
- joint_angles = joint_angles + Kp * \
- ang_diff(joint_goal_angles, joint_angles) * dt
- else:
- state = WAIT_FOR_NEW_GOAL
- solution_found = False
-
- arm.update_joints(joint_angles)
-
-
-def inverse_kinematics(link_lengths, joint_angles, goal_pos):
- """
- Calculates the inverse kinematics using the Jacobian inverse method.
- """
- for iteration in range(N_ITERATIONS):
- current_pos = forward_kinematics(link_lengths, joint_angles)
- errors, distance = distance_to_goal(current_pos, goal_pos)
- if distance < 0.1:
- print("Solution found in %d iterations." % iteration)
- return joint_angles, True
- J = jacobian_inverse(link_lengths, joint_angles)
- joint_angles = joint_angles + np.matmul(J, errors)
- return joint_angles, False
-
-
-def get_random_goal():
- from random import random
- SAREA = 15.0
- return [SAREA * random() - SAREA / 2.0,
- SAREA * random() - SAREA / 2.0]
-
-
-def animation():
- link_lengths = [1] * N_LINKS
- joint_angles = np.array([0] * N_LINKS)
- goal_pos = get_random_goal()
- arm = NLinkArm(link_lengths, joint_angles, goal_pos, show_animation)
- state = WAIT_FOR_NEW_GOAL
- solution_found = False
-
- i_goal = 0
- while True:
- old_goal = np.array(goal_pos)
- goal_pos = np.array(arm.goal)
- end_effector = arm.end_effector
- errors, distance = distance_to_goal(end_effector, goal_pos)
-
- # State machine to allow changing of goal before current goal has been reached
- if state is WAIT_FOR_NEW_GOAL:
-
- if distance > 0.1 and not solution_found:
- joint_goal_angles, solution_found = inverse_kinematics(
- link_lengths, joint_angles, goal_pos)
- if not solution_found:
- print("Solution could not be found.")
- state = WAIT_FOR_NEW_GOAL
- arm.goal = get_random_goal()
- elif solution_found:
- state = MOVING_TO_GOAL
- elif state is MOVING_TO_GOAL:
- if distance > 0.1 and all(old_goal == goal_pos):
- joint_angles = joint_angles + Kp * \
- ang_diff(joint_goal_angles, joint_angles) * dt
- else:
- state = WAIT_FOR_NEW_GOAL
- solution_found = False
- arm.goal = get_random_goal()
- i_goal += 1
-
- if i_goal >= 5:
- break
-
- arm.update_joints(joint_angles)
-
-
-def forward_kinematics(link_lengths, joint_angles):
- x = y = 0
- for i in range(1, N_LINKS + 1):
- x += link_lengths[i - 1] * np.cos(np.sum(joint_angles[:i]))
- y += link_lengths[i - 1] * np.sin(np.sum(joint_angles[:i]))
- return np.array([x, y]).T
-
-
-def jacobian_inverse(link_lengths, joint_angles):
- J = np.zeros((2, N_LINKS))
- for i in range(N_LINKS):
- J[0, i] = 0
- J[1, i] = 0
- for j in range(i, N_LINKS):
- J[0, i] -= link_lengths[j] * np.sin(np.sum(joint_angles[:j]))
- J[1, i] += link_lengths[j] * np.cos(np.sum(joint_angles[:j]))
-
- return np.linalg.pinv(J)
-
-
-def distance_to_goal(current_pos, goal_pos):
- x_diff = goal_pos[0] - current_pos[0]
- y_diff = goal_pos[1] - current_pos[1]
- return np.array([x_diff, y_diff]).T, np.hypot(x_diff, y_diff)
-
-
-def ang_diff(theta1, theta2):
- """
- Returns the difference between two angles in the range -pi to +pi
- """
- return angle_mod(theta1 - theta2)
-
-
-if __name__ == '__main__':
- # main()
- animation()
diff --git a/ArmNavigation/rrt_star_seven_joint_arm_control/rrt_star_seven_joint_arm_control.py b/ArmNavigation/rrt_star_seven_joint_arm_control/rrt_star_seven_joint_arm_control.py
deleted file mode 100755
index 3bc2a5ec1d7..00000000000
--- a/ArmNavigation/rrt_star_seven_joint_arm_control/rrt_star_seven_joint_arm_control.py
+++ /dev/null
@@ -1,405 +0,0 @@
-"""
-RRT* path planner for a seven joint arm
-Author: Mahyar Abdeetedal (mahyaret)
-"""
-import math
-import random
-import numpy as np
-import matplotlib.pyplot as plt
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from n_joint_arm_3d.NLinkArm3d import NLinkArm
-
-show_animation = True
-verbose = False
-
-
-class RobotArm(NLinkArm):
- def get_points(self, joint_angle_list):
- self.set_joint_angles(joint_angle_list)
-
- x_list = []
- y_list = []
- z_list = []
-
- trans = np.identity(4)
-
- x_list.append(trans[0, 3])
- y_list.append(trans[1, 3])
- z_list.append(trans[2, 3])
- for i in range(len(self.link_list)):
- trans = np.dot(trans, self.link_list[i].transformation_matrix())
- x_list.append(trans[0, 3])
- y_list.append(trans[1, 3])
- z_list.append(trans[2, 3])
-
- return x_list, y_list, z_list
-
-
-class RRTStar:
- """
- Class for RRT Star planning
- """
-
- class Node:
- def __init__(self, x):
- self.x = x
- self.parent = None
- self.cost = 0.0
-
- def __init__(self, start, goal, robot, obstacle_list, rand_area,
- expand_dis=.30,
- path_resolution=.1,
- goal_sample_rate=20,
- max_iter=300,
- connect_circle_dist=50.0
- ):
- """
- Setting Parameter
-
- start:Start Position [q1,...,qn]
- goal:Goal Position [q1,...,qn]
- obstacleList:obstacle Positions [[x,y,z,size],...]
- randArea:Random Sampling Area [min,max]
-
- """
- self.start = self.Node(start)
- self.end = self.Node(goal)
- self.dimension = len(start)
- self.min_rand = rand_area[0]
- self.max_rand = rand_area[1]
- self.expand_dis = expand_dis
- self.path_resolution = path_resolution
- self.goal_sample_rate = goal_sample_rate
- self.max_iter = max_iter
- self.robot = robot
- self.obstacle_list = obstacle_list
- self.connect_circle_dist = connect_circle_dist
- self.goal_node = self.Node(goal)
- self.node_list = []
- if show_animation:
- self.ax = plt.axes(projection='3d')
-
- def planning(self, animation=False, search_until_max_iter=False):
- """
- rrt star path planning
-
- animation: flag for animation on or off
- search_until_max_iter: search until max iteration for path
- improving or not
- """
-
- self.node_list = [self.start]
- for i in range(self.max_iter):
- if verbose:
- print("Iter:", i, ", number of nodes:", len(self.node_list))
- rnd = self.get_random_node()
- nearest_ind = self.get_nearest_node_index(self.node_list, rnd)
- new_node = self.steer(self.node_list[nearest_ind],
- rnd,
- self.expand_dis)
-
- if self.check_collision(new_node, self.robot, self.obstacle_list):
- near_inds = self.find_near_nodes(new_node)
- new_node = self.choose_parent(new_node, near_inds)
- if new_node:
- self.node_list.append(new_node)
- self.rewire(new_node, near_inds)
-
- if animation and i % 5 == 0 and self.dimension <= 3:
- self.draw_graph(rnd)
-
- if (not search_until_max_iter) and new_node:
- last_index = self.search_best_goal_node()
- if last_index is not None:
- return self.generate_final_course(last_index)
- if verbose:
- print("reached max iteration")
-
- last_index = self.search_best_goal_node()
- if last_index is not None:
- return self.generate_final_course(last_index)
-
- return None
-
- def choose_parent(self, new_node, near_inds):
- if not near_inds:
- return None
-
- # search nearest cost in near_inds
- costs = []
- for i in near_inds:
- near_node = self.node_list[i]
- t_node = self.steer(near_node, new_node)
- if t_node and self.check_collision(t_node,
- self.robot,
- self.obstacle_list):
- costs.append(self.calc_new_cost(near_node, new_node))
- else:
- costs.append(float("inf")) # the cost of collision node
- min_cost = min(costs)
-
- if min_cost == float("inf"):
- print("There is no good path.(min_cost is inf)")
- return None
-
- min_ind = near_inds[costs.index(min_cost)]
- new_node = self.steer(self.node_list[min_ind], new_node)
- new_node.parent = self.node_list[min_ind]
- new_node.cost = min_cost
-
- return new_node
-
- def search_best_goal_node(self):
- dist_to_goal_list = [self.calc_dist_to_goal(n.x)
- for n in self.node_list]
- goal_inds = [dist_to_goal_list.index(i)
- for i in dist_to_goal_list if i <= self.expand_dis]
-
- safe_goal_inds = []
- for goal_ind in goal_inds:
- t_node = self.steer(self.node_list[goal_ind], self.goal_node)
- if self.check_collision(t_node, self.robot, self.obstacle_list):
- safe_goal_inds.append(goal_ind)
-
- if not safe_goal_inds:
- return None
-
- min_cost = min([self.node_list[i].cost for i in safe_goal_inds])
- for i in safe_goal_inds:
- if self.node_list[i].cost == min_cost:
- return i
-
- return None
-
- def find_near_nodes(self, new_node):
- nnode = len(self.node_list) + 1
- r = self.connect_circle_dist * math.sqrt(math.log(nnode) / nnode)
- # if expand_dist exists, search vertices in
- # a range no more than expand_dist
- if hasattr(self, 'expand_dis'):
- r = min(r, self.expand_dis)
- dist_list = [np.sum((np.array(node.x) - np.array(new_node.x)) ** 2)
- for node in self.node_list]
- near_inds = [dist_list.index(i) for i in dist_list if i <= r ** 2]
- return near_inds
-
- def rewire(self, new_node, near_inds):
- for i in near_inds:
- near_node = self.node_list[i]
- edge_node = self.steer(new_node, near_node)
- if not edge_node:
- continue
- edge_node.cost = self.calc_new_cost(new_node, near_node)
-
- no_collision = self.check_collision(edge_node,
- self.robot,
- self.obstacle_list)
- improved_cost = near_node.cost > edge_node.cost
-
- if no_collision and improved_cost:
- self.node_list[i] = edge_node
- self.propagate_cost_to_leaves(new_node)
-
- def calc_new_cost(self, from_node, to_node):
- d, _, _ = self.calc_distance_and_angle(from_node, to_node)
- return from_node.cost + d
-
- def propagate_cost_to_leaves(self, parent_node):
-
- for node in self.node_list:
- if node.parent == parent_node:
- node.cost = self.calc_new_cost(parent_node, node)
- self.propagate_cost_to_leaves(node)
-
- def generate_final_course(self, goal_ind):
- path = [self.end.x]
- node = self.node_list[goal_ind]
- while node.parent is not None:
- path.append(node.x)
- node = node.parent
- path.append(node.x)
- reversed(path)
- return path
-
- def calc_dist_to_goal(self, x):
- distance = np.linalg.norm(np.array(x) - np.array(self.end.x))
- return distance
-
- def get_random_node(self):
- if random.randint(0, 100) > self.goal_sample_rate:
- rnd = self.Node(np.random.uniform(self.min_rand,
- self.max_rand,
- self.dimension))
- else: # goal point sampling
- rnd = self.Node(self.end.x)
- return rnd
-
- def steer(self, from_node, to_node, extend_length=float("inf")):
- new_node = self.Node(list(from_node.x))
- d, phi, theta = self.calc_distance_and_angle(new_node, to_node)
-
- new_node.path_x = [list(new_node.x)]
-
- if extend_length > d:
- extend_length = d
-
- n_expand = math.floor(extend_length / self.path_resolution)
-
- start, end = np.array(from_node.x), np.array(to_node.x)
- v = end - start
- u = v / (np.sqrt(np.sum(v ** 2)))
- for _ in range(n_expand):
- new_node.x += u * self.path_resolution
- new_node.path_x.append(list(new_node.x))
-
- d, _, _ = self.calc_distance_and_angle(new_node, to_node)
- if d <= self.path_resolution:
- new_node.path_x.append(list(to_node.x))
-
- new_node.parent = from_node
-
- return new_node
-
- def draw_graph(self, rnd=None):
- plt.cla()
- self.ax.axis([-1, 1, -1, 1, -1, 1])
- self.ax.set_zlim(0, 1)
- self.ax.grid(True)
- for (ox, oy, oz, size) in self.obstacle_list:
- self.plot_sphere(self.ax, ox, oy, oz, size=size)
- if self.dimension > 3:
- return self.ax
- if rnd is not None:
- self.ax.plot([rnd.x[0]], [rnd.x[1]], [rnd.x[2]], "^k")
- for node in self.node_list:
- if node.parent:
- path = np.array(node.path_x)
- plt.plot(path[:, 0], path[:, 1], path[:, 2], "-g")
- self.ax.plot([self.start.x[0]], [self.start.x[1]],
- [self.start.x[2]], "xr")
- self.ax.plot([self.end.x[0]], [self.end.x[1]], [self.end.x[2]], "xr")
- plt.pause(0.01)
- return self.ax
-
- @staticmethod
- def get_nearest_node_index(node_list, rnd_node):
- dlist = [np.sum((np.array(node.x) - np.array(rnd_node.x))**2)
- for node in node_list]
- minind = dlist.index(min(dlist))
-
- return minind
-
- @staticmethod
- def plot_sphere(ax, x, y, z, size=1, color="k"):
- u, v = np.mgrid[0:2*np.pi:20j, 0:np.pi:10j]
- xl = x+size*np.cos(u)*np.sin(v)
- yl = y+size*np.sin(u)*np.sin(v)
- zl = z+size*np.cos(v)
- ax.plot_wireframe(xl, yl, zl, color=color)
-
- @staticmethod
- def calc_distance_and_angle(from_node, to_node):
- dx = to_node.x[0] - from_node.x[0]
- dy = to_node.x[1] - from_node.x[1]
- dz = to_node.x[2] - from_node.x[2]
- d = np.sqrt(np.sum((np.array(to_node.x) - np.array(from_node.x))**2))
- phi = math.atan2(dy, dx)
- theta = math.atan2(math.hypot(dx, dy), dz)
- return d, phi, theta
-
- @staticmethod
- def calc_distance_and_angle2(from_node, to_node):
- dx = to_node.x[0] - from_node.x[0]
- dy = to_node.x[1] - from_node.x[1]
- dz = to_node.x[2] - from_node.x[2]
- d = math.sqrt(dx**2 + dy**2 + dz**2)
- phi = math.atan2(dy, dx)
- theta = math.atan2(math.hypot(dx, dy), dz)
- return d, phi, theta
-
- @staticmethod
- def check_collision(node, robot, obstacleList):
-
- if node is None:
- return False
-
- for (ox, oy, oz, size) in obstacleList:
- for x in node.path_x:
- x_list, y_list, z_list = robot.get_points(x)
- dx_list = [ox - x_point for x_point in x_list]
- dy_list = [oy - y_point for y_point in y_list]
- dz_list = [oz - z_point for z_point in z_list]
- d_list = [dx * dx + dy * dy + dz * dz
- for (dx, dy, dz) in zip(dx_list,
- dy_list,
- dz_list)]
-
- if min(d_list) <= size ** 2:
- return False # collision
-
- return True # safe
-
-
-def main():
- print("Start " + __file__)
-
- # init NLinkArm with Denavit-Hartenberg parameters of panda
- # https://frankaemika.github.io/docs/control_parameters.html
- # [theta, alpha, a, d]
- seven_joint_arm = RobotArm([[0., math.pi/2., 0., .333],
- [0., -math.pi/2., 0., 0.],
- [0., math.pi/2., 0.0825, 0.3160],
- [0., -math.pi/2., -0.0825, 0.],
- [0., math.pi/2., 0., 0.3840],
- [0., math.pi/2., 0.088, 0.],
- [0., 0., 0., 0.107]])
- # ====Search Path with RRT====
- obstacle_list = [
- (-.3, -.3, .7, .1),
- (.0, -.3, .7, .1),
- (.2, -.1, .3, .15),
- ] # [x,y,size(radius)]
- start = [0 for _ in range(len(seven_joint_arm.link_list))]
- end = [1.5 for _ in range(len(seven_joint_arm.link_list))]
- # Set Initial parameters
- rrt_star = RRTStar(start=start,
- goal=end,
- rand_area=[0, 2],
- max_iter=200,
- robot=seven_joint_arm,
- obstacle_list=obstacle_list)
- path = rrt_star.planning(animation=show_animation,
- search_until_max_iter=False)
-
- if path is None:
- print("Cannot find path.")
- else:
- print("Found path!")
-
- # Draw final path
- if show_animation:
- ax = rrt_star.draw_graph()
-
- # Plot final configuration
- x_points, y_points, z_points = seven_joint_arm.get_points(path[-1])
- ax.plot([x for x in x_points],
- [y for y in y_points],
- [z for z in z_points],
- "o-", color="red", ms=5, mew=0.5)
-
- for i, q in enumerate(path):
- x_points, y_points, z_points = seven_joint_arm.get_points(q)
- ax.plot([x for x in x_points],
- [y for y in y_points],
- [z for z in z_points],
- "o-", color="grey", ms=4, mew=0.5)
- plt.pause(0.1)
-
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/ArmNavigation/two_joint_arm_to_point_control/two_joint_arm_to_point_control.py b/ArmNavigation/two_joint_arm_to_point_control/two_joint_arm_to_point_control.py
deleted file mode 100644
index c2227f18e35..00000000000
--- a/ArmNavigation/two_joint_arm_to_point_control/two_joint_arm_to_point_control.py
+++ /dev/null
@@ -1,145 +0,0 @@
-"""
-Inverse kinematics of a two-joint arm
-Left-click the plot to set the goal position of the end effector
-
-Author: Daniel Ingram (daniel-s-ingram)
- Atsushi Sakai (@Atsushi_twi)
-
-Ref: P. I. Corke, "Robotics, Vision & Control", Springer 2017,
- ISBN 978-3-319-54413-7 p102
-- [Robotics, Vision and Control]
-(https://link.springer.com/book/10.1007/978-3-642-20144-8)
-
-"""
-
-import matplotlib.pyplot as plt
-import numpy as np
-import math
-from utils.angle import angle_mod
-
-
-# Simulation parameters
-Kp = 15
-dt = 0.01
-
-# Link lengths
-l1 = l2 = 1
-
-# Set initial goal position to the initial end-effector position
-x = 2
-y = 0
-
-show_animation = True
-
-if show_animation:
- plt.ion()
-
-
-def two_joint_arm(GOAL_TH=0.0, theta1=0.0, theta2=0.0):
- """
- Computes the inverse kinematics for a planar 2DOF arm
- When out of bounds, rewrite x and y with last correct values
- """
- global x, y
- x_prev, y_prev = None, None
- while True:
- try:
- if x is not None and y is not None:
- x_prev = x
- y_prev = y
- if np.hypot(x, y) > (l1 + l2):
- theta2_goal = 0
- else:
- theta2_goal = np.arccos(
- (x**2 + y**2 - l1**2 - l2**2) / (2 * l1 * l2))
- tmp = math.atan2(l2 * np.sin(theta2_goal),
- (l1 + l2 * np.cos(theta2_goal)))
- theta1_goal = math.atan2(y, x) - tmp
-
- if theta1_goal < 0:
- theta2_goal = -theta2_goal
- tmp = math.atan2(l2 * np.sin(theta2_goal),
- (l1 + l2 * np.cos(theta2_goal)))
- theta1_goal = math.atan2(y, x) - tmp
-
- theta1 = theta1 + Kp * ang_diff(theta1_goal, theta1) * dt
- theta2 = theta2 + Kp * ang_diff(theta2_goal, theta2) * dt
- except ValueError as e:
- print("Unreachable goal"+e)
- except TypeError:
- x = x_prev
- y = y_prev
-
- wrist = plot_arm(theta1, theta2, x, y)
-
- # check goal
- d2goal = None
- if x is not None and y is not None:
- d2goal = np.hypot(wrist[0] - x, wrist[1] - y)
-
- if abs(d2goal) < GOAL_TH and x is not None:
- return theta1, theta2
-
-
-def plot_arm(theta1, theta2, target_x, target_y): # pragma: no cover
- shoulder = np.array([0, 0])
- elbow = shoulder + np.array([l1 * np.cos(theta1), l1 * np.sin(theta1)])
- wrist = elbow + \
- np.array([l2 * np.cos(theta1 + theta2), l2 * np.sin(theta1 + theta2)])
-
- if show_animation:
- plt.cla()
-
- plt.plot([shoulder[0], elbow[0]], [shoulder[1], elbow[1]], 'k-')
- plt.plot([elbow[0], wrist[0]], [elbow[1], wrist[1]], 'k-')
-
- plt.plot(shoulder[0], shoulder[1], 'ro')
- plt.plot(elbow[0], elbow[1], 'ro')
- plt.plot(wrist[0], wrist[1], 'ro')
-
- plt.plot([wrist[0], target_x], [wrist[1], target_y], 'g--')
- plt.plot(target_x, target_y, 'g*')
-
- plt.xlim(-2, 2)
- plt.ylim(-2, 2)
-
- plt.show()
- plt.pause(dt)
-
- return wrist
-
-
-def ang_diff(theta1, theta2):
- # Returns the difference between two angles in the range -pi to +pi
- return angle_mod(theta1 - theta2)
-
-
-def click(event): # pragma: no cover
- global x, y
- x = event.xdata
- y = event.ydata
-
-
-def animation():
- from random import random
- global x, y
- theta1 = theta2 = 0.0
- for i in range(5):
- x = 2.0 * random() - 1.0
- y = 2.0 * random() - 1.0
- theta1, theta2 = two_joint_arm(
- GOAL_TH=0.01, theta1=theta1, theta2=theta2)
-
-
-def main(): # pragma: no cover
- fig = plt.figure()
- fig.canvas.mpl_connect("button_press_event", click)
- # for stopping simulation with the esc key.
- fig.canvas.mpl_connect('key_release_event', lambda event: [
- exit(0) if event.key == 'escape' else None])
- two_joint_arm()
-
-
-if __name__ == "__main__":
- # animation()
- main()
diff --git a/Bipedal/__init__.py b/Bipedal/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/Bipedal/bipedal_planner/__init__.py b/Bipedal/bipedal_planner/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/Bipedal/bipedal_planner/bipedal_planner.py b/Bipedal/bipedal_planner/bipedal_planner.py
deleted file mode 100644
index c34357df678..00000000000
--- a/Bipedal/bipedal_planner/bipedal_planner.py
+++ /dev/null
@@ -1,205 +0,0 @@
-"""
-Bipedal Walking with modifying designated footsteps
-author: Takayuki Murooka (takayuki5168)
-"""
-import numpy as np
-import math
-from matplotlib import pyplot as plt
-import matplotlib.patches as pat
-from mpl_toolkits.mplot3d import Axes3D
-import mpl_toolkits.mplot3d.art3d as art3d
-
-
-class BipedalPlanner(object):
- def __init__(self):
- self.act_p = [] # actual footstep positions
- self.ref_p = [] # reference footstep positions
- self.com_trajectory = []
- self.ref_footsteps = None
- self.g = 9.8
-
- def set_ref_footsteps(self, ref_footsteps):
- self.ref_footsteps = ref_footsteps
-
- def inverted_pendulum(self, x, x_dot, px_star, y, y_dot, py_star, z_c,
- time_width):
- time_split = 100
-
- for i in range(time_split):
- delta_time = time_width / time_split
-
- x_dot2 = self.g / z_c * (x - px_star)
- x += x_dot * delta_time
- x_dot += x_dot2 * delta_time
-
- y_dot2 = self.g / z_c * (y - py_star)
- y += y_dot * delta_time
- y_dot += y_dot2 * delta_time
-
- if i % 10 == 0:
- self.com_trajectory.append([x, y])
-
- return x, x_dot, y, y_dot
-
- def walk(self, t_sup=0.8, z_c=0.8, a=10, b=1, plot=False):
- if self.ref_footsteps is None:
- print("No footsteps")
- return
-
- # set up plotter
- if plot:
- fig = plt.figure()
- ax = Axes3D(fig)
- fig.add_axes(ax)
- com_trajectory_for_plot = []
-
- px, py = 0.0, 0.0 # reference footstep position
- px_star, py_star = px, py # modified footstep position
- xi, xi_dot, yi, yi_dot = 0.0, 0.0, 0.01, 0.0
- time = 0.0
- n = 0
- self.ref_p.append([px, py, 0])
- self.act_p.append([px, py, 0])
- for i in range(len(self.ref_footsteps)):
- # simulate x, y and those of dot of inverted pendulum
- xi, xi_dot, yi, yi_dot = self.inverted_pendulum(
- xi, xi_dot, px_star, yi, yi_dot, py_star, z_c, t_sup)
-
- # update time
- time += t_sup
- n += 1
-
- # calculate px, py, x_, y_, vx_, vy_
- f_x, f_y, f_theta = self.ref_footsteps[n - 1]
- rotate_mat = np.array([[math.cos(f_theta), -math.sin(f_theta)],
- [math.sin(f_theta), math.cos(f_theta)]])
-
- if n == len(self.ref_footsteps):
- f_x_next, f_y_next, f_theta_next = 0., 0., 0.
- else:
- f_x_next, f_y_next, f_theta_next = self.ref_footsteps[n]
- rotate_mat_next = np.array(
- [[math.cos(f_theta_next), -math.sin(f_theta_next)],
- [math.sin(f_theta_next), math.cos(f_theta_next)]])
-
- Tc = math.sqrt(z_c / self.g)
- C = math.cosh(t_sup / Tc)
- S = math.sinh(t_sup / Tc)
-
- px, py = list(np.array([px, py])
- + np.dot(rotate_mat,
- np.array([f_x, -1 * math.pow(-1, n) * f_y])
- ))
- x_, y_ = list(np.dot(rotate_mat_next, np.array(
- [f_x_next / 2., math.pow(-1, n) * f_y_next / 2.])))
- vx_, vy_ = list(np.dot(rotate_mat_next, np.array(
- [(1 + C) / (Tc * S) * x_, (C - 1) / (Tc * S) * y_])))
- self.ref_p.append([px, py, f_theta])
-
- # calculate reference COM
- xd, xd_dot = px + x_, vx_
- yd, yd_dot = py + y_, vy_
-
- # calculate modified footsteps
- D = a * math.pow(C - 1, 2) + b * math.pow(S / Tc, 2)
- px_star = -a * (C - 1) / D * (xd - C * xi - Tc * S * xi_dot) \
- - b * S / (Tc * D) * (xd_dot - S / Tc * xi - C * xi_dot)
- py_star = -a * (C - 1) / D * (yd - C * yi - Tc * S * yi_dot) \
- - b * S / (Tc * D) * (yd_dot - S / Tc * yi - C * yi_dot)
- self.act_p.append([px_star, py_star, f_theta])
-
- # plot
- if plot:
- self.plot_animation(ax, com_trajectory_for_plot, px_star,
- py_star, z_c)
- if plot:
- plt.show()
-
- def plot_animation(self, ax, com_trajectory_for_plot, px_star, py_star,
- z_c): # pragma: no cover
- # for plot trajectory, plot in for loop
- for c in range(len(self.com_trajectory)):
- if c > len(com_trajectory_for_plot):
- # set up plotter
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event:
- [exit(0) if event.key == 'escape' else None])
- ax.set_zlim(0, z_c * 2)
- ax.set_xlim(0, 1)
- ax.set_ylim(-0.5, 0.5)
-
- # update com_trajectory_for_plot
- com_trajectory_for_plot.append(self.com_trajectory[c])
-
- # plot com
- ax.plot([p[0] for p in com_trajectory_for_plot],
- [p[1] for p in com_trajectory_for_plot], [
- 0 for _ in com_trajectory_for_plot],
- color="red")
-
- # plot inverted pendulum
- ax.plot([px_star, com_trajectory_for_plot[-1][0]],
- [py_star, com_trajectory_for_plot[-1][1]],
- [0, z_c], color="green", linewidth=3)
- ax.scatter([com_trajectory_for_plot[-1][0]],
- [com_trajectory_for_plot[-1][1]],
- [z_c], color="green", s=300)
-
- # foot rectangle for self.ref_p
- foot_width = 0.06
- foot_height = 0.04
- for j in range(len(self.ref_p)):
- angle = self.ref_p[j][2] + \
- math.atan2(foot_height,
- foot_width) - math.pi
- r = math.sqrt(
- math.pow(foot_width / 3., 2) + math.pow(
- foot_height / 2., 2))
- rec = pat.Rectangle(xy=(
- self.ref_p[j][0] + r * math.cos(angle),
- self.ref_p[j][1] + r * math.sin(angle)),
- width=foot_width,
- height=foot_height,
- angle=self.ref_p[j][
- 2] * 180 / math.pi,
- color="blue", fill=False,
- ls=":")
- ax.add_patch(rec)
- art3d.pathpatch_2d_to_3d(rec, z=0, zdir="z")
-
- # foot rectangle for self.act_p
- for j in range(len(self.act_p)):
- angle = self.act_p[j][2] + \
- math.atan2(foot_height,
- foot_width) - math.pi
- r = math.sqrt(
- math.pow(foot_width / 3., 2) + math.pow(
- foot_height / 2., 2))
- rec = pat.Rectangle(xy=(
- self.act_p[j][0] + r * math.cos(angle),
- self.act_p[j][1] + r * math.sin(angle)),
- width=foot_width,
- height=foot_height,
- angle=self.act_p[j][
- 2] * 180 / math.pi,
- color="blue", fill=False)
- ax.add_patch(rec)
- art3d.pathpatch_2d_to_3d(rec, z=0, zdir="z")
-
- plt.draw()
- plt.pause(0.001)
-
-
-if __name__ == "__main__":
- bipedal_planner = BipedalPlanner()
-
- footsteps = [[0.0, 0.2, 0.0],
- [0.3, 0.2, 0.0],
- [0.3, 0.2, 0.2],
- [0.3, 0.2, 0.2],
- [0.0, 0.2, 0.2]]
- bipedal_planner.set_ref_footsteps(footsteps)
- bipedal_planner.walk(plot=True)
diff --git a/CODE_OF_CONDUCT.md b/CODE_OF_CONDUCT.md
deleted file mode 100644
index e8c4702596b..00000000000
--- a/CODE_OF_CONDUCT.md
+++ /dev/null
@@ -1,76 +0,0 @@
-# Contributor Covenant Code of Conduct
-
-## Our Pledge
-
-In the interest of fostering an open and welcoming environment, we as
-contributors and maintainers pledge to making participation in our project and
-our community a harassment-free experience for everyone, regardless of age, body
-size, disability, ethnicity, sex characteristics, gender identity and expression,
-level of experience, education, socio-economic status, nationality, personal
-appearance, race, religion, or sexual identity and orientation.
-
-## Our Standards
-
-Examples of behavior that contributes to creating a positive environment
-include:
-
-* Using welcoming and inclusive language
-* Being respectful of differing viewpoints and experiences
-* Gracefully accepting constructive criticism
-* Focusing on what is best for the community
-* Showing empathy towards other community members
-
-Examples of unacceptable behavior by participants include:
-
-* The use of sexualized language or imagery and unwelcome sexual attention or
- advances
-* Trolling, insulting/derogatory comments, and personal or political attacks
-* Public or private harassment
-* Publishing others' private information, such as a physical or electronic
- address, without explicit permission
-* Other conduct which could reasonably be considered inappropriate in a
- professional setting
-
-## Our Responsibilities
-
-Project maintainers are responsible for clarifying the standards of acceptable
-behavior and are expected to take appropriate and fair corrective action in
-response to any instances of unacceptable behavior.
-
-Project maintainers have the right and responsibility to remove, edit, or
-reject comments, commits, code, wiki edits, issues, and other contributions
-that are not aligned to this Code of Conduct, or to ban temporarily or
-permanently any contributor for other behaviors that they deem inappropriate,
-threatening, offensive, or harmful.
-
-## Scope
-
-This Code of Conduct applies both within project spaces and in public spaces
-when an individual is representing the project or its community. Examples of
-representing a project or community include using an official project e-mail
-address, posting via an official social media account, or acting as an appointed
-representative at an online or offline event. Representation of a project may be
-further defined and clarified by project maintainers.
-
-## Enforcement
-
-Instances of abusive, harassing, or otherwise unacceptable behavior may be
-reported by contacting the project team at asakaig@gmail.com. All
-complaints will be reviewed and investigated and will result in a response that
-is deemed necessary and appropriate to the circumstances. The project team is
-obligated to maintain confidentiality with regard to the reporter of an incident.
-Further details of specific enforcement policies may be posted separately.
-
-Project maintainers who do not follow or enforce the Code of Conduct in good
-faith may face temporary or permanent repercussions as determined by other
-members of the project's leadership.
-
-## Attribution
-
-This Code of Conduct is adapted from the [Contributor Covenant][homepage], version 1.4,
-available at https://www.contributor-covenant.org/version/1/4/code-of-conduct.html
-
-[homepage]: https://www.contributor-covenant.org
-
-For answers to common questions about this code of conduct, see
-https://www.contributor-covenant.org/faq
diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md
deleted file mode 100644
index 3bcc499e6ae..00000000000
--- a/CONTRIBUTING.md
+++ /dev/null
@@ -1,5 +0,0 @@
-# Contributing
-
-:+1::tada: First of all, thank you very much for taking the time to contribute! :tada::+1:
-
-Please check this document for contribution: [How to contribute — PythonRobotics documentation](https://atsushisakai.github.io/PythonRobotics/modules/0_getting_started/3_how_to_contribute.html)
diff --git a/InvertedPendulum/inverted_pendulum_lqr_control.py b/InvertedPendulum/inverted_pendulum_lqr_control.py
deleted file mode 100644
index c4380530b81..00000000000
--- a/InvertedPendulum/inverted_pendulum_lqr_control.py
+++ /dev/null
@@ -1,192 +0,0 @@
-"""
-Inverted Pendulum LQR control
-author: Trung Kien - letrungkien.k53.hut@gmail.com
-"""
-
-import math
-import time
-
-import matplotlib.pyplot as plt
-import numpy as np
-from numpy.linalg import inv, eig
-
-# Model parameters
-
-l_bar = 2.0 # length of bar
-M = 1.0 # [kg]
-m = 0.3 # [kg]
-g = 9.8 # [m/s^2]
-
-nx = 4 # number of state
-nu = 1 # number of input
-Q = np.diag([0.0, 1.0, 1.0, 0.0]) # state cost matrix
-R = np.diag([0.01]) # input cost matrix
-
-delta_t = 0.1 # time tick [s]
-sim_time = 5.0 # simulation time [s]
-
-show_animation = True
-
-
-def main():
- x0 = np.array([
- [0.0],
- [0.0],
- [0.3],
- [0.0]
- ])
-
- x = np.copy(x0)
- time = 0.0
-
- while sim_time > time:
- time += delta_t
-
- # calc control input
- u = lqr_control(x)
-
- # simulate inverted pendulum cart
- x = simulation(x, u)
-
- if show_animation:
- plt.clf()
- px = float(x[0, 0])
- theta = float(x[2, 0])
- plot_cart(px, theta)
- plt.xlim([-5.0, 2.0])
- plt.pause(0.001)
-
- print("Finish")
- print(f"x={float(x[0, 0]):.2f} [m] , theta={math.degrees(x[2, 0]):.2f} [deg]")
- if show_animation:
- plt.show()
-
-
-def simulation(x, u):
- A, B = get_model_matrix()
- x = A @ x + B @ u
-
- return x
-
-
-def solve_DARE(A, B, Q, R, maxiter=150, eps=0.01):
- """
- Solve a discrete time_Algebraic Riccati equation (DARE)
- """
- P = Q
-
- for i in range(maxiter):
- Pn = A.T @ P @ A - A.T @ P @ B @ \
- inv(R + B.T @ P @ B) @ B.T @ P @ A + Q
- if (abs(Pn - P)).max() < eps:
- break
- P = Pn
-
- return Pn
-
-
-def dlqr(A, B, Q, R):
- """
- Solve the discrete time lqr controller.
- x[k+1] = A x[k] + B u[k]
- cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
- # ref Bertsekas, p.151
- """
-
- # first, try to solve the ricatti equation
- P = solve_DARE(A, B, Q, R)
-
- # compute the LQR gain
- K = inv(B.T @ P @ B + R) @ (B.T @ P @ A)
-
- eigVals, eigVecs = eig(A - B @ K)
- return K, P, eigVals
-
-
-def lqr_control(x):
- A, B = get_model_matrix()
- start = time.time()
- K, _, _ = dlqr(A, B, Q, R)
- u = -K @ x
- elapsed_time = time.time() - start
- print(f"calc time:{elapsed_time:.6f} [sec]")
- return u
-
-
-def get_numpy_array_from_matrix(x):
- """
- get build-in list from matrix
- """
- return np.array(x).flatten()
-
-
-def get_model_matrix():
- A = np.array([
- [0.0, 1.0, 0.0, 0.0],
- [0.0, 0.0, m * g / M, 0.0],
- [0.0, 0.0, 0.0, 1.0],
- [0.0, 0.0, g * (M + m) / (l_bar * M), 0.0]
- ])
- A = np.eye(nx) + delta_t * A
-
- B = np.array([
- [0.0],
- [1.0 / M],
- [0.0],
- [1.0 / (l_bar * M)]
- ])
- B = delta_t * B
-
- return A, B
-
-
-def flatten(a):
- return np.array(a).flatten()
-
-
-def plot_cart(xt, theta):
- cart_w = 1.0
- cart_h = 0.5
- radius = 0.1
-
- cx = np.array([-cart_w / 2.0, cart_w / 2.0, cart_w /
- 2.0, -cart_w / 2.0, -cart_w / 2.0])
- cy = np.array([0.0, 0.0, cart_h, cart_h, 0.0])
- cy += radius * 2.0
-
- cx = cx + xt
-
- bx = np.array([0.0, l_bar * math.sin(-theta)])
- bx += xt
- by = np.array([cart_h, l_bar * math.cos(-theta) + cart_h])
- by += radius * 2.0
-
- angles = np.arange(0.0, math.pi * 2.0, math.radians(3.0))
- ox = np.array([radius * math.cos(a) for a in angles])
- oy = np.array([radius * math.sin(a) for a in angles])
-
- rwx = np.copy(ox) + cart_w / 4.0 + xt
- rwy = np.copy(oy) + radius
- lwx = np.copy(ox) - cart_w / 4.0 + xt
- lwy = np.copy(oy) + radius
-
- wx = np.copy(ox) + bx[-1]
- wy = np.copy(oy) + by[-1]
-
- plt.plot(flatten(cx), flatten(cy), "-b")
- plt.plot(flatten(bx), flatten(by), "-k")
- plt.plot(flatten(rwx), flatten(rwy), "-k")
- plt.plot(flatten(lwx), flatten(lwy), "-k")
- plt.plot(flatten(wx), flatten(wy), "-k")
- plt.title(f"x: {xt:.2f} , theta: {math.degrees(theta):.2f}")
-
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
-
- plt.axis("equal")
-
-
-if __name__ == '__main__':
- main()
diff --git a/InvertedPendulum/inverted_pendulum_mpc_control.py b/InvertedPendulum/inverted_pendulum_mpc_control.py
deleted file mode 100644
index 9a5fa2ab414..00000000000
--- a/InvertedPendulum/inverted_pendulum_mpc_control.py
+++ /dev/null
@@ -1,187 +0,0 @@
-"""
-Inverted Pendulum MPC control
-author: Atsushi Sakai
-"""
-
-import math
-import time
-
-import cvxpy
-import matplotlib.pyplot as plt
-import numpy as np
-
-# Model parameters
-
-l_bar = 2.0 # length of bar
-M = 1.0 # [kg]
-m = 0.3 # [kg]
-g = 9.8 # [m/s^2]
-
-nx = 4 # number of state
-nu = 1 # number of input
-Q = np.diag([0.0, 1.0, 1.0, 0.0]) # state cost matrix
-R = np.diag([0.01]) # input cost matrix
-
-T = 30 # Horizon length
-delta_t = 0.1 # time tick
-sim_time = 5.0 # simulation time [s]
-
-show_animation = True
-
-
-def main():
- x0 = np.array([
- [0.0],
- [0.0],
- [0.3],
- [0.0]
- ])
-
- x = np.copy(x0)
- time = 0.0
-
- while sim_time > time:
- time += delta_t
-
- # calc control input
- opt_x, opt_delta_x, opt_theta, opt_delta_theta, opt_input = \
- mpc_control(x)
-
- # get input
- u = opt_input[0]
-
- # simulate inverted pendulum cart
- x = simulation(x, u)
-
- if show_animation:
- plt.clf()
- px = float(x[0, 0])
- theta = float(x[2, 0])
- plot_cart(px, theta)
- plt.xlim([-5.0, 2.0])
- plt.pause(0.001)
-
- print("Finish")
- print(f"x={float(x[0, 0]):.2f} [m] , theta={math.degrees(x[2, 0]):.2f} [deg]")
- if show_animation:
- plt.show()
-
-
-def simulation(x, u):
- A, B = get_model_matrix()
- x = np.dot(A, x) + np.dot(B, u)
-
- return x
-
-
-def mpc_control(x0):
- x = cvxpy.Variable((nx, T + 1))
- u = cvxpy.Variable((nu, T))
-
- A, B = get_model_matrix()
-
- cost = 0.0
- constr = []
- for t in range(T):
- cost += cvxpy.quad_form(x[:, t + 1], Q)
- cost += cvxpy.quad_form(u[:, t], R)
- constr += [x[:, t + 1] == A @ x[:, t] + B @ u[:, t]]
-
- constr += [x[:, 0] == x0[:, 0]]
- prob = cvxpy.Problem(cvxpy.Minimize(cost), constr)
-
- start = time.time()
- prob.solve(verbose=False)
- elapsed_time = time.time() - start
- print(f"calc time:{elapsed_time:.6f} [sec]")
-
- if prob.status == cvxpy.OPTIMAL:
- ox = get_numpy_array_from_matrix(x.value[0, :])
- dx = get_numpy_array_from_matrix(x.value[1, :])
- theta = get_numpy_array_from_matrix(x.value[2, :])
- d_theta = get_numpy_array_from_matrix(x.value[3, :])
-
- ou = get_numpy_array_from_matrix(u.value[0, :])
- else:
- ox, dx, theta, d_theta, ou = None, None, None, None, None
-
- return ox, dx, theta, d_theta, ou
-
-
-def get_numpy_array_from_matrix(x):
- """
- get build-in list from matrix
- """
- return np.array(x).flatten()
-
-
-def get_model_matrix():
- A = np.array([
- [0.0, 1.0, 0.0, 0.0],
- [0.0, 0.0, m * g / M, 0.0],
- [0.0, 0.0, 0.0, 1.0],
- [0.0, 0.0, g * (M + m) / (l_bar * M), 0.0]
- ])
- A = np.eye(nx) + delta_t * A
-
- B = np.array([
- [0.0],
- [1.0 / M],
- [0.0],
- [1.0 / (l_bar * M)]
- ])
- B = delta_t * B
-
- return A, B
-
-
-def flatten(a):
- return np.array(a).flatten()
-
-
-def plot_cart(xt, theta):
- cart_w = 1.0
- cart_h = 0.5
- radius = 0.1
-
- cx = np.array([-cart_w / 2.0, cart_w / 2.0, cart_w /
- 2.0, -cart_w / 2.0, -cart_w / 2.0])
- cy = np.array([0.0, 0.0, cart_h, cart_h, 0.0])
- cy += radius * 2.0
-
- cx = cx + xt
-
- bx = np.array([0.0, l_bar * math.sin(-theta)])
- bx += xt
- by = np.array([cart_h, l_bar * math.cos(-theta) + cart_h])
- by += radius * 2.0
-
- angles = np.arange(0.0, math.pi * 2.0, math.radians(3.0))
- ox = np.array([radius * math.cos(a) for a in angles])
- oy = np.array([radius * math.sin(a) for a in angles])
-
- rwx = np.copy(ox) + cart_w / 4.0 + xt
- rwy = np.copy(oy) + radius
- lwx = np.copy(ox) - cart_w / 4.0 + xt
- lwy = np.copy(oy) + radius
-
- wx = np.copy(ox) + bx[-1]
- wy = np.copy(oy) + by[-1]
-
- plt.plot(flatten(cx), flatten(cy), "-b")
- plt.plot(flatten(bx), flatten(by), "-k")
- plt.plot(flatten(rwx), flatten(rwy), "-k")
- plt.plot(flatten(lwx), flatten(lwy), "-k")
- plt.plot(flatten(wx), flatten(wy), "-k")
- plt.title(f"x: {xt:.2f} , theta: {math.degrees(theta):.2f}")
-
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
-
- plt.axis("equal")
-
-
-if __name__ == '__main__':
- main()
diff --git a/LICENSE b/LICENSE
deleted file mode 100644
index 1c9b928b543..00000000000
--- a/LICENSE
+++ /dev/null
@@ -1,22 +0,0 @@
-The MIT License (MIT)
-
-Copyright (c) 2016 - now Atsushi Sakai and other contributors:
-https://github.com/AtsushiSakai/PythonRobotics/contributors
-
-Permission is hereby granted, free of charge, to any person obtaining a copy
-of this software and associated documentation files (the "Software"), to deal
-in the Software without restriction, including without limitation the rights
-to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
-copies of the Software, and to permit persons to whom the Software is
-furnished to do so, subject to the following conditions:
-
-The above copyright notice and this permission notice shall be included in all
-copies or substantial portions of the Software.
-
-THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
-IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
-FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
-AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
-LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
-OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
-SOFTWARE.
diff --git a/Localization/__init__.py b/Localization/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/Localization/cubature_kalman_filter/cubature_kalman_filter.py b/Localization/cubature_kalman_filter/cubature_kalman_filter.py
deleted file mode 100644
index 0fc4c937600..00000000000
--- a/Localization/cubature_kalman_filter/cubature_kalman_filter.py
+++ /dev/null
@@ -1,246 +0,0 @@
-"""
-Cubature Kalman filter using Constant Turn Rate and Velocity (CTRV) model
-Fuse sensor data from IMU and GPS to obtain accurate position
-
-https://ieeexplore.ieee.org/document/4982682
-
-Author: Raghuram Shankar
-
-state matrix: 2D x-y position, yaw, velocity and yaw rate
-measurement matrix: 2D x-y position, velocity and yaw rate
-
-dt: Duration of time step
-N: Number of time steps
-show_final: Flag for showing final result
-show_animation: Flag for showing each animation frame
-show_ellipse: Flag for showing covariance ellipse
-z_noise: Measurement noise
-x_0: Prior state estimate matrix
-P_0: Prior state estimate covariance matrix
-q: Process noise covariance
-hx: Measurement model matrix
-r: Sensor noise covariance
-SP: Sigma Points
-W: Weights
-
-x_est: State estimate
-P_est: State estimate covariance
-x_true: Ground truth value of state
-x_true_cat: Concatenate all ground truth states
-x_est_cat: Concatenate all state estimates
-z_cat: Concatenate all measurements
-
-"""
-
-import math
-import matplotlib.pyplot as plt
-import numpy as np
-from scipy.linalg import sqrtm
-
-
-dt = 0.1
-N = 100
-
-show_final = 1
-show_animation = 0
-show_ellipse = 0
-
-
-z_noise = np.array([[0.1, 0.0, 0.0, 0.0], # x position [m]
- [0.0, 0.1, 0.0, 0.0], # y position [m]
- [0.0, 0.0, 0.1, 0.0], # velocity [m/s]
- [0.0, 0.0, 0.0, 0.1]]) # yaw rate [rad/s]
-
-
-x_0 = np.array([[0.0], # x position [m]
- [0.0], # y position [m]
- [0.0], # yaw [rad]
- [1.0], # velocity [m/s]
- [0.1]]) # yaw rate [rad/s]
-
-
-p_0 = np.array([[1e-3, 0.0, 0.0, 0.0, 0.0],
- [0.0, 1e-3, 0.0, 0.0, 0.0],
- [0.0, 0.0, 1.0, 0.0, 0.0],
- [0.0, 0.0, 0.0, 1.0, 0.0],
- [0.0, 0.0, 0.0, 0.0, 1.0]])
-
-
-q = np.array([[1e-11, 0.0, 0.0, 0.0, 0.0],
- [0.0, 1e-11, 0.0, 0.0, 0.0],
- [0.0, 0.0, np.deg2rad(1e-4), 0.0, 0.0],
- [0.0, 0.0, 0.0, 1e-4, 0.0],
- [0.0, 0.0, 0.0, 0.0, np.deg2rad(1e-4)]])
-
-
-hx = np.array([[1.0, 0.0, 0.0, 0.0, 0.0],
- [0.0, 1.0, 0.0, 0.0, 0.0],
- [0.0, 0.0, 0.0, 1.0, 0.0],
- [0.0, 0.0, 0.0, 0.0, 1.0]])
-
-
-r = np.array([[0.015, 0.0, 0.0, 0.0],
- [0.0, 0.010, 0.0, 0.0],
- [0.0, 0.0, 0.1, 0.0],
- [0.0, 0.0, 0.0, 0.01]])**2
-
-
-def cubature_kalman_filter(x_est, p_est, z):
- x_pred, p_pred = cubature_prediction(x_est, p_est)
- x_upd, p_upd = cubature_update(x_pred, p_pred, z)
- return x_upd, p_upd
-
-
-def f(x):
- """
- Motion Model
- References:
- http://fusion.isif.org/proceedings/fusion08CD/papers/1569107835.pdf
- https://github.com/balzer82/Kalman
- """
- x[0] = x[0] + (x[3]/x[4]) * (np.sin(x[4] * dt + x[2]) - np.sin(x[2]))
- x[1] = x[1] + (x[3]/x[4]) * (- np.cos(x[4] * dt + x[2]) + np.cos(x[2]))
- x[2] = x[2] + x[4] * dt
- x[3] = x[3]
- x[4] = x[4]
- return x
-
-
-def h(x):
- """Measurement Model"""
- x = hx @ x
- return x
-
-
-def sigma(x, p):
- """
- Unscented Transform with Cubature Rule
- Generate 2n Sigma Points to represent the nonlinear motion
- Assign Weights to each Sigma Point, Wi = 1/2n
- Cubature Rule - Special Case of Unscented Transform
- W0 = 0, no extra tuning parameters, no negative weights
- """
- n = np.shape(x)[0]
- SP = np.zeros((n, 2*n))
- W = np.zeros((1, 2*n))
- for i in range(n):
- SD = sqrtm(p)
- SP[:, i] = (x + (math.sqrt(n) * SD[:, i]).reshape((n, 1))).flatten()
- SP[:, i+n] = (x - (math.sqrt(n) * SD[:, i]).reshape((n, 1))).flatten()
- W[:, i] = 1/(2*n)
- W[:, i+n] = W[:, i]
- return SP, W
-
-
-def cubature_prediction(x_pred, p_pred):
- n = np.shape(x_pred)[0]
- [SP, W] = sigma(x_pred, p_pred)
- x_pred = np.zeros((n, 1))
- p_pred = q
- for i in range(2*n):
- x_pred = x_pred + (f(SP[:, i]).reshape((n, 1)) * W[0, i])
- for i in range(2*n):
- p_step = (f(SP[:, i]).reshape((n, 1)) - x_pred)
- p_pred = p_pred + (p_step @ p_step.T * W[0, i])
- return x_pred, p_pred
-
-
-def cubature_update(x_pred, p_pred, z):
- n = np.shape(x_pred)[0]
- m = np.shape(z)[0]
- [SP, W] = sigma(x_pred, p_pred)
- y_k = np.zeros((m, 1))
- P_xy = np.zeros((n, m))
- s = r
- for i in range(2*n):
- y_k = y_k + (h(SP[:, i]).reshape((m, 1)) * W[0, i])
- for i in range(2*n):
- p_step = (h(SP[:, i]).reshape((m, 1)) - y_k)
- P_xy = P_xy + ((SP[:, i]).reshape((n, 1)) -
- x_pred) @ p_step.T * W[0, i]
- s = s + p_step @ p_step.T * W[0, i]
- x_pred = x_pred + P_xy @ np.linalg.pinv(s) @ (z - y_k)
- p_pred = p_pred - P_xy @ np.linalg.pinv(s) @ P_xy.T
- return x_pred, p_pred
-
-
-def generate_measurement(x_true):
- gz = hx @ x_true
- z = gz + z_noise @ np.random.randn(4, 1)
- return z
-
-
-def plot_animation(i, x_true_cat, x_est_cat, z):
- if i == 0:
- plt.plot(x_true_cat[0], x_true_cat[1], '.r')
- plt.plot(x_est_cat[0], x_est_cat[1], '.b')
- else:
- plt.plot(x_true_cat[0:, 0], x_true_cat[0:, 1], 'r')
- plt.plot(x_est_cat[0:, 0], x_est_cat[0:, 1], 'b')
- plt.plot(z[0], z[1], '+g')
- plt.grid(True)
- plt.pause(0.001)
-
-
-def plot_ellipse(x_est, p_est):
- phi = np.linspace(0, 2 * math.pi, 100)
- p_ellipse = np.array(
- [[p_est[0, 0], p_est[0, 1]], [p_est[1, 0], p_est[1, 1]]])
- x0 = 3 * sqrtm(p_ellipse)
- xy_1 = np.array([])
- xy_2 = np.array([])
- for i in range(100):
- arr = np.array([[math.sin(phi[i])], [math.cos(phi[i])]])
- arr = x0 @ arr
- xy_1 = np.hstack([xy_1, arr[0]])
- xy_2 = np.hstack([xy_2, arr[1]])
- plt.plot(xy_1 + x_est[0], xy_2 + x_est[1], 'r')
- plt.pause(0.00001)
-
-
-def plot_final(x_true_cat, x_est_cat, z_cat):
- fig = plt.figure()
- subplot = fig.add_subplot(111)
- subplot.plot(x_true_cat[0:, 0], x_true_cat[0:, 1],
- 'r', label='True Position')
- subplot.plot(x_est_cat[0:, 0], x_est_cat[0:, 1],
- 'b', label='Estimated Position')
- subplot.plot(z_cat[0:, 0], z_cat[0:, 1], '+g', label='Noisy Measurements')
- subplot.set_xlabel('x [m]')
- subplot.set_ylabel('y [m]')
- subplot.set_title('Cubature Kalman Filter - CTRV Model')
- subplot.legend(loc='upper left', shadow=True, fontsize='large')
- plt.grid(True)
- plt.show()
-
-
-def main():
- print(__file__ + " start!!")
- x_est = x_0
- p_est = p_0
- x_true = x_0
- x_true_cat = np.array([x_0[0, 0], x_0[1, 0]])
- x_est_cat = np.array([x_0[0, 0], x_0[1, 0]])
- z_cat = np.array([x_0[0, 0], x_0[1, 0]])
- for i in range(N):
- x_true = f(x_true)
- z = generate_measurement(x_true)
- if i == (N - 1) and show_final == 1:
- show_final_flag = 1
- else:
- show_final_flag = 0
- if show_animation == 1:
- plot_animation(i, x_true_cat, x_est_cat, z)
- if show_ellipse == 1:
- plot_ellipse(x_est[0:2], p_est)
- if show_final_flag == 1:
- plot_final(x_true_cat, x_est_cat, z_cat)
- x_est, p_est = cubature_kalman_filter(x_est, p_est, z)
- x_true_cat = np.vstack((x_true_cat, x_true[0:2].T))
- x_est_cat = np.vstack((x_est_cat, x_est[0:2].T))
- z_cat = np.vstack((z_cat, z[0:2].T))
- print('CKF Over')
-
-
-if __name__ == '__main__':
- main()
diff --git a/Localization/ensemble_kalman_filter/ensemble_kalman_filter.py b/Localization/ensemble_kalman_filter/ensemble_kalman_filter.py
deleted file mode 100644
index 2bab3b49c1c..00000000000
--- a/Localization/ensemble_kalman_filter/ensemble_kalman_filter.py
+++ /dev/null
@@ -1,246 +0,0 @@
-"""
-
-Ensemble Kalman Filter(EnKF) localization sample
-
-author: Ryohei Sasaki(rsasaki0109)
-
-Ref:
-Ensemble Kalman filtering
-(https://rmets.onlinelibrary.wiley.com/doi/10.1256/qj.05.135)
-
-"""
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import math
-import matplotlib.pyplot as plt
-import numpy as np
-from utils.angle import angle_mod
-
-from utils.angle import rot_mat_2d
-
-# Simulation parameter
-Q_sim = np.diag([0.2, np.deg2rad(1.0)]) ** 2
-R_sim = np.diag([1.0, np.deg2rad(30.0)]) ** 2
-
-DT = 0.1 # time tick [s]
-SIM_TIME = 50.0 # simulation time [s]
-MAX_RANGE = 20.0 # maximum observation range
-
-# Ensemble Kalman filter parameter
-NP = 20 # Number of Particle
-
-show_animation = True
-
-
-def calc_input():
- v = 1.0 # [m/s]
- yaw_rate = 0.1 # [rad/s]
- u = np.array([[v, yaw_rate]]).T
- return u
-
-
-def observation(xTrue, xd, u, RFID):
- xTrue = motion_model(xTrue, u)
-
- z = np.zeros((0, 4))
-
- for i in range(len(RFID[:, 0])):
-
- dx = RFID[i, 0] - xTrue[0, 0]
- dy = RFID[i, 1] - xTrue[1, 0]
- d = math.hypot(dx, dy)
- angle = pi_2_pi(math.atan2(dy, dx) - xTrue[2, 0])
- if d <= MAX_RANGE:
- dn = d + np.random.randn() * Q_sim[0, 0] ** 0.5 # add noise
- angle_with_noise = angle + np.random.randn() * Q_sim[1, 1] ** 0.5
- zi = np.array([dn, angle_with_noise, RFID[i, 0], RFID[i, 1]])
- z = np.vstack((z, zi))
-
- # add noise to input
- ud = np.array([[
- u[0, 0] + np.random.randn() * R_sim[0, 0] ** 0.5,
- u[1, 0] + np.random.randn() * R_sim[1, 1] ** 0.5]]).T
-
- xd = motion_model(xd, ud)
- return xTrue, z, xd, ud
-
-
-def motion_model(x, u):
- F = np.array([[1.0, 0, 0, 0],
- [0, 1.0, 0, 0],
- [0, 0, 1.0, 0],
- [0, 0, 0, 0]])
-
- B = np.array([[DT * math.cos(x[2, 0]), 0],
- [DT * math.sin(x[2, 0]), 0],
- [0.0, DT],
- [1.0, 0.0]])
- x = F.dot(x) + B.dot(u)
-
- return x
-
-
-def observe_landmark_position(x, landmarks):
- landmarks_pos = np.zeros((2 * landmarks.shape[0], 1))
- for (i, lm) in enumerate(landmarks):
- index = 2 * i
- q = Q_sim[0, 0] ** 0.5
- landmarks_pos[index] = x[0, 0] + lm[0] * math.cos(
- x[2, 0] + lm[1]) + np.random.randn() * q / np.sqrt(2)
- landmarks_pos[index + 1] = x[1, 0] + lm[0] * math.sin(
- x[2, 0] + lm[1]) + np.random.randn() * q / np.sqrt(2)
- return landmarks_pos
-
-
-def calc_covariance(xEst, px):
- cov = np.zeros((3, 3))
-
- for i in range(px.shape[1]):
- dx = (px[:, i] - xEst)[0:3]
- cov += dx.dot(dx.T)
- cov /= NP
-
- return cov
-
-
-def enkf_localization(px, z, u):
- """
- Localization with Ensemble Kalman filter
- """
- pz = np.zeros((z.shape[0] * 2, NP)) # Particle store of z
- for ip in range(NP):
- x = np.array([px[:, ip]]).T
-
- # Predict with random input sampling
- ud1 = u[0, 0] + np.random.randn() * R_sim[0, 0] ** 0.5
- ud2 = u[1, 0] + np.random.randn() * R_sim[1, 1] ** 0.5
- ud = np.array([[ud1, ud2]]).T
- x = motion_model(x, ud)
- px[:, ip] = x[:, 0]
- z_pos = observe_landmark_position(x, z)
- pz[:, ip] = z_pos[:, 0]
-
- x_ave = np.mean(px, axis=1)
- x_dif = px - np.tile(x_ave, (NP, 1)).T
-
- z_ave = np.mean(pz, axis=1)
- z_dif = pz - np.tile(z_ave, (NP, 1)).T
-
- U = 1 / (NP - 1) * x_dif @ z_dif.T
- V = 1 / (NP - 1) * z_dif @ z_dif.T
-
- K = U @ np.linalg.inv(V) # Kalman Gain
-
- z_lm_pos = z[:, [2, 3]].reshape(-1, )
-
- px_hat = px + K @ (np.tile(z_lm_pos, (NP, 1)).T - pz)
-
- xEst = np.average(px_hat, axis=1).reshape(4, 1)
- PEst = calc_covariance(xEst, px_hat)
-
- return xEst, PEst, px_hat
-
-
-def plot_covariance_ellipse(xEst, PEst): # pragma: no cover
- Pxy = PEst[0:2, 0:2]
- eig_val, eig_vec = np.linalg.eig(Pxy)
-
- if eig_val[0] >= eig_val[1]:
- big_ind = 0
- small_ind = 1
- else:
- big_ind = 1
- small_ind = 0
-
- t = np.arange(0, 2 * math.pi + 0.1, 0.1)
-
- # eig_val[big_ind] or eiq_val[small_ind] were occasionally negative
- # numbers extremely close to 0 (~10^-20), catch these cases and set
- # the respective variable to 0
- try:
- a = math.sqrt(eig_val[big_ind])
- except ValueError:
- a = 0
-
- try:
- b = math.sqrt(eig_val[small_ind])
- except ValueError:
- b = 0
-
- x = [a * math.cos(it) for it in t]
- y = [b * math.sin(it) for it in t]
- angle = math.atan2(eig_vec[1, big_ind], eig_vec[0, big_ind])
- fx = np.stack([x, y]).T @ rot_mat_2d(angle)
-
- px = np.array(fx[:, 0] + xEst[0, 0]).flatten()
- py = np.array(fx[:, 1] + xEst[1, 0]).flatten()
- plt.plot(px, py, "--r")
-
-
-def pi_2_pi(angle):
- return angle_mod(angle)
-
-
-def main():
- print(__file__ + " start!!")
-
- time = 0.0
-
- # RF_ID positions [x, y]
- RF_ID = np.array([[10.0, 0.0],
- [10.0, 10.0],
- [0.0, 15.0],
- [-5.0, 20.0]])
-
- # State Vector [x y yaw v]'
- xEst = np.zeros((4, 1))
- xTrue = np.zeros((4, 1))
- px = np.zeros((4, NP)) # Particle store of x
-
- xDR = np.zeros((4, 1)) # Dead reckoning
-
- # history
- hxEst = xEst
- hxTrue = xTrue
- hxDR = xTrue
-
- while SIM_TIME >= time:
- time += DT
- u = calc_input()
-
- xTrue, z, xDR, ud = observation(xTrue, xDR, u, RF_ID)
-
- xEst, PEst, px = enkf_localization(px, z, ud)
-
- # store data history
- hxEst = np.hstack((hxEst, xEst))
- hxDR = np.hstack((hxDR, xDR))
- hxTrue = np.hstack((hxTrue, xTrue))
-
- if show_animation:
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
-
- for i in range(len(z[:, 0])):
- plt.plot([xTrue[0, 0], z[i, 2]], [xTrue[1, 0], z[i, 3]], "-k")
- plt.plot(RF_ID[:, 0], RF_ID[:, 1], "*k")
- plt.plot(px[0, :], px[1, :], ".r")
- plt.plot(np.array(hxTrue[0, :]).flatten(),
- np.array(hxTrue[1, :]).flatten(), "-b")
- plt.plot(np.array(hxDR[0, :]).flatten(),
- np.array(hxDR[1, :]).flatten(), "-k")
- plt.plot(np.array(hxEst[0, :]).flatten(),
- np.array(hxEst[1, :]).flatten(), "-r")
- plot_covariance_ellipse(xEst, PEst)
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.001)
-
-
-if __name__ == '__main__':
- main()
diff --git a/Localization/extended_kalman_filter/ekf_with_velocity_correction.py b/Localization/extended_kalman_filter/ekf_with_velocity_correction.py
deleted file mode 100644
index 5dd97830fc4..00000000000
--- a/Localization/extended_kalman_filter/ekf_with_velocity_correction.py
+++ /dev/null
@@ -1,198 +0,0 @@
-"""
-
-Extended kalman filter (EKF) localization with velocity correction sample
-
-author: Atsushi Sakai (@Atsushi_twi)
-modified by: Ryohei Sasaki (@rsasaki0109)
-
-"""
-import sys
-import pathlib
-
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import math
-import matplotlib.pyplot as plt
-import numpy as np
-
-from utils.plot import plot_covariance_ellipse
-
-# Covariance for EKF simulation
-Q = np.diag([
- 0.1, # variance of location on x-axis
- 0.1, # variance of location on y-axis
- np.deg2rad(1.0), # variance of yaw angle
- 0.4, # variance of velocity
- 0.1 # variance of scale factor
-]) ** 2 # predict state covariance
-R = np.diag([0.1, 0.1]) ** 2 # Observation x,y position covariance
-
-# Simulation parameter
-INPUT_NOISE = np.diag([0.1, np.deg2rad(5.0)]) ** 2
-GPS_NOISE = np.diag([0.05, 0.05]) ** 2
-
-DT = 0.1 # time tick [s]
-SIM_TIME = 50.0 # simulation time [s]
-
-show_animation = True
-
-
-def calc_input():
- v = 1.0 # [m/s]
- yawrate = 0.1 # [rad/s]
- u = np.array([[v], [yawrate]])
- return u
-
-
-def observation(xTrue, xd, u):
- xTrue = motion_model(xTrue, u)
-
- # add noise to gps x-y
- z = observation_model(xTrue) + GPS_NOISE @ np.random.randn(2, 1)
-
- # add noise to input
- ud = u + INPUT_NOISE @ np.random.randn(2, 1)
-
- xd = motion_model(xd, ud)
-
- return xTrue, z, xd, ud
-
-
-def motion_model(x, u):
- F = np.array([[1.0, 0, 0, 0, 0],
- [0, 1.0, 0, 0, 0],
- [0, 0, 1.0, 0, 0],
- [0, 0, 0, 0, 0],
- [0, 0, 0, 0, 1.0]])
-
- B = np.array([[DT * math.cos(x[2, 0]) * x[4, 0], 0],
- [DT * math.sin(x[2, 0]) * x[4, 0], 0],
- [0.0, DT],
- [1.0, 0.0],
- [0.0, 0.0]])
-
- x = F @ x + B @ u
-
- return x
-
-
-def observation_model(x):
- H = np.array([
- [1, 0, 0, 0, 0],
- [0, 1, 0, 0, 0]
- ])
- z = H @ x
-
- return z
-
-
-def jacob_f(x, u):
- """
- Jacobian of Motion Model
-
- motion model
- x_{t+1} = x_t+v*s*dt*cos(yaw)
- y_{t+1} = y_t+v*s*dt*sin(yaw)
- yaw_{t+1} = yaw_t+omega*dt
- v_{t+1} = v{t}
- s_{t+1} = s{t}
- so
- dx/dyaw = -v*s*dt*sin(yaw)
- dx/dv = dt*s*cos(yaw)
- dx/ds = dt*v*cos(yaw)
- dy/dyaw = v*s*dt*cos(yaw)
- dy/dv = dt*s*sin(yaw)
- dy/ds = dt*v*sin(yaw)
- """
- yaw = x[2, 0]
- v = u[0, 0]
- s = x[4, 0]
- jF = np.array([
- [1.0, 0.0, -DT * v * s * math.sin(yaw), DT * s * math.cos(yaw), DT * v * math.cos(yaw)],
- [0.0, 1.0, DT * v * s * math.cos(yaw), DT * s * math.sin(yaw), DT * v * math.sin(yaw)],
- [0.0, 0.0, 1.0, 0.0, 0.0],
- [0.0, 0.0, 0.0, 1.0, 0.0],
- [0.0, 0.0, 0.0, 0.0, 1.0]])
- return jF
-
-
-def jacob_h():
- jH = np.array([[1, 0, 0, 0, 0],
- [0, 1, 0, 0, 0]])
- return jH
-
-
-def ekf_estimation(xEst, PEst, z, u):
- # Predict
- xPred = motion_model(xEst, u)
- jF = jacob_f(xEst, u)
- PPred = jF @ PEst @ jF.T + Q
-
- # Update
- jH = jacob_h()
- zPred = observation_model(xPred)
- y = z - zPred
- S = jH @ PPred @ jH.T + R
- K = PPred @ jH.T @ np.linalg.inv(S)
- xEst = xPred + K @ y
- PEst = (np.eye(len(xEst)) - K @ jH) @ PPred
- return xEst, PEst
-
-
-def main():
- print(__file__ + " start!!")
-
- time = 0.0
-
- # State Vector [x y yaw v s]'
- xEst = np.zeros((5, 1))
- xEst[4, 0] = 1.0 # Initial scale factor
- xTrue = np.zeros((5, 1))
- true_scale_factor = 0.9 # True scale factor
- xTrue[4, 0] = true_scale_factor
- PEst = np.eye(5)
-
- xDR = np.zeros((5, 1)) # Dead reckoning
-
- # history
- hxEst = xEst
- hxTrue = xTrue
- hxDR = xTrue
- hz = np.zeros((2, 1))
-
- while SIM_TIME >= time:
- time += DT
- u = calc_input()
-
- xTrue, z, xDR, ud = observation(xTrue, xDR, u)
-
- xEst, PEst = ekf_estimation(xEst, PEst, z, ud)
-
- # store data history
- hxEst = np.hstack((hxEst, xEst))
- hxDR = np.hstack((hxDR, xDR))
- hxTrue = np.hstack((hxTrue, xTrue))
- hz = np.hstack((hz, z))
- estimated_scale_factor = hxEst[4, -1]
- if show_animation:
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(hz[0, :], hz[1, :], ".g")
- plt.plot(hxTrue[0, :].flatten(),
- hxTrue[1, :].flatten(), "-b")
- plt.plot(hxDR[0, :].flatten(),
- hxDR[1, :].flatten(), "-k")
- plt.plot(hxEst[0, :].flatten(),
- hxEst[1, :].flatten(), "-r")
- plt.text(0.45, 0.85, f"True Velocity Scale Factor: {true_scale_factor:.2f}", ha='left', va='top', transform=plt.gca().transAxes)
- plt.text(0.45, 0.95, f"Estimated Velocity Scale Factor: {estimated_scale_factor:.2f}", ha='left', va='top', transform=plt.gca().transAxes)
- plot_covariance_ellipse(xEst[0, 0], xEst[1, 0], PEst)
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.001)
-
-
-if __name__ == '__main__':
- main()
diff --git a/Localization/extended_kalman_filter/extended_kalman_filter.py b/Localization/extended_kalman_filter/extended_kalman_filter.py
deleted file mode 100644
index d9ece6c6f38..00000000000
--- a/Localization/extended_kalman_filter/extended_kalman_filter.py
+++ /dev/null
@@ -1,190 +0,0 @@
-"""
-
-Extended kalman filter (EKF) localization sample
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-import sys
-import pathlib
-
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import math
-import matplotlib.pyplot as plt
-import numpy as np
-
-from utils.plot import plot_covariance_ellipse
-
-# Covariance for EKF simulation
-Q = np.diag([
- 0.1, # variance of location on x-axis
- 0.1, # variance of location on y-axis
- np.deg2rad(1.0), # variance of yaw angle
- 1.0 # variance of velocity
-]) ** 2 # predict state covariance
-R = np.diag([1.0, 1.0]) ** 2 # Observation x,y position covariance
-
-# Simulation parameter
-INPUT_NOISE = np.diag([1.0, np.deg2rad(30.0)]) ** 2
-GPS_NOISE = np.diag([0.5, 0.5]) ** 2
-
-DT = 0.1 # time tick [s]
-SIM_TIME = 50.0 # simulation time [s]
-
-show_animation = True
-
-
-def calc_input():
- v = 1.0 # [m/s]
- yawrate = 0.1 # [rad/s]
- u = np.array([[v], [yawrate]])
- return u
-
-
-def observation(xTrue, xd, u):
- xTrue = motion_model(xTrue, u)
-
- # add noise to gps x-y
- z = observation_model(xTrue) + GPS_NOISE @ np.random.randn(2, 1)
-
- # add noise to input
- ud = u + INPUT_NOISE @ np.random.randn(2, 1)
-
- xd = motion_model(xd, ud)
-
- return xTrue, z, xd, ud
-
-
-def motion_model(x, u):
- F = np.array([[1.0, 0, 0, 0],
- [0, 1.0, 0, 0],
- [0, 0, 1.0, 0],
- [0, 0, 0, 0]])
-
- B = np.array([[DT * math.cos(x[2, 0]), 0],
- [DT * math.sin(x[2, 0]), 0],
- [0.0, DT],
- [1.0, 0.0]])
-
- x = F @ x + B @ u
-
- return x
-
-
-def observation_model(x):
- H = np.array([
- [1, 0, 0, 0],
- [0, 1, 0, 0]
- ])
-
- z = H @ x
-
- return z
-
-
-def jacob_f(x, u):
- """
- Jacobian of Motion Model
-
- motion model
- x_{t+1} = x_t+v*dt*cos(yaw)
- y_{t+1} = y_t+v*dt*sin(yaw)
- yaw_{t+1} = yaw_t+omega*dt
- v_{t+1} = v{t}
- so
- dx/dyaw = -v*dt*sin(yaw)
- dx/dv = dt*cos(yaw)
- dy/dyaw = v*dt*cos(yaw)
- dy/dv = dt*sin(yaw)
- """
- yaw = x[2, 0]
- v = u[0, 0]
- jF = np.array([
- [1.0, 0.0, -DT * v * math.sin(yaw), DT * math.cos(yaw)],
- [0.0, 1.0, DT * v * math.cos(yaw), DT * math.sin(yaw)],
- [0.0, 0.0, 1.0, 0.0],
- [0.0, 0.0, 0.0, 1.0]])
-
- return jF
-
-
-def jacob_h():
- # Jacobian of Observation Model
- jH = np.array([
- [1, 0, 0, 0],
- [0, 1, 0, 0]
- ])
-
- return jH
-
-
-def ekf_estimation(xEst, PEst, z, u):
- # Predict
- xPred = motion_model(xEst, u)
- jF = jacob_f(xEst, u)
- PPred = jF @ PEst @ jF.T + Q
-
- # Update
- jH = jacob_h()
- zPred = observation_model(xPred)
- y = z - zPred
- S = jH @ PPred @ jH.T + R
- K = PPred @ jH.T @ np.linalg.inv(S)
- xEst = xPred + K @ y
- PEst = (np.eye(len(xEst)) - K @ jH) @ PPred
- return xEst, PEst
-
-
-def main():
- print(__file__ + " start!!")
-
- time = 0.0
-
- # State Vector [x y yaw v]'
- xEst = np.zeros((4, 1))
- xTrue = np.zeros((4, 1))
- PEst = np.eye(4)
-
- xDR = np.zeros((4, 1)) # Dead reckoning
-
- # history
- hxEst = xEst
- hxTrue = xTrue
- hxDR = xTrue
- hz = np.zeros((2, 1))
-
- while SIM_TIME >= time:
- time += DT
- u = calc_input()
-
- xTrue, z, xDR, ud = observation(xTrue, xDR, u)
-
- xEst, PEst = ekf_estimation(xEst, PEst, z, ud)
-
- # store data history
- hxEst = np.hstack((hxEst, xEst))
- hxDR = np.hstack((hxDR, xDR))
- hxTrue = np.hstack((hxTrue, xTrue))
- hz = np.hstack((hz, z))
-
- if show_animation:
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(hz[0, :], hz[1, :], ".g")
- plt.plot(hxTrue[0, :].flatten(),
- hxTrue[1, :].flatten(), "-b")
- plt.plot(hxDR[0, :].flatten(),
- hxDR[1, :].flatten(), "-k")
- plt.plot(hxEst[0, :].flatten(),
- hxEst[1, :].flatten(), "-r")
- plot_covariance_ellipse(xEst[0, 0], xEst[1, 0], PEst)
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.001)
-
-
-if __name__ == '__main__':
- main()
diff --git a/Localization/histogram_filter/histogram_filter.py b/Localization/histogram_filter/histogram_filter.py
deleted file mode 100644
index 17cfc2e14c7..00000000000
--- a/Localization/histogram_filter/histogram_filter.py
+++ /dev/null
@@ -1,265 +0,0 @@
-"""
-
-Histogram Filter 2D localization example
-
-
-In this simulation, x,y are unknown, yaw is known.
-
-Initial position is not needed.
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import copy
-import math
-
-import matplotlib.pyplot as plt
-import matplotlib as mpl
-import numpy as np
-from scipy.ndimage import gaussian_filter
-from scipy.stats import norm
-
-# Parameters
-EXTEND_AREA = 10.0 # [m] grid map extended length
-SIM_TIME = 50.0 # simulation time [s]
-DT = 0.1 # time tick [s]
-MAX_RANGE = 10.0 # maximum observation range
-MOTION_STD = 1.0 # standard deviation for motion gaussian distribution
-RANGE_STD = 3.0 # standard deviation for observation gaussian distribution
-
-# grid map param
-XY_RESOLUTION = 0.5 # xy grid resolution
-MIN_X = -15.0
-MIN_Y = -5.0
-MAX_X = 15.0
-MAX_Y = 25.0
-
-# simulation parameters
-NOISE_RANGE = 2.0 # [m] 1σ range noise parameter
-NOISE_SPEED = 0.5 # [m/s] 1σ speed noise parameter
-
-show_animation = True
-
-
-class GridMap:
-
- def __init__(self):
- self.data = None
- self.xy_resolution = None
- self.min_x = None
- self.min_y = None
- self.max_x = None
- self.max_y = None
- self.x_w = None
- self.y_w = None
- self.dx = 0.0 # movement distance
- self.dy = 0.0 # movement distance
-
-
-def histogram_filter_localization(grid_map, u, z, yaw):
- grid_map = motion_update(grid_map, u, yaw)
-
- grid_map = observation_update(grid_map, z, RANGE_STD)
-
- return grid_map
-
-
-def calc_gaussian_observation_pdf(grid_map, z, iz, ix, iy, std):
- # predicted range
- x = ix * grid_map.xy_resolution + grid_map.min_x
- y = iy * grid_map.xy_resolution + grid_map.min_y
- d = math.hypot(x - z[iz, 1], y - z[iz, 2])
-
- # likelihood
- pdf = norm.pdf(d - z[iz, 0], 0.0, std)
-
- return pdf
-
-
-def observation_update(grid_map, z, std):
- for iz in range(z.shape[0]):
- for ix in range(grid_map.x_w):
- for iy in range(grid_map.y_w):
- grid_map.data[ix][iy] *= calc_gaussian_observation_pdf(
- grid_map, z, iz, ix, iy, std)
-
- grid_map = normalize_probability(grid_map)
-
- return grid_map
-
-
-def calc_control_input():
- v = 1.0 # [m/s]
- yaw_rate = 0.1 # [rad/s]
- u = np.array([v, yaw_rate]).reshape(2, 1)
- return u
-
-
-def motion_model(x, u):
- F = np.array([[1.0, 0, 0, 0],
- [0, 1.0, 0, 0],
- [0, 0, 1.0, 0],
- [0, 0, 0, 0]])
-
- B = np.array([[DT * math.cos(x[2, 0]), 0],
- [DT * math.sin(x[2, 0]), 0],
- [0.0, DT],
- [1.0, 0.0]])
-
- x = F @ x + B @ u
-
- return x
-
-
-def draw_heat_map(data, mx, my):
- max_value = max([max(i_data) for i_data in data])
- plt.grid(False)
- plt.pcolor(mx, my, data, vmax=max_value, cmap=mpl.colormaps["Blues"])
- plt.axis("equal")
-
-
-def observation(xTrue, u, RFID):
- xTrue = motion_model(xTrue, u)
-
- z = np.zeros((0, 3))
-
- for i in range(len(RFID[:, 0])):
-
- dx = xTrue[0, 0] - RFID[i, 0]
- dy = xTrue[1, 0] - RFID[i, 1]
- d = math.hypot(dx, dy)
- if d <= MAX_RANGE:
- # add noise to range observation
- dn = d + np.random.randn() * NOISE_RANGE
- zi = np.array([dn, RFID[i, 0], RFID[i, 1]])
- z = np.vstack((z, zi))
-
- # add noise to speed
- ud = u[:, :]
- ud[0] += np.random.randn() * NOISE_SPEED
-
- return xTrue, z, ud
-
-
-def normalize_probability(grid_map):
- sump = sum([sum(i_data) for i_data in grid_map.data])
-
- for ix in range(grid_map.x_w):
- for iy in range(grid_map.y_w):
- grid_map.data[ix][iy] /= sump
-
- return grid_map
-
-
-def init_grid_map(xy_resolution, min_x, min_y, max_x, max_y):
- grid_map = GridMap()
-
- grid_map.xy_resolution = xy_resolution
- grid_map.min_x = min_x
- grid_map.min_y = min_y
- grid_map.max_x = max_x
- grid_map.max_y = max_y
- grid_map.x_w = int(round((grid_map.max_x - grid_map.min_x)
- / grid_map.xy_resolution))
- grid_map.y_w = int(round((grid_map.max_y - grid_map.min_y)
- / grid_map.xy_resolution))
-
- grid_map.data = [[1.0 for _ in range(grid_map.y_w)]
- for _ in range(grid_map.x_w)]
- grid_map = normalize_probability(grid_map)
-
- return grid_map
-
-
-def map_shift(grid_map, x_shift, y_shift):
- tmp_grid_map = copy.deepcopy(grid_map.data)
-
- for ix in range(grid_map.x_w):
- for iy in range(grid_map.y_w):
- nix = ix + x_shift
- niy = iy + y_shift
-
- if 0 <= nix < grid_map.x_w and 0 <= niy < grid_map.y_w:
- grid_map.data[ix + x_shift][iy + y_shift] =\
- tmp_grid_map[ix][iy]
-
- return grid_map
-
-
-def motion_update(grid_map, u, yaw):
- grid_map.dx += DT * math.cos(yaw) * u[0]
- grid_map.dy += DT * math.sin(yaw) * u[0]
-
- x_shift = grid_map.dx // grid_map.xy_resolution
- y_shift = grid_map.dy // grid_map.xy_resolution
-
- if abs(x_shift) >= 1.0 or abs(y_shift) >= 1.0: # map should be shifted
- grid_map = map_shift(grid_map, int(x_shift[0]), int(y_shift[0]))
- grid_map.dx -= x_shift * grid_map.xy_resolution
- grid_map.dy -= y_shift * grid_map.xy_resolution
-
- # Add motion noise
- grid_map.data = gaussian_filter(grid_map.data, sigma=MOTION_STD)
-
- return grid_map
-
-
-def calc_grid_index(grid_map):
- mx, my = np.mgrid[slice(grid_map.min_x - grid_map.xy_resolution / 2.0,
- grid_map.max_x + grid_map.xy_resolution / 2.0,
- grid_map.xy_resolution),
- slice(grid_map.min_y - grid_map.xy_resolution / 2.0,
- grid_map.max_y + grid_map.xy_resolution / 2.0,
- grid_map.xy_resolution)]
-
- return mx, my
-
-
-def main():
- print(__file__ + " start!!")
-
- # RF_ID positions [x, y]
- RF_ID = np.array([[10.0, 0.0],
- [10.0, 10.0],
- [0.0, 15.0],
- [-5.0, 20.0]])
-
- time = 0.0
-
- xTrue = np.zeros((4, 1))
- grid_map = init_grid_map(XY_RESOLUTION, MIN_X, MIN_Y, MAX_X, MAX_Y)
- mx, my = calc_grid_index(grid_map) # for grid map visualization
-
- while SIM_TIME >= time:
- time += DT
- print(f"{time=:.1f}")
-
- u = calc_control_input()
-
- yaw = xTrue[2, 0] # Orientation is known
- xTrue, z, ud = observation(xTrue, u, RF_ID)
-
- grid_map = histogram_filter_localization(grid_map, u, z, yaw)
-
- if show_animation:
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- draw_heat_map(grid_map.data, mx, my)
- plt.plot(xTrue[0, :], xTrue[1, :], "xr")
- plt.plot(RF_ID[:, 0], RF_ID[:, 1], ".k")
- for i in range(z.shape[0]):
- plt.plot([xTrue[0, 0], z[i, 1]],
- [xTrue[1, 0], z[i, 2]],
- "-k")
- plt.title("Time[s]:" + str(time)[0: 4])
- plt.pause(0.1)
-
- print("Done")
-
-
-if __name__ == '__main__':
- main()
diff --git a/Localization/particle_filter/particle_filter.py b/Localization/particle_filter/particle_filter.py
deleted file mode 100644
index ba54a3d12b5..00000000000
--- a/Localization/particle_filter/particle_filter.py
+++ /dev/null
@@ -1,263 +0,0 @@
-"""
-
-Particle Filter localization sample
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import math
-
-import matplotlib.pyplot as plt
-import numpy as np
-
-from utils.angle import rot_mat_2d
-
-# Estimation parameter of PF
-Q = np.diag([0.2]) ** 2 # range error
-R = np.diag([2.0, np.deg2rad(40.0)]) ** 2 # input error
-
-# Simulation parameter
-Q_sim = np.diag([0.2]) ** 2
-R_sim = np.diag([1.0, np.deg2rad(30.0)]) ** 2
-
-DT = 0.1 # time tick [s]
-SIM_TIME = 50.0 # simulation time [s]
-MAX_RANGE = 20.0 # maximum observation range
-
-# Particle filter parameter
-NP = 100 # Number of Particle
-NTh = NP / 2.0 # Number of particle for re-sampling
-
-show_animation = True
-
-
-def calc_input():
- v = 1.0 # [m/s]
- yaw_rate = 0.1 # [rad/s]
- u = np.array([[v, yaw_rate]]).T
- return u
-
-
-def observation(x_true, xd, u, rf_id):
- x_true = motion_model(x_true, u)
-
- # add noise to gps x-y
- z = np.zeros((0, 3))
-
- for i in range(len(rf_id[:, 0])):
-
- dx = x_true[0, 0] - rf_id[i, 0]
- dy = x_true[1, 0] - rf_id[i, 1]
- d = math.hypot(dx, dy)
- if d <= MAX_RANGE:
- dn = d + np.random.randn() * Q_sim[0, 0] ** 0.5 # add noise
- zi = np.array([[dn, rf_id[i, 0], rf_id[i, 1]]])
- z = np.vstack((z, zi))
-
- # add noise to input
- ud1 = u[0, 0] + np.random.randn() * R_sim[0, 0] ** 0.5
- ud2 = u[1, 0] + np.random.randn() * R_sim[1, 1] ** 0.5
- ud = np.array([[ud1, ud2]]).T
-
- xd = motion_model(xd, ud)
-
- return x_true, z, xd, ud
-
-
-def motion_model(x, u):
- F = np.array([[1.0, 0, 0, 0],
- [0, 1.0, 0, 0],
- [0, 0, 1.0, 0],
- [0, 0, 0, 0]])
-
- B = np.array([[DT * math.cos(x[2, 0]), 0],
- [DT * math.sin(x[2, 0]), 0],
- [0.0, DT],
- [1.0, 0.0]])
-
- x = F.dot(x) + B.dot(u)
-
- return x
-
-
-def gauss_likelihood(x, sigma):
- p = 1.0 / math.sqrt(2.0 * math.pi * sigma ** 2) * \
- math.exp(-x ** 2 / (2 * sigma ** 2))
-
- return p
-
-
-def calc_covariance(x_est, px, pw):
- """
- calculate covariance matrix
- see ipynb doc
- """
- cov = np.zeros((4, 4))
- n_particle = px.shape[1]
- for i in range(n_particle):
- dx = (px[:, i:i + 1] - x_est)
- cov += pw[0, i] * dx @ dx.T
- cov *= 1.0 / (1.0 - pw @ pw.T)
-
- return cov
-
-
-def pf_localization(px, pw, z, u):
- """
- Localization with Particle filter
- """
-
- for ip in range(NP):
- x = np.array([px[:, ip]]).T
- w = pw[0, ip]
-
- # Predict with random input sampling
- ud1 = u[0, 0] + np.random.randn() * R[0, 0] ** 0.5
- ud2 = u[1, 0] + np.random.randn() * R[1, 1] ** 0.5
- ud = np.array([[ud1, ud2]]).T
- x = motion_model(x, ud)
-
- # Calc Importance Weight
- for i in range(len(z[:, 0])):
- dx = x[0, 0] - z[i, 1]
- dy = x[1, 0] - z[i, 2]
- pre_z = math.hypot(dx, dy)
- dz = pre_z - z[i, 0]
- w = w * gauss_likelihood(dz, math.sqrt(Q[0, 0]))
-
- px[:, ip] = x[:, 0]
- pw[0, ip] = w
-
- pw = pw / pw.sum() # normalize
-
- x_est = px.dot(pw.T)
- p_est = calc_covariance(x_est, px, pw)
-
- N_eff = 1.0 / (pw.dot(pw.T))[0, 0] # Effective particle number
- if N_eff < NTh:
- px, pw = re_sampling(px, pw)
- return x_est, p_est, px, pw
-
-
-def re_sampling(px, pw):
- """
- low variance re-sampling
- """
-
- w_cum = np.cumsum(pw)
- base = np.arange(0.0, 1.0, 1 / NP)
- re_sample_id = base + np.random.uniform(0, 1 / NP)
- indexes = []
- ind = 0
- for ip in range(NP):
- while re_sample_id[ip] > w_cum[ind]:
- ind += 1
- indexes.append(ind)
-
- px = px[:, indexes]
- pw = np.zeros((1, NP)) + 1.0 / NP # init weight
-
- return px, pw
-
-
-def plot_covariance_ellipse(x_est, p_est): # pragma: no cover
- p_xy = p_est[0:2, 0:2]
- eig_val, eig_vec = np.linalg.eig(p_xy)
-
- if eig_val[0] >= eig_val[1]:
- big_ind = 0
- small_ind = 1
- else:
- big_ind = 1
- small_ind = 0
-
- t = np.arange(0, 2 * math.pi + 0.1, 0.1)
-
- # eig_val[big_ind] or eiq_val[small_ind] were occasionally negative
- # numbers extremely close to 0 (~10^-20), catch these cases and set the
- # respective variable to 0
- try:
- a = math.sqrt(eig_val[big_ind])
- except ValueError:
- a = 0
-
- try:
- b = math.sqrt(eig_val[small_ind])
- except ValueError:
- b = 0
-
- x = [a * math.cos(it) for it in t]
- y = [b * math.sin(it) for it in t]
- angle = math.atan2(eig_vec[1, big_ind], eig_vec[0, big_ind])
- fx = rot_mat_2d(angle) @ np.array([[x, y]])
- px = np.array(fx[:, 0] + x_est[0, 0]).flatten()
- py = np.array(fx[:, 1] + x_est[1, 0]).flatten()
- plt.plot(px, py, "--r")
-
-
-def main():
- print(__file__ + " start!!")
-
- time = 0.0
-
- # RF_ID positions [x, y]
- rf_id = np.array([[10.0, 0.0],
- [10.0, 10.0],
- [0.0, 15.0],
- [-5.0, 20.0]])
-
- # State Vector [x y yaw v]'
- x_est = np.zeros((4, 1))
- x_true = np.zeros((4, 1))
-
- px = np.zeros((4, NP)) # Particle store
- pw = np.zeros((1, NP)) + 1.0 / NP # Particle weight
- x_dr = np.zeros((4, 1)) # Dead reckoning
-
- # history
- h_x_est = x_est
- h_x_true = x_true
- h_x_dr = x_true
-
- while SIM_TIME >= time:
- time += DT
- u = calc_input()
-
- x_true, z, x_dr, ud = observation(x_true, x_dr, u, rf_id)
-
- x_est, PEst, px, pw = pf_localization(px, pw, z, ud)
-
- # store data history
- h_x_est = np.hstack((h_x_est, x_est))
- h_x_dr = np.hstack((h_x_dr, x_dr))
- h_x_true = np.hstack((h_x_true, x_true))
-
- if show_animation:
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
-
- for i in range(len(z[:, 0])):
- plt.plot([x_true[0, 0], z[i, 1]], [x_true[1, 0], z[i, 2]], "-k")
- plt.plot(rf_id[:, 0], rf_id[:, 1], "*k")
- plt.plot(px[0, :], px[1, :], ".r")
- plt.plot(np.array(h_x_true[0, :]).flatten(),
- np.array(h_x_true[1, :]).flatten(), "-b")
- plt.plot(np.array(h_x_dr[0, :]).flatten(),
- np.array(h_x_dr[1, :]).flatten(), "-k")
- plt.plot(np.array(h_x_est[0, :]).flatten(),
- np.array(h_x_est[1, :]).flatten(), "-r")
- plot_covariance_ellipse(x_est, PEst)
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.001)
-
-
-if __name__ == '__main__':
- main()
diff --git a/Localization/unscented_kalman_filter/unscented_kalman_filter.py b/Localization/unscented_kalman_filter/unscented_kalman_filter.py
deleted file mode 100644
index 4af748ec71e..00000000000
--- a/Localization/unscented_kalman_filter/unscented_kalman_filter.py
+++ /dev/null
@@ -1,264 +0,0 @@
-"""
-
-Unscented kalman filter (UKF) localization sample
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import math
-
-import matplotlib.pyplot as plt
-import numpy as np
-import scipy.linalg
-
-from utils.angle import rot_mat_2d
-
-# Covariance for UKF simulation
-Q = np.diag([
- 0.1, # variance of location on x-axis
- 0.1, # variance of location on y-axis
- np.deg2rad(1.0), # variance of yaw angle
- 1.0 # variance of velocity
-]) ** 2 # predict state covariance
-R = np.diag([1.0, 1.0]) ** 2 # Observation x,y position covariance
-
-# Simulation parameter
-INPUT_NOISE = np.diag([1.0, np.deg2rad(30.0)]) ** 2
-GPS_NOISE = np.diag([0.5, 0.5]) ** 2
-
-DT = 0.1 # time tick [s]
-SIM_TIME = 50.0 # simulation time [s]
-
-# UKF Parameter
-ALPHA = 0.001
-BETA = 2
-KAPPA = 0
-
-show_animation = True
-
-
-def calc_input():
- v = 1.0 # [m/s]
- yawRate = 0.1 # [rad/s]
- u = np.array([[v, yawRate]]).T
- return u
-
-
-def observation(xTrue, xd, u):
- xTrue = motion_model(xTrue, u)
-
- # add noise to gps x-y
- z = observation_model(xTrue) + GPS_NOISE @ np.random.randn(2, 1)
-
- # add noise to input
- ud = u + INPUT_NOISE @ np.random.randn(2, 1)
-
- xd = motion_model(xd, ud)
-
- return xTrue, z, xd, ud
-
-
-def motion_model(x, u):
- F = np.array([[1.0, 0, 0, 0],
- [0, 1.0, 0, 0],
- [0, 0, 1.0, 0],
- [0, 0, 0, 0]])
-
- B = np.array([[DT * math.cos(x[2, 0]), 0],
- [DT * math.sin(x[2, 0]), 0],
- [0.0, DT],
- [1.0, 0.0]])
-
- x = F @ x + B @ u
-
- return x
-
-
-def observation_model(x):
- H = np.array([
- [1, 0, 0, 0],
- [0, 1, 0, 0]
- ])
-
- z = H @ x
-
- return z
-
-
-def generate_sigma_points(xEst, PEst, gamma):
- sigma = xEst
- Psqrt = scipy.linalg.sqrtm(PEst)
- n = len(xEst[:, 0])
- # Positive direction
- for i in range(n):
- sigma = np.hstack((sigma, xEst + gamma * Psqrt[:, i:i + 1]))
-
- # Negative direction
- for i in range(n):
- sigma = np.hstack((sigma, xEst - gamma * Psqrt[:, i:i + 1]))
-
- return sigma
-
-
-def predict_sigma_motion(sigma, u):
- """
- Sigma Points prediction with motion model
- """
- for i in range(sigma.shape[1]):
- sigma[:, i:i + 1] = motion_model(sigma[:, i:i + 1], u)
-
- return sigma
-
-
-def predict_sigma_observation(sigma):
- """
- Sigma Points prediction with observation model
- """
- for i in range(sigma.shape[1]):
- sigma[0:2, i] = observation_model(sigma[:, i])
-
- sigma = sigma[0:2, :]
-
- return sigma
-
-
-def calc_sigma_covariance(x, sigma, wc, Pi):
- nSigma = sigma.shape[1]
- d = sigma - x[0:sigma.shape[0]]
- P = Pi
- for i in range(nSigma):
- P = P + wc[0, i] * d[:, i:i + 1] @ d[:, i:i + 1].T
- return P
-
-
-def calc_pxz(sigma, x, z_sigma, zb, wc):
- nSigma = sigma.shape[1]
- dx = sigma - x
- dz = z_sigma - zb[0:2]
- P = np.zeros((dx.shape[0], dz.shape[0]))
-
- for i in range(nSigma):
- P = P + wc[0, i] * dx[:, i:i + 1] @ dz[:, i:i + 1].T
-
- return P
-
-
-def ukf_estimation(xEst, PEst, z, u, wm, wc, gamma):
- # Predict
- sigma = generate_sigma_points(xEst, PEst, gamma)
- sigma = predict_sigma_motion(sigma, u)
- xPred = (wm @ sigma.T).T
- PPred = calc_sigma_covariance(xPred, sigma, wc, Q)
-
- # Update
- zPred = observation_model(xPred)
- y = z - zPred
- sigma = generate_sigma_points(xPred, PPred, gamma)
- zb = (wm @ sigma.T).T
- z_sigma = predict_sigma_observation(sigma)
- st = calc_sigma_covariance(zb, z_sigma, wc, R)
- Pxz = calc_pxz(sigma, xPred, z_sigma, zb, wc)
- K = Pxz @ np.linalg.inv(st)
- xEst = xPred + K @ y
- PEst = PPred - K @ st @ K.T
-
- return xEst, PEst
-
-
-def plot_covariance_ellipse(xEst, PEst): # pragma: no cover
- Pxy = PEst[0:2, 0:2]
- eigval, eigvec = np.linalg.eig(Pxy)
-
- if eigval[0] >= eigval[1]:
- bigind = 0
- smallind = 1
- else:
- bigind = 1
- smallind = 0
-
- t = np.arange(0, 2 * math.pi + 0.1, 0.1)
- a = math.sqrt(eigval[bigind])
- b = math.sqrt(eigval[smallind])
- x = [a * math.cos(it) for it in t]
- y = [b * math.sin(it) for it in t]
- angle = math.atan2(eigvec[1, bigind], eigvec[0, bigind])
- fx = rot_mat_2d(angle) @ np.array([x, y])
- px = np.array(fx[0, :] + xEst[0, 0]).flatten()
- py = np.array(fx[1, :] + xEst[1, 0]).flatten()
- plt.plot(px, py, "--r")
-
-
-def setup_ukf(nx):
- lamb = ALPHA ** 2 * (nx + KAPPA) - nx
- # calculate weights
- wm = [lamb / (lamb + nx)]
- wc = [(lamb / (lamb + nx)) + (1 - ALPHA ** 2 + BETA)]
- for i in range(2 * nx):
- wm.append(1.0 / (2 * (nx + lamb)))
- wc.append(1.0 / (2 * (nx + lamb)))
- gamma = math.sqrt(nx + lamb)
-
- wm = np.array([wm])
- wc = np.array([wc])
-
- return wm, wc, gamma
-
-
-def main():
- print(__file__ + " start!!")
-
- nx = 4 # State Vector [x y yaw v]'
- xEst = np.zeros((nx, 1))
- xTrue = np.zeros((nx, 1))
- PEst = np.eye(nx)
- xDR = np.zeros((nx, 1)) # Dead reckoning
-
- wm, wc, gamma = setup_ukf(nx)
-
- # history
- hxEst = xEst
- hxTrue = xTrue
- hxDR = xTrue
- hz = np.zeros((2, 1))
-
- time = 0.0
-
- while SIM_TIME >= time:
- time += DT
- u = calc_input()
-
- xTrue, z, xDR, ud = observation(xTrue, xDR, u)
-
- xEst, PEst = ukf_estimation(xEst, PEst, z, ud, wm, wc, gamma)
-
- # store data history
- hxEst = np.hstack((hxEst, xEst))
- hxDR = np.hstack((hxDR, xDR))
- hxTrue = np.hstack((hxTrue, xTrue))
- hz = np.hstack((hz, z))
-
- if show_animation:
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(hz[0, :], hz[1, :], ".g")
- plt.plot(np.array(hxTrue[0, :]).flatten(),
- np.array(hxTrue[1, :]).flatten(), "-b")
- plt.plot(np.array(hxDR[0, :]).flatten(),
- np.array(hxDR[1, :]).flatten(), "-k")
- plt.plot(np.array(hxEst[0, :]).flatten(),
- np.array(hxEst[1, :]).flatten(), "-r")
- plot_covariance_ellipse(xEst, PEst)
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.001)
-
-
-if __name__ == '__main__':
- main()
diff --git a/Mapping/DistanceMap/distance_map.py b/Mapping/DistanceMap/distance_map.py
deleted file mode 100644
index 0dcc7380c54..00000000000
--- a/Mapping/DistanceMap/distance_map.py
+++ /dev/null
@@ -1,202 +0,0 @@
-"""
-Distance Map
-
-author: Wang Zheng (@Aglargil)
-
-Ref:
-
-- [Distance Map]
-(https://cs.brown.edu/people/pfelzens/papers/dt-final.pdf)
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-import scipy
-
-INF = 1e20
-ENABLE_PLOT = True
-
-
-def compute_sdf_scipy(obstacles):
- """
- Compute the signed distance field (SDF) from a boolean field using scipy.
- This function has the same functionality as compute_sdf.
- However, by using scipy.ndimage.distance_transform_edt, it can compute much faster.
-
- Example: 500×500 map
- • compute_sdf: 3 sec
- • compute_sdf_scipy: 0.05 sec
-
- Parameters
- ----------
- obstacles : array_like
- A 2D boolean array where '1' represents obstacles and '0' represents free space.
-
- Returns
- -------
- array_like
- A 2D array representing the signed distance field, where positive values indicate distance
- to the nearest obstacle, and negative values indicate distance to the nearest free space.
- """
- # distance_transform_edt use '0' as obstacles, so we need to convert the obstacles to '0'
- a = scipy.ndimage.distance_transform_edt(obstacles == 0)
- b = scipy.ndimage.distance_transform_edt(obstacles == 1)
- return a - b
-
-
-def compute_udf_scipy(obstacles):
- """
- Compute the unsigned distance field (UDF) from a boolean field using scipy.
- This function has the same functionality as compute_udf.
- However, by using scipy.ndimage.distance_transform_edt, it can compute much faster.
-
- Example: 500×500 map
- • compute_udf: 1.5 sec
- • compute_udf_scipy: 0.02 sec
-
- Parameters
- ----------
- obstacles : array_like
- A 2D boolean array where '1' represents obstacles and '0' represents free space.
-
- Returns
- -------
- array_like
- A 2D array of distances from the nearest obstacle, with the same dimensions as `bool_field`.
- """
- return scipy.ndimage.distance_transform_edt(obstacles == 0)
-
-
-def compute_sdf(obstacles):
- """
- Compute the signed distance field (SDF) from a boolean field.
-
- Parameters
- ----------
- obstacles : array_like
- A 2D boolean array where '1' represents obstacles and '0' represents free space.
-
- Returns
- -------
- array_like
- A 2D array representing the signed distance field, where positive values indicate distance
- to the nearest obstacle, and negative values indicate distance to the nearest free space.
- """
- a = compute_udf(obstacles)
- b = compute_udf(obstacles == 0)
- return a - b
-
-
-def compute_udf(obstacles):
- """
- Compute the unsigned distance field (UDF) from a boolean field.
-
- Parameters
- ----------
- obstacles : array_like
- A 2D boolean array where '1' represents obstacles and '0' represents free space.
-
- Returns
- -------
- array_like
- A 2D array of distances from the nearest obstacle, with the same dimensions as `bool_field`.
- """
- edt = obstacles.copy()
- if not np.all(np.isin(edt, [0, 1])):
- raise ValueError("Input array should only contain 0 and 1")
- edt = np.where(edt == 0, INF, edt)
- edt = np.where(edt == 1, 0, edt)
- for row in range(len(edt)):
- dt(edt[row])
- edt = edt.T
- for row in range(len(edt)):
- dt(edt[row])
- edt = edt.T
- return np.sqrt(edt)
-
-
-def dt(d):
- """
- Compute 1D distance transform under the squared Euclidean distance
-
- Parameters
- ----------
- d : array_like
- Input array containing the distances.
-
- Returns:
- --------
- d : array_like
- The transformed array with computed distances.
- """
- v = np.zeros(len(d) + 1)
- z = np.zeros(len(d) + 1)
- k = 0
- v[0] = 0
- z[0] = -INF
- z[1] = INF
- for q in range(1, len(d)):
- s = ((d[q] + q * q) - (d[int(v[k])] + v[k] * v[k])) / (2 * q - 2 * v[k])
- while s <= z[k]:
- k = k - 1
- s = ((d[q] + q * q) - (d[int(v[k])] + v[k] * v[k])) / (2 * q - 2 * v[k])
- k = k + 1
- v[k] = q
- z[k] = s
- z[k + 1] = INF
- k = 0
- for q in range(len(d)):
- while z[k + 1] < q:
- k = k + 1
- dx = q - v[k]
- d[q] = dx * dx + d[int(v[k])]
-
-
-def main():
- obstacles = np.array(
- [
- [1, 0, 0, 0, 0],
- [0, 1, 1, 1, 0],
- [0, 1, 1, 1, 0],
- [0, 0, 1, 1, 0],
- [0, 0, 1, 0, 0],
- [0, 0, 0, 0, 0],
- [0, 0, 0, 0, 0],
- [0, 0, 0, 0, 0],
- [0, 0, 1, 0, 0],
- [0, 0, 0, 0, 0],
- [0, 0, 0, 0, 0],
- ]
- )
-
- # Compute the signed distance field
- sdf = compute_sdf(obstacles)
- udf = compute_udf(obstacles)
-
- if ENABLE_PLOT:
- _, (ax1, ax2, ax3) = plt.subplots(1, 3, figsize=(15, 5))
-
- obstacles_plot = ax1.imshow(obstacles, cmap="binary")
- ax1.set_title("Obstacles")
- ax1.set_xlabel("x")
- ax1.set_ylabel("y")
- plt.colorbar(obstacles_plot, ax=ax1)
-
- udf_plot = ax2.imshow(udf, cmap="viridis")
- ax2.set_title("Unsigned Distance Field")
- ax2.set_xlabel("x")
- ax2.set_ylabel("y")
- plt.colorbar(udf_plot, ax=ax2)
-
- sdf_plot = ax3.imshow(sdf, cmap="RdBu")
- ax3.set_title("Signed Distance Field")
- ax3.set_xlabel("x")
- ax3.set_ylabel("y")
- plt.colorbar(sdf_plot, ax=ax3)
-
- plt.tight_layout()
- plt.show()
-
-
-if __name__ == "__main__":
- main()
diff --git a/Mapping/__init__.py b/Mapping/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/Mapping/circle_fitting/circle_fitting.py b/Mapping/circle_fitting/circle_fitting.py
deleted file mode 100644
index 2eba5501273..00000000000
--- a/Mapping/circle_fitting/circle_fitting.py
+++ /dev/null
@@ -1,141 +0,0 @@
-"""
-
-Object shape recognition with circle fitting
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import matplotlib.pyplot as plt
-import math
-import random
-import numpy as np
-
-show_animation = True
-
-
-def circle_fitting(x, y):
- """
- Circle Fitting with least squared
- input: point x-y positions
- output cxe x center position
- cye y center position
- re radius of circle
- error: prediction error
- """
-
- sumx = sum(x)
- sumy = sum(y)
- sumx2 = sum([ix ** 2 for ix in x])
- sumy2 = sum([iy ** 2 for iy in y])
- sumxy = sum([ix * iy for (ix, iy) in zip(x, y)])
-
- F = np.array([[sumx2, sumxy, sumx],
- [sumxy, sumy2, sumy],
- [sumx, sumy, len(x)]])
-
- G = np.array([[-sum([ix ** 3 + ix * iy ** 2 for (ix, iy) in zip(x, y)])],
- [-sum([ix ** 2 * iy + iy ** 3 for (ix, iy) in zip(x, y)])],
- [-sum([ix ** 2 + iy ** 2 for (ix, iy) in zip(x, y)])]])
-
- T = np.linalg.inv(F).dot(G)
-
- cxe = float(T[0, 0] / -2)
- cye = float(T[1, 0] / -2)
- re = math.sqrt(cxe**2 + cye**2 - T[2, 0])
-
- error = sum([np.hypot(cxe - ix, cye - iy) - re for (ix, iy) in zip(x, y)])
-
- return (cxe, cye, re, error)
-
-
-def get_sample_points(cx, cy, cr, angle_reso):
- x, y, angle, r = [], [], [], []
-
- # points sampling
- for theta in np.arange(0.0, 2.0 * math.pi, angle_reso):
- nx = cx + cr * math.cos(theta)
- ny = cy + cr * math.sin(theta)
- nangle = math.atan2(ny, nx)
- nr = math.hypot(nx, ny) * random.uniform(0.95, 1.05)
-
- x.append(nx)
- y.append(ny)
- angle.append(nangle)
- r.append(nr)
-
- # ray casting filter
- rx, ry = ray_casting_filter(x, y, angle, r, angle_reso)
-
- return rx, ry
-
-
-def ray_casting_filter(xl, yl, thetal, rangel, angle_reso):
- rx, ry = [], []
- rangedb = [float("inf") for _ in range(
- int(math.floor((math.pi * 2.0) / angle_reso)) + 1)]
-
- for i, _ in enumerate(thetal):
- angleid = math.floor(thetal[i] / angle_reso)
-
- if rangedb[angleid] > rangel[i]:
- rangedb[angleid] = rangel[i]
-
- for i, _ in enumerate(rangedb):
- t = i * angle_reso
- if rangedb[i] != float("inf"):
- rx.append(rangedb[i] * math.cos(t))
- ry.append(rangedb[i] * math.sin(t))
-
- return rx, ry
-
-
-def plot_circle(x, y, size, color="-b"): # pragma: no cover
- deg = list(range(0, 360, 5))
- deg.append(0)
- xl = [x + size * math.cos(np.deg2rad(d)) for d in deg]
- yl = [y + size * math.sin(np.deg2rad(d)) for d in deg]
- plt.plot(xl, yl, color)
-
-
-def main():
-
- # simulation parameters
- simtime = 15.0 # simulation time
- dt = 1.0 # time tick
-
- cx = -2.0 # initial x position of obstacle
- cy = -8.0 # initial y position of obstacle
- cr = 1.0 # obstacle radious
- theta = np.deg2rad(30.0) # obstacle moving direction
- angle_reso = np.deg2rad(3.0) # sensor angle resolution
-
- time = 0.0
- while time <= simtime:
- time += dt
-
- cx += math.cos(theta)
- cy += math.cos(theta)
-
- x, y = get_sample_points(cx, cy, cr, angle_reso)
-
- ex, ey, er, error = circle_fitting(x, y)
- print("Error:", error)
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.axis("equal")
- plt.plot(0.0, 0.0, "*r")
- plot_circle(cx, cy, cr)
- plt.plot(x, y, "xr")
- plot_circle(ex, ey, er, "-r")
- plt.pause(dt)
-
- print("Done")
-
-
-if __name__ == '__main__':
- main()
diff --git a/Mapping/gaussian_grid_map/gaussian_grid_map.py b/Mapping/gaussian_grid_map/gaussian_grid_map.py
deleted file mode 100644
index b7664f1acbb..00000000000
--- a/Mapping/gaussian_grid_map/gaussian_grid_map.py
+++ /dev/null
@@ -1,86 +0,0 @@
-"""
-
-2D gaussian grid map sample
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import math
-import numpy as np
-import matplotlib.pyplot as plt
-from scipy.stats import norm
-
-EXTEND_AREA = 10.0 # [m] grid map extention length
-
-show_animation = True
-
-
-def generate_gaussian_grid_map(ox, oy, xyreso, std):
-
- minx, miny, maxx, maxy, xw, yw = calc_grid_map_config(ox, oy, xyreso)
-
- gmap = [[0.0 for i in range(yw)] for i in range(xw)]
-
- for ix in range(xw):
- for iy in range(yw):
-
- x = ix * xyreso + minx
- y = iy * xyreso + miny
-
- # Search minimum distance
- mindis = float("inf")
- for (iox, ioy) in zip(ox, oy):
- d = math.hypot(iox - x, ioy - y)
- if mindis >= d:
- mindis = d
-
- pdf = (1.0 - norm.cdf(mindis, 0.0, std))
- gmap[ix][iy] = pdf
-
- return gmap, minx, maxx, miny, maxy
-
-
-def calc_grid_map_config(ox, oy, xyreso):
- minx = round(min(ox) - EXTEND_AREA / 2.0)
- miny = round(min(oy) - EXTEND_AREA / 2.0)
- maxx = round(max(ox) + EXTEND_AREA / 2.0)
- maxy = round(max(oy) + EXTEND_AREA / 2.0)
- xw = int(round((maxx - minx) / xyreso))
- yw = int(round((maxy - miny) / xyreso))
-
- return minx, miny, maxx, maxy, xw, yw
-
-
-def draw_heatmap(data, minx, maxx, miny, maxy, xyreso):
- x, y = np.mgrid[slice(minx - xyreso / 2.0, maxx + xyreso / 2.0, xyreso),
- slice(miny - xyreso / 2.0, maxy + xyreso / 2.0, xyreso)]
- plt.pcolor(x, y, data, vmax=1.0, cmap=plt.cm.Blues)
- plt.axis("equal")
-
-
-def main():
- print(__file__ + " start!!")
-
- xyreso = 0.5 # xy grid resolution
- STD = 5.0 # standard diviation for gaussian distribution
-
- for i in range(5):
- ox = (np.random.rand(4) - 0.5) * 10.0
- oy = (np.random.rand(4) - 0.5) * 10.0
- gmap, minx, maxx, miny, maxy = generate_gaussian_grid_map(
- ox, oy, xyreso, STD)
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- draw_heatmap(gmap, minx, maxx, miny, maxy, xyreso)
- plt.plot(ox, oy, "xr")
- plt.plot(0.0, 0.0, "ob")
- plt.pause(1.0)
-
-
-if __name__ == '__main__':
- main()
diff --git a/Mapping/grid_map_lib/__init__.py b/Mapping/grid_map_lib/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/Mapping/grid_map_lib/grid_map_lib.py b/Mapping/grid_map_lib/grid_map_lib.py
deleted file mode 100644
index d08d8ec5ba4..00000000000
--- a/Mapping/grid_map_lib/grid_map_lib.py
+++ /dev/null
@@ -1,312 +0,0 @@
-"""
-
-Grid map library in python
-
-author: Atsushi Sakai
-
-"""
-from functools import total_ordering
-import matplotlib.pyplot as plt
-import numpy as np
-
-
-@total_ordering
-class FloatGrid:
-
- def __init__(self, init_val=0.0):
- self.data = init_val
-
- def get_float_data(self):
- return self.data
-
- def __eq__(self, other):
- if not isinstance(other, FloatGrid):
- return NotImplemented
- return self.get_float_data() == other.get_float_data()
-
- def __lt__(self, other):
- if not isinstance(other, FloatGrid):
- return NotImplemented
- return self.get_float_data() < other.get_float_data()
-
-
-class GridMap:
- """
- GridMap class
- """
-
- def __init__(self, width, height, resolution,
- center_x, center_y, init_val=FloatGrid(0.0)):
- """__init__
-
- :param width: number of grid for width
- :param height: number of grid for height
- :param resolution: grid resolution [m]
- :param center_x: center x position [m]
- :param center_y: center y position [m]
- :param init_val: initial value for all grid
- """
- self.width = width
- self.height = height
- self.resolution = resolution
- self.center_x = center_x
- self.center_y = center_y
-
- self.left_lower_x = self.center_x - self.width / 2.0 * self.resolution
- self.left_lower_y = self.center_y - self.height / 2.0 * self.resolution
-
- self.n_data = self.width * self.height
- self.data = [init_val] * self.n_data
- self.data_type = type(init_val)
-
- def get_value_from_xy_index(self, x_ind, y_ind):
- """get_value_from_xy_index
-
- when the index is out of grid map area, return None
-
- :param x_ind: x index
- :param y_ind: y index
- """
-
- grid_ind = self.calc_grid_index_from_xy_index(x_ind, y_ind)
-
- if 0 <= grid_ind < self.n_data:
- return self.data[grid_ind]
- else:
- return None
-
- def get_xy_index_from_xy_pos(self, x_pos, y_pos):
- """get_xy_index_from_xy_pos
-
- :param x_pos: x position [m]
- :param y_pos: y position [m]
- """
- x_ind = self.calc_xy_index_from_position(
- x_pos, self.left_lower_x, self.width)
- y_ind = self.calc_xy_index_from_position(
- y_pos, self.left_lower_y, self.height)
-
- return x_ind, y_ind
-
- def set_value_from_xy_pos(self, x_pos, y_pos, val):
- """set_value_from_xy_pos
-
- return bool flag, which means setting value is succeeded or not
-
- :param x_pos: x position [m]
- :param y_pos: y position [m]
- :param val: grid value
- """
-
- x_ind, y_ind = self.get_xy_index_from_xy_pos(x_pos, y_pos)
-
- if (not x_ind) or (not y_ind):
- return False # NG
-
- flag = self.set_value_from_xy_index(x_ind, y_ind, val)
-
- return flag
-
- def set_value_from_xy_index(self, x_ind, y_ind, val):
- """set_value_from_xy_index
-
- return bool flag, which means setting value is succeeded or not
-
- :param x_ind: x index
- :param y_ind: y index
- :param val: grid value
- """
-
- if (x_ind is None) or (y_ind is None):
- return False, False
-
- grid_ind = int(y_ind * self.width + x_ind)
-
- if 0 <= grid_ind < self.n_data and isinstance(val, self.data_type):
- self.data[grid_ind] = val
- return True # OK
- else:
- return False # NG
-
- def set_value_from_polygon(self, pol_x, pol_y, val, inside=True):
- """set_value_from_polygon
-
- Setting value inside or outside polygon
-
- :param pol_x: x position list for a polygon
- :param pol_y: y position list for a polygon
- :param val: grid value
- :param inside: setting data inside or outside
- """
-
- # making ring polygon
- if (pol_x[0] != pol_x[-1]) or (pol_y[0] != pol_y[-1]):
- np.append(pol_x, pol_x[0])
- np.append(pol_y, pol_y[0])
-
- # setting value for all grid
- for x_ind in range(self.width):
- for y_ind in range(self.height):
- x_pos, y_pos = self.calc_grid_central_xy_position_from_xy_index(
- x_ind, y_ind)
-
- flag = self.check_inside_polygon(x_pos, y_pos, pol_x, pol_y)
-
- if flag is inside:
- self.set_value_from_xy_index(x_ind, y_ind, val)
-
- def calc_grid_index_from_xy_index(self, x_ind, y_ind):
- grid_ind = int(y_ind * self.width + x_ind)
- return grid_ind
-
- def calc_xy_index_from_grid_index(self, grid_ind):
- y_ind, x_ind = divmod(grid_ind, self.width)
- return x_ind, y_ind
-
- def calc_grid_index_from_xy_pos(self, x_pos, y_pos):
- """get_xy_index_from_xy_pos
-
- :param x_pos: x position [m]
- :param y_pos: y position [m]
- """
- x_ind = self.calc_xy_index_from_position(
- x_pos, self.left_lower_x, self.width)
- y_ind = self.calc_xy_index_from_position(
- y_pos, self.left_lower_y, self.height)
-
- return self.calc_grid_index_from_xy_index(x_ind, y_ind)
-
- def calc_grid_central_xy_position_from_grid_index(self, grid_ind):
- x_ind, y_ind = self.calc_xy_index_from_grid_index(grid_ind)
- return self.calc_grid_central_xy_position_from_xy_index(x_ind, y_ind)
-
- def calc_grid_central_xy_position_from_xy_index(self, x_ind, y_ind):
- x_pos = self.calc_grid_central_xy_position_from_index(
- x_ind, self.left_lower_x)
- y_pos = self.calc_grid_central_xy_position_from_index(
- y_ind, self.left_lower_y)
-
- return x_pos, y_pos
-
- def calc_grid_central_xy_position_from_index(self, index, lower_pos):
- return lower_pos + index * self.resolution + self.resolution / 2.0
-
- def calc_xy_index_from_position(self, pos, lower_pos, max_index):
- ind = int(np.floor((pos - lower_pos) / self.resolution))
- if 0 <= ind <= max_index:
- return ind
- else:
- return None
-
- def check_occupied_from_xy_index(self, x_ind, y_ind, occupied_val):
-
- val = self.get_value_from_xy_index(x_ind, y_ind)
-
- if val is None or val >= occupied_val:
- return True
- else:
- return False
-
- def expand_grid(self, occupied_val=FloatGrid(1.0)):
- x_inds, y_inds, values = [], [], []
-
- for ix in range(self.width):
- for iy in range(self.height):
- if self.check_occupied_from_xy_index(ix, iy, occupied_val):
- x_inds.append(ix)
- y_inds.append(iy)
- values.append(self.get_value_from_xy_index(ix, iy))
-
- for (ix, iy, value) in zip(x_inds, y_inds, values):
- self.set_value_from_xy_index(ix + 1, iy, val=value)
- self.set_value_from_xy_index(ix, iy + 1, val=value)
- self.set_value_from_xy_index(ix + 1, iy + 1, val=value)
- self.set_value_from_xy_index(ix - 1, iy, val=value)
- self.set_value_from_xy_index(ix, iy - 1, val=value)
- self.set_value_from_xy_index(ix - 1, iy - 1, val=value)
-
- @staticmethod
- def check_inside_polygon(iox, ioy, x, y):
-
- n_point = len(x) - 1
- inside = False
- for i1 in range(n_point):
- i2 = (i1 + 1) % (n_point + 1)
-
- if x[i1] >= x[i2]:
- min_x, max_x = x[i2], x[i1]
- else:
- min_x, max_x = x[i1], x[i2]
- if not min_x <= iox < max_x:
- continue
-
- tmp1 = (y[i2] - y[i1]) / (x[i2] - x[i1])
- if (y[i1] + tmp1 * (iox - x[i1]) - ioy) > 0.0:
- inside = not inside
-
- return inside
-
- def print_grid_map_info(self):
- print("width:", self.width)
- print("height:", self.height)
- print("resolution:", self.resolution)
- print("center_x:", self.center_x)
- print("center_y:", self.center_y)
- print("left_lower_x:", self.left_lower_x)
- print("left_lower_y:", self.left_lower_y)
- print("n_data:", self.n_data)
-
- def plot_grid_map(self, ax=None):
- float_data_array = np.array([d.get_float_data() for d in self.data])
- grid_data = np.reshape(float_data_array, (self.height, self.width))
- if not ax:
- fig, ax = plt.subplots()
- heat_map = ax.pcolor(grid_data, cmap="Blues", vmin=0.0, vmax=1.0)
- plt.axis("equal")
-
- return heat_map
-
-
-def polygon_set_demo():
- ox = [0.0, 4.35, 20.0, 50.0, 100.0, 130.0, 40.0]
- oy = [0.0, -4.15, -20.0, 0.0, 30.0, 60.0, 80.0]
-
- grid_map = GridMap(600, 290, 0.7, 60.0, 30.5)
-
- grid_map.set_value_from_polygon(ox, oy, FloatGrid(1.0), inside=False)
-
- grid_map.plot_grid_map()
-
- plt.axis("equal")
- plt.grid(True)
-
-
-def position_set_demo():
- grid_map = GridMap(100, 120, 0.5, 10.0, -0.5)
-
- grid_map.set_value_from_xy_pos(10.1, -1.1, FloatGrid(1.0))
- grid_map.set_value_from_xy_pos(10.1, -0.1, FloatGrid(1.0))
- grid_map.set_value_from_xy_pos(10.1, 1.1, FloatGrid(1.0))
- grid_map.set_value_from_xy_pos(11.1, 0.1, FloatGrid(1.0))
- grid_map.set_value_from_xy_pos(10.1, 0.1, FloatGrid(1.0))
- grid_map.set_value_from_xy_pos(9.1, 0.1, FloatGrid(1.0))
-
- grid_map.plot_grid_map()
-
- plt.axis("equal")
- plt.grid(True)
-
-
-def main():
- print("start!!")
-
- position_set_demo()
- polygon_set_demo()
-
- plt.show()
-
- print("done!!")
-
-
-if __name__ == '__main__':
- main()
diff --git a/Mapping/kmeans_clustering/kmeans_clustering.py b/Mapping/kmeans_clustering/kmeans_clustering.py
deleted file mode 100644
index e18960e9903..00000000000
--- a/Mapping/kmeans_clustering/kmeans_clustering.py
+++ /dev/null
@@ -1,149 +0,0 @@
-"""
-
-Object clustering with k-means algorithm
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import math
-import matplotlib.pyplot as plt
-import random
-
-# k means parameters
-MAX_LOOP = 10
-DCOST_TH = 0.1
-show_animation = True
-
-
-def kmeans_clustering(rx, ry, nc):
- clusters = Clusters(rx, ry, nc)
- clusters.calc_centroid()
-
- pre_cost = float("inf")
- for loop in range(MAX_LOOP):
- print("loop:", loop)
- cost = clusters.update_clusters()
- clusters.calc_centroid()
-
- d_cost = abs(cost - pre_cost)
- if d_cost < DCOST_TH:
- break
- pre_cost = cost
-
- return clusters
-
-
-class Clusters:
-
- def __init__(self, x, y, n_label):
- self.x = x
- self.y = y
- self.n_data = len(self.x)
- self.n_label = n_label
- self.labels = [random.randint(0, n_label - 1)
- for _ in range(self.n_data)]
- self.center_x = [0.0 for _ in range(n_label)]
- self.center_y = [0.0 for _ in range(n_label)]
-
- def plot_cluster(self):
- for label in set(self.labels):
- x, y = self._get_labeled_x_y(label)
- plt.plot(x, y, ".")
-
- def calc_centroid(self):
- for label in set(self.labels):
- x, y = self._get_labeled_x_y(label)
- n_data = len(x)
- self.center_x[label] = sum(x) / n_data
- self.center_y[label] = sum(y) / n_data
-
- def update_clusters(self):
- cost = 0.0
-
- for ip in range(self.n_data):
- px = self.x[ip]
- py = self.y[ip]
-
- dx = [icx - px for icx in self.center_x]
- dy = [icy - py for icy in self.center_y]
-
- dist_list = [math.hypot(idx, idy) for (idx, idy) in zip(dx, dy)]
- min_dist = min(dist_list)
- min_id = dist_list.index(min_dist)
- self.labels[ip] = min_id
- cost += min_dist
-
- return cost
-
- def _get_labeled_x_y(self, target_label):
- x = [self.x[i] for i, label in enumerate(self.labels) if label == target_label]
- y = [self.y[i] for i, label in enumerate(self.labels) if label == target_label]
- return x, y
-
-
-def calc_raw_data(cx, cy, n_points, rand_d):
- rx, ry = [], []
-
- for (icx, icy) in zip(cx, cy):
- for _ in range(n_points):
- rx.append(icx + rand_d * (random.random() - 0.5))
- ry.append(icy + rand_d * (random.random() - 0.5))
-
- return rx, ry
-
-
-def update_positions(cx, cy):
- # object moving parameters
- DX1 = 0.4
- DY1 = 0.5
- DX2 = -0.3
- DY2 = -0.5
-
- cx[0] += DX1
- cy[0] += DY1
- cx[1] += DX2
- cy[1] += DY2
-
- return cx, cy
-
-
-def main():
- print(__file__ + " start!!")
-
- cx = [0.0, 8.0]
- cy = [0.0, 8.0]
- n_points = 10
- rand_d = 3.0
- n_cluster = 2
- sim_time = 15.0
- dt = 1.0
- time = 0.0
-
- while time <= sim_time:
- print("Time:", time)
- time += dt
-
- # objects moving simulation
- cx, cy = update_positions(cx, cy)
- raw_x, raw_y = calc_raw_data(cx, cy, n_points, rand_d)
-
- clusters = kmeans_clustering(raw_x, raw_y, n_cluster)
-
- # for animation
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- clusters.plot_cluster()
- plt.plot(cx, cy, "or")
- plt.xlim(-2.0, 10.0)
- plt.ylim(-2.0, 10.0)
- plt.pause(dt)
-
- print("Done")
-
-
-if __name__ == '__main__':
- main()
diff --git a/Mapping/lidar_to_grid_map/lidar01.csv b/Mapping/lidar_to_grid_map/lidar01.csv
deleted file mode 100644
index 1f6b3f5cd9f..00000000000
--- a/Mapping/lidar_to_grid_map/lidar01.csv
+++ /dev/null
@@ -1,154 +0,0 @@
-0.008450416037156572,0.5335
-0.046902201120156306,0.5345
-0.08508127850753233,0.537
-0.1979822644959155,0.2605
-0.21189035697274505,0.2625
-0.2587960806200922,0.26475
-0.3043382657893199,0.2675
-0.34660795861105775,0.27075
-0.43632879047139106,0.59
-0.4739624524675188,0.60025
-0.5137777760286397,0.611
-0.5492297764597742,0.6265
-0.5895905154121426,0.64
-0.6253152235389017,0.6565
-0.6645851317087743,0.676
-0.6997644244442851,0.6975
-0.7785769484796541,0.3345
-0.7772134100015329,0.74575
-0.8652979956881222,0.3315
-0.8996591653367609,0.31775
-0.9397471965935056,0.31275
-0.9847439663714841,0.31125
-1.0283771976713423,0.31325
-1.0641019057981014,0.31975
-1.1009174447073562,0.3335
-1.2012738766970301,0.92275
-1.2397256617800307,0.95325
-1.2779047391674068,0.9865
-1.316629231946031,1.01775
-1.3561718478115274,1.011
-1.3948963405901518,1.0055
-1.4330754179775278,1.00225
-1.4731634492342724,0.99975
-1.5113425266216485,0.9975
-1.5517032655740168,1.001
-1.5896096352657691,1.00275
-1.6288795434356418,1.008
-1.6684221593011381,1.0135
-1.7066012366885142,1.022
-1.7453257294671385,1.02875
-1.7862318838107551,0.9935
-1.8257744996762515,1.0025
-1.8661352386286207,0.96075
-1.9045870237116205,0.92125
-1.9465840088377355,0.8855
-1.986944747790103,0.85725
-2.025669240568728,0.832
-2.065757271825472,0.80675
-2.1066634261690886,0.78875
-2.1464787497302105,0.7705
-2.1865667809869542,0.75625
-2.2261093968524506,0.74475
-2.2683790896741876,0.68275
-2.3090125363221823,0.6375
-2.3510095214482956,0.59925
-2.3916429680962885,0.5665
-2.4330945378311526,0.538
-2.4783640153047557,0.50825
-2.5203610004308707,0.4875
-2.562903400948233,0.46825
-2.599173524466238,0.45
-2.642806755766097,0.4355
-2.685076448587836,0.42275
-2.722437402888339,0.4125
-2.766888757275069,0.40125
-2.8007045115324587,0.39525
-2.841883373571701,0.385
-2.8819714048284446,0.3805
-2.922332143780814,0.38575
-2.9637837135156797,0.38425
-3.0005992524249336,0.36575
-3.0401418682904318,0.3765
-3.079957191851552,0.3915
-3.115409192282687,0.408
-3.154679100452558,0.4265
-3.184949654666836,0.447
-3.2242195628367085,0.4715
-3.2574899017028507,0.49875
-3.2959416867858504,0.52875
-3.3292120256519926,0.564
-3.3665729799524957,0.6055
-3.4031158111661277,0.6515
-3.438022396206014,0.70675
-3.4756560582021407,0.771
-3.513562427893893,0.77075
-3.5522869206725183,0.7785
-3.621827383056667,0.79575
-3.65918833735717,0.8045
-3.697367414744546,0.81725
-3.7377281536969154,0.83325
-3.775634523388667,0.8415
-3.8135408930804187,0.85575
-3.8522653858590425,0.87325
-3.8898990478551703,0.88725
-3.9299870791119154,0.906
-3.9665299103255465,0.9265
-4.006072526191043,0.94575
-4.043978895882795,0.97175
-4.081885265574547,1.02075
-4.1206097583531704,1.046
-4.1587888357405465,1.07025
-4.196422497736674,1.097
-4.234874282819675,1.12575
-4.286688744988257,0.73475
-4.324322406984384,0.72225
-4.364410438241129,0.731
-4.405862007975994,0.7405
-4.44267754688525,0.749
-4.484129116620115,0.76025
-4.522853609398739,0.76825
-4.560759979090491,0.77125
-4.5989390564778665,0.77725
-4.640117918517108,0.782
-4.679115118991357,0.78425
-4.717294196378733,0.789
-4.757109519939853,0.78825
-4.796652135805349,0.7855
-4.8337403824102285,0.786
-4.871646752101981,0.78275
-4.9109166602718535,0.7785
-4.950186568441726,0.7635
-4.990274599698471,0.74725
-5.028180969390222,0.737
-5.0677235852557185,0.72575
-5.109720570381833,0.71525
-5.149263186247329,0.70625
-5.1863514328522085,0.69975
-5.230530079543315,0.693
-5.269799987713188,0.68925
-5.307979065100563,0.68425
-5.347248973270435,0.68275
-5.386518881440308,0.68075
-5.426606912697053,0.68175
-5.465604113171301,0.67825
-5.502419652080556,0.6835
-5.543871221815422,0.6885
-5.580959468420302,0.67925
-5.624319992024535,0.6555
-5.660044700151294,0.639
-5.700950854494911,0.623
-5.740220762664784,0.6075
-5.783581286269018,0.59475
-5.820124117482649,0.58475
-5.861848394913139,0.57325
-5.899209349213642,0.565
-5.938751965079138,0.55525
-5.9782945809446355,0.55175
-6.017564489114507,0.546
-6.059288766544997,0.5405
-6.097467843932373,0.53825
-6.139464829058487,0.534
-6.176825783358991,0.5325
-6.215822983833238,0.53125
-6.252911230438118,0.53075
\ No newline at end of file
diff --git a/Mapping/lidar_to_grid_map/lidar_to_grid_map.py b/Mapping/lidar_to_grid_map/lidar_to_grid_map.py
deleted file mode 100644
index ad987392f5d..00000000000
--- a/Mapping/lidar_to_grid_map/lidar_to_grid_map.py
+++ /dev/null
@@ -1,240 +0,0 @@
-"""
-
-LIDAR to 2D grid map example
-
-author: Erno Horvath, Csaba Hajdu based on Atsushi Sakai's scripts
-
-"""
-
-import math
-from collections import deque
-
-import matplotlib.pyplot as plt
-import numpy as np
-
-EXTEND_AREA = 1.0
-
-
-def file_read(f):
- """
- Reading LIDAR laser beams (angles and corresponding distance data)
- """
- with open(f) as data:
- measures = [line.split(",") for line in data]
- angles = []
- distances = []
- for measure in measures:
- angles.append(float(measure[0]))
- distances.append(float(measure[1]))
- angles = np.array(angles)
- distances = np.array(distances)
- return angles, distances
-
-
-def bresenham(start, end):
- """
- Implementation of Bresenham's line drawing algorithm
- See en.wikipedia.org/wiki/Bresenham's_line_algorithm
- Bresenham's Line Algorithm
- Produces a np.array from start and end (original from roguebasin.com)
- >>> points1 = bresenham((4, 4), (6, 10))
- >>> print(points1)
- np.array([[4,4], [4,5], [5,6], [5,7], [5,8], [6,9], [6,10]])
- """
- # setup initial conditions
- x1, y1 = start
- x2, y2 = end
- dx = x2 - x1
- dy = y2 - y1
- is_steep = abs(dy) > abs(dx) # determine how steep the line is
- if is_steep: # rotate line
- x1, y1 = y1, x1
- x2, y2 = y2, x2
- # swap start and end points if necessary and store swap state
- swapped = False
- if x1 > x2:
- x1, x2 = x2, x1
- y1, y2 = y2, y1
- swapped = True
- dx = x2 - x1 # recalculate differentials
- dy = y2 - y1 # recalculate differentials
- error = int(dx / 2.0) # calculate error
- y_step = 1 if y1 < y2 else -1
- # iterate over bounding box generating points between start and end
- y = y1
- points = []
- for x in range(x1, x2 + 1):
- coord = [y, x] if is_steep else (x, y)
- points.append(coord)
- error -= abs(dy)
- if error < 0:
- y += y_step
- error += dx
- if swapped: # reverse the list if the coordinates were swapped
- points.reverse()
- points = np.array(points)
- return points
-
-
-def calc_grid_map_config(ox, oy, xy_resolution):
- """
- Calculates the size, and the maximum distances according to the the
- measurement center
- """
- min_x = round(min(ox) - EXTEND_AREA / 2.0)
- min_y = round(min(oy) - EXTEND_AREA / 2.0)
- max_x = round(max(ox) + EXTEND_AREA / 2.0)
- max_y = round(max(oy) + EXTEND_AREA / 2.0)
- xw = int(round((max_x - min_x) / xy_resolution))
- yw = int(round((max_y - min_y) / xy_resolution))
- print("The grid map is ", xw, "x", yw, ".")
- return min_x, min_y, max_x, max_y, xw, yw
-
-
-def atan_zero_to_twopi(y, x):
- angle = math.atan2(y, x)
- if angle < 0.0:
- angle += math.pi * 2.0
- return angle
-
-
-def init_flood_fill(center_point, obstacle_points, xy_points, min_coord,
- xy_resolution):
- """
- center_point: center point
- obstacle_points: detected obstacles points (x,y)
- xy_points: (x,y) point pairs
- """
- center_x, center_y = center_point
- prev_ix, prev_iy = center_x - 1, center_y
- ox, oy = obstacle_points
- xw, yw = xy_points
- min_x, min_y = min_coord
- occupancy_map = (np.ones((xw, yw))) * 0.5
- for (x, y) in zip(ox, oy):
- # x coordinate of the the occupied area
- ix = int(round((x - min_x) / xy_resolution))
- # y coordinate of the the occupied area
- iy = int(round((y - min_y) / xy_resolution))
- free_area = bresenham((prev_ix, prev_iy), (ix, iy))
- for fa in free_area:
- occupancy_map[fa[0]][fa[1]] = 0 # free area 0.0
- prev_ix = ix
- prev_iy = iy
- return occupancy_map
-
-
-def flood_fill(center_point, occupancy_map):
- """
- center_point: starting point (x,y) of fill
- occupancy_map: occupancy map generated from Bresenham ray-tracing
- """
- # Fill empty areas with queue method
- sx, sy = occupancy_map.shape
- fringe = deque()
- fringe.appendleft(center_point)
- while fringe:
- n = fringe.pop()
- nx, ny = n
- # West
- if nx > 0:
- if occupancy_map[nx - 1, ny] == 0.5:
- occupancy_map[nx - 1, ny] = 0.0
- fringe.appendleft((nx - 1, ny))
- # East
- if nx < sx - 1:
- if occupancy_map[nx + 1, ny] == 0.5:
- occupancy_map[nx + 1, ny] = 0.0
- fringe.appendleft((nx + 1, ny))
- # North
- if ny > 0:
- if occupancy_map[nx, ny - 1] == 0.5:
- occupancy_map[nx, ny - 1] = 0.0
- fringe.appendleft((nx, ny - 1))
- # South
- if ny < sy - 1:
- if occupancy_map[nx, ny + 1] == 0.5:
- occupancy_map[nx, ny + 1] = 0.0
- fringe.appendleft((nx, ny + 1))
-
-
-def generate_ray_casting_grid_map(ox, oy, xy_resolution, breshen=True):
- """
- The breshen boolean tells if it's computed with bresenham ray casting
- (True) or with flood fill (False)
- """
- min_x, min_y, max_x, max_y, x_w, y_w = calc_grid_map_config(
- ox, oy, xy_resolution)
- # default 0.5 -- [[0.5 for i in range(y_w)] for i in range(x_w)]
- occupancy_map = np.ones((x_w, y_w)) / 2
- center_x = int(
- round(-min_x / xy_resolution)) # center x coordinate of the grid map
- center_y = int(
- round(-min_y / xy_resolution)) # center y coordinate of the grid map
- # occupancy grid computed with bresenham ray casting
- if breshen:
- for (x, y) in zip(ox, oy):
- # x coordinate of the the occupied area
- ix = int(round((x - min_x) / xy_resolution))
- # y coordinate of the the occupied area
- iy = int(round((y - min_y) / xy_resolution))
- laser_beams = bresenham((center_x, center_y), (
- ix, iy)) # line form the lidar to the occupied point
- for laser_beam in laser_beams:
- occupancy_map[laser_beam[0]][
- laser_beam[1]] = 0.0 # free area 0.0
- occupancy_map[ix][iy] = 1.0 # occupied area 1.0
- occupancy_map[ix + 1][iy] = 1.0 # extend the occupied area
- occupancy_map[ix][iy + 1] = 1.0 # extend the occupied area
- occupancy_map[ix + 1][iy + 1] = 1.0 # extend the occupied area
- # occupancy grid computed with with flood fill
- else:
- occupancy_map = init_flood_fill((center_x, center_y), (ox, oy),
- (x_w, y_w),
- (min_x, min_y), xy_resolution)
- flood_fill((center_x, center_y), occupancy_map)
- occupancy_map = np.array(occupancy_map, dtype=float)
- for (x, y) in zip(ox, oy):
- ix = int(round((x - min_x) / xy_resolution))
- iy = int(round((y - min_y) / xy_resolution))
- occupancy_map[ix][iy] = 1.0 # occupied area 1.0
- occupancy_map[ix + 1][iy] = 1.0 # extend the occupied area
- occupancy_map[ix][iy + 1] = 1.0 # extend the occupied area
- occupancy_map[ix + 1][iy + 1] = 1.0 # extend the occupied area
- return occupancy_map, min_x, max_x, min_y, max_y, xy_resolution
-
-
-def main():
- """
- Example usage
- """
- print(__file__, "start")
- xy_resolution = 0.02 # x-y grid resolution
- ang, dist = file_read("lidar01.csv")
- ox = np.sin(ang) * dist
- oy = np.cos(ang) * dist
- occupancy_map, min_x, max_x, min_y, max_y, xy_resolution = \
- generate_ray_casting_grid_map(ox, oy, xy_resolution, True)
- xy_res = np.array(occupancy_map).shape
- plt.figure(1, figsize=(10, 4))
- plt.subplot(122)
- plt.imshow(occupancy_map, cmap="PiYG_r")
- # cmap = "binary" "PiYG_r" "PiYG_r" "bone" "bone_r" "RdYlGn_r"
- plt.clim(-0.4, 1.4)
- plt.gca().set_xticks(np.arange(-.5, xy_res[1], 1), minor=True)
- plt.gca().set_yticks(np.arange(-.5, xy_res[0], 1), minor=True)
- plt.grid(True, which="minor", color="w", linewidth=0.6, alpha=0.5)
- plt.colorbar()
- plt.subplot(121)
- plt.plot([oy, np.zeros(np.size(oy))], [ox, np.zeros(np.size(oy))], "ro-")
- plt.axis("equal")
- plt.plot(0.0, 0.0, "ob")
- plt.gca().set_aspect("equal", "box")
- bottom, top = plt.ylim() # return the current y-lim
- plt.ylim((top, bottom)) # rescale y axis, to match the grid orientation
- plt.grid(True)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/Mapping/ndt_map/ndt_map.py b/Mapping/ndt_map/ndt_map.py
deleted file mode 100644
index f4f32996625..00000000000
--- a/Mapping/ndt_map/ndt_map.py
+++ /dev/null
@@ -1,135 +0,0 @@
-"""
-Normal Distribution Transform (NDTGrid) mapping sample
-"""
-import matplotlib.pyplot as plt
-import numpy as np
-from collections import defaultdict
-
-from Mapping.grid_map_lib.grid_map_lib import GridMap
-from utils.plot import plot_covariance_ellipse
-
-
-class NDTMap:
- """
- Normal Distribution Transform (NDT) map class
-
- :param ox: obstacle x position list
- :param oy: obstacle y position list
- :param resolution: grid resolution [m]
- """
-
- class NDTGrid:
- """
- NDT grid
- """
-
- def __init__(self):
- #: Number of points in the NDTGrid grid
- self.n_points = 0
- #: Mean x position of points in the NDTGrid cell
- self.mean_x = None
- #: Mean y position of points in the NDTGrid cell
- self.mean_y = None
- #: Center x position of the NDT grid
- self.center_grid_x = None
- #: Center y position of the NDT grid
- self.center_grid_y = None
- #: Covariance matrix of the NDT grid
- self.covariance = None
- #: Eigen vectors of the NDT grid
- self.eig_vec = None
- #: Eigen values of the NDT grid
- self.eig_values = None
-
- def __init__(self, ox, oy, resolution):
- #: Minimum number of points in the NDT grid
- self.min_n_points = 3
- #: Resolution of the NDT grid [m]
- self.resolution = resolution
- width = int((max(ox) - min(ox))/resolution) + 3 # rounding up + right and left margin
- height = int((max(oy) - min(oy))/resolution) + 3
- center_x = np.mean(ox)
- center_y = np.mean(oy)
- self.ox = ox
- self.oy = oy
- #: NDT grid index map
- self.grid_index_map = self._create_grid_index_map(ox, oy)
-
- #: NDT grid map. Each grid contains NDTGrid object
- self._construct_grid_map(center_x, center_y, height, ox, oy, resolution, width)
-
- def _construct_grid_map(self, center_x, center_y, height, ox, oy, resolution, width):
- self.grid_map = GridMap(width, height, resolution, center_x, center_y, self.NDTGrid())
- for grid_index, inds in self.grid_index_map.items():
- ndt = self.NDTGrid()
- ndt.n_points = len(inds)
- if ndt.n_points >= self.min_n_points:
- ndt.mean_x = np.mean(ox[inds])
- ndt.mean_y = np.mean(oy[inds])
- ndt.center_grid_x, ndt.center_grid_y = \
- self.grid_map.calc_grid_central_xy_position_from_grid_index(grid_index)
- ndt.covariance = np.cov(ox[inds], oy[inds])
- ndt.eig_values, ndt.eig_vec = np.linalg.eig(ndt.covariance)
- self.grid_map.data[grid_index] = ndt
-
- def _create_grid_index_map(self, ox, oy):
- grid_index_map = defaultdict(list)
- for i in range(len(ox)):
- grid_index = self.grid_map.calc_grid_index_from_xy_pos(ox[i], oy[i])
- grid_index_map[grid_index].append(i)
- return grid_index_map
-
-
-def create_dummy_observation_data():
- ox = []
- oy = []
- # left corridor
- for y in range(-50, 50):
- ox.append(-20.0)
- oy.append(y)
- # right corridor 1
- for y in range(-50, 0):
- ox.append(20.0)
- oy.append(y)
- # right corridor 2
- for x in range(20, 50):
- ox.append(x)
- oy.append(0)
- # right corridor 3
- for x in range(20, 50):
- ox.append(x)
- oy.append(x/2.0+10)
- # right corridor 4
- for y in range(20, 50):
- ox.append(20)
- oy.append(y)
- ox = np.array(ox)
- oy = np.array(oy)
- # Adding random noize
- ox += np.random.rand(len(ox)) * 1.0
- oy += np.random.rand(len(ox)) * 1.0
- return ox, oy
-
-
-def main():
- print(__file__ + " start!!")
-
- ox, oy = create_dummy_observation_data()
- grid_resolution = 10.0
- ndt_map = NDTMap(ox, oy, grid_resolution)
-
- # plot raw observation
- plt.plot(ox, oy, ".r")
-
- # plot grid clustering
- [plt.plot(ox[inds], oy[inds], "x") for inds in ndt_map.grid_index_map.values()]
-
- # plot ndt grid map
- [plot_covariance_ellipse(ndt.mean_x, ndt.mean_y, ndt.covariance, color="-k") for ndt in ndt_map.grid_map.data if ndt.n_points > 0]
-
- plt.axis("equal")
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/Mapping/normal_vector_estimation/normal_vector_estimation.py b/Mapping/normal_vector_estimation/normal_vector_estimation.py
deleted file mode 100644
index 996ba3ffee5..00000000000
--- a/Mapping/normal_vector_estimation/normal_vector_estimation.py
+++ /dev/null
@@ -1,177 +0,0 @@
-import numpy as np
-from matplotlib import pyplot as plt
-
-from utils.plot import plot_3d_vector_arrow, plot_triangle, set_equal_3d_axis
-
-show_animation = True
-
-
-def calc_normal_vector(p1, p2, p3):
- """Calculate normal vector of triangle
-
- Parameters
- ----------
- p1 : np.array
- 3D point
- p2 : np.array
- 3D point
- p3 : np.array
- 3D point
-
- Returns
- -------
- normal_vector : np.array
- normal vector (3,)
-
- """
- # calculate two vectors of triangle
- v1 = p2 - p1
- v2 = p3 - p1
-
- # calculate normal vector
- normal_vector = np.cross(v1, v2)
-
- # normalize vector
- normal_vector = normal_vector / np.linalg.norm(normal_vector)
-
- return normal_vector
-
-
-def sample_3d_points_from_a_plane(num_samples, normal):
- points_2d = np.random.normal(size=(num_samples, 2)) # 2D points on a plane
- d = 0
- for i in range(len(points_2d)):
- point_3d = np.append(points_2d[i], 0)
- d += normal @ point_3d
- d /= len(points_2d)
-
- points_3d = np.zeros((len(points_2d), 3))
- for i in range(len(points_2d)):
- point_2d = np.append(points_2d[i], 0)
- projection_length = (d - normal @ point_2d) / np.linalg.norm(normal)
- points_3d[i] = point_2d + projection_length * normal
-
- return points_3d
-
-
-def distance_to_plane(point, normal, origin):
- dot_product = np.dot(normal, point) - np.dot(normal, origin)
- if np.isclose(dot_product, 0):
- return 0.0
- else:
- distance = abs(dot_product) / np.linalg.norm(normal)
- return distance
-
-
-def ransac_normal_vector_estimation(points_3d, inlier_radio_th=0.7,
- inlier_dist=0.1, p=0.99):
- """
- RANSAC based normal vector estimation
-
- Parameters
- ----------
- points_3d : np.array
- 3D points (N, 3)
- inlier_radio_th : float
- Inlier ratio threshold. If inlier ratio is larger than this value,
- the iteration is stopped. Default is 0.7.
- inlier_dist : float
- Inlier distance threshold. If distance between points and estimated
- plane is smaller than this value, the point is inlier. Default is 0.1.
- p : float
- Probability that at least one of the sets of random samples does not
- include an outlier. If this probability is near 1, the iteration
- number is large. Default is 0.99.
-
- Returns
- -------
- center_vector : np.array
- Center of estimated plane. (3,)
- normal_vector : np.array
- Normal vector of estimated plane. (3,)
-
- """
- center = np.mean(points_3d, axis=0)
-
- max_iter = int(np.floor(np.log(1.0-p)/np.log(1.0-(1.0-inlier_radio_th)**3)))
-
- for ite in range(max_iter):
- # Random sampling
- sampled_ids = np.random.choice(points_3d.shape[0], size=3,
- replace=False)
- sampled_points = points_3d[sampled_ids, :]
- p1 = sampled_points[0, :]
- p2 = sampled_points[1, :]
- p3 = sampled_points[2, :]
- normal_vector = calc_normal_vector(p1, p2, p3)
-
- # calc inlier ratio
- n_inliner = 0
- for i in range(points_3d.shape[0]):
- p = points_3d[i, :]
- if distance_to_plane(p, normal_vector, center) <= inlier_dist:
- n_inliner += 1
- inlier_ratio = n_inliner / points_3d.shape[0]
- print(f"Iter:{ite}, {inlier_ratio=}")
- if inlier_ratio > inlier_radio_th:
- return center, normal_vector
-
- return center, None
-
-
-def main1():
- p1 = np.array([0.0, 0.0, 1.0])
- p2 = np.array([1.0, 1.0, 0.0])
- p3 = np.array([0.0, 1.0, 0.0])
-
- center = np.mean([p1, p2, p3], axis=0)
- normal_vector = calc_normal_vector(p1, p2, p3)
- print(f"{center=}")
- print(f"{normal_vector=}")
-
- if show_animation:
- fig = plt.figure()
- ax = fig.add_subplot(projection='3d')
- set_equal_3d_axis(ax, [0.0, 2.5], [0.0, 2.5], [0.0, 3.0])
- plot_triangle(p1, p2, p3, ax)
- ax.plot(center[0], center[1], center[2], "ro")
- plot_3d_vector_arrow(ax, center, center + normal_vector)
- plt.show()
-
-
-def main2(rng=None):
- true_normal = np.array([0, 1, 1])
- true_normal = true_normal / np.linalg.norm(true_normal)
- num_samples = 100
- noise_scale = 0.1
-
- points_3d = sample_3d_points_from_a_plane(num_samples, true_normal)
- # add random noise
- points_3d += np.random.normal(size=points_3d.shape, scale=noise_scale)
-
- print(f"{points_3d.shape=}")
-
- center, estimated_normal = ransac_normal_vector_estimation(
- points_3d, inlier_dist=noise_scale)
-
- if estimated_normal is None:
- print("Failed to estimate normal vector")
- return
-
- print(f"{true_normal=}")
- print(f"{estimated_normal=}")
-
- if show_animation:
- fig = plt.figure()
- ax = fig.add_subplot(projection='3d')
- ax.plot(points_3d[:, 0], points_3d[:, 1], points_3d[:, 2], ".r")
- plot_3d_vector_arrow(ax, center, center + true_normal)
- plot_3d_vector_arrow(ax, center, center + estimated_normal)
- set_equal_3d_axis(ax, [-3.0, 3.0], [-3.0, 3.0], [-3.0, 3.0])
- plt.title("RANSAC based Normal vector estimation")
- plt.show()
-
-
-if __name__ == '__main__':
- # main1()
- main2()
diff --git a/Mapping/point_cloud_sampling/point_cloud_sampling.py b/Mapping/point_cloud_sampling/point_cloud_sampling.py
deleted file mode 100644
index df7cde41c06..00000000000
--- a/Mapping/point_cloud_sampling/point_cloud_sampling.py
+++ /dev/null
@@ -1,168 +0,0 @@
-"""
-Point cloud sampling example codes. This code supports
-- Voxel point sampling
-- Farthest point sampling
-- Poisson disk sampling
-
-"""
-import matplotlib.pyplot as plt
-import numpy as np
-import numpy.typing as npt
-from collections import defaultdict
-
-do_plot = True
-
-
-def voxel_point_sampling(original_points: npt.NDArray, voxel_size: float):
- """
- Voxel Point Sampling function.
- This function sample N-dimensional points with voxel grid.
- Points in a same voxel grid will be merged by mean operation for sampling.
-
- Parameters
- ----------
- original_points : (M, N) N-dimensional points for sampling.
- The number of points is M.
- voxel_size : voxel grid size
-
- Returns
- -------
- sampled points (M', N)
- """
- voxel_dict = defaultdict(list)
- for i in range(original_points.shape[0]):
- xyz = original_points[i, :]
- xyz_index = tuple(xyz // voxel_size)
- voxel_dict[xyz_index].append(xyz)
- points = np.vstack([np.mean(v, axis=0) for v in voxel_dict.values()])
- return points
-
-
-def farthest_point_sampling(orig_points: npt.NDArray,
- n_points: int, seed: int):
- """
- Farthest point sampling function
- This function sample N-dimensional points with the farthest point policy.
-
- Parameters
- ----------
- orig_points : (M, N) N-dimensional points for sampling.
- The number of points is M.
- n_points : number of points for sampling
- seed : random seed number
-
- Returns
- -------
- sampled points (n_points, N)
-
- """
- rng = np.random.default_rng(seed)
- n_orig_points = orig_points.shape[0]
- first_point_id = rng.choice(range(n_orig_points))
- min_distances = np.ones(n_orig_points) * float("inf")
- selected_ids = [first_point_id]
- while len(selected_ids) < n_points:
- base_point = orig_points[selected_ids[-1], :]
- distances = np.linalg.norm(orig_points[np.newaxis, :] - base_point,
- axis=2).flatten()
- min_distances = np.minimum(min_distances, distances)
- distances_rank = np.argsort(-min_distances) # Farthest order
- for i in distances_rank: # From the farthest point
- if i not in selected_ids: # if not selected yes, select it
- selected_ids.append(i)
- break
- return orig_points[selected_ids, :]
-
-
-def poisson_disk_sampling(orig_points: npt.NDArray, n_points: int,
- min_distance: float, seed: int, MAX_ITER=1000):
- """
- Poisson disk sampling function
- This function sample N-dimensional points randomly until the number of
- points keeping minimum distance between selected points.
-
- Parameters
- ----------
- orig_points : (M, N) N-dimensional points for sampling.
- The number of points is M.
- n_points : number of points for sampling
- min_distance : minimum distance between selected points.
- seed : random seed number
- MAX_ITER : Maximum number of iteration. Default is 1000.
-
- Returns
- -------
- sampled points (n_points or less, N)
- """
- rng = np.random.default_rng(seed)
- selected_id = rng.choice(range(orig_points.shape[0]))
- selected_ids = [selected_id]
- loop = 0
- while len(selected_ids) < n_points and loop <= MAX_ITER:
- selected_id = rng.choice(range(orig_points.shape[0]))
- base_point = orig_points[selected_id, :]
- distances = np.linalg.norm(
- orig_points[np.newaxis, selected_ids] - base_point,
- axis=2).flatten()
- if min(distances) >= min_distance:
- selected_ids.append(selected_id)
- loop += 1
- if len(selected_ids) != n_points:
- print("Could not find the specified number of points...")
-
- return orig_points[selected_ids, :]
-
-
-def plot_sampled_points(original_points, sampled_points, method_name):
- fig = plt.figure()
- ax = fig.add_subplot(projection='3d')
- ax.scatter(original_points[:, 0], original_points[:, 1],
- original_points[:, 2], marker=".", label="Original points")
- ax.scatter(sampled_points[:, 0], sampled_points[:, 1],
- sampled_points[:, 2], marker="o",
- label="Filtered points")
- plt.legend()
- plt.title(method_name)
- plt.axis("equal")
-
-
-def main():
- n_points = 1000
- seed = 1234
- rng = np.random.default_rng(seed)
-
- x = rng.normal(0.0, 10.0, n_points)
- y = rng.normal(0.0, 1.0, n_points)
- z = rng.normal(0.0, 10.0, n_points)
- original_points = np.vstack((x, y, z)).T
- print(f"{original_points.shape=}")
- print("Voxel point sampling")
- voxel_size = 20.0
- voxel_sampling_points = voxel_point_sampling(original_points, voxel_size)
- print(f"{voxel_sampling_points.shape=}")
-
- print("Farthest point sampling")
- n_points = 20
- farthest_sampling_points = farthest_point_sampling(original_points,
- n_points, seed)
- print(f"{farthest_sampling_points.shape=}")
-
- print("Poisson disk sampling")
- n_points = 20
- min_distance = 10.0
- poisson_disk_points = poisson_disk_sampling(original_points, n_points,
- min_distance, seed)
- print(f"{poisson_disk_points.shape=}")
-
- if do_plot:
- plot_sampled_points(original_points, voxel_sampling_points,
- "Voxel point sampling")
- plot_sampled_points(original_points, farthest_sampling_points,
- "Farthest point sampling")
- plot_sampled_points(original_points, poisson_disk_points,
- "poisson disk sampling")
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/Mapping/raycasting_grid_map/raycasting_grid_map.py b/Mapping/raycasting_grid_map/raycasting_grid_map.py
deleted file mode 100644
index 8ce37b925b0..00000000000
--- a/Mapping/raycasting_grid_map/raycasting_grid_map.py
+++ /dev/null
@@ -1,137 +0,0 @@
-"""
-
-Ray casting 2D grid map example
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import math
-import numpy as np
-import matplotlib.pyplot as plt
-
-EXTEND_AREA = 10.0
-
-show_animation = True
-
-
-def calc_grid_map_config(ox, oy, xyreso):
- minx = round(min(ox) - EXTEND_AREA / 2.0)
- miny = round(min(oy) - EXTEND_AREA / 2.0)
- maxx = round(max(ox) + EXTEND_AREA / 2.0)
- maxy = round(max(oy) + EXTEND_AREA / 2.0)
- xw = int(round((maxx - minx) / xyreso))
- yw = int(round((maxy - miny) / xyreso))
-
- return minx, miny, maxx, maxy, xw, yw
-
-
-class precastDB:
-
- def __init__(self):
- self.px = 0.0
- self.py = 0.0
- self.d = 0.0
- self.angle = 0.0
- self.ix = 0
- self.iy = 0
-
- def __str__(self):
- return str(self.px) + "," + str(self.py) + "," + str(self.d) + "," + str(self.angle)
-
-
-def atan_zero_to_twopi(y, x):
- angle = math.atan2(y, x)
- if angle < 0.0:
- angle += math.pi * 2.0
-
- return angle
-
-
-def precasting(minx, miny, xw, yw, xyreso, yawreso):
-
- precast = [[] for i in range(int(round((math.pi * 2.0) / yawreso)) + 1)]
-
- for ix in range(xw):
- for iy in range(yw):
- px = ix * xyreso + minx
- py = iy * xyreso + miny
-
- d = math.hypot(px, py)
- angle = atan_zero_to_twopi(py, px)
- angleid = int(math.floor(angle / yawreso))
-
- pc = precastDB()
-
- pc.px = px
- pc.py = py
- pc.d = d
- pc.ix = ix
- pc.iy = iy
- pc.angle = angle
-
- precast[angleid].append(pc)
-
- return precast
-
-
-def generate_ray_casting_grid_map(ox, oy, xyreso, yawreso):
-
- minx, miny, maxx, maxy, xw, yw = calc_grid_map_config(ox, oy, xyreso)
-
- pmap = [[0.0 for i in range(yw)] for i in range(xw)]
-
- precast = precasting(minx, miny, xw, yw, xyreso, yawreso)
-
- for (x, y) in zip(ox, oy):
-
- d = math.hypot(x, y)
- angle = atan_zero_to_twopi(y, x)
- angleid = int(math.floor(angle / yawreso))
-
- gridlist = precast[angleid]
-
- ix = int(round((x - minx) / xyreso))
- iy = int(round((y - miny) / xyreso))
-
- for grid in gridlist:
- if grid.d > d:
- pmap[grid.ix][grid.iy] = 0.5
-
- pmap[ix][iy] = 1.0
-
- return pmap, minx, maxx, miny, maxy, xyreso
-
-
-def draw_heatmap(data, minx, maxx, miny, maxy, xyreso):
- x, y = np.mgrid[slice(minx - xyreso / 2.0, maxx + xyreso / 2.0, xyreso),
- slice(miny - xyreso / 2.0, maxy + xyreso / 2.0, xyreso)]
- plt.pcolor(x, y, data, vmax=1.0, cmap=plt.cm.Blues)
- plt.axis("equal")
-
-
-def main():
- print(__file__ + " start!!")
-
- xyreso = 0.25 # x-y grid resolution [m]
- yawreso = np.deg2rad(10.0) # yaw angle resolution [rad]
-
- for i in range(5):
- ox = (np.random.rand(4) - 0.5) * 10.0
- oy = (np.random.rand(4) - 0.5) * 10.0
- pmap, minx, maxx, miny, maxy, xyreso = generate_ray_casting_grid_map(
- ox, oy, xyreso, yawreso)
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- draw_heatmap(pmap, minx, maxx, miny, maxy, xyreso)
- plt.plot(ox, oy, "xr")
- plt.plot(0.0, 0.0, "ob")
- plt.pause(1.0)
-
-
-if __name__ == '__main__':
- main()
diff --git a/Mapping/rectangle_fitting/__init_.py b/Mapping/rectangle_fitting/__init_.py
deleted file mode 100644
index 2194d4c3033..00000000000
--- a/Mapping/rectangle_fitting/__init_.py
+++ /dev/null
@@ -1,3 +0,0 @@
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent))
diff --git a/Mapping/rectangle_fitting/rectangle_fitting.py b/Mapping/rectangle_fitting/rectangle_fitting.py
deleted file mode 100644
index 177f0788718..00000000000
--- a/Mapping/rectangle_fitting/rectangle_fitting.py
+++ /dev/null
@@ -1,291 +0,0 @@
-"""
-
-Object shape recognition with L-shape fitting
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-Ref:
-- Efficient L-Shape Fitting for Vehicle Detection Using Laser Scanners -
-The Robotics Institute Carnegie Mellon University
-https://www.ri.cmu.edu/publications/
-efficient-l-shape-fitting-for-vehicle-detection-using-laser-scanners/
-
-"""
-
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import matplotlib.pyplot as plt
-import numpy as np
-import itertools
-from enum import Enum
-
-from utils.angle import rot_mat_2d
-
-from Mapping.rectangle_fitting.simulator \
- import VehicleSimulator, LidarSimulator
-
-show_animation = True
-
-
-class LShapeFitting:
- """
- LShapeFitting class. You can use this class by initializing the class and
- changing the parameters, and then calling the fitting method.
-
- """
-
- class Criteria(Enum):
- AREA = 1
- CLOSENESS = 2
- VARIANCE = 3
-
- def __init__(self):
- """
- Default parameter settings
- """
- #: Fitting criteria parameter
- self.criteria = self.Criteria.VARIANCE
- #: Minimum distance for closeness criteria parameter [m]
- self.min_dist_of_closeness_criteria = 0.01
- #: Angle difference parameter [deg]
- self.d_theta_deg_for_search = 1.0
- #: Range segmentation parameter [m]
- self.R0 = 3.0
- #: Range segmentation parameter [m]
- self.Rd = 0.001
-
- def fitting(self, ox, oy):
- """
- Fitting L-shape model to object points
-
- Parameters
- ----------
- ox : x positions of range points from an object
- oy : y positions of range points from an object
-
- Returns
- -------
- rects: Fitting rectangles
- id_sets: id sets of each cluster
-
- """
- # step1: Adaptive Range Segmentation
- id_sets = self._adoptive_range_segmentation(ox, oy)
-
- # step2 Rectangle search
- rects = []
- for ids in id_sets: # for each cluster
- cx = [ox[i] for i in range(len(ox)) if i in ids]
- cy = [oy[i] for i in range(len(oy)) if i in ids]
- rects.append(self._rectangle_search(cx, cy))
-
- return rects, id_sets
-
- @staticmethod
- def _calc_area_criterion(c1, c2):
- c1_max, c1_min, c2_max, c2_min = LShapeFitting._find_min_max(c1, c2)
- alpha = -(c1_max - c1_min) * (c2_max - c2_min)
- return alpha
-
- def _calc_closeness_criterion(self, c1, c2):
- c1_max, c1_min, c2_max, c2_min = LShapeFitting._find_min_max(c1, c2)
-
- # Vectorization
- d1 = np.minimum(c1_max - c1, c1 - c1_min)
- d2 = np.minimum(c2_max - c2, c2 - c2_min)
- d = np.maximum(np.minimum(d1, d2), self.min_dist_of_closeness_criteria)
- beta = (1.0 / d).sum()
-
- return beta
-
- @staticmethod
- def _calc_variance_criterion(c1, c2):
- c1_max, c1_min, c2_max, c2_min = LShapeFitting._find_min_max(c1, c2)
-
- # Vectorization
- d1 = np.minimum(c1_max - c1, c1 - c1_min)
- d2 = np.minimum(c2_max - c2, c2 - c2_min)
- e1 = d1[d1 < d2]
- e2 = d2[d1 >= d2]
- v1 = - np.var(e1) if len(e1) > 0 else 0.
- v2 = - np.var(e2) if len(e2) > 0 else 0.
- gamma = v1 + v2
-
- return gamma
-
- @staticmethod
- def _find_min_max(c1, c2):
- c1_max = max(c1)
- c2_max = max(c2)
- c1_min = min(c1)
- c2_min = min(c2)
- return c1_max, c1_min, c2_max, c2_min
-
- def _rectangle_search(self, x, y):
-
- xy = np.array([x, y]).T
-
- d_theta = np.deg2rad(self.d_theta_deg_for_search)
- min_cost = (-float('inf'), None)
- for theta in np.arange(0.0, np.pi / 2.0 - d_theta, d_theta):
-
- c = xy @ rot_mat_2d(theta)
- c1 = c[:, 0]
- c2 = c[:, 1]
-
- # Select criteria
- cost = 0.0
- if self.criteria == self.Criteria.AREA:
- cost = self._calc_area_criterion(c1, c2)
- elif self.criteria == self.Criteria.CLOSENESS:
- cost = self._calc_closeness_criterion(c1, c2)
- elif self.criteria == self.Criteria.VARIANCE:
- cost = self._calc_variance_criterion(c1, c2)
-
- if min_cost[0] < cost:
- min_cost = (cost, theta)
-
- # calc best rectangle
- sin_s = np.sin(min_cost[1])
- cos_s = np.cos(min_cost[1])
-
- c1_s = xy @ np.array([cos_s, sin_s]).T
- c2_s = xy @ np.array([-sin_s, cos_s]).T
-
- rect = RectangleData()
- rect.a[0] = cos_s
- rect.b[0] = sin_s
- rect.c[0] = min(c1_s)
- rect.a[1] = -sin_s
- rect.b[1] = cos_s
- rect.c[1] = min(c2_s)
- rect.a[2] = cos_s
- rect.b[2] = sin_s
- rect.c[2] = max(c1_s)
- rect.a[3] = -sin_s
- rect.b[3] = cos_s
- rect.c[3] = max(c2_s)
-
- return rect
-
- def _adoptive_range_segmentation(self, ox, oy):
-
- # Setup initial cluster
- segment_list = []
- for i, _ in enumerate(ox):
- c = set()
- r = self.R0 + self.Rd * np.linalg.norm([ox[i], oy[i]])
- for j, _ in enumerate(ox):
- d = np.hypot(ox[i] - ox[j], oy[i] - oy[j])
- if d <= r:
- c.add(j)
- segment_list.append(c)
-
- # Merge cluster
- while True:
- no_change = True
- for (c1, c2) in list(itertools.permutations(range(len(segment_list)), 2)):
- if segment_list[c1] & segment_list[c2]:
- segment_list[c1] = (segment_list[c1] | segment_list.pop(c2))
- no_change = False
- break
- if no_change:
- break
-
- return segment_list
-
-
-class RectangleData:
-
- def __init__(self):
- self.a = [None] * 4
- self.b = [None] * 4
- self.c = [None] * 4
-
- self.rect_c_x = [None] * 5
- self.rect_c_y = [None] * 5
-
- def plot(self):
- self.calc_rect_contour()
- plt.plot(self.rect_c_x, self.rect_c_y, "-r")
-
- def calc_rect_contour(self):
-
- self.rect_c_x[0], self.rect_c_y[0] = self.calc_cross_point(
- self.a[0:2], self.b[0:2], self.c[0:2])
- self.rect_c_x[1], self.rect_c_y[1] = self.calc_cross_point(
- self.a[1:3], self.b[1:3], self.c[1:3])
- self.rect_c_x[2], self.rect_c_y[2] = self.calc_cross_point(
- self.a[2:4], self.b[2:4], self.c[2:4])
- self.rect_c_x[3], self.rect_c_y[3] = self.calc_cross_point(
- [self.a[3], self.a[0]], [self.b[3], self.b[0]], [self.c[3], self.c[0]])
- self.rect_c_x[4], self.rect_c_y[4] = self.rect_c_x[0], self.rect_c_y[0]
-
- @staticmethod
- def calc_cross_point(a, b, c):
- x = (b[0] * -c[1] - b[1] * -c[0]) / (a[0] * b[1] - a[1] * b[0])
- y = (a[1] * -c[0] - a[0] * -c[1]) / (a[0] * b[1] - a[1] * b[0])
- return x, y
-
-
-def main():
-
- # simulation parameters
- sim_time = 30.0 # simulation time
- dt = 0.2 # time tick
-
- angle_resolution = np.deg2rad(3.0) # sensor angle resolution
-
- v1 = VehicleSimulator(-10.0, 0.0, np.deg2rad(90.0),
- 0.0, 50.0 / 3.6, 3.0, 5.0)
- v2 = VehicleSimulator(20.0, 10.0, np.deg2rad(180.0),
- 0.0, 50.0 / 3.6, 4.0, 10.0)
-
- l_shape_fitting = LShapeFitting()
- lidar_sim = LidarSimulator()
-
- time = 0.0
- while time <= sim_time:
- time += dt
-
- v1.update(dt, 0.1, 0.0)
- v2.update(dt, 0.1, -0.05)
-
- ox, oy = lidar_sim.get_observation_points([v1, v2], angle_resolution)
-
- rects, id_sets = l_shape_fitting.fitting(ox, oy)
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.axis("equal")
- plt.plot(0.0, 0.0, "*r")
- v1.plot()
- v2.plot()
-
- # Plot range observation
- for ids in id_sets:
- x = [ox[i] for i in range(len(ox)) if i in ids]
- y = [oy[i] for i in range(len(ox)) if i in ids]
-
- for (ix, iy) in zip(x, y):
- plt.plot([0.0, ix], [0.0, iy], "-og")
-
- plt.plot([ox[i] for i in range(len(ox)) if i in ids],
- [oy[i] for i in range(len(ox)) if i in ids],
- "o")
- for rect in rects:
- rect.plot()
-
- plt.pause(0.1)
-
- print("Done")
-
-
-if __name__ == '__main__':
- main()
diff --git a/Mapping/rectangle_fitting/simulator.py b/Mapping/rectangle_fitting/simulator.py
deleted file mode 100644
index aa32ae1b1fc..00000000000
--- a/Mapping/rectangle_fitting/simulator.py
+++ /dev/null
@@ -1,140 +0,0 @@
-"""
-
-Simulator
-
-author: Atsushi Sakai
-
-"""
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import numpy as np
-import matplotlib.pyplot as plt
-import math
-import random
-
-from utils.angle import rot_mat_2d
-
-
-class VehicleSimulator:
-
- def __init__(self, i_x, i_y, i_yaw, i_v, max_v, w, L):
- self.x = i_x
- self.y = i_y
- self.yaw = i_yaw
- self.v = i_v
- self.max_v = max_v
- self.W = w
- self.L = L
- self._calc_vehicle_contour()
-
- def update(self, dt, a, omega):
- self.x += self.v * np.cos(self.yaw) * dt
- self.y += self.v * np.sin(self.yaw) * dt
- self.yaw += omega * dt
- self.v += a * dt
- if self.v >= self.max_v:
- self.v = self.max_v
-
- def plot(self):
- plt.plot(self.x, self.y, ".b")
-
- # convert global coordinate
- gx, gy = self.calc_global_contour()
- plt.plot(gx, gy, "--b")
-
- def calc_global_contour(self):
- gxy = np.stack([self.vc_x, self.vc_y]).T @ rot_mat_2d(self.yaw)
- gx = gxy[:, 0] + self.x
- gy = gxy[:, 1] + self.y
-
- return gx, gy
-
- def _calc_vehicle_contour(self):
-
- self.vc_x = []
- self.vc_y = []
-
- self.vc_x.append(self.L / 2.0)
- self.vc_y.append(self.W / 2.0)
-
- self.vc_x.append(self.L / 2.0)
- self.vc_y.append(-self.W / 2.0)
-
- self.vc_x.append(-self.L / 2.0)
- self.vc_y.append(-self.W / 2.0)
-
- self.vc_x.append(-self.L / 2.0)
- self.vc_y.append(self.W / 2.0)
-
- self.vc_x.append(self.L / 2.0)
- self.vc_y.append(self.W / 2.0)
-
- self.vc_x, self.vc_y = self._interpolate(self.vc_x, self.vc_y)
-
- @staticmethod
- def _interpolate(x, y):
- rx, ry = [], []
- d_theta = 0.05
- for i in range(len(x) - 1):
- rx.extend([(1.0 - theta) * x[i] + theta * x[i + 1]
- for theta in np.arange(0.0, 1.0, d_theta)])
- ry.extend([(1.0 - theta) * y[i] + theta * y[i + 1]
- for theta in np.arange(0.0, 1.0, d_theta)])
-
- rx.extend([(1.0 - theta) * x[len(x) - 1] + theta * x[1]
- for theta in np.arange(0.0, 1.0, d_theta)])
- ry.extend([(1.0 - theta) * y[len(y) - 1] + theta * y[1]
- for theta in np.arange(0.0, 1.0, d_theta)])
-
- return rx, ry
-
-
-class LidarSimulator:
-
- def __init__(self):
- self.range_noise = 0.01
-
- def get_observation_points(self, v_list, angle_resolution):
- x, y, angle, r = [], [], [], []
-
- # store all points
- for v in v_list:
-
- gx, gy = v.calc_global_contour()
-
- for vx, vy in zip(gx, gy):
- v_angle = math.atan2(vy, vx)
- vr = np.hypot(vx, vy) * random.uniform(1.0 - self.range_noise,
- 1.0 + self.range_noise)
-
- x.append(vx)
- y.append(vy)
- angle.append(v_angle)
- r.append(vr)
-
- # ray casting filter
- rx, ry = self.ray_casting_filter(angle, r, angle_resolution)
-
- return rx, ry
-
- @staticmethod
- def ray_casting_filter(theta_l, range_l, angle_resolution):
- rx, ry = [], []
- range_db = [float("inf") for _ in range(
- int(np.floor((np.pi * 2.0) / angle_resolution)) + 1)]
-
- for i in range(len(theta_l)):
- angle_id = int(round(theta_l[i] / angle_resolution))
-
- if range_db[angle_id] > range_l[i]:
- range_db[angle_id] = range_l[i]
-
- for i in range(len(range_db)):
- t = i * angle_resolution
- if range_db[i] != float("inf"):
- rx.append(range_db[i] * np.cos(t))
- ry.append(range_db[i] * np.sin(t))
-
- return rx, ry
diff --git a/MissionPlanning/BehaviorTree/behavior_tree.py b/MissionPlanning/BehaviorTree/behavior_tree.py
deleted file mode 100644
index 59f4c713f1b..00000000000
--- a/MissionPlanning/BehaviorTree/behavior_tree.py
+++ /dev/null
@@ -1,690 +0,0 @@
-"""
-Behavior Tree
-
-author: Wang Zheng (@Aglargil)
-
-Ref:
-
-- [Behavior Tree](https://en.wikipedia.org/wiki/Behavior_tree_(artificial_intelligence,_robotics_and_control))
-"""
-
-import time
-import xml.etree.ElementTree as ET
-from enum import Enum
-
-
-class Status(Enum):
- SUCCESS = "success"
- FAILURE = "failure"
- RUNNING = "running"
-
-
-class NodeType(Enum):
- CONTROL_NODE = "ControlNode"
- ACTION_NODE = "ActionNode"
- DECORATOR_NODE = "DecoratorNode"
-
-
-class Node:
- """
- Base class for all nodes in a behavior tree.
- """
-
- def __init__(self, name):
- self.name = name
- self.status = None
-
- def tick(self) -> Status:
- """
- Tick the node.
-
- Returns:
- Status: The status of the node.
- """
- raise ValueError("Node is not implemented")
-
- def tick_and_set_status(self) -> Status:
- """
- Tick the node and set the status.
-
- Returns:
- Status: The status of the node.
- """
- self.status = self.tick()
- return self.status
-
- def reset(self):
- """
- Reset the node.
- """
- self.status = None
-
- def reset_children(self):
- """
- Reset the children of the node.
- """
- pass
-
-
-class ControlNode(Node):
- """
- Base class for all control nodes in a behavior tree.
-
- Control nodes manage the execution flow of their child nodes according to specific rules.
- They typically have multiple children and determine which children to execute and in what order.
- """
-
- def __init__(self, name):
- super().__init__(name)
- self.children = []
- self.type = NodeType.CONTROL_NODE
-
- def not_set_children_raise_error(self):
- if len(self.children) == 0:
- raise ValueError("Children are not set")
-
- def reset_children(self):
- for child in self.children:
- child.reset()
-
-
-class SequenceNode(ControlNode):
- """
- Executes child nodes in sequence until one fails or all succeed.
-
- Returns:
- - Returns FAILURE if any child returns FAILURE
- - Returns SUCCESS when all children have succeeded
- - Returns RUNNING when a child is still running or when moving to the next child
-
- Example:
- .. code-block:: xml
-
- <Sequence>
- <Action1 />
- <Action2 />
- </Sequence>
- """
-
- def __init__(self, name):
- super().__init__(name)
- self.current_child_index = 0
-
- def tick(self) -> Status:
- self.not_set_children_raise_error()
-
- if self.current_child_index >= len(self.children):
- self.reset_children()
- return Status.SUCCESS
- status = self.children[self.current_child_index].tick_and_set_status()
- if status == Status.FAILURE:
- self.reset_children()
- return Status.FAILURE
- elif status == Status.SUCCESS:
- self.current_child_index += 1
- return Status.RUNNING
- elif status == Status.RUNNING:
- return Status.RUNNING
- else:
- raise ValueError("Unknown status")
-
-
-class SelectorNode(ControlNode):
- """
- Executes child nodes in sequence until one succeeds or all fail.
-
- Returns:
- - Returns SUCCESS if any child returns SUCCESS
- - Returns FAILURE when all children have failed
- - Returns RUNNING when a child is still running or when moving to the next child
-
- Examples:
- .. code-block:: xml
-
- <Selector>
- <Action1 />
- <Action2 />
- </Selector>
- """
-
- def __init__(self, name):
- super().__init__(name)
- self.current_child_index = 0
-
- def tick(self) -> Status:
- self.not_set_children_raise_error()
-
- if self.current_child_index >= len(self.children):
- self.reset_children()
- return Status.FAILURE
- status = self.children[self.current_child_index].tick_and_set_status()
- if status == Status.SUCCESS:
- self.reset_children()
- return Status.SUCCESS
- elif status == Status.FAILURE:
- self.current_child_index += 1
- return Status.RUNNING
- elif status == Status.RUNNING:
- return Status.RUNNING
- else:
- raise ValueError("Unknown status")
-
-
-class WhileDoElseNode(ControlNode):
- """
- Conditional execution node with three parts: condition, do, and optional else.
-
- Returns:
- First executes the condition node (child[0])
- If condition succeeds, executes do node (child[1]) and returns RUNNING
- If condition fails, executes else node (child[2]) if present and returns result of else node
- If condition fails and there is no else node, returns SUCCESS
-
- Example:
- .. code-block:: xml
-
- <WhileDoElse>
- <Condition />
- <Do />
- <Else />
- </WhileDoElse>
- """
-
- def __init__(self, name):
- super().__init__(name)
-
- def tick(self) -> Status:
- if len(self.children) != 3 and len(self.children) != 2:
- raise ValueError("WhileDoElseNode must have exactly 3 or 2 children")
-
- condition_node = self.children[0]
- do_node = self.children[1]
- else_node = self.children[2] if len(self.children) == 3 else None
-
- condition_status = condition_node.tick_and_set_status()
- if condition_status == Status.SUCCESS:
- do_node.tick_and_set_status()
- return Status.RUNNING
- elif condition_status == Status.FAILURE:
- if else_node is not None:
- else_status = else_node.tick_and_set_status()
- if else_status == Status.SUCCESS:
- self.reset_children()
- return Status.SUCCESS
- elif else_status == Status.FAILURE:
- self.reset_children()
- return Status.FAILURE
- elif else_status == Status.RUNNING:
- return Status.RUNNING
- else:
- raise ValueError("Unknown status")
- else:
- self.reset_children()
- return Status.SUCCESS
- else:
- raise ValueError("Unknown status")
-
-
-class ActionNode(Node):
- """
- Base class for all action nodes in a behavior tree.
-
- Action nodes are responsible for performing specific tasks or actions.
- They do not have children and are typically used to execute logic or operations.
- """
-
- def __init__(self, name):
- super().__init__(name)
- self.type = NodeType.ACTION_NODE
-
-
-class SleepNode(ActionNode):
- """
- Sleep node that sleeps for a specified duration.
-
- Returns:
- Returns SUCCESS after the specified duration has passed
- Returns RUNNING if the duration has not yet passed
-
- Example:
- .. code-block:: xml
-
- <Sleep sec="1.5" />
- """
-
- def __init__(self, name, duration):
- super().__init__(name)
- self.duration = duration
- self.start_time = None
-
- def tick(self) -> Status:
- if self.start_time is None:
- self.start_time = time.time()
- if time.time() - self.start_time > self.duration:
- return Status.SUCCESS
- return Status.RUNNING
-
-
-class EchoNode(ActionNode):
- """
- Echo node that prints a message to the console.
-
- Returns:
- Returns SUCCESS after the message has been printed
-
- Example:
- .. code-block:: xml
-
- <Echo message="Hello, World!" />
- """
-
- def __init__(self, name, message):
- super().__init__(name)
- self.message = message
-
- def tick(self) -> Status:
- print(self.name, self.message)
- return Status.SUCCESS
-
-
-class DecoratorNode(Node):
- """
- Base class for all decorator nodes in a behavior tree.
-
- Decorator nodes modify the behavior of their child node.
- They must have a single child and can alter the status of the child node.
- """
-
- def __init__(self, name):
- super().__init__(name)
- self.type = NodeType.DECORATOR_NODE
- self.child = None
-
- def not_set_child_raise_error(self):
- if self.child is None:
- raise ValueError("Child is not set")
-
- def reset_children(self):
- self.child.reset()
-
-
-class InverterNode(DecoratorNode):
- """
- Inverter node that inverts the status of its child node.
-
- Returns:
- - Returns SUCCESS if the child returns FAILURE
- - Returns FAILURE if the child returns SUCCESS
- - Returns RUNNING if the child returns RUNNING
-
- Examples:
- .. code-block:: xml
-
- <Inverter>
- <Action />
- </Inverter>
- """
-
- def __init__(self, name):
- super().__init__(name)
-
- def tick(self) -> Status:
- self.not_set_child_raise_error()
- status = self.child.tick_and_set_status()
- return Status.SUCCESS if status == Status.FAILURE else Status.FAILURE
-
-
-class TimeoutNode(DecoratorNode):
- """
- Timeout node that fails if the child node takes too long to execute
-
- Returns:
- - FAILURE: If the timeout duration has been exceeded
- - Child's status: Otherwise, passes through the status of the child node
-
- Example:
- .. code-block:: xml
-
- <Timeout sec="1.5">
- <Action />
- </Timeout>
- """
-
- def __init__(self, name, timeout):
- super().__init__(name)
- self.timeout = timeout
- self.start_time = None
-
- def tick(self) -> Status:
- self.not_set_child_raise_error()
- if self.start_time is None:
- self.start_time = time.time()
- if time.time() - self.start_time > self.timeout:
- return Status.FAILURE
- print(f"{self.name} is running")
- return self.child.tick_and_set_status()
-
-
-class DelayNode(DecoratorNode):
- """
- Delay node that delays the execution of its child node for a specified duration.
-
- Returns:
- - Returns RUNNING if the duration has not yet passed
- - Returns child's status after the duration has passed
-
- Example:
- .. code-block:: xml
-
- <Delay sec="1.5">
- <Action />
- </Delay>
- """
-
- def __init__(self, name, delay):
- super().__init__(name)
- self.delay = delay
- self.start_time = None
-
- def tick(self) -> Status:
- self.not_set_child_raise_error()
- if self.start_time is None:
- self.start_time = time.time()
- if time.time() - self.start_time > self.delay:
- return self.child.tick_and_set_status()
- return Status.RUNNING
-
-
-class ForceSuccessNode(DecoratorNode):
- """
- ForceSuccess node that always returns SUCCESS.
-
- Returns:
- - Returns RUNNING if the child returns RUNNING
- - Returns SUCCESS if the child returns SUCCESS or FAILURE
- """
-
- def __init__(self, name):
- super().__init__(name)
-
- def tick(self) -> Status:
- self.not_set_child_raise_error()
- status = self.child.tick_and_set_status()
- if status == Status.FAILURE:
- return Status.SUCCESS
- return status
-
-
-class ForceFailureNode(DecoratorNode):
- """
- ForceFailure node that always returns FAILURE.
-
- Returns:
- - Returns RUNNING if the child returns RUNNING
- - Returns FAILURE if the child returns SUCCESS or FAILURE
- """
-
- def __init__(self, name):
- super().__init__(name)
-
- def tick(self) -> Status:
- self.not_set_child_raise_error()
- status = self.child.tick_and_set_status()
- if status == Status.SUCCESS:
- return Status.FAILURE
- return status
-
-
-class BehaviorTree:
- """
- Behavior tree class that manages the execution of a behavior tree.
- """
-
- def __init__(self, root):
- self.root = root
-
- def tick(self):
- """
- Tick once on the behavior tree.
- """
- self.root.tick_and_set_status()
-
- def reset(self):
- """
- Reset the behavior tree.
- """
- self.root.reset()
-
- def tick_while_running(self, interval=None, enable_print=True):
- """
- Tick the behavior tree while it is running.
-
- Args:
- interval (float, optional): The interval between ticks. Defaults to None.
- enable_print (bool, optional): Whether to print the behavior tree. Defaults to True.
- """
- while self.root.tick_and_set_status() == Status.RUNNING:
- if enable_print:
- self.print_tree()
- if interval is not None:
- time.sleep(interval)
- if enable_print:
- self.print_tree()
-
- def to_text(self, root, indent=0):
- """
- Recursively convert the behavior tree to a text representation.
- """
- current_text = ""
- if root.status == Status.RUNNING:
- # yellow
- current_text = "\033[93m" + root.name + "\033[0m"
- elif root.status == Status.SUCCESS:
- # green
- current_text = "\033[92m" + root.name + "\033[0m"
- elif root.status == Status.FAILURE:
- # red
- current_text = "\033[91m" + root.name + "\033[0m"
- else:
- current_text = root.name
- if root.type == NodeType.CONTROL_NODE:
- current_text = " " * indent + "[" + current_text + "]\n"
- for child in root.children:
- current_text += self.to_text(child, indent + 2)
- elif root.type == NodeType.DECORATOR_NODE:
- current_text = " " * indent + "(" + current_text + ")\n"
- current_text += self.to_text(root.child, indent + 2)
- elif root.type == NodeType.ACTION_NODE:
- current_text = " " * indent + "<" + current_text + ">\n"
- return current_text
-
- def print_tree(self):
- """
- Print the behavior tree.
-
- Node print format:
- Action: <Action>
- Decorator: (Decorator)
- Control: [Control]
-
- Node status colors:
- Yellow: RUNNING
- Green: SUCCESS
- Red: FAILURE
- """
- text = self.to_text(self.root)
- text = text.strip()
- print("\033[94m" + "Behavior Tree" + "\033[0m")
- print(text)
- print("\033[94m" + "Behavior Tree" + "\033[0m")
-
-
-class BehaviorTreeFactory:
- """
- Factory class for creating behavior trees from XML strings.
- """
-
- def __init__(self):
- self.node_builders = {}
- # Control nodes
- self.register_node_builder(
- "Sequence",
- lambda node: SequenceNode(node.attrib.get("name", SequenceNode.__name__)),
- )
- self.register_node_builder(
- "Selector",
- lambda node: SelectorNode(node.attrib.get("name", SelectorNode.__name__)),
- )
- self.register_node_builder(
- "WhileDoElse",
- lambda node: WhileDoElseNode(
- node.attrib.get("name", WhileDoElseNode.__name__)
- ),
- )
- # Decorator nodes
- self.register_node_builder(
- "Inverter",
- lambda node: InverterNode(node.attrib.get("name", InverterNode.__name__)),
- )
- self.register_node_builder(
- "Timeout",
- lambda node: TimeoutNode(
- node.attrib.get("name", SelectorNode.__name__),
- float(node.attrib["sec"]),
- ),
- )
- self.register_node_builder(
- "Delay",
- lambda node: DelayNode(
- node.attrib.get("name", DelayNode.__name__),
- float(node.attrib["sec"]),
- ),
- )
- self.register_node_builder(
- "ForceSuccess",
- lambda node: ForceSuccessNode(
- node.attrib.get("name", ForceSuccessNode.__name__)
- ),
- )
- self.register_node_builder(
- "ForceFailure",
- lambda node: ForceFailureNode(
- node.attrib.get("name", ForceFailureNode.__name__)
- ),
- )
- # Action nodes
- self.register_node_builder(
- "Sleep",
- lambda node: SleepNode(
- node.attrib.get("name", SleepNode.__name__),
- float(node.attrib["sec"]),
- ),
- )
- self.register_node_builder(
- "Echo",
- lambda node: EchoNode(
- node.attrib.get("name", EchoNode.__name__),
- node.attrib["message"],
- ),
- )
-
- def register_node_builder(self, node_name, builder):
- """
- Register a builder for a node
-
- Args:
- node_name (str): The name of the node.
- builder (function): The builder function.
-
- Example:
- .. code-block:: python
-
- factory = BehaviorTreeFactory()
- factory.register_node_builder(
- "MyNode",
- lambda node: MyNode(
- node.attrib.get("name", MyNode.__name__),
- node.attrib["my_param"],
- ),
- )
- """
- self.node_builders[node_name] = builder
-
- def build_node(self, node):
- """
- Build a node from an XML element.
-
- Args:
- node (Element): The XML element to build the node from.
-
- Returns:
- BehaviorTree Node: the built node
- """
- if node.tag in self.node_builders:
- root = self.node_builders[node.tag](node)
- if root.type == NodeType.CONTROL_NODE:
- if len(node) <= 0:
- raise ValueError(f"{root.name} Control node must have children")
- for child in node:
- root.children.append(self.build_node(child))
- elif root.type == NodeType.DECORATOR_NODE:
- if len(node) != 1:
- raise ValueError(
- f"{root.name} Decorator node must have exactly one child"
- )
- root.child = self.build_node(node[0])
- elif root.type == NodeType.ACTION_NODE:
- if len(node) != 0:
- raise ValueError(f"{root.name} Action node must have no children")
- return root
- else:
- raise ValueError(f"Unknown node type: {node.tag}")
-
- def build_tree(self, xml_string):
- """
- Build a behavior tree from an XML string.
-
- Args:
- xml_string (str): The XML string containing the behavior tree.
-
- Returns:
- BehaviorTree: The behavior tree.
- """
- xml_tree = ET.fromstring(xml_string)
- root = self.build_node(xml_tree)
- return BehaviorTree(root)
-
- def build_tree_from_file(self, file_path):
- """
- Build a behavior tree from a file.
-
- Args:
- file_path (str): The path to the file containing the behavior tree.
-
- Returns:
- BehaviorTree: The behavior tree.
- """
- with open(file_path) as file:
- xml_string = file.read()
- return self.build_tree(xml_string)
-
-
-xml_string = """
- <Sequence name="Sequence">
- <Echo name="Echo0" message="Hello, World0!" />
- <Delay name="Delay" sec="1.5">
- <Echo name="Echo1" message="Hello, World1!" />
- </Delay>
- <Echo name="Echo2" message="Hello, World2!" />
- </Sequence>
- """
-
-
-def main():
- factory = BehaviorTreeFactory()
- tree = factory.build_tree(xml_string)
- tree.tick_while_running()
-
-
-if __name__ == "__main__":
- main()
diff --git a/MissionPlanning/BehaviorTree/robot_behavior_case.py b/MissionPlanning/BehaviorTree/robot_behavior_case.py
deleted file mode 100644
index 6c39aa76b24..00000000000
--- a/MissionPlanning/BehaviorTree/robot_behavior_case.py
+++ /dev/null
@@ -1,247 +0,0 @@
-"""
-Robot Behavior Tree Case
-
-This file demonstrates how to use a behavior tree to control robot behavior.
-"""
-
-from behavior_tree import (
- BehaviorTreeFactory,
- Status,
- ActionNode,
-)
-import time
-import random
-import os
-
-
-class CheckBatteryNode(ActionNode):
- """
- Node to check robot battery level
-
- If battery level is below threshold, returns FAILURE, otherwise returns SUCCESS
- """
-
- def __init__(self, name, threshold=20):
- super().__init__(name)
- self.threshold = threshold
- self.battery_level = 100 # Initial battery level is 100%
-
- def tick(self):
- # Simulate battery level decreasing
- self.battery_level -= random.randint(1, 5)
- print(f"Current battery level: {self.battery_level}%")
-
- if self.battery_level <= self.threshold:
- return Status.FAILURE
- return Status.SUCCESS
-
-
-class ChargeBatteryNode(ActionNode):
- """
- Node to charge the robot's battery
- """
-
- def __init__(self, name, charge_rate=10):
- super().__init__(name)
- self.charge_rate = charge_rate
- self.charging_time = 0
-
- def tick(self):
- # Simulate charging process
- if self.charging_time == 0:
- print("Starting to charge...")
-
- self.charging_time += 1
- charge_amount = self.charge_rate * self.charging_time
-
- if charge_amount >= 100:
- print("Charging complete! Battery level: 100%")
- self.charging_time = 0
- return Status.SUCCESS
- else:
- print(f"Charging in progress... Battery level: {min(charge_amount, 100)}%")
- return Status.RUNNING
-
-
-class MoveToPositionNode(ActionNode):
- """
- Node to move to a specified position
- """
-
- def __init__(self, name, position, move_duration=2):
- super().__init__(name)
- self.position = position
- self.move_duration = move_duration
- self.start_time = None
-
- def tick(self):
- if self.start_time is None:
- self.start_time = time.time()
- print(f"Starting movement to position {self.position}")
-
- elapsed_time = time.time() - self.start_time
-
- if elapsed_time >= self.move_duration:
- print(f"Arrived at position {self.position}")
- self.start_time = None
- return Status.SUCCESS
- else:
- print(
- f"Moving to position {self.position}... {int(elapsed_time / self.move_duration * 100)}% complete"
- )
- return Status.RUNNING
-
-
-class DetectObstacleNode(ActionNode):
- """
- Node to detect obstacles
- """
-
- def __init__(self, name, obstacle_probability=0.3):
- super().__init__(name)
- self.obstacle_probability = obstacle_probability
-
- def tick(self):
- # Use random probability to simulate obstacle detection
- if random.random() < self.obstacle_probability:
- print("Obstacle detected!")
- return Status.SUCCESS
- else:
- print("No obstacle detected")
- return Status.FAILURE
-
-
-class AvoidObstacleNode(ActionNode):
- """
- Node to avoid obstacles
- """
-
- def __init__(self, name, avoid_duration=1.5):
- super().__init__(name)
- self.avoid_duration = avoid_duration
- self.start_time = None
-
- def tick(self):
- if self.start_time is None:
- self.start_time = time.time()
- print("Starting obstacle avoidance...")
-
- elapsed_time = time.time() - self.start_time
-
- if elapsed_time >= self.avoid_duration:
- print("Obstacle avoidance complete")
- self.start_time = None
- return Status.SUCCESS
- else:
- print("Avoiding obstacle...")
- return Status.RUNNING
-
-
-class PerformTaskNode(ActionNode):
- """
- Node to perform a specific task
- """
-
- def __init__(self, name, task_name, task_duration=3):
- super().__init__(name)
- self.task_name = task_name
- self.task_duration = task_duration
- self.start_time = None
-
- def tick(self):
- if self.start_time is None:
- self.start_time = time.time()
- print(f"Starting task: {self.task_name}")
-
- elapsed_time = time.time() - self.start_time
-
- if elapsed_time >= self.task_duration:
- print(f"Task complete: {self.task_name}")
- self.start_time = None
- return Status.SUCCESS
- else:
- print(
- f"Performing task: {self.task_name}... {int(elapsed_time / self.task_duration * 100)}% complete"
- )
- return Status.RUNNING
-
-
-def create_robot_behavior_tree():
- """
- Create robot behavior tree
- """
-
- factory = BehaviorTreeFactory()
-
- # Register custom nodes
- factory.register_node_builder(
- "CheckBattery",
- lambda node: CheckBatteryNode(
- node.attrib.get("name", "CheckBattery"),
- int(node.attrib.get("threshold", "20")),
- ),
- )
-
- factory.register_node_builder(
- "ChargeBattery",
- lambda node: ChargeBatteryNode(
- node.attrib.get("name", "ChargeBattery"),
- int(node.attrib.get("charge_rate", "10")),
- ),
- )
-
- factory.register_node_builder(
- "MoveToPosition",
- lambda node: MoveToPositionNode(
- node.attrib.get("name", "MoveToPosition"),
- node.attrib.get("position", "Unknown Position"),
- float(node.attrib.get("move_duration", "2")),
- ),
- )
-
- factory.register_node_builder(
- "DetectObstacle",
- lambda node: DetectObstacleNode(
- node.attrib.get("name", "DetectObstacle"),
- float(node.attrib.get("obstacle_probability", "0.3")),
- ),
- )
-
- factory.register_node_builder(
- "AvoidObstacle",
- lambda node: AvoidObstacleNode(
- node.attrib.get("name", "AvoidObstacle"),
- float(node.attrib.get("avoid_duration", "1.5")),
- ),
- )
-
- factory.register_node_builder(
- "PerformTask",
- lambda node: PerformTaskNode(
- node.attrib.get("name", "PerformTask"),
- node.attrib.get("task_name", "Unknown Task"),
- float(node.attrib.get("task_duration", "3")),
- ),
- )
- # Read XML from file
- xml_path = os.path.join(os.path.dirname(__file__), "robot_behavior_tree.xml")
- return factory.build_tree_from_file(xml_path)
-
-
-def main():
- """
- Main function: Create and run the robot behavior tree
- """
- print("Creating robot behavior tree...")
- tree = create_robot_behavior_tree()
-
- print("\nStarting robot behavior tree execution...\n")
- # Run for a period of time or until completion
-
- tree.tick_while_running(interval=0.01)
-
- print("\nBehavior tree execution complete!")
-
-
-if __name__ == "__main__":
- main()
diff --git a/MissionPlanning/BehaviorTree/robot_behavior_tree.xml b/MissionPlanning/BehaviorTree/robot_behavior_tree.xml
deleted file mode 100644
index 0bca76a3ff9..00000000000
--- a/MissionPlanning/BehaviorTree/robot_behavior_tree.xml
+++ /dev/null
@@ -1,57 +0,0 @@
-<Selector name="Robot Main Controller">
- <!-- Charge battery when power is low -->
- <Sequence name="Battery Management">
- <Inverter name="Low Battery Detection">
- <CheckBattery name="Check Battery" threshold="30" />
- </Inverter>
- <Echo name="Low Battery Warning" message="Battery level low! Charging needed" />
- <ChargeBattery name="Charge Battery" charge_rate="20" />
- </Sequence>
- <!-- Main task sequence -->
- <Sequence name="Patrol Task">
- <Echo name="Start Task" message="Starting patrol task" />
- <!-- Move to position A -->
- <Sequence name="Move to Position A">
- <MoveToPosition name="Move to A" position="A" move_duration="2" />
- <!-- Handle obstacles -->
- <Selector name="Obstacle Handling A">
- <Sequence name="Obstacle Present">
- <DetectObstacle name="Detect Obstacle" obstacle_probability="0.3" />
- <AvoidObstacle name="Avoid Obstacle" avoid_duration="1.5" />
- </Sequence>
- <Echo name="No Obstacle" message="Path clear" />
- </Selector>
- <PerformTask name="Position A Task" task_name="Check Device Status" task_duration="2" />
- </Sequence>
- <!-- Move to position B -->
- <Sequence name="Move to Position B">
- <Delay name="Short Wait" sec="1">
- <Echo name="Prepare Movement" message="Preparing to move to next position" />
- </Delay>
- <MoveToPosition name="Move to B" position="B" move_duration="3" />
- <!-- Handle obstacles with timeout -->
- <Timeout name="Limited Time Obstacle Handling" sec="2">
- <Sequence name="Obstacle Present">
- <DetectObstacle name="Detect Obstacle" obstacle_probability="0.4" />
- <AvoidObstacle name="Avoid Obstacle" avoid_duration="1.8" />
- </Sequence>
- </Timeout>
- <PerformTask name="Position B Task" task_name="Data Collection" task_duration="2.5" />
- </Sequence>
- <!-- Move to position C -->
- <WhileDoElse name="Conditional Move to C">
- <CheckBattery name="Check Sufficient Battery" threshold="50" />
- <Sequence name="Perform Position C Task">
- <MoveToPosition name="Move to C" position="C" move_duration="2.5" />
- <ForceSuccess name="Ensure Completion">
- <PerformTask name="Position C Task" task_name="Environment Monitoring"
- task_duration="2" />
- </ForceSuccess>
- </Sequence>
- <Echo name="Skip Position C" message="Insufficient power, skipping position C task" />
- </WhileDoElse>
- <Echo name="Complete Patrol" message="Patrol task completed, returning to charging station" />
- <MoveToPosition name="Return to Charging Station" position="Charging Station"
- move_duration="4" />
- </Sequence>
-</Selector>
\ No newline at end of file
diff --git a/MissionPlanning/StateMachine/robot_behavior_case.py b/MissionPlanning/StateMachine/robot_behavior_case.py
deleted file mode 100644
index 03ee60ae9fd..00000000000
--- a/MissionPlanning/StateMachine/robot_behavior_case.py
+++ /dev/null
@@ -1,111 +0,0 @@
-"""
-A case study of robot behavior using state machine
-
-author: Wang Zheng (@Aglargil)
-"""
-
-from state_machine import StateMachine
-
-
-class Robot:
- def __init__(self):
- self.battery = 100
- self.task_progress = 0
-
- # Initialize state machine
- self.machine = StateMachine("robot_sm", self)
-
- # Add state transition rules
- self.machine.add_transition(
- src_state="patrolling",
- event="detect_task",
- dst_state="executing_task",
- guard=None,
- action=None,
- )
-
- self.machine.add_transition(
- src_state="executing_task",
- event="task_complete",
- dst_state="patrolling",
- guard=None,
- action="reset_task",
- )
-
- self.machine.add_transition(
- src_state="executing_task",
- event="low_battery",
- dst_state="returning_to_base",
- guard="is_battery_low",
- )
-
- self.machine.add_transition(
- src_state="returning_to_base",
- event="reach_base",
- dst_state="charging",
- guard=None,
- action=None,
- )
-
- self.machine.add_transition(
- src_state="charging",
- event="charge_complete",
- dst_state="patrolling",
- guard=None,
- action="battery_full",
- )
-
- # Set initial state
- self.machine.set_current_state("patrolling")
-
- def is_battery_low(self):
- """Battery level check condition"""
- return self.battery < 30
-
- def reset_task(self):
- """Reset task progress"""
- self.task_progress = 0
- print("[Action] Task progress has been reset")
-
- # Modify state entry callback naming convention (add state_ prefix)
- def on_enter_executing_task(self):
- print("\n------ Start Executing Task ------")
- print(f"Current battery: {self.battery}%")
- while self.machine.get_current_state().name == "executing_task":
- self.task_progress += 10
- self.battery -= 25
- print(
- f"Task progress: {self.task_progress}%, Remaining battery: {self.battery}%"
- )
-
- if self.task_progress >= 100:
- self.machine.process("task_complete")
- break
- elif self.is_battery_low():
- self.machine.process("low_battery")
- break
-
- def on_enter_returning_to_base(self):
- print("\nLow battery, returning to charging station...")
- self.machine.process("reach_base")
-
- def on_enter_charging(self):
- print("\n------ Charging ------")
- self.battery = 100
- print("Charging complete!")
- self.machine.process("charge_complete")
-
-
-# Keep the test section structure the same, only modify the trigger method
-if __name__ == "__main__":
- robot = Robot()
- print(robot.machine.generate_plantuml())
-
- print(f"Initial state: {robot.machine.get_current_state().name}")
- print("------------")
-
- # Trigger task detection event
- robot.machine.process("detect_task")
-
- print("\n------------")
- print(f"Final state: {robot.machine.get_current_state().name}")
diff --git a/MissionPlanning/StateMachine/state_machine.py b/MissionPlanning/StateMachine/state_machine.py
deleted file mode 100644
index de72f0f4517..00000000000
--- a/MissionPlanning/StateMachine/state_machine.py
+++ /dev/null
@@ -1,294 +0,0 @@
-"""
-State Machine
-
-author: Wang Zheng (@Aglargil)
-
-Ref:
-
-- [State Machine]
-(https://en.wikipedia.org/wiki/Finite-state_machine)
-"""
-
-import string
-from urllib.request import urlopen, Request
-from base64 import b64encode
-from zlib import compress
-from io import BytesIO
-from collections.abc import Callable
-from matplotlib.image import imread
-from matplotlib import pyplot as plt
-
-
-def deflate_and_encode(plantuml_text):
- """
- zlib compress the plantuml text and encode it for the plantuml server.
-
- Ref: https://plantuml.com/en/text-encoding
- """
- plantuml_alphabet = (
- string.digits + string.ascii_uppercase + string.ascii_lowercase + "-_"
- )
- base64_alphabet = (
- string.ascii_uppercase + string.ascii_lowercase + string.digits + "+/"
- )
- b64_to_plantuml = bytes.maketrans(
- base64_alphabet.encode("utf-8"), plantuml_alphabet.encode("utf-8")
- )
- zlibbed_str = compress(plantuml_text.encode("utf-8"))
- compressed_string = zlibbed_str[2:-4]
- return b64encode(compressed_string).translate(b64_to_plantuml).decode("utf-8")
-
-
-class State:
- def __init__(self, name, on_enter=None, on_exit=None):
- self.name = name
- self.on_enter = on_enter
- self.on_exit = on_exit
-
- def enter(self):
- print(f"entering <{self.name}>")
- if self.on_enter:
- self.on_enter()
-
- def exit(self):
- print(f"exiting <{self.name}>")
- if self.on_exit:
- self.on_exit()
-
-
-class StateMachine:
- def __init__(self, name: str, model=object):
- """Initialize the state machine.
-
- Args:
- name (str): Name of the state machine.
- model (object, optional): Model object used to automatically look up callback functions
- for states and transitions:
- State callbacks: Automatically searches for 'on_enter_<state>' and 'on_exit_<state>' methods.
- Transition callbacks: When action or guard parameters are strings, looks up corresponding methods in the model.
-
- Example:
- >>> class MyModel:
- ... def on_enter_idle(self):
- ... print("Entering idle state")
- ... def on_exit_idle(self):
- ... print("Exiting idle state")
- ... def can_start(self):
- ... return True
- ... def on_start(self):
- ... print("Starting operation")
- >>> model = MyModel()
- >>> machine = StateMachine("my_machine", model)
- """
- self._name = name
- self._states = {}
- self._events = {}
- self._transition_table = {}
- self._model = model
- self._state: State = None
-
- def _register_event(self, event: str):
- self._events[event] = event
-
- def _get_state(self, name):
- return self._states[name]
-
- def _get_event(self, name):
- return self._events[name]
-
- def _has_event(self, event: str):
- return event in self._events
-
- def add_transition(
- self,
- src_state: str | State,
- event: str,
- dst_state: str | State,
- guard: str | Callable = None,
- action: str | Callable = None,
- ) -> None:
- """Add a transition to the state machine.
-
- Args:
- src_state (str | State): The source state where the transition begins.
- Can be either a state name or a State object.
- event (str): The event that triggers this transition.
- dst_state (str | State): The destination state where the transition ends.
- Can be either a state name or a State object.
- guard (str | Callable, optional): Guard condition for the transition.
- If callable: Function that returns bool.
- If str: Name of a method in the model class.
- If returns True: Transition proceeds.
- If returns False: Transition is skipped.
- action (str | Callable, optional): Action to execute during transition.
- If callable: Function to execute.
- If str: Name of a method in the model class.
- Executed after guard passes and before entering new state.
-
- Example:
- >>> machine.add_transition(
- ... src_state="idle",
- ... event="start",
- ... dst_state="running",
- ... guard="can_start",
- ... action="on_start"
- ... )
- """
- # Convert string parameters to objects if necessary
- self.register_state(src_state)
- self._register_event(event)
- self.register_state(dst_state)
-
- def get_state_obj(state):
- return state if isinstance(state, State) else self._get_state(state)
-
- def get_callable(func):
- return func if callable(func) else getattr(self._model, func, None)
-
- src_state_obj = get_state_obj(src_state)
- dst_state_obj = get_state_obj(dst_state)
-
- guard_func = get_callable(guard) if guard else None
- action_func = get_callable(action) if action else None
- self._transition_table[(src_state_obj.name, event)] = (
- dst_state_obj,
- guard_func,
- action_func,
- )
-
- def state_transition(self, src_state: State, event: str):
- if (src_state.name, event) not in self._transition_table:
- raise ValueError(
- f"|{self._name}| invalid transition: <{src_state.name}> : [{event}]"
- )
-
- dst_state, guard, action = self._transition_table[(src_state.name, event)]
-
- def call_guard(guard):
- if callable(guard):
- return guard()
- else:
- return True
-
- def call_action(action):
- if callable(action):
- action()
-
- if call_guard(guard):
- call_action(action)
- if src_state.name != dst_state.name:
- print(
- f"|{self._name}| transitioning from <{src_state.name}> to <{dst_state.name}>"
- )
- src_state.exit()
- self._state = dst_state
- dst_state.enter()
- else:
- print(
- f"|{self._name}| skipping transition from <{src_state.name}> to <{dst_state.name}> because guard failed"
- )
-
- def register_state(self, state: str | State, on_enter=None, on_exit=None):
- """Register a state in the state machine.
-
- Args:
- state (str | State): The state to register. Can be either a string (state name)
- or a State object.
- on_enter (Callable, optional): Callback function to be executed when entering the state.
- If state is a string and on_enter is None, it will look for
- a method named 'on_enter_<state>' in the model.
- on_exit (Callable, optional): Callback function to be executed when exiting the state.
- If state is a string and on_exit is None, it will look for
- a method named 'on_exit_<state>' in the model.
- Example:
- >>> machine.register_state("idle", on_enter=on_enter_idle, on_exit=on_exit_idle)
- >>> machine.register_state(State("running", on_enter=on_enter_running, on_exit=on_exit_running))
- """
- if isinstance(state, str):
- if on_enter is None:
- on_enter = getattr(self._model, "on_enter_" + state, None)
- if on_exit is None:
- on_exit = getattr(self._model, "on_exit_" + state, None)
- self._states[state] = State(state, on_enter, on_exit)
- return
-
- self._states[state.name] = state
-
- def set_current_state(self, state: State | str):
- if isinstance(state, str):
- self._state = self._get_state(state)
- else:
- self._state = state
-
- def get_current_state(self):
- return self._state
-
- def process(self, event: str) -> None:
- """Process an event in the state machine.
-
- Args:
- event: Event name.
-
- Example:
- >>> machine.process("start")
- """
- if self._state is None:
- raise ValueError("State machine is not initialized")
-
- if self._has_event(event):
- self.state_transition(self._state, event)
- else:
- raise ValueError(f"Invalid event: {event}")
-
- def generate_plantuml(self) -> str:
- """Generate PlantUML state diagram representation of the state machine.
-
- Returns:
- str: PlantUML state diagram code.
- """
- if self._state is None:
- raise ValueError("State machine is not initialized")
-
- plant_uml = ["@startuml"]
- plant_uml.append("[*] --> " + self._state.name)
-
- # Generate transitions
- for (src_state, event), (
- dst_state,
- guard,
- action,
- ) in self._transition_table.items():
- transition = f"{src_state} --> {dst_state.name} : {event}"
-
- # Add guard and action if present
- conditions = []
- if guard:
- guard_name = guard.__name__ if callable(guard) else guard
- conditions.append(f"[{guard_name}]")
- if action:
- action_name = action.__name__ if callable(action) else action
- conditions.append(f"/ {action_name}")
-
- if conditions:
- transition += "\\n" + " ".join(conditions)
-
- plant_uml.append(transition)
-
- plant_uml.append("@enduml")
- plant_uml_text = "\n".join(plant_uml)
-
- try:
- url = f"http://www.plantuml.com/plantuml/img/{deflate_and_encode(plant_uml_text)}"
- headers = {"User-Agent": "Mozilla/5.0"}
- request = Request(url, headers=headers)
-
- with urlopen(request) as response:
- content = response.read()
-
- plt.imshow(imread(BytesIO(content), format="png"))
- plt.axis("off")
- plt.show()
- except Exception as e:
- print(f"Error showing PlantUML: {e}")
-
- return plant_uml_text
diff --git a/PathPlanning/AStar/a_star.py b/PathPlanning/AStar/a_star.py
deleted file mode 100644
index 6d203504327..00000000000
--- a/PathPlanning/AStar/a_star.py
+++ /dev/null
@@ -1,282 +0,0 @@
-"""
-
-A* grid planning
-
-author: Atsushi Sakai(@Atsushi_twi)
- Nikos Kanargias (nkana@tee.gr)
-
-See Wikipedia article (https://en.wikipedia.org/wiki/A*_search_algorithm)
-
-"""
-
-import math
-
-import matplotlib.pyplot as plt
-
-show_animation = True
-
-
-class AStarPlanner:
-
- def __init__(self, ox, oy, resolution, rr):
- """
- Initialize grid map for a star planning
-
- ox: x position list of Obstacles [m]
- oy: y position list of Obstacles [m]
- resolution: grid resolution [m]
- rr: robot radius[m]
- """
-
- self.resolution = resolution
- self.rr = rr
- self.min_x, self.min_y = 0, 0
- self.max_x, self.max_y = 0, 0
- self.obstacle_map = None
- self.x_width, self.y_width = 0, 0
- self.motion = self.get_motion_model()
- self.calc_obstacle_map(ox, oy)
-
- class Node:
- def __init__(self, x, y, cost, parent_index):
- self.x = x # index of grid
- self.y = y # index of grid
- self.cost = cost
- self.parent_index = parent_index
-
- def __str__(self):
- return str(self.x) + "," + str(self.y) + "," + str(
- self.cost) + "," + str(self.parent_index)
-
- def planning(self, sx, sy, gx, gy):
- """
- A star path search
-
- input:
- s_x: start x position [m]
- s_y: start y position [m]
- gx: goal x position [m]
- gy: goal y position [m]
-
- output:
- rx: x position list of the final path
- ry: y position list of the final path
- """
-
- start_node = self.Node(self.calc_xy_index(sx, self.min_x),
- self.calc_xy_index(sy, self.min_y), 0.0, -1)
- goal_node = self.Node(self.calc_xy_index(gx, self.min_x),
- self.calc_xy_index(gy, self.min_y), 0.0, -1)
-
- open_set, closed_set = dict(), dict()
- open_set[self.calc_grid_index(start_node)] = start_node
-
- while True:
- if len(open_set) == 0:
- print("Open set is empty..")
- break
-
- c_id = min(
- open_set,
- key=lambda o: open_set[o].cost + self.calc_heuristic(goal_node,
- open_set[
- o]))
- current = open_set[c_id]
-
- # show graph
- if show_animation: # pragma: no cover
- plt.plot(self.calc_grid_position(current.x, self.min_x),
- self.calc_grid_position(current.y, self.min_y), "xc")
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(
- 0) if event.key == 'escape' else None])
- if len(closed_set.keys()) % 10 == 0:
- plt.pause(0.001)
-
- if current.x == goal_node.x and current.y == goal_node.y:
- print("Find goal")
- goal_node.parent_index = current.parent_index
- goal_node.cost = current.cost
- break
-
- # Remove the item from the open set
- del open_set[c_id]
-
- # Add it to the closed set
- closed_set[c_id] = current
-
- # expand_grid search grid based on motion model
- for i, _ in enumerate(self.motion):
- node = self.Node(current.x + self.motion[i][0],
- current.y + self.motion[i][1],
- current.cost + self.motion[i][2], c_id)
- n_id = self.calc_grid_index(node)
-
- # If the node is not safe, do nothing
- if not self.verify_node(node):
- continue
-
- if n_id in closed_set:
- continue
-
- if n_id not in open_set:
- open_set[n_id] = node # discovered a new node
- else:
- if open_set[n_id].cost > node.cost:
- # This path is the best until now. record it
- open_set[n_id] = node
-
- rx, ry = self.calc_final_path(goal_node, closed_set)
-
- return rx, ry
-
- def calc_final_path(self, goal_node, closed_set):
- # generate final course
- rx, ry = [self.calc_grid_position(goal_node.x, self.min_x)], [
- self.calc_grid_position(goal_node.y, self.min_y)]
- parent_index = goal_node.parent_index
- while parent_index != -1:
- n = closed_set[parent_index]
- rx.append(self.calc_grid_position(n.x, self.min_x))
- ry.append(self.calc_grid_position(n.y, self.min_y))
- parent_index = n.parent_index
-
- return rx, ry
-
- @staticmethod
- def calc_heuristic(n1, n2):
- w = 1.0 # weight of heuristic
- d = w * math.hypot(n1.x - n2.x, n1.y - n2.y)
- return d
-
- def calc_grid_position(self, index, min_position):
- """
- calc grid position
-
- :param index:
- :param min_position:
- :return:
- """
- pos = index * self.resolution + min_position
- return pos
-
- def calc_xy_index(self, position, min_pos):
- return round((position - min_pos) / self.resolution)
-
- def calc_grid_index(self, node):
- return (node.y - self.min_y) * self.x_width + (node.x - self.min_x)
-
- def verify_node(self, node):
- px = self.calc_grid_position(node.x, self.min_x)
- py = self.calc_grid_position(node.y, self.min_y)
-
- if px < self.min_x:
- return False
- elif py < self.min_y:
- return False
- elif px >= self.max_x:
- return False
- elif py >= self.max_y:
- return False
-
- # collision check
- if self.obstacle_map[node.x][node.y]:
- return False
-
- return True
-
- def calc_obstacle_map(self, ox, oy):
-
- self.min_x = round(min(ox))
- self.min_y = round(min(oy))
- self.max_x = round(max(ox))
- self.max_y = round(max(oy))
- print("min_x:", self.min_x)
- print("min_y:", self.min_y)
- print("max_x:", self.max_x)
- print("max_y:", self.max_y)
-
- self.x_width = round((self.max_x - self.min_x) / self.resolution)
- self.y_width = round((self.max_y - self.min_y) / self.resolution)
- print("x_width:", self.x_width)
- print("y_width:", self.y_width)
-
- # obstacle map generation
- self.obstacle_map = [[False for _ in range(self.y_width)]
- for _ in range(self.x_width)]
- for ix in range(self.x_width):
- x = self.calc_grid_position(ix, self.min_x)
- for iy in range(self.y_width):
- y = self.calc_grid_position(iy, self.min_y)
- for iox, ioy in zip(ox, oy):
- d = math.hypot(iox - x, ioy - y)
- if d <= self.rr:
- self.obstacle_map[ix][iy] = True
- break
-
- @staticmethod
- def get_motion_model():
- # dx, dy, cost
- motion = [[1, 0, 1],
- [0, 1, 1],
- [-1, 0, 1],
- [0, -1, 1],
- [-1, -1, math.sqrt(2)],
- [-1, 1, math.sqrt(2)],
- [1, -1, math.sqrt(2)],
- [1, 1, math.sqrt(2)]]
-
- return motion
-
-
-def main():
- print(__file__ + " start!!")
-
- # start and goal position
- sx = 10.0 # [m]
- sy = 10.0 # [m]
- gx = 50.0 # [m]
- gy = 50.0 # [m]
- grid_size = 2.0 # [m]
- robot_radius = 1.0 # [m]
-
- # set obstacle positions
- ox, oy = [], []
- for i in range(-10, 60):
- ox.append(i)
- oy.append(-10.0)
- for i in range(-10, 60):
- ox.append(60.0)
- oy.append(i)
- for i in range(-10, 61):
- ox.append(i)
- oy.append(60.0)
- for i in range(-10, 61):
- ox.append(-10.0)
- oy.append(i)
- for i in range(-10, 40):
- ox.append(20.0)
- oy.append(i)
- for i in range(0, 40):
- ox.append(40.0)
- oy.append(60.0 - i)
-
- if show_animation: # pragma: no cover
- plt.plot(ox, oy, ".k")
- plt.plot(sx, sy, "og")
- plt.plot(gx, gy, "xb")
- plt.grid(True)
- plt.axis("equal")
-
- a_star = AStarPlanner(ox, oy, grid_size, robot_radius)
- rx, ry = a_star.planning(sx, sy, gx, gy)
-
- if show_animation: # pragma: no cover
- plt.plot(rx, ry, "-r")
- plt.pause(0.001)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/AStar/a_star_searching_from_two_side.py b/PathPlanning/AStar/a_star_searching_from_two_side.py
deleted file mode 100644
index f43cea71b42..00000000000
--- a/PathPlanning/AStar/a_star_searching_from_two_side.py
+++ /dev/null
@@ -1,369 +0,0 @@
-"""
-A* algorithm
-Author: Weicent
-randomly generate obstacles, start and goal point
-searching path from start and end simultaneously
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-import math
-
-show_animation = True
-
-
-class Node:
- """node with properties of g, h, coordinate and parent node"""
-
- def __init__(self, G=0, H=0, coordinate=None, parent=None):
- self.G = G
- self.H = H
- self.F = G + H
- self.parent = parent
- self.coordinate = coordinate
-
- def reset_f(self):
- self.F = self.G + self.H
-
-
-def hcost(node_coordinate, goal):
- dx = abs(node_coordinate[0] - goal[0])
- dy = abs(node_coordinate[1] - goal[1])
- hcost = dx + dy
- return hcost
-
-
-def gcost(fixed_node, update_node_coordinate):
- dx = abs(fixed_node.coordinate[0] - update_node_coordinate[0])
- dy = abs(fixed_node.coordinate[1] - update_node_coordinate[1])
- gc = math.hypot(dx, dy) # gc = move from fixed_node to update_node
- gcost = fixed_node.G + gc # gcost = move from start point to update_node
- return gcost
-
-
-def boundary_and_obstacles(start, goal, top_vertex, bottom_vertex, obs_number):
- """
- :param start: start coordinate
- :param goal: goal coordinate
- :param top_vertex: top right vertex coordinate of boundary
- :param bottom_vertex: bottom left vertex coordinate of boundary
- :param obs_number: number of obstacles generated in the map
- :return: boundary_obstacle array, obstacle list
- """
- # below can be merged into a rectangle boundary
- ay = list(range(bottom_vertex[1], top_vertex[1]))
- ax = [bottom_vertex[0]] * len(ay)
- cy = ay
- cx = [top_vertex[0]] * len(cy)
- bx = list(range(bottom_vertex[0] + 1, top_vertex[0]))
- by = [bottom_vertex[1]] * len(bx)
- dx = [bottom_vertex[0]] + bx + [top_vertex[0]]
- dy = [top_vertex[1]] * len(dx)
-
- # generate random obstacles
- ob_x = np.random.randint(bottom_vertex[0] + 1,
- top_vertex[0], obs_number).tolist()
- ob_y = np.random.randint(bottom_vertex[1] + 1,
- top_vertex[1], obs_number).tolist()
- # x y coordinate in certain order for boundary
- x = ax + bx + cx + dx
- y = ay + by + cy + dy
- obstacle = np.vstack((ob_x, ob_y)).T.tolist()
- # remove start and goal coordinate in obstacle list
- obstacle = [coor for coor in obstacle if coor != start and coor != goal]
- obs_array = np.array(obstacle)
- bound = np.vstack((x, y)).T
- bound_obs = np.vstack((bound, obs_array))
- return bound_obs, obstacle
-
-
-def find_neighbor(node, ob, closed):
- # Convert obstacles to a set for faster lookup
- ob_set = set(map(tuple, ob.tolist()))
- neighbor_set = set()
-
- # Generate neighbors within the 3x3 grid around the node
- for x in range(node.coordinate[0] - 1, node.coordinate[0] + 2):
- for y in range(node.coordinate[1] - 1, node.coordinate[1] + 2):
- coord = (x, y)
- if coord not in ob_set and coord != tuple(node.coordinate):
- neighbor_set.add(coord)
-
- # Define neighbors in cardinal and diagonal directions
- top_nei = (node.coordinate[0], node.coordinate[1] + 1)
- bottom_nei = (node.coordinate[0], node.coordinate[1] - 1)
- left_nei = (node.coordinate[0] - 1, node.coordinate[1])
- right_nei = (node.coordinate[0] + 1, node.coordinate[1])
- lt_nei = (node.coordinate[0] - 1, node.coordinate[1] + 1)
- rt_nei = (node.coordinate[0] + 1, node.coordinate[1] + 1)
- lb_nei = (node.coordinate[0] - 1, node.coordinate[1] - 1)
- rb_nei = (node.coordinate[0] + 1, node.coordinate[1] - 1)
-
- # Remove neighbors that violate diagonal motion rules
- if top_nei in ob_set and left_nei in ob_set:
- neighbor_set.discard(lt_nei)
- if top_nei in ob_set and right_nei in ob_set:
- neighbor_set.discard(rt_nei)
- if bottom_nei in ob_set and left_nei in ob_set:
- neighbor_set.discard(lb_nei)
- if bottom_nei in ob_set and right_nei in ob_set:
- neighbor_set.discard(rb_nei)
-
- # Filter out neighbors that are in the closed set
- closed_set = set(map(tuple, closed))
- neighbor_set -= closed_set
-
- return list(neighbor_set)
-
-
-
-def find_node_index(coordinate, node_list):
- # find node index in the node list via its coordinate
- ind = 0
- for node in node_list:
- if node.coordinate == coordinate:
- target_node = node
- ind = node_list.index(target_node)
- break
- return ind
-
-
-def find_path(open_list, closed_list, goal, obstacle):
- # searching for the path, update open and closed list
- # obstacle = obstacle and boundary
- flag = len(open_list)
- for i in range(flag):
- node = open_list[0]
- open_coordinate_list = [node.coordinate for node in open_list]
- closed_coordinate_list = [node.coordinate for node in closed_list]
- temp = find_neighbor(node, obstacle, closed_coordinate_list)
- for element in temp:
- if element in closed_list:
- continue
- elif element in open_coordinate_list:
- # if node in open list, update g value
- ind = open_coordinate_list.index(element)
- new_g = gcost(node, element)
- if new_g <= open_list[ind].G:
- open_list[ind].G = new_g
- open_list[ind].reset_f()
- open_list[ind].parent = node
- else: # new coordinate, create corresponding node
- ele_node = Node(coordinate=element, parent=node,
- G=gcost(node, element), H=hcost(element, goal))
- open_list.append(ele_node)
- open_list.remove(node)
- closed_list.append(node)
- open_list.sort(key=lambda x: x.F)
- return open_list, closed_list
-
-
-def node_to_coordinate(node_list):
- # convert node list into coordinate list and array
- coordinate_list = [node.coordinate for node in node_list]
- return coordinate_list
-
-
-def check_node_coincide(close_ls1, closed_ls2):
- """
- :param close_ls1: node closed list for searching from start
- :param closed_ls2: node closed list for searching from end
- :return: intersect node list for above two
- """
- # check if node in close_ls1 intersect with node in closed_ls2
- cl1 = node_to_coordinate(close_ls1)
- cl2 = node_to_coordinate(closed_ls2)
- intersect_ls = [node for node in cl1 if node in cl2]
- return intersect_ls
-
-
-def find_surrounding(coordinate, obstacle):
- # find obstacles around node, help to draw the borderline
- boundary: list = []
- for x in range(coordinate[0] - 1, coordinate[0] + 2):
- for y in range(coordinate[1] - 1, coordinate[1] + 2):
- if [x, y] in obstacle:
- boundary.append([x, y])
- return boundary
-
-
-def get_border_line(node_closed_ls, obstacle):
- # if no path, find border line which confine goal or robot
- border: list = []
- coordinate_closed_ls = node_to_coordinate(node_closed_ls)
- for coordinate in coordinate_closed_ls:
- temp = find_surrounding(coordinate, obstacle)
- border = border + temp
- border_ary = np.array(border)
- return border_ary
-
-
-def get_path(org_list, goal_list, coordinate):
- # get path from start to end
- path_org: list = []
- path_goal: list = []
- ind = find_node_index(coordinate, org_list)
- node = org_list[ind]
- while node != org_list[0]:
- path_org.append(node.coordinate)
- node = node.parent
- path_org.append(org_list[0].coordinate)
- ind = find_node_index(coordinate, goal_list)
- node = goal_list[ind]
- while node != goal_list[0]:
- path_goal.append(node.coordinate)
- node = node.parent
- path_goal.append(goal_list[0].coordinate)
- path_org.reverse()
- path = path_org + path_goal
- path = np.array(path)
- return path
-
-
-def random_coordinate(bottom_vertex, top_vertex):
- # generate random coordinates inside maze
- coordinate = [np.random.randint(bottom_vertex[0] + 1, top_vertex[0]),
- np.random.randint(bottom_vertex[1] + 1, top_vertex[1])]
- return coordinate
-
-
-def draw(close_origin, close_goal, start, end, bound):
- # plot the map
- if not close_goal.tolist(): # ensure the close_goal not empty
- # in case of the obstacle number is really large (>4500), the
- # origin is very likely blocked at the first search, and then
- # the program is over and the searching from goal to origin
- # will not start, which remain the closed_list for goal == []
- # in order to plot the map, add the end coordinate to array
- close_goal = np.array([end])
- plt.cla()
- plt.gcf().set_size_inches(11, 9, forward=True)
- plt.axis('equal')
- plt.plot(close_origin[:, 0], close_origin[:, 1], 'oy')
- plt.plot(close_goal[:, 0], close_goal[:, 1], 'og')
- plt.plot(bound[:, 0], bound[:, 1], 'sk')
- plt.plot(end[0], end[1], '*b', label='Goal')
- plt.plot(start[0], start[1], '^b', label='Origin')
- plt.legend()
- plt.pause(0.0001)
-
-
-def draw_control(org_closed, goal_closed, flag, start, end, bound, obstacle):
- """
- control the plot process, evaluate if the searching finished
- flag == 0 : draw the searching process and plot path
- flag == 1 or 2 : start or end is blocked, draw the border line
- """
- stop_loop = 0 # stop sign for the searching
- org_closed_ls = node_to_coordinate(org_closed)
- org_array = np.array(org_closed_ls)
- goal_closed_ls = node_to_coordinate(goal_closed)
- goal_array = np.array(goal_closed_ls)
- path = None
- if show_animation: # draw the searching process
- draw(org_array, goal_array, start, end, bound)
- if flag == 0:
- node_intersect = check_node_coincide(org_closed, goal_closed)
- if node_intersect: # a path is find
- path = get_path(org_closed, goal_closed, node_intersect[0])
- stop_loop = 1
- print('Path found!')
- if show_animation: # draw the path
- plt.plot(path[:, 0], path[:, 1], '-r')
- plt.title('Robot Arrived', size=20, loc='center')
- plt.pause(0.01)
- plt.show()
- elif flag == 1: # start point blocked first
- stop_loop = 1
- print('There is no path to the goal! Start point is blocked!')
- elif flag == 2: # end point blocked first
- stop_loop = 1
- print('There is no path to the goal! End point is blocked!')
- if show_animation: # blocked case, draw the border line
- info = 'There is no path to the goal!' \
- ' Robot&Goal are split by border' \
- ' shown in red \'x\'!'
- if flag == 1:
- border = get_border_line(org_closed, obstacle)
- plt.plot(border[:, 0], border[:, 1], 'xr')
- plt.title(info, size=14, loc='center')
- plt.pause(0.01)
- plt.show()
- elif flag == 2:
- border = get_border_line(goal_closed, obstacle)
- plt.plot(border[:, 0], border[:, 1], 'xr')
- plt.title(info, size=14, loc='center')
- plt.pause(0.01)
- plt.show()
- return stop_loop, path
-
-
-def searching_control(start, end, bound, obstacle):
- """manage the searching process, start searching from two side"""
- # initial origin node and end node
- origin = Node(coordinate=start, H=hcost(start, end))
- goal = Node(coordinate=end, H=hcost(end, start))
- # list for searching from origin to goal
- origin_open: list = [origin]
- origin_close: list = []
- # list for searching from goal to origin
- goal_open = [goal]
- goal_close: list = []
- # initial target
- target_goal = end
- # flag = 0 (not blocked) 1 (start point blocked) 2 (end point blocked)
- flag = 0 # init flag
- path = None
- while True:
- # searching from start to end
- origin_open, origin_close = \
- find_path(origin_open, origin_close, target_goal, bound)
- if not origin_open: # no path condition
- flag = 1 # origin node is blocked
- draw_control(origin_close, goal_close, flag, start, end, bound,
- obstacle)
- break
- # update target for searching from end to start
- target_origin = min(origin_open, key=lambda x: x.F).coordinate
-
- # searching from end to start
- goal_open, goal_close = \
- find_path(goal_open, goal_close, target_origin, bound)
- if not goal_open: # no path condition
- flag = 2 # goal is blocked
- draw_control(origin_close, goal_close, flag, start, end, bound,
- obstacle)
- break
- # update target for searching from start to end
- target_goal = min(goal_open, key=lambda x: x.F).coordinate
-
- # continue searching, draw the process
- stop_sign, path = draw_control(origin_close, goal_close, flag, start,
- end, bound, obstacle)
- if stop_sign:
- break
- return path
-
-
-def main(obstacle_number=1500):
- print(__file__ + ' start!')
-
- top_vertex = [60, 60] # top right vertex of boundary
- bottom_vertex = [0, 0] # bottom left vertex of boundary
-
- # generate start and goal point randomly
- start = random_coordinate(bottom_vertex, top_vertex)
- end = random_coordinate(bottom_vertex, top_vertex)
-
- # generate boundary and obstacles
- bound, obstacle = boundary_and_obstacles(start, end, top_vertex,
- bottom_vertex,
- obstacle_number)
-
- path = searching_control(start, end, bound, obstacle)
- if not show_animation:
- print(path)
-
-
-if __name__ == '__main__':
- main(obstacle_number=1500)
diff --git a/PathPlanning/AStar/a_star_variants.py b/PathPlanning/AStar/a_star_variants.py
deleted file mode 100644
index e0053ee2249..00000000000
--- a/PathPlanning/AStar/a_star_variants.py
+++ /dev/null
@@ -1,483 +0,0 @@
-"""
-a star variants
-author: Sarim Mehdi(muhammadsarim.mehdi@studio.unibo.it)
-Source: http://theory.stanford.edu/~amitp/GameProgramming/Variations.html
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-show_animation = True
-use_beam_search = False
-use_iterative_deepening = False
-use_dynamic_weighting = False
-use_theta_star = False
-use_jump_point = False
-
-beam_capacity = 30
-max_theta = 5
-only_corners = False
-max_corner = 5
-w, epsilon, upper_bound_depth = 1, 4, 500
-
-
-def draw_horizontal_line(start_x, start_y, length, o_x, o_y, o_dict):
- for i in range(start_x, start_x + length):
- for j in range(start_y, start_y + 2):
- o_x.append(i)
- o_y.append(j)
- o_dict[(i, j)] = True
-
-
-def draw_vertical_line(start_x, start_y, length, o_x, o_y, o_dict):
- for i in range(start_x, start_x + 2):
- for j in range(start_y, start_y + length):
- o_x.append(i)
- o_y.append(j)
- o_dict[(i, j)] = True
-
-
-def in_line_of_sight(obs_grid, x1, y1, x2, y2):
- t = 0
- while t <= 0.5:
- xt = (1 - t) * x1 + t * x2
- yt = (1 - t) * y1 + t * y2
- if obs_grid[(int(xt), int(yt))]:
- return False, None
- xt = (1 - t) * x2 + t * x1
- yt = (1 - t) * y2 + t * y1
- if obs_grid[(int(xt), int(yt))]:
- return False, None
- t += 0.001
- dist = np.linalg.norm(np.array([x1, y1] - np.array([x2, y2])))
- return True, dist
-
-
-def key_points(o_dict):
- offsets1 = [(1, 0), (0, 1), (-1, 0), (1, 0)]
- offsets2 = [(1, 1), (-1, 1), (-1, -1), (1, -1)]
- offsets3 = [(0, 1), (-1, 0), (0, -1), (0, -1)]
- c_list = []
- for grid_point, obs_status in o_dict.items():
- if obs_status:
- continue
- empty_space = True
- x, y = grid_point
- for i in [-1, 0, 1]:
- for j in [-1, 0, 1]:
- if (x + i, y + j) not in o_dict.keys():
- continue
- if o_dict[(x + i, y + j)]:
- empty_space = False
- break
- if empty_space:
- continue
- for offset1, offset2, offset3 in zip(offsets1, offsets2, offsets3):
- i1, j1 = offset1
- i2, j2 = offset2
- i3, j3 = offset3
- if ((x + i1, y + j1) not in o_dict.keys()) or \
- ((x + i2, y + j2) not in o_dict.keys()) or \
- ((x + i3, y + j3) not in o_dict.keys()):
- continue
- obs_count = 0
- if o_dict[(x + i1, y + j1)]:
- obs_count += 1
- if o_dict[(x + i2, y + j2)]:
- obs_count += 1
- if o_dict[(x + i3, y + j3)]:
- obs_count += 1
- if obs_count == 3 or obs_count == 1:
- c_list.append((x, y))
- if show_animation:
- plt.plot(x, y, ".y")
- break
- if only_corners:
- return c_list
-
- e_list = []
- for corner in c_list:
- x1, y1 = corner
- for other_corner in c_list:
- x2, y2 = other_corner
- if x1 == x2 and y1 == y2:
- continue
- reachable, _ = in_line_of_sight(o_dict, x1, y1, x2, y2)
- if not reachable:
- continue
- x_m, y_m = int((x1 + x2) / 2), int((y1 + y2) / 2)
- e_list.append((x_m, y_m))
- if show_animation:
- plt.plot(x_m, y_m, ".y")
- return c_list + e_list
-
-
-class SearchAlgo:
- def __init__(self, obs_grid, goal_x, goal_y, start_x, start_y,
- limit_x, limit_y, corner_list=None):
- self.start_pt = [start_x, start_y]
- self.goal_pt = [goal_x, goal_y]
- self.obs_grid = obs_grid
- g_cost, h_cost = 0, self.get_hval(start_x, start_y, goal_x, goal_y)
- f_cost = g_cost + h_cost
- self.all_nodes, self.open_set = {}, []
-
- if use_jump_point:
- for corner in corner_list:
- i, j = corner
- h_c = self.get_hval(i, j, goal_x, goal_y)
- self.all_nodes[(i, j)] = {'pos': [i, j], 'pred': None,
- 'gcost': np.inf, 'hcost': h_c,
- 'fcost': np.inf,
- 'open': True, 'in_open_list': False}
- self.all_nodes[tuple(self.goal_pt)] = \
- {'pos': self.goal_pt, 'pred': None,
- 'gcost': np.inf, 'hcost': 0, 'fcost': np.inf,
- 'open': True, 'in_open_list': True}
- else:
- for i in range(limit_x):
- for j in range(limit_y):
- h_c = self.get_hval(i, j, goal_x, goal_y)
- self.all_nodes[(i, j)] = {'pos': [i, j], 'pred': None,
- 'gcost': np.inf, 'hcost': h_c,
- 'fcost': np.inf,
- 'open': True,
- 'in_open_list': False}
- self.all_nodes[tuple(self.start_pt)] = \
- {'pos': self.start_pt, 'pred': None,
- 'gcost': g_cost, 'hcost': h_cost, 'fcost': f_cost,
- 'open': True, 'in_open_list': True}
- self.open_set.append(self.all_nodes[tuple(self.start_pt)])
-
- @staticmethod
- def get_hval(x1, y1, x2, y2):
- x, y = x1, y1
- val = 0
- while x != x2 or y != y2:
- if x != x2 and y != y2:
- val += 14
- else:
- val += 10
- x, y = x + np.sign(x2 - x), y + np.sign(y2 - y)
- return val
-
- def get_farthest_point(self, x, y, i, j):
- i_temp, j_temp = i, j
- counter = 1
- got_goal = False
- while not self.obs_grid[(x + i_temp, y + j_temp)] and \
- counter < max_theta:
- i_temp += i
- j_temp += j
- counter += 1
- if [x + i_temp, y + j_temp] == self.goal_pt:
- got_goal = True
- break
- if (x + i_temp, y + j_temp) not in self.obs_grid.keys():
- break
- return i_temp - 2*i, j_temp - 2*j, counter, got_goal
-
- def jump_point(self):
- """Jump point: Instead of exploring all empty spaces of the
- map, just explore the corners."""
-
- goal_found = False
- while len(self.open_set) > 0:
- self.open_set = sorted(self.open_set, key=lambda x: x['fcost'])
- lowest_f = self.open_set[0]['fcost']
- lowest_h = self.open_set[0]['hcost']
- lowest_g = self.open_set[0]['gcost']
- p = 0
- for p_n in self.open_set[1:]:
- if p_n['fcost'] == lowest_f and \
- p_n['gcost'] < lowest_g:
- lowest_g = p_n['gcost']
- p += 1
- elif p_n['fcost'] == lowest_f and \
- p_n['gcost'] == lowest_g and \
- p_n['hcost'] < lowest_h:
- lowest_h = p_n['hcost']
- p += 1
- else:
- break
- current_node = self.all_nodes[tuple(self.open_set[p]['pos'])]
- x1, y1 = current_node['pos']
-
- for cand_pt, cand_node in self.all_nodes.items():
- x2, y2 = cand_pt
- if x1 == x2 and y1 == y2:
- continue
- if np.linalg.norm(np.array([x1, y1] -
- np.array([x2, y2]))) > max_corner:
- continue
- reachable, offset = in_line_of_sight(self.obs_grid, x1,
- y1, x2, y2)
- if not reachable:
- continue
-
- if list(cand_pt) == self.goal_pt:
- current_node['open'] = False
- self.all_nodes[tuple(cand_pt)]['pred'] = \
- current_node['pos']
- goal_found = True
- break
-
- g_cost = offset + current_node['gcost']
- h_cost = self.all_nodes[cand_pt]['hcost']
- f_cost = g_cost + h_cost
- cand_pt = tuple(cand_pt)
- if f_cost < self.all_nodes[cand_pt]['fcost']:
- self.all_nodes[cand_pt]['pred'] = current_node['pos']
- self.all_nodes[cand_pt]['gcost'] = g_cost
- self.all_nodes[cand_pt]['fcost'] = f_cost
- if not self.all_nodes[cand_pt]['in_open_list']:
- self.open_set.append(self.all_nodes[cand_pt])
- self.all_nodes[cand_pt]['in_open_list'] = True
- if show_animation:
- plt.plot(cand_pt[0], cand_pt[1], "r*")
-
- if goal_found:
- break
- if show_animation:
- plt.pause(0.001)
- if goal_found:
- current_node = self.all_nodes[tuple(self.goal_pt)]
- while goal_found:
- if current_node['pred'] is None:
- break
- x = [current_node['pos'][0], current_node['pred'][0]]
- y = [current_node['pos'][1], current_node['pred'][1]]
- current_node = self.all_nodes[tuple(current_node['pred'])]
- if show_animation:
- plt.plot(x, y, "b")
- plt.pause(0.001)
- if goal_found:
- break
-
- current_node['open'] = False
- current_node['in_open_list'] = False
- if show_animation:
- plt.plot(current_node['pos'][0], current_node['pos'][1], "g*")
- del self.open_set[p]
- current_node['fcost'], current_node['hcost'] = np.inf, np.inf
- if show_animation:
- plt.title('Jump Point')
- plt.show()
-
- def a_star(self):
- """Beam search: Maintain an open list of just 30 nodes.
- If more than 30 nodes, then get rid of nodes with high
- f values.
- Iterative deepening: At every iteration, get a cut-off
- value for the f cost. This cut-off is minimum of the f
- value of all nodes whose f value is higher than the
- current cut-off value. Nodes with f value higher than
- the current cut off value are not put in the open set.
- Dynamic weighting: Multiply heuristic with the following:
- (1 + epsilon - (epsilon*d)/N) where d is the current
- iteration of loop and N is upper bound on number of
- iterations.
- Theta star: Same as A star but you don't need to move
- one neighbor at a time. In fact, you can look for the
- next node as far out as you can as long as there is a
- clear line of sight from your current node to that node."""
- if show_animation:
- if use_beam_search:
- plt.title('A* with beam search')
- elif use_iterative_deepening:
- plt.title('A* with iterative deepening')
- elif use_dynamic_weighting:
- plt.title('A* with dynamic weighting')
- elif use_theta_star:
- plt.title('Theta*')
- else:
- plt.title('A*')
-
- goal_found = False
- curr_f_thresh = np.inf
- depth = 0
- no_valid_f = False
- w = None
- while len(self.open_set) > 0:
- self.open_set = sorted(self.open_set, key=lambda x: x['fcost'])
- lowest_f = self.open_set[0]['fcost']
- lowest_h = self.open_set[0]['hcost']
- lowest_g = self.open_set[0]['gcost']
- p = 0
- for p_n in self.open_set[1:]:
- if p_n['fcost'] == lowest_f and \
- p_n['gcost'] < lowest_g:
- lowest_g = p_n['gcost']
- p += 1
- elif p_n['fcost'] == lowest_f and \
- p_n['gcost'] == lowest_g and \
- p_n['hcost'] < lowest_h:
- lowest_h = p_n['hcost']
- p += 1
- else:
- break
- current_node = self.all_nodes[tuple(self.open_set[p]['pos'])]
-
- while len(self.open_set) > beam_capacity and use_beam_search:
- del self.open_set[-1]
-
- f_cost_list = []
- if use_dynamic_weighting:
- w = (1 + epsilon - epsilon*depth/upper_bound_depth)
- for i in range(-1, 2):
- for j in range(-1, 2):
- x, y = current_node['pos']
- if (i == 0 and j == 0) or \
- ((x + i, y + j) not in self.obs_grid.keys()):
- continue
- if (i, j) in [(1, 0), (0, 1), (-1, 0), (0, -1)]:
- offset = 10
- else:
- offset = 14
- if use_theta_star:
- new_i, new_j, counter, goal_found = \
- self.get_farthest_point(x, y, i, j)
- offset = offset * counter
- cand_pt = [current_node['pos'][0] + new_i,
- current_node['pos'][1] + new_j]
- else:
- cand_pt = [current_node['pos'][0] + i,
- current_node['pos'][1] + j]
-
- if use_theta_star and goal_found:
- current_node['open'] = False
- cand_pt = self.goal_pt
- self.all_nodes[tuple(cand_pt)]['pred'] = \
- current_node['pos']
- break
-
- if cand_pt == self.goal_pt:
- current_node['open'] = False
- self.all_nodes[tuple(cand_pt)]['pred'] = \
- current_node['pos']
- goal_found = True
- break
-
- cand_pt = tuple(cand_pt)
- no_valid_f = self.update_node_cost(cand_pt, curr_f_thresh,
- current_node,
- f_cost_list, no_valid_f,
- offset, w)
- if goal_found:
- break
- if show_animation:
- plt.pause(0.001)
- if goal_found:
- current_node = self.all_nodes[tuple(self.goal_pt)]
- while goal_found:
- if current_node['pred'] is None:
- break
- if use_theta_star or use_jump_point:
- x, y = [current_node['pos'][0], current_node['pred'][0]], \
- [current_node['pos'][1], current_node['pred'][1]]
- if show_animation:
- plt.plot(x, y, "b")
- else:
- if show_animation:
- plt.plot(current_node['pred'][0],
- current_node['pred'][1], "b*")
- current_node = self.all_nodes[tuple(current_node['pred'])]
- if goal_found:
- break
-
- if use_iterative_deepening and f_cost_list:
- curr_f_thresh = min(f_cost_list)
- if use_iterative_deepening and not f_cost_list:
- curr_f_thresh = np.inf
- if use_iterative_deepening and not f_cost_list and no_valid_f:
- current_node['fcost'], current_node['hcost'] = np.inf, np.inf
- continue
-
- current_node['open'] = False
- current_node['in_open_list'] = False
- if show_animation:
- plt.plot(current_node['pos'][0], current_node['pos'][1], "g*")
- del self.open_set[p]
- current_node['fcost'], current_node['hcost'] = np.inf, np.inf
- depth += 1
- if show_animation:
- plt.show()
-
- def update_node_cost(self, cand_pt, curr_f_thresh, current_node,
- f_cost_list, no_valid_f, offset, w):
- if not self.obs_grid[tuple(cand_pt)] and \
- self.all_nodes[cand_pt]['open']:
- g_cost = offset + current_node['gcost']
- h_cost = self.all_nodes[cand_pt]['hcost']
- if use_dynamic_weighting:
- h_cost = h_cost * w
- f_cost = g_cost + h_cost
- if f_cost < self.all_nodes[cand_pt]['fcost'] and \
- f_cost <= curr_f_thresh:
- f_cost_list.append(f_cost)
- self.all_nodes[cand_pt]['pred'] = \
- current_node['pos']
- self.all_nodes[cand_pt]['gcost'] = g_cost
- self.all_nodes[cand_pt]['fcost'] = f_cost
- if not self.all_nodes[cand_pt]['in_open_list']:
- self.open_set.append(self.all_nodes[cand_pt])
- self.all_nodes[cand_pt]['in_open_list'] = True
- if show_animation:
- plt.plot(cand_pt[0], cand_pt[1], "r*")
- if curr_f_thresh < f_cost < \
- self.all_nodes[cand_pt]['fcost']:
- no_valid_f = True
- return no_valid_f
-
-
-def main():
- # set obstacle positions
- obs_dict = {}
- for i in range(51):
- for j in range(51):
- obs_dict[(i, j)] = False
- o_x, o_y = [], []
-
- s_x = 5.0
- s_y = 5.0
- g_x = 35.0
- g_y = 45.0
-
- # draw outer border of maze
- draw_vertical_line(0, 0, 50, o_x, o_y, obs_dict)
- draw_vertical_line(48, 0, 50, o_x, o_y, obs_dict)
- draw_horizontal_line(0, 0, 50, o_x, o_y, obs_dict)
- draw_horizontal_line(0, 48, 50, o_x, o_y, obs_dict)
-
- # draw inner walls
- all_x = [10, 10, 10, 15, 20, 20, 30, 30, 35, 30, 40, 45]
- all_y = [10, 30, 45, 20, 5, 40, 10, 40, 5, 40, 10, 25]
- all_len = [10, 10, 5, 10, 10, 5, 20, 10, 25, 10, 35, 15]
- for x, y, l in zip(all_x, all_y, all_len):
- draw_vertical_line(x, y, l, o_x, o_y, obs_dict)
-
- all_x[:], all_y[:], all_len[:] = [], [], []
- all_x = [35, 40, 15, 10, 45, 20, 10, 15, 25, 45, 10, 30, 10, 40]
- all_y = [5, 10, 15, 20, 20, 25, 30, 35, 35, 35, 40, 40, 45, 45]
- all_len = [10, 5, 10, 10, 5, 5, 10, 5, 10, 5, 10, 5, 5, 5]
- for x, y, l in zip(all_x, all_y, all_len):
- draw_horizontal_line(x, y, l, o_x, o_y, obs_dict)
-
- if show_animation:
- plt.plot(o_x, o_y, ".k")
- plt.plot(s_x, s_y, "og")
- plt.plot(g_x, g_y, "xb")
- plt.grid(True)
-
- if use_jump_point:
- keypoint_list = key_points(obs_dict)
- search_obj = SearchAlgo(obs_dict, g_x, g_y, s_x, s_y, 101, 101,
- keypoint_list)
- search_obj.jump_point()
- else:
- search_obj = SearchAlgo(obs_dict, g_x, g_y, s_x, s_y, 101, 101)
- search_obj.a_star()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/BSplinePath/bspline_path.py b/PathPlanning/BSplinePath/bspline_path.py
deleted file mode 100644
index a2a396efaa7..00000000000
--- a/PathPlanning/BSplinePath/bspline_path.py
+++ /dev/null
@@ -1,152 +0,0 @@
-"""
-
-Path Planner with B-Spline
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import numpy as np
-import matplotlib.pyplot as plt
-import scipy.interpolate as interpolate
-
-from utils.plot import plot_curvature
-
-
-def approximate_b_spline_path(x: list,
- y: list,
- n_path_points: int,
- degree: int = 3,
- s=None,
- ) -> tuple:
- """
- Approximate points with a B-Spline path
-
- Parameters
- ----------
- x : array_like
- x position list of approximated points
- y : array_like
- y position list of approximated points
- n_path_points : int
- number of path points
- degree : int, optional
- B Spline curve degree. Must be 2<= k <= 5. Default: 3.
- s : int, optional
- smoothing parameter. If this value is bigger, the path will be
- smoother, but it will be less accurate. If this value is smaller,
- the path will be more accurate, but it will be less smooth.
- When `s` is 0, it is equivalent to the interpolation. Default is None,
- in this case `s` will be `len(x)`.
-
- Returns
- -------
- x : array
- x positions of the result path
- y : array
- y positions of the result path
- heading : array
- heading of the result path
- curvature : array
- curvature of the result path
-
- """
- distances = _calc_distance_vector(x, y)
-
- spl_i_x = interpolate.UnivariateSpline(distances, x, k=degree, s=s)
- spl_i_y = interpolate.UnivariateSpline(distances, y, k=degree, s=s)
-
- sampled = np.linspace(0.0, distances[-1], n_path_points)
- return _evaluate_spline(sampled, spl_i_x, spl_i_y)
-
-
-def interpolate_b_spline_path(x, y,
- n_path_points: int,
- degree: int = 3) -> tuple:
- """
- Interpolate x-y points with a B-Spline path
-
- Parameters
- ----------
- x : array_like
- x positions of interpolated points
- y : array_like
- y positions of interpolated points
- n_path_points : int
- number of path points
- degree : int, optional
- B-Spline degree. Must be 2<= k <= 5. Default: 3
-
- Returns
- -------
- x : array
- x positions of the result path
- y : array
- y positions of the result path
- heading : array
- heading of the result path
- curvature : array
- curvature of the result path
-
- """
- return approximate_b_spline_path(x, y, n_path_points, degree, s=0.0)
-
-
-def _calc_distance_vector(x, y):
- dx, dy = np.diff(x), np.diff(y)
- distances = np.cumsum([np.hypot(idx, idy) for idx, idy in zip(dx, dy)])
- distances = np.concatenate(([0.0], distances))
- distances /= distances[-1]
- return distances
-
-
-def _evaluate_spline(sampled, spl_i_x, spl_i_y):
- x = spl_i_x(sampled)
- y = spl_i_y(sampled)
- dx = spl_i_x.derivative(1)(sampled)
- dy = spl_i_y.derivative(1)(sampled)
- heading = np.arctan2(dy, dx)
- ddx = spl_i_x.derivative(2)(sampled)
- ddy = spl_i_y.derivative(2)(sampled)
- curvature = (ddy * dx - ddx * dy) / np.power(dx * dx + dy * dy, 2.0 / 3.0)
- return np.array(x), y, heading, curvature,
-
-
-def main():
- print(__file__ + " start!!")
- # way points
- way_point_x = [-1.0, 3.0, 4.0, 2.0, 1.0]
- way_point_y = [0.0, -3.0, 1.0, 1.0, 3.0]
- n_course_point = 50 # sampling number
-
- plt.subplots()
- rax, ray, heading, curvature = approximate_b_spline_path(
- way_point_x, way_point_y, n_course_point, s=0.5)
- plt.plot(rax, ray, '-r', label="Approximated B-Spline path")
- plot_curvature(rax, ray, heading, curvature)
-
- plt.title("B-Spline approximation")
- plt.plot(way_point_x, way_point_y, '-og', label="way points")
- plt.grid(True)
- plt.legend()
- plt.axis("equal")
-
- plt.subplots()
- rix, riy, heading, curvature = interpolate_b_spline_path(
- way_point_x, way_point_y, n_course_point)
- plt.plot(rix, riy, '-b', label="Interpolated B-Spline path")
- plot_curvature(rix, riy, heading, curvature)
-
- plt.title("B-Spline interpolation")
- plt.plot(way_point_x, way_point_y, '-og', label="way points")
- plt.grid(True)
- plt.legend()
- plt.axis("equal")
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/BatchInformedRRTStar/batch_informed_rrtstar.py b/PathPlanning/BatchInformedRRTStar/batch_informed_rrtstar.py
deleted file mode 100644
index 92c3a58761a..00000000000
--- a/PathPlanning/BatchInformedRRTStar/batch_informed_rrtstar.py
+++ /dev/null
@@ -1,635 +0,0 @@
-"""
-Batch Informed Trees based path planning:
-Uses a heuristic to efficiently search increasingly dense
-RGGs while reusing previous information. Provides faster
-convergence that RRT*, Informed RRT* and other sampling based
-methods.
-
-Uses lazy connecting by combining sampling based methods and A*
-like incremental graph search algorithms.
-
-author: Karan Chawla(@karanchawla)
- Atsushi Sakai(@Atsushi_twi)
-
-Reference: https://arxiv.org/abs/1405.5848
-"""
-
-import math
-import random
-
-import matplotlib.pyplot as plt
-import numpy as np
-
-show_animation = True
-
-
-class RTree:
- # Class to represent the explicit tree created
- # while sampling through the state space
-
- def __init__(self, start=None, lowerLimit=None, upperLimit=None,
- resolution=1.0):
-
- if upperLimit is None:
- upperLimit = [10, 10]
- if lowerLimit is None:
- lowerLimit = [0, 0]
- if start is None:
- start = [0, 0]
- self.vertices = dict()
- self.edges = []
- self.start = start
- self.lowerLimit = lowerLimit
- self.upperLimit = upperLimit
- self.dimension = len(lowerLimit)
- self.num_cells = [0] * self.dimension
- self.resolution = resolution
- # compute the number of grid cells based on the limits and
- # resolution given
- for idx in range(self.dimension):
- self.num_cells[idx] = np.ceil(
- (upperLimit[idx] - lowerLimit[idx]) / resolution)
-
- vertex_id = self.real_world_to_node_id(start)
- self.vertices[vertex_id] = []
-
- @staticmethod
- def get_root_id():
- # return the id of the root of the tree
- return 0
-
- def add_vertex(self, vertex):
- # add a vertex to the tree
- vertex_id = self.real_world_to_node_id(vertex)
- self.vertices[vertex_id] = []
- return vertex_id
-
- def add_edge(self, v, x):
- # create an edge between v and x vertices
- if (v, x) not in self.edges:
- self.edges.append((v, x))
- # since the tree is undirected
- self.vertices[v].append(x)
- self.vertices[x].append(v)
-
- def real_coords_to_grid_coord(self, real_coord):
- # convert real world coordinates to grid space
- # depends on the resolution of the grid
- # the output is the same as real world coords if the resolution
- # is set to 1
- coord = [0] * self.dimension
- for i in range(len(coord)):
- start = self.lowerLimit[i] # start of the grid space
- coord[i] = int(np.around((real_coord[i] - start) / self.resolution))
- return coord
-
- def grid_coordinate_to_node_id(self, coord):
- # This function maps a grid coordinate to a unique
- # node id
- nodeId = 0
- for i in range(len(coord) - 1, -1, -1):
- product = 1
- for j in range(0, i):
- product = product * self.num_cells[j]
- nodeId = nodeId + coord[i] * product
- return nodeId
-
- def real_world_to_node_id(self, real_coord):
- # first convert the given coordinates to grid space and then
- # convert the grid space coordinates to a unique node id
- return self.grid_coordinate_to_node_id(
- self.real_coords_to_grid_coord(real_coord))
-
- def grid_coord_to_real_world_coord(self, coord):
- # This function maps a grid coordinate in discrete space
- # to a configuration in the full configuration space
- config = [0] * self.dimension
- for i in range(0, len(coord)):
- # start of the real world / configuration space
- start = self.lowerLimit[i]
- # step from the coordinate in the grid
- grid_step = self.resolution * coord[i]
- config[i] = start + grid_step
- return config
-
- def node_id_to_grid_coord(self, node_id):
- # This function maps a node id to the associated
- # grid coordinate
- coord = [0] * len(self.lowerLimit)
- for i in range(len(coord) - 1, -1, -1):
- # Get the product of the grid space maximums
- prod = 1
- for j in range(0, i):
- prod = prod * self.num_cells[j]
- coord[i] = np.floor(node_id / prod)
- node_id = node_id - (coord[i] * prod)
- return coord
-
- def node_id_to_real_world_coord(self, nid):
- # This function maps a node in discrete space to a configuration
- # in the full configuration space
- return self.grid_coord_to_real_world_coord(
- self.node_id_to_grid_coord(nid))
-
-
-class BITStar:
-
- def __init__(self, start, goal,
- obstacleList, randArea, eta=2.0,
- maxIter=80):
- self.start = start
- self.goal = goal
-
- self.min_rand = randArea[0]
- self.max_rand = randArea[1]
- self.max_iIter = maxIter
- self.obstacleList = obstacleList
- self.startId = None
- self.goalId = None
-
- self.vertex_queue = []
- self.edge_queue = []
- self.samples = dict()
- self.g_scores = dict()
- self.f_scores = dict()
- self.nodes = dict()
- self.r = float('inf')
- self.eta = eta # tunable parameter
- self.unit_ball_measure = 1
- self.old_vertices = []
-
- # initialize tree
- lowerLimit = [randArea[0], randArea[0]]
- upperLimit = [randArea[1], randArea[1]]
- self.tree = RTree(start=start, lowerLimit=lowerLimit,
- upperLimit=upperLimit, resolution=0.01)
-
- def setup_planning(self):
- self.startId = self.tree.real_world_to_node_id(self.start)
- self.goalId = self.tree.real_world_to_node_id(self.goal)
-
- # add goal to the samples
- self.samples[self.goalId] = self.goal
- self.g_scores[self.goalId] = float('inf')
- self.f_scores[self.goalId] = 0
-
- # add the start id to the tree
- self.tree.add_vertex(self.start)
- self.g_scores[self.startId] = 0
- self.f_scores[self.startId] = self.compute_heuristic_cost(
- self.startId, self.goalId)
-
- # max length we expect to find in our 'informed' sample space, starts as infinite
- cBest = self.g_scores[self.goalId]
-
- # Computing the sampling space
- cMin = math.hypot(self.start[0] - self.goal[0],
- self.start[1] - self.goal[1]) / 1.5
- xCenter = np.array([[(self.start[0] + self.goal[0]) / 2.0],
- [(self.start[1] + self.goal[1]) / 2.0], [0]])
- a1 = np.array([[(self.goal[0] - self.start[0]) / cMin],
- [(self.goal[1] - self.start[1]) / cMin], [0]])
- eTheta = math.atan2(a1[1, 0], a1[0, 0])
- # first column of identity matrix transposed
- id1_t = np.array([1.0, 0.0, 0.0]).reshape(1, 3)
- M = np.dot(a1, id1_t)
- U, S, Vh = np.linalg.svd(M, True, True)
- C = np.dot(np.dot(U, np.diag(
- [1.0, 1.0, np.linalg.det(U) * np.linalg.det(np.transpose(Vh))])),
- Vh)
-
- self.samples.update(self.informed_sample(
- 200, cBest, cMin, xCenter, C))
-
- return eTheta, cMin, xCenter, C, cBest
-
- def setup_sample(self, iterations, foundGoal, cMin, xCenter, C, cBest):
-
- if len(self.vertex_queue) == 0 and len(self.edge_queue) == 0:
- print("Batch: ", iterations)
- # Using informed rrt star way of computing the samples
- self.r = 2.0
- if iterations != 0:
- if foundGoal:
- # a better way to do this would be to make number of samples
- # a function of cMin
- m = 200
- self.samples = dict()
- self.samples[self.goalId] = self.goal
- else:
- m = 100
- cBest = self.g_scores[self.goalId]
- self.samples.update(self.informed_sample(
- m, cBest, cMin, xCenter, C))
-
- # make the old vertices the new vertices
- self.old_vertices += self.tree.vertices.keys()
- # add the vertices to the vertex queue
- for nid in self.tree.vertices.keys():
- if nid not in self.vertex_queue:
- self.vertex_queue.append(nid)
- return cBest
-
- def plan(self, animation=True):
-
- eTheta, cMin, xCenter, C, cBest = self.setup_planning()
- iterations = 0
-
- foundGoal = False
- # run until done
- while iterations < self.max_iIter:
- cBest = self.setup_sample(iterations,
- foundGoal, cMin, xCenter, C, cBest)
- # expand the best vertices until an edge is better than the vertex
- # this is done because the vertex cost represents the lower bound
- # on the edge cost
- while self.best_vertex_queue_value() <= \
- self.best_edge_queue_value():
- self.expand_vertex(self.best_in_vertex_queue())
-
- # add the best edge to the tree
- bestEdge = self.best_in_edge_queue()
- self.edge_queue.remove(bestEdge)
-
- # Check if this can improve the current solution
- estimatedCostOfVertex = self.g_scores[bestEdge[
- 0]] + self.compute_distance_cost(
- bestEdge[0], bestEdge[1]) + self.compute_heuristic_cost(
- bestEdge[1], self.goalId)
- estimatedCostOfEdge = self.compute_distance_cost(
- self.startId, bestEdge[0]) + self.compute_heuristic_cost(
- bestEdge[0], bestEdge[1]) + self.compute_heuristic_cost(
- bestEdge[1], self.goalId)
- actualCostOfEdge = self.g_scores[
- bestEdge[0]] + self.compute_distance_cost(
- bestEdge[0], bestEdge[1])
-
- f1 = estimatedCostOfVertex < self.g_scores[self.goalId]
- f2 = estimatedCostOfEdge < self.g_scores[self.goalId]
- f3 = actualCostOfEdge < self.g_scores[self.goalId]
-
- if f1 and f2 and f3:
- # connect this edge
- firstCoord = self.tree.node_id_to_real_world_coord(
- bestEdge[0])
- secondCoord = self.tree.node_id_to_real_world_coord(
- bestEdge[1])
- path = self.connect(firstCoord, secondCoord)
- lastEdge = self.tree.real_world_to_node_id(secondCoord)
- if path is None or len(path) == 0:
- continue
- nextCoord = path[len(path) - 1, :]
- nextCoordPathId = self.tree.real_world_to_node_id(
- nextCoord)
- bestEdge = (bestEdge[0], nextCoordPathId)
- if bestEdge[1] in self.tree.vertices.keys():
- continue
- else:
- try:
- del self.samples[bestEdge[1]]
- except KeyError:
- # invalid sample key
- pass
- eid = self.tree.add_vertex(nextCoord)
- self.vertex_queue.append(eid)
- if eid == self.goalId or bestEdge[0] == self.goalId or \
- bestEdge[1] == self.goalId:
- print("Goal found")
- foundGoal = True
-
- self.tree.add_edge(bestEdge[0], bestEdge[1])
-
- g_score = self.compute_distance_cost(
- bestEdge[0], bestEdge[1])
- self.g_scores[bestEdge[1]] = g_score + self.g_scores[
- bestEdge[0]]
- self.f_scores[
- bestEdge[1]] = g_score + self.compute_heuristic_cost(
- bestEdge[1], self.goalId)
- self.update_graph()
-
- # visualize new edge
- if animation:
- self.draw_graph(xCenter=xCenter, cBest=cBest,
- cMin=cMin, eTheta=eTheta,
- samples=self.samples.values(),
- start=firstCoord, end=secondCoord)
-
- self.remove_queue(lastEdge, bestEdge)
-
- else:
- print("Nothing good")
- self.edge_queue = []
- self.vertex_queue = []
-
- iterations += 1
-
- print("Finding the path")
- return self.find_final_path()
-
- def find_final_path(self):
- plan = [self.goal]
- currId = self.goalId
- while currId != self.startId:
- plan.append(self.tree.node_id_to_real_world_coord(currId))
- try:
- currId = self.nodes[currId]
- except KeyError:
- print("cannot find Path")
- return []
-
- plan.append(self.start)
- plan = plan[::-1] # reverse the plan
-
- return plan
-
- def remove_queue(self, lastEdge, bestEdge):
- for edge in self.edge_queue:
- if edge[1] == bestEdge[1]:
- dist_cost = self.compute_distance_cost(edge[1], bestEdge[1])
- if self.g_scores[edge[1]] + dist_cost >= \
- self.g_scores[self.goalId]:
- if (lastEdge, bestEdge[1]) in self.edge_queue:
- self.edge_queue.remove(
- (lastEdge, bestEdge[1]))
-
- def connect(self, start, end):
- # A function which attempts to extend from a start coordinates
- # to goal coordinates
- steps = int(self.compute_distance_cost(
- self.tree.real_world_to_node_id(start),
- self.tree.real_world_to_node_id(end)) * 10)
- x = np.linspace(start[0], end[0], num=steps)
- y = np.linspace(start[1], end[1], num=steps)
- for i in range(len(x)):
- if self._collision_check(x[i], y[i]):
- if i == 0:
- return None
- # if collision, send path until collision
- return np.vstack((x[0:i], y[0:i])).transpose()
-
- return np.vstack((x, y)).transpose()
-
- def _collision_check(self, x, y):
- for (ox, oy, size) in self.obstacleList:
- dx = ox - x
- dy = oy - y
- d = dx * dx + dy * dy
- if d <= size ** 2:
- return True # collision
- return False
-
- def compute_heuristic_cost(self, start_id, goal_id):
- # Using Manhattan distance as heuristic
- start = np.array(self.tree.node_id_to_real_world_coord(start_id))
- goal = np.array(self.tree.node_id_to_real_world_coord(goal_id))
-
- return np.linalg.norm(start - goal, 2)
-
- def compute_distance_cost(self, vid, xid):
- # L2 norm distance
- start = np.array(self.tree.node_id_to_real_world_coord(vid))
- stop = np.array(self.tree.node_id_to_real_world_coord(xid))
-
- return np.linalg.norm(stop - start, 2)
-
- # Sample free space confined in the radius of ball R
- def informed_sample(self, m, cMax, cMin, xCenter, C):
- samples = dict()
- print("g_Score goal id: ", self.g_scores[self.goalId])
- for i in range(m + 1):
- if cMax < float('inf'):
- r = [cMax / 2.0,
- math.sqrt(cMax ** 2 - cMin ** 2) / 2.0,
- math.sqrt(cMax ** 2 - cMin ** 2) / 2.0]
- L = np.diag(r)
- xBall = self.sample_unit_ball()
- rnd = np.dot(np.dot(C, L), xBall) + xCenter
- rnd = [rnd[(0, 0)], rnd[(1, 0)]]
- random_id = self.tree.real_world_to_node_id(rnd)
- samples[random_id] = rnd
- else:
- rnd = self.sample_free_space()
- random_id = self.tree.real_world_to_node_id(rnd)
- samples[random_id] = rnd
- return samples
-
- # Sample point in a unit ball
- @staticmethod
- def sample_unit_ball():
- a = random.random()
- b = random.random()
-
- if b < a:
- a, b = b, a
-
- sample = (b * math.cos(2 * math.pi * a / b),
- b * math.sin(2 * math.pi * a / b))
- return np.array([[sample[0]], [sample[1]], [0]])
-
- def sample_free_space(self):
- rnd = [random.uniform(self.min_rand, self.max_rand),
- random.uniform(self.min_rand, self.max_rand)]
-
- return rnd
-
- def best_vertex_queue_value(self):
- if len(self.vertex_queue) == 0:
- return float('inf')
- values = [self.g_scores[v]
- + self.compute_heuristic_cost(v, self.goalId) for v in
- self.vertex_queue]
- values.sort()
- return values[0]
-
- def best_edge_queue_value(self):
- if len(self.edge_queue) == 0:
- return float('inf')
- # return the best value in the queue by score g_tau[v] + c(v,x) + h(x)
- values = [self.g_scores[e[0]] + self.compute_distance_cost(e[0], e[1])
- + self.compute_heuristic_cost(e[1], self.goalId) for e in
- self.edge_queue]
- values.sort(reverse=True)
- return values[0]
-
- def best_in_vertex_queue(self):
- # return the best value in the vertex queue
- v_plus_values = [(v, self.g_scores[v] +
- self.compute_heuristic_cost(v, self.goalId))
- for v in self.vertex_queue]
- v_plus_values = sorted(v_plus_values, key=lambda x: x[1])
- # print(v_plus_values)
- return v_plus_values[0][0]
-
- def best_in_edge_queue(self):
- e_and_values = [
- (e[0], e[1], self.g_scores[e[0]] + self.compute_distance_cost(
- e[0], e[1]) + self.compute_heuristic_cost(e[1], self.goalId))
- for e in self.edge_queue]
- e_and_values = sorted(e_and_values, key=lambda x: x[2])
-
- return e_and_values[0][0], e_and_values[0][1]
-
- def expand_vertex(self, vid):
- self.vertex_queue.remove(vid)
-
- # get the coordinates for given vid
- currCoord = np.array(self.tree.node_id_to_real_world_coord(vid))
-
- # get the nearest value in vertex for every one in samples where difference is
- # less than the radius
- neighbors = []
- for sid, s_coord in self.samples.items():
- s_coord = np.array(s_coord)
- if np.linalg.norm(s_coord - currCoord, 2) <= self.r and sid != vid:
- neighbors.append((sid, s_coord))
-
- # add an edge to the edge queue is the path might improve the solution
- for neighbor in neighbors:
- sid = neighbor[0]
- h_cost = self.compute_heuristic_cost(sid, self.goalId)
- estimated_f_score = self.compute_distance_cost(
- self.startId, vid) + h_cost + self.compute_distance_cost(vid,
- sid)
- if estimated_f_score < self.g_scores[self.goalId]:
- self.edge_queue.append((vid, sid))
-
- # add the vertex to the edge queue
- self.add_vertex_to_edge_queue(vid, currCoord)
-
- def add_vertex_to_edge_queue(self, vid, currCoord):
- if vid not in self.old_vertices:
- neighbors = []
- for v, edges in self.tree.vertices.items():
- if v != vid and (v, vid) not in self.edge_queue and \
- (vid, v) not in self.edge_queue:
- v_coord = self.tree.node_id_to_real_world_coord(v)
- if np.linalg.norm(currCoord - v_coord, 2) <= self.r:
- neighbors.append((vid, v_coord))
-
- for neighbor in neighbors:
- sid = neighbor[0]
- estimated_f_score = self.compute_distance_cost(
- self.startId, vid) + self.compute_distance_cost(
- vid, sid) + self.compute_heuristic_cost(sid, self.goalId)
- if estimated_f_score < self.g_scores[self.goalId] and (
- self.g_scores[vid] +
- self.compute_distance_cost(vid, sid)) < \
- self.g_scores[sid]:
- self.edge_queue.append((vid, sid))
-
- def update_graph(self):
- closedSet = []
- openSet = []
- currId = self.startId
- openSet.append(currId)
-
- while len(openSet) != 0:
- # get the element with lowest f_score
- currId = min(openSet, key=lambda x: self.f_scores[x])
-
- # remove element from open set
- openSet.remove(currId)
-
- # Check if we're at the goal
- if currId == self.goalId:
- break
-
- if currId not in closedSet:
- closedSet.append(currId)
-
- # find a non visited successor to the current node
- successors = self.tree.vertices[currId]
- for successor in successors:
- if successor in closedSet:
- continue
- else:
- # calculate tentative g score
- g_score = self.g_scores[currId] + \
- self.compute_distance_cost(currId, successor)
- if successor not in openSet:
- # add the successor to open set
- openSet.append(successor)
- elif g_score >= self.g_scores[successor]:
- continue
-
- # update g and f scores
- self.g_scores[successor] = g_score
- self.f_scores[
- successor] = g_score + self.compute_heuristic_cost(
- successor, self.goalId)
-
- # store the parent and child
- self.nodes[successor] = currId
-
- def draw_graph(self, xCenter=None, cBest=None, cMin=None, eTheta=None,
- samples=None, start=None, end=None):
- plt.clf()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- for rnd in samples:
- if rnd is not None:
- plt.plot(rnd[0], rnd[1], "^k")
- if cBest != float('inf'):
- self.plot_ellipse(xCenter, cBest, cMin, eTheta)
-
- if start is not None and end is not None:
- plt.plot([start[0], start[1]], [end[0], end[1]], "-g")
-
- for (ox, oy, size) in self.obstacleList:
- plt.plot(ox, oy, "ok", ms=30 * size)
-
- plt.plot(self.start[0], self.start[1], "xr")
- plt.plot(self.goal[0], self.goal[1], "xr")
- plt.axis([-2, 15, -2, 15])
- plt.grid(True)
- plt.pause(0.01)
-
- @staticmethod
- def plot_ellipse(xCenter, cBest, cMin, eTheta): # pragma: no cover
-
- a = math.sqrt(cBest ** 2 - cMin ** 2) / 2.0
- b = cBest / 2.0
- angle = math.pi / 2.0 - eTheta
- cx = xCenter[0]
- cy = xCenter[1]
-
- t = np.arange(0, 2 * math.pi + 0.1, 0.1)
- x = [a * math.cos(it) for it in t]
- y = [b * math.sin(it) for it in t]
- R = np.array([[math.cos(angle), math.sin(angle)],
- [-math.sin(angle), math.cos(angle)]])
- fx = R @ np.array([x, y])
- px = np.array(fx[0, :] + cx).flatten()
- py = np.array(fx[1, :] + cy).flatten()
- plt.plot(cx, cy, "xc")
- plt.plot(px, py, "--c")
-
-
-def main(maxIter=80):
- print("Starting Batch Informed Trees Star planning")
- obstacleList = [
- (5, 5, 0.5),
- (9, 6, 1),
- (7, 5, 1),
- (1, 5, 1),
- (3, 6, 1),
- (7, 9, 1)
- ]
-
- bitStar = BITStar(start=[-1, 0], goal=[3, 8], obstacleList=obstacleList,
- randArea=[-2, 15], maxIter=maxIter)
- path = bitStar.plan(animation=show_animation)
- print("Done")
-
- if show_animation:
- plt.plot([x for (x, y) in path], [y for (x, y) in path], '-r')
- plt.grid(True)
- plt.pause(0.05)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/BezierPath/bezier_path.py b/PathPlanning/BezierPath/bezier_path.py
deleted file mode 100644
index 46faf1f3106..00000000000
--- a/PathPlanning/BezierPath/bezier_path.py
+++ /dev/null
@@ -1,215 +0,0 @@
-"""
-
-Path planning with Bezier curve.
-
-author: Atsushi Sakai(@Atsushi_twi)
-
-"""
-
-import matplotlib.pyplot as plt
-import numpy as np
-import scipy.special
-
-show_animation = True
-
-
-def calc_4points_bezier_path(sx, sy, syaw, ex, ey, eyaw, offset):
- """
- Compute control points and path given start and end position.
-
- :param sx: (float) x-coordinate of the starting point
- :param sy: (float) y-coordinate of the starting point
- :param syaw: (float) yaw angle at start
- :param ex: (float) x-coordinate of the ending point
- :param ey: (float) y-coordinate of the ending point
- :param eyaw: (float) yaw angle at the end
- :param offset: (float)
- :return: (numpy array, numpy array)
- """
- dist = np.hypot(sx - ex, sy - ey) / offset
- control_points = np.array(
- [[sx, sy],
- [sx + dist * np.cos(syaw), sy + dist * np.sin(syaw)],
- [ex - dist * np.cos(eyaw), ey - dist * np.sin(eyaw)],
- [ex, ey]])
-
- path = calc_bezier_path(control_points, n_points=100)
-
- return path, control_points
-
-
-def calc_bezier_path(control_points, n_points=100):
- """
- Compute bezier path (trajectory) given control points.
-
- :param control_points: (numpy array)
- :param n_points: (int) number of points in the trajectory
- :return: (numpy array)
- """
- traj = []
- for t in np.linspace(0, 1, n_points):
- traj.append(bezier(t, control_points))
-
- return np.array(traj)
-
-
-def bernstein_poly(n, i, t):
- """
- Bernstein polynom.
-
- :param n: (int) polynom degree
- :param i: (int)
- :param t: (float)
- :return: (float)
- """
- return scipy.special.comb(n, i) * t ** i * (1 - t) ** (n - i)
-
-
-def bezier(t, control_points):
- """
- Return one point on the bezier curve.
-
- :param t: (float) number in [0, 1]
- :param control_points: (numpy array)
- :return: (numpy array) Coordinates of the point
- """
- n = len(control_points) - 1
- return np.sum([bernstein_poly(n, i, t) * control_points[i] for i in range(n + 1)], axis=0)
-
-
-def bezier_derivatives_control_points(control_points, n_derivatives):
- """
- Compute control points of the successive derivatives of a given bezier curve.
-
- A derivative of a bezier curve is a bezier curve.
- See https://pomax.github.io/bezierinfo/#derivatives
- for detailed explanations
-
- :param control_points: (numpy array)
- :param n_derivatives: (int)
- e.g., n_derivatives=2 -> compute control points for first and second derivatives
- :return: ([numpy array])
- """
- w = {0: control_points}
- for i in range(n_derivatives):
- n = len(w[i])
- w[i + 1] = np.array([(n - 1) * (w[i][j + 1] - w[i][j])
- for j in range(n - 1)])
- return w
-
-
-def curvature(dx, dy, ddx, ddy):
- """
- Compute curvature at one point given first and second derivatives.
-
- :param dx: (float) First derivative along x axis
- :param dy: (float)
- :param ddx: (float) Second derivative along x axis
- :param ddy: (float)
- :return: (float)
- """
- return (dx * ddy - dy * ddx) / (dx ** 2 + dy ** 2) ** (3 / 2)
-
-
-def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"): # pragma: no cover
- """Plot arrow."""
- if not isinstance(x, float):
- for (ix, iy, iyaw) in zip(x, y, yaw):
- plot_arrow(ix, iy, iyaw)
- else:
- plt.arrow(x, y, length * np.cos(yaw), length * np.sin(yaw),
- fc=fc, ec=ec, head_width=width, head_length=width)
- plt.plot(x, y)
-
-
-def main():
- """Plot an example bezier curve."""
- start_x = 10.0 # [m]
- start_y = 1.0 # [m]
- start_yaw = np.radians(180.0) # [rad]
-
- end_x = -0.0 # [m]
- end_y = -3.0 # [m]
- end_yaw = np.radians(-45.0) # [rad]
- offset = 3.0
-
- path, control_points = calc_4points_bezier_path(
- start_x, start_y, start_yaw, end_x, end_y, end_yaw, offset)
-
- # Note: alternatively, instead of specifying start and end position
- # you can directly define n control points and compute the path:
- # control_points = np.array([[5., 1.], [-2.78, 1.], [-11.5, -4.5], [-6., -8.]])
- # path = calc_bezier_path(control_points, n_points=100)
-
- # Display the tangent, normal and radius of cruvature at a given point
- t = 0.86 # Number in [0, 1]
- x_target, y_target = bezier(t, control_points)
- derivatives_cp = bezier_derivatives_control_points(control_points, 2)
- point = bezier(t, control_points)
- dt = bezier(t, derivatives_cp[1])
- ddt = bezier(t, derivatives_cp[2])
- # Radius of curvature
- radius = 1 / curvature(dt[0], dt[1], ddt[0], ddt[1])
- # Normalize derivative
- dt /= np.linalg.norm(dt, 2)
- tangent = np.array([point, point + dt])
- normal = np.array([point, point + [- dt[1], dt[0]]])
- curvature_center = point + np.array([- dt[1], dt[0]]) * radius
- circle = plt.Circle(tuple(curvature_center), radius,
- color=(0, 0.8, 0.8), fill=False, linewidth=1)
-
- assert path.T[0][0] == start_x, "path is invalid"
- assert path.T[1][0] == start_y, "path is invalid"
- assert path.T[0][-1] == end_x, "path is invalid"
- assert path.T[1][-1] == end_y, "path is invalid"
-
- if show_animation: # pragma: no cover
- fig, ax = plt.subplots()
- ax.plot(path.T[0], path.T[1], label="Bezier Path")
- ax.plot(control_points.T[0], control_points.T[1],
- '--o', label="Control Points")
- ax.plot(x_target, y_target)
- ax.plot(tangent[:, 0], tangent[:, 1], label="Tangent")
- ax.plot(normal[:, 0], normal[:, 1], label="Normal")
- ax.add_artist(circle)
- plot_arrow(start_x, start_y, start_yaw)
- plot_arrow(end_x, end_y, end_yaw)
- ax.legend()
- ax.axis("equal")
- ax.grid(True)
- plt.show()
-
-
-def main2():
- """Show the effect of the offset."""
- start_x = 10.0 # [m]
- start_y = 1.0 # [m]
- start_yaw = np.radians(180.0) # [rad]
-
- end_x = -0.0 # [m]
- end_y = -3.0 # [m]
- end_yaw = np.radians(-45.0) # [rad]
-
- for offset in np.arange(1.0, 5.0, 1.0):
- path, control_points = calc_4points_bezier_path(
- start_x, start_y, start_yaw, end_x, end_y, end_yaw, offset)
- assert path.T[0][0] == start_x, "path is invalid"
- assert path.T[1][0] == start_y, "path is invalid"
- assert path.T[0][-1] == end_x, "path is invalid"
- assert path.T[1][-1] == end_y, "path is invalid"
-
- if show_animation: # pragma: no cover
- plt.plot(path.T[0], path.T[1], label="Offset=" + str(offset))
-
- if show_animation: # pragma: no cover
- plot_arrow(start_x, start_y, start_yaw)
- plot_arrow(end_x, end_y, end_yaw)
- plt.legend()
- plt.axis("equal")
- plt.grid(True)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
- # main2()
diff --git a/PathPlanning/BidirectionalAStar/bidirectional_a_star.py b/PathPlanning/BidirectionalAStar/bidirectional_a_star.py
deleted file mode 100644
index 5387cca1ad9..00000000000
--- a/PathPlanning/BidirectionalAStar/bidirectional_a_star.py
+++ /dev/null
@@ -1,347 +0,0 @@
-"""
-
-Bidirectional A* grid planning
-
-author: Erwin Lejeune (@spida_rwin)
-
-See Wikipedia article (https://en.wikipedia.org/wiki/Bidirectional_search)
-
-"""
-
-import math
-
-import matplotlib.pyplot as plt
-
-show_animation = True
-
-
-class BidirectionalAStarPlanner:
-
- def __init__(self, ox, oy, resolution, rr):
- """
- Initialize grid map for a star planning
-
- ox: x position list of Obstacles [m]
- oy: y position list of Obstacles [m]
- resolution: grid resolution [m]
- rr: robot radius[m]
- """
-
- self.min_x, self.min_y = None, None
- self.max_x, self.max_y = None, None
- self.x_width, self.y_width, self.obstacle_map = None, None, None
- self.resolution = resolution
- self.rr = rr
- self.calc_obstacle_map(ox, oy)
- self.motion = self.get_motion_model()
-
- class Node:
- def __init__(self, x, y, cost, parent_index):
- self.x = x # index of grid
- self.y = y # index of grid
- self.cost = cost
- self.parent_index = parent_index
-
- def __str__(self):
- return str(self.x) + "," + str(self.y) + "," + str(
- self.cost) + "," + str(self.parent_index)
-
- def planning(self, sx, sy, gx, gy):
- """
- Bidirectional A star path search
-
- input:
- s_x: start x position [m]
- s_y: start y position [m]
- gx: goal x position [m]
- gy: goal y position [m]
-
- output:
- rx: x position list of the final path
- ry: y position list of the final path
- """
-
- start_node = self.Node(self.calc_xy_index(sx, self.min_x),
- self.calc_xy_index(sy, self.min_y), 0.0, -1)
- goal_node = self.Node(self.calc_xy_index(gx, self.min_x),
- self.calc_xy_index(gy, self.min_y), 0.0, -1)
-
- open_set_A, closed_set_A = dict(), dict()
- open_set_B, closed_set_B = dict(), dict()
- open_set_A[self.calc_grid_index(start_node)] = start_node
- open_set_B[self.calc_grid_index(goal_node)] = goal_node
-
- current_A = start_node
- current_B = goal_node
- meet_point_A, meet_point_B = None, None
-
- while True:
- if len(open_set_A) == 0:
- print("Open set A is empty..")
- break
-
- if len(open_set_B) == 0:
- print("Open set B is empty..")
- break
-
- c_id_A = min(
- open_set_A,
- key=lambda o: self.find_total_cost(open_set_A, o, current_B))
-
- current_A = open_set_A[c_id_A]
-
- c_id_B = min(
- open_set_B,
- key=lambda o: self.find_total_cost(open_set_B, o, current_A))
-
- current_B = open_set_B[c_id_B]
-
- # show graph
- if show_animation: # pragma: no cover
- plt.plot(self.calc_grid_position(current_A.x, self.min_x),
- self.calc_grid_position(current_A.y, self.min_y),
- "xc")
- plt.plot(self.calc_grid_position(current_B.x, self.min_x),
- self.calc_grid_position(current_B.y, self.min_y),
- "xc")
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if len(closed_set_A.keys()) % 10 == 0:
- plt.pause(0.001)
-
- if current_A.x == current_B.x and current_A.y == current_B.y:
- print("Found goal")
- meet_point_A = current_A
- meet_point_B = current_B
- break
-
- # Remove the item from the open set
- del open_set_A[c_id_A]
- del open_set_B[c_id_B]
-
- # Add it to the closed set
- closed_set_A[c_id_A] = current_A
- closed_set_B[c_id_B] = current_B
-
- # expand_grid search grid based on motion model
- for i, _ in enumerate(self.motion):
-
- c_nodes = [self.Node(current_A.x + self.motion[i][0],
- current_A.y + self.motion[i][1],
- current_A.cost + self.motion[i][2],
- c_id_A),
- self.Node(current_B.x + self.motion[i][0],
- current_B.y + self.motion[i][1],
- current_B.cost + self.motion[i][2],
- c_id_B)]
-
- n_ids = [self.calc_grid_index(c_nodes[0]),
- self.calc_grid_index(c_nodes[1])]
-
- # If the node is not safe, do nothing
- continue_ = self.check_nodes_and_sets(c_nodes, closed_set_A,
- closed_set_B, n_ids)
-
- if not continue_[0]:
- if n_ids[0] not in open_set_A:
- # discovered a new node
- open_set_A[n_ids[0]] = c_nodes[0]
- else:
- if open_set_A[n_ids[0]].cost > c_nodes[0].cost:
- # This path is the best until now. record it
- open_set_A[n_ids[0]] = c_nodes[0]
-
- if not continue_[1]:
- if n_ids[1] not in open_set_B:
- # discovered a new node
- open_set_B[n_ids[1]] = c_nodes[1]
- else:
- if open_set_B[n_ids[1]].cost > c_nodes[1].cost:
- # This path is the best until now. record it
- open_set_B[n_ids[1]] = c_nodes[1]
-
- rx, ry = self.calc_final_bidirectional_path(
- meet_point_A, meet_point_B, closed_set_A, closed_set_B)
-
- return rx, ry
-
- # takes two sets and two meeting nodes and return the optimal path
- def calc_final_bidirectional_path(self, n1, n2, setA, setB):
- rx_A, ry_A = self.calc_final_path(n1, setA)
- rx_B, ry_B = self.calc_final_path(n2, setB)
-
- rx_A.reverse()
- ry_A.reverse()
-
- rx = rx_A + rx_B
- ry = ry_A + ry_B
-
- return rx, ry
-
- def calc_final_path(self, goal_node, closed_set):
- # generate final course
- rx, ry = [self.calc_grid_position(goal_node.x, self.min_x)], \
- [self.calc_grid_position(goal_node.y, self.min_y)]
- parent_index = goal_node.parent_index
- while parent_index != -1:
- n = closed_set[parent_index]
- rx.append(self.calc_grid_position(n.x, self.min_x))
- ry.append(self.calc_grid_position(n.y, self.min_y))
- parent_index = n.parent_index
-
- return rx, ry
-
- def check_nodes_and_sets(self, c_nodes, closedSet_A, closedSet_B, n_ids):
- continue_ = [False, False]
- if not self.verify_node(c_nodes[0]) or n_ids[0] in closedSet_A:
- continue_[0] = True
-
- if not self.verify_node(c_nodes[1]) or n_ids[1] in closedSet_B:
- continue_[1] = True
-
- return continue_
-
- @staticmethod
- def calc_heuristic(n1, n2):
- w = 1.0 # weight of heuristic
- d = w * math.hypot(n1.x - n2.x, n1.y - n2.y)
- return d
-
- def find_total_cost(self, open_set, lambda_, n1):
- g_cost = open_set[lambda_].cost
- h_cost = self.calc_heuristic(n1, open_set[lambda_])
- f_cost = g_cost + h_cost
- return f_cost
-
- def calc_grid_position(self, index, min_position):
- """
- calc grid position
-
- :param index:
- :param min_position:
- :return:
- """
- pos = index * self.resolution + min_position
- return pos
-
- def calc_xy_index(self, position, min_pos):
- return round((position - min_pos) / self.resolution)
-
- def calc_grid_index(self, node):
- return (node.y - self.min_y) * self.x_width + (node.x - self.min_x)
-
- def verify_node(self, node):
- px = self.calc_grid_position(node.x, self.min_x)
- py = self.calc_grid_position(node.y, self.min_y)
-
- if px < self.min_x:
- return False
- elif py < self.min_y:
- return False
- elif px >= self.max_x:
- return False
- elif py >= self.max_y:
- return False
-
- # collision check
- if self.obstacle_map[node.x][node.y]:
- return False
-
- return True
-
- def calc_obstacle_map(self, ox, oy):
-
- self.min_x = round(min(ox))
- self.min_y = round(min(oy))
- self.max_x = round(max(ox))
- self.max_y = round(max(oy))
- print("min_x:", self.min_x)
- print("min_y:", self.min_y)
- print("max_x:", self.max_x)
- print("max_y:", self.max_y)
-
- self.x_width = round((self.max_x - self.min_x) / self.resolution)
- self.y_width = round((self.max_y - self.min_y) / self.resolution)
- print("x_width:", self.x_width)
- print("y_width:", self.y_width)
-
- # obstacle map generation
- self.obstacle_map = [[False for _ in range(self.y_width)]
- for _ in range(self.x_width)]
- for ix in range(self.x_width):
- x = self.calc_grid_position(ix, self.min_x)
- for iy in range(self.y_width):
- y = self.calc_grid_position(iy, self.min_y)
- for iox, ioy in zip(ox, oy):
- d = math.hypot(iox - x, ioy - y)
- if d <= self.rr:
- self.obstacle_map[ix][iy] = True
- break
-
- @staticmethod
- def get_motion_model():
- # dx, dy, cost
- motion = [[1, 0, 1],
- [0, 1, 1],
- [-1, 0, 1],
- [0, -1, 1],
- [-1, -1, math.sqrt(2)],
- [-1, 1, math.sqrt(2)],
- [1, -1, math.sqrt(2)],
- [1, 1, math.sqrt(2)]]
-
- return motion
-
-
-def main():
- print(__file__ + " start!!")
-
- # start and goal position
- sx = 10.0 # [m]
- sy = 10.0 # [m]
- gx = 50.0 # [m]
- gy = 50.0 # [m]
- grid_size = 2.0 # [m]
- robot_radius = 1.0 # [m]
-
- # set obstacle positions
- ox, oy = [], []
- for i in range(-10, 60):
- ox.append(i)
- oy.append(-10.0)
- for i in range(-10, 60):
- ox.append(60.0)
- oy.append(i)
- for i in range(-10, 61):
- ox.append(i)
- oy.append(60.0)
- for i in range(-10, 61):
- ox.append(-10.0)
- oy.append(i)
- for i in range(-10, 40):
- ox.append(20.0)
- oy.append(i)
- for i in range(0, 40):
- ox.append(40.0)
- oy.append(60.0 - i)
-
- if show_animation: # pragma: no cover
- plt.plot(ox, oy, ".k")
- plt.plot(sx, sy, "og")
- plt.plot(gx, gy, "ob")
- plt.grid(True)
- plt.axis("equal")
-
- bidir_a_star = BidirectionalAStarPlanner(ox, oy, grid_size, robot_radius)
- rx, ry = bidir_a_star.planning(sx, sy, gx, gy)
-
- if show_animation: # pragma: no cover
- plt.plot(rx, ry, "-r")
- plt.pause(.0001)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/BidirectionalBreadthFirstSearch/bidirectional_breadth_first_search.py b/PathPlanning/BidirectionalBreadthFirstSearch/bidirectional_breadth_first_search.py
deleted file mode 100644
index 60a8c5e1704..00000000000
--- a/PathPlanning/BidirectionalBreadthFirstSearch/bidirectional_breadth_first_search.py
+++ /dev/null
@@ -1,317 +0,0 @@
-"""
-
-Bidirectional Breadth-First grid planning
-
-author: Erwin Lejeune (@spida_rwin)
-
-See Wikipedia article (https://en.wikipedia.org/wiki/Breadth-first_search)
-
-"""
-
-import math
-
-import matplotlib.pyplot as plt
-
-show_animation = True
-
-
-class BidirectionalBreadthFirstSearchPlanner:
-
- def __init__(self, ox, oy, resolution, rr):
- """
- Initialize grid map for bfs planning
-
- ox: x position list of Obstacles [m]
- oy: y position list of Obstacles [m]
- resolution: grid resolution [m]
- rr: robot radius[m]
- """
-
- self.min_x, self.min_y = None, None
- self.max_x, self.max_y = None, None
- self.x_width, self.y_width, self.obstacle_map = None, None, None
- self.resolution = resolution
- self.rr = rr
- self.calc_obstacle_map(ox, oy)
- self.motion = self.get_motion_model()
-
- class Node:
- def __init__(self, x, y, cost, parent_index, parent):
- self.x = x # index of grid
- self.y = y # index of grid
- self.cost = cost
- self.parent_index = parent_index
- self.parent = parent
-
- def __str__(self):
- return str(self.x) + "," + str(self.y) + "," + str(
- self.cost) + "," + str(self.parent_index)
-
- def planning(self, sx, sy, gx, gy):
- """
- Bidirectional Breadth First search based planning
-
- input:
- s_x: start x position [m]
- s_y: start y position [m]
- gx: goal x position [m]
- gy: goal y position [m]
-
- output:
- rx: x position list of the final path
- ry: y position list of the final path
- """
-
- start_node = self.Node(self.calc_xy_index(sx, self.min_x),
- self.calc_xy_index(sy, self.min_y), 0.0, -1,
- None)
- goal_node = self.Node(self.calc_xy_index(gx, self.min_x),
- self.calc_xy_index(gy, self.min_y), 0.0, -1,
- None)
-
- open_set_A, closed_set_A = dict(), dict()
- open_set_B, closed_set_B = dict(), dict()
- open_set_B[self.calc_grid_index(goal_node)] = goal_node
- open_set_A[self.calc_grid_index(start_node)] = start_node
-
- meet_point_A, meet_point_B = None, None
-
- while True:
- if len(open_set_A) == 0:
- print("Open set A is empty..")
- break
-
- if len(open_set_B) == 0:
- print("Open set B is empty")
- break
-
- current_A = open_set_A.pop(list(open_set_A.keys())[0])
- current_B = open_set_B.pop(list(open_set_B.keys())[0])
-
- c_id_A = self.calc_grid_index(current_A)
- c_id_B = self.calc_grid_index(current_B)
-
- closed_set_A[c_id_A] = current_A
- closed_set_B[c_id_B] = current_B
-
- # show graph
- if show_animation: # pragma: no cover
- plt.plot(self.calc_grid_position(current_A.x, self.min_x),
- self.calc_grid_position(current_A.y, self.min_y),
- "xc")
- plt.plot(self.calc_grid_position(current_B.x, self.min_x),
- self.calc_grid_position(current_B.y, self.min_y),
- "xc")
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if len(closed_set_A.keys()) % 10 == 0:
- plt.pause(0.001)
-
- if c_id_A in closed_set_B:
- print("Find goal")
- meet_point_A = closed_set_A[c_id_A]
- meet_point_B = closed_set_B[c_id_A]
- break
-
- elif c_id_B in closed_set_A:
- print("Find goal")
- meet_point_A = closed_set_A[c_id_B]
- meet_point_B = closed_set_B[c_id_B]
- break
-
- # expand_grid search grid based on motion model
- for i, _ in enumerate(self.motion):
- breakA = False
- breakB = False
-
- node_A = self.Node(current_A.x + self.motion[i][0],
- current_A.y + self.motion[i][1],
- current_A.cost + self.motion[i][2],
- c_id_A, None)
- node_B = self.Node(current_B.x + self.motion[i][0],
- current_B.y + self.motion[i][1],
- current_B.cost + self.motion[i][2],
- c_id_B, None)
-
- n_id_A = self.calc_grid_index(node_A)
- n_id_B = self.calc_grid_index(node_B)
-
- # If the node is not safe, do nothing
- if not self.verify_node(node_A):
- breakA = True
-
- if not self.verify_node(node_B):
- breakB = True
-
- if (n_id_A not in closed_set_A) and \
- (n_id_A not in open_set_A) and (not breakA):
- node_A.parent = current_A
- open_set_A[n_id_A] = node_A
-
- if (n_id_B not in closed_set_B) and \
- (n_id_B not in open_set_B) and (not breakB):
- node_B.parent = current_B
- open_set_B[n_id_B] = node_B
-
- rx, ry = self.calc_final_path_bidir(
- meet_point_A, meet_point_B, closed_set_A, closed_set_B)
- return rx, ry
-
- # takes both set and meeting nodes and calculate optimal path
- def calc_final_path_bidir(self, n1, n2, setA, setB):
- rxA, ryA = self.calc_final_path(n1, setA)
- rxB, ryB = self.calc_final_path(n2, setB)
-
- rxA.reverse()
- ryA.reverse()
-
- rx = rxA + rxB
- ry = ryA + ryB
-
- return rx, ry
-
- def calc_final_path(self, goal_node, closed_set):
- # generate final course
- rx, ry = [self.calc_grid_position(goal_node.x, self.min_x)], [
- self.calc_grid_position(goal_node.y, self.min_y)]
- n = closed_set[goal_node.parent_index]
- while n is not None:
- rx.append(self.calc_grid_position(n.x, self.min_x))
- ry.append(self.calc_grid_position(n.y, self.min_y))
- n = n.parent
-
- return rx, ry
-
- def calc_grid_position(self, index, min_position):
- """
- calc grid position
-
- :param index:
- :param min_position:
- :return:
- """
- pos = index * self.resolution + min_position
- return pos
-
- def calc_xy_index(self, position, min_pos):
- return round((position - min_pos) / self.resolution)
-
- def calc_grid_index(self, node):
- return (node.y - self.min_y) * self.x_width + (node.x - self.min_x)
-
- def verify_node(self, node):
- px = self.calc_grid_position(node.x, self.min_x)
- py = self.calc_grid_position(node.y, self.min_y)
-
- if px < self.min_x:
- return False
- elif py < self.min_y:
- return False
- elif px >= self.max_x:
- return False
- elif py >= self.max_y:
- return False
-
- # collision check
- if self.obstacle_map[node.x][node.y]:
- return False
-
- return True
-
- def calc_obstacle_map(self, ox, oy):
-
- self.min_x = round(min(ox))
- self.min_y = round(min(oy))
- self.max_x = round(max(ox))
- self.max_y = round(max(oy))
- print("min_x:", self.min_x)
- print("min_y:", self.min_y)
- print("max_x:", self.max_x)
- print("max_y:", self.max_y)
-
- self.x_width = round((self.max_x - self.min_x) / self.resolution)
- self.y_width = round((self.max_y - self.min_y) / self.resolution)
- print("x_width:", self.x_width)
- print("y_width:", self.y_width)
-
- # obstacle map generation
- self.obstacle_map = [[False for _ in range(self.y_width)]
- for _ in range(self.x_width)]
- for ix in range(self.x_width):
- x = self.calc_grid_position(ix, self.min_x)
- for iy in range(self.y_width):
- y = self.calc_grid_position(iy, self.min_y)
- for iox, ioy in zip(ox, oy):
- d = math.hypot(iox - x, ioy - y)
- if d <= self.rr:
- self.obstacle_map[ix][iy] = True
- break
-
- @staticmethod
- def get_motion_model():
- # dx, dy, cost
- motion = [[1, 0, 1],
- [0, 1, 1],
- [-1, 0, 1],
- [0, -1, 1],
- [-1, -1, math.sqrt(2)],
- [-1, 1, math.sqrt(2)],
- [1, -1, math.sqrt(2)],
- [1, 1, math.sqrt(2)]]
-
- return motion
-
-
-def main():
- print(__file__ + " start!!")
-
- # start and goal position
- sx = 10.0 # [m]
- sy = 10.0 # [m]
- gx = 50.0 # [m]
- gy = 50.0 # [m]
- grid_size = 2.0 # [m]
- robot_radius = 1.0 # [m]
-
- # set obstacle positions
- ox, oy = [], []
- for i in range(-10, 60):
- ox.append(i)
- oy.append(-10.0)
- for i in range(-10, 60):
- ox.append(60.0)
- oy.append(i)
- for i in range(-10, 61):
- ox.append(i)
- oy.append(60.0)
- for i in range(-10, 61):
- ox.append(-10.0)
- oy.append(i)
- for i in range(-10, 40):
- ox.append(20.0)
- oy.append(i)
- for i in range(0, 40):
- ox.append(40.0)
- oy.append(60.0 - i)
-
- if show_animation: # pragma: no cover
- plt.plot(ox, oy, ".k")
- plt.plot(sx, sy, "og")
- plt.plot(gx, gy, "ob")
- plt.grid(True)
- plt.axis("equal")
-
- bi_bfs = BidirectionalBreadthFirstSearchPlanner(
- ox, oy, grid_size, robot_radius)
- rx, ry = bi_bfs.planning(sx, sy, gx, gy)
-
- if show_animation: # pragma: no cover
- plt.plot(rx, ry, "-r")
- plt.pause(0.01)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/BreadthFirstSearch/breadth_first_search.py b/PathPlanning/BreadthFirstSearch/breadth_first_search.py
deleted file mode 100644
index ad994732a55..00000000000
--- a/PathPlanning/BreadthFirstSearch/breadth_first_search.py
+++ /dev/null
@@ -1,258 +0,0 @@
-"""
-
-Breadth-First grid planning
-
-author: Erwin Lejeune (@spida_rwin)
-
-See Wikipedia article (https://en.wikipedia.org/wiki/Breadth-first_search)
-
-"""
-
-import math
-
-import matplotlib.pyplot as plt
-
-show_animation = True
-
-
-class BreadthFirstSearchPlanner:
-
- def __init__(self, ox, oy, reso, rr):
- """
- Initialize grid map for bfs planning
-
- ox: x position list of Obstacles [m]
- oy: y position list of Obstacles [m]
- resolution: grid resolution [m]
- rr: robot radius[m]
- """
-
- self.reso = reso
- self.rr = rr
- self.calc_obstacle_map(ox, oy)
- self.motion = self.get_motion_model()
-
- class Node:
- def __init__(self, x, y, cost, parent_index, parent):
- self.x = x # index of grid
- self.y = y # index of grid
- self.cost = cost
- self.parent_index = parent_index
- self.parent = parent
-
- def __str__(self):
- return str(self.x) + "," + str(self.y) + "," + str(
- self.cost) + "," + str(self.parent_index)
-
- def planning(self, sx, sy, gx, gy):
- """
- Breadth First search based planning
-
- input:
- s_x: start x position [m]
- s_y: start y position [m]
- gx: goal x position [m]
- gy: goal y position [m]
-
- output:
- rx: x position list of the final path
- ry: y position list of the final path
- """
-
- nstart = self.Node(self.calc_xyindex(sx, self.minx),
- self.calc_xyindex(sy, self.miny), 0.0, -1, None)
- ngoal = self.Node(self.calc_xyindex(gx, self.minx),
- self.calc_xyindex(gy, self.miny), 0.0, -1, None)
-
- open_set, closed_set = dict(), dict()
- open_set[self.calc_grid_index(nstart)] = nstart
-
- while True:
- if len(open_set) == 0:
- print("Open set is empty..")
- break
-
- current = open_set.pop(list(open_set.keys())[0])
-
- c_id = self.calc_grid_index(current)
-
- closed_set[c_id] = current
-
- # show graph
- if show_animation: # pragma: no cover
- plt.plot(self.calc_grid_position(current.x, self.minx),
- self.calc_grid_position(current.y, self.miny), "xc")
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event:
- [exit(0) if event.key == 'escape'
- else None])
- if len(closed_set.keys()) % 10 == 0:
- plt.pause(0.001)
-
- if current.x == ngoal.x and current.y == ngoal.y:
- print("Find goal")
- ngoal.parent_index = current.parent_index
- ngoal.cost = current.cost
- break
-
- # expand_grid search grid based on motion model
- for i, _ in enumerate(self.motion):
- node = self.Node(current.x + self.motion[i][0],
- current.y + self.motion[i][1],
- current.cost + self.motion[i][2], c_id, None)
- n_id = self.calc_grid_index(node)
-
- # If the node is not safe, do nothing
- if not self.verify_node(node):
- continue
-
- if (n_id not in closed_set) and (n_id not in open_set):
- node.parent = current
- open_set[n_id] = node
-
- rx, ry = self.calc_final_path(ngoal, closed_set)
- return rx, ry
-
- def calc_final_path(self, ngoal, closedset):
- # generate final course
- rx, ry = [self.calc_grid_position(ngoal.x, self.minx)], [
- self.calc_grid_position(ngoal.y, self.miny)]
- n = closedset[ngoal.parent_index]
- while n is not None:
- rx.append(self.calc_grid_position(n.x, self.minx))
- ry.append(self.calc_grid_position(n.y, self.miny))
- n = n.parent
-
- return rx, ry
-
- def calc_grid_position(self, index, minp):
- """
- calc grid position
-
- :param index:
- :param minp:
- :return:
- """
- pos = index * self.reso + minp
- return pos
-
- def calc_xyindex(self, position, min_pos):
- return round((position - min_pos) / self.reso)
-
- def calc_grid_index(self, node):
- return (node.y - self.miny) * self.xwidth + (node.x - self.minx)
-
- def verify_node(self, node):
- px = self.calc_grid_position(node.x, self.minx)
- py = self.calc_grid_position(node.y, self.miny)
-
- if px < self.minx:
- return False
- elif py < self.miny:
- return False
- elif px >= self.maxx:
- return False
- elif py >= self.maxy:
- return False
-
- # collision check
- if self.obmap[node.x][node.y]:
- return False
-
- return True
-
- def calc_obstacle_map(self, ox, oy):
-
- self.minx = round(min(ox))
- self.miny = round(min(oy))
- self.maxx = round(max(ox))
- self.maxy = round(max(oy))
- print("min_x:", self.minx)
- print("min_y:", self.miny)
- print("max_x:", self.maxx)
- print("max_y:", self.maxy)
-
- self.xwidth = round((self.maxx - self.minx) / self.reso)
- self.ywidth = round((self.maxy - self.miny) / self.reso)
- print("x_width:", self.xwidth)
- print("y_width:", self.ywidth)
-
- # obstacle map generation
- self.obmap = [[False for _ in range(self.ywidth)]
- for _ in range(self.xwidth)]
- for ix in range(self.xwidth):
- x = self.calc_grid_position(ix, self.minx)
- for iy in range(self.ywidth):
- y = self.calc_grid_position(iy, self.miny)
- for iox, ioy in zip(ox, oy):
- d = math.hypot(iox - x, ioy - y)
- if d <= self.rr:
- self.obmap[ix][iy] = True
- break
-
- @staticmethod
- def get_motion_model():
- # dx, dy, cost
- motion = [[1, 0, 1],
- [0, 1, 1],
- [-1, 0, 1],
- [0, -1, 1],
- [-1, -1, math.sqrt(2)],
- [-1, 1, math.sqrt(2)],
- [1, -1, math.sqrt(2)],
- [1, 1, math.sqrt(2)]]
-
- return motion
-
-
-def main():
- print(__file__ + " start!!")
-
- # start and goal position
- sx = 10.0 # [m]
- sy = 10.0 # [m]
- gx = 50.0 # [m]
- gy = 50.0 # [m]
- grid_size = 2.0 # [m]
- robot_radius = 1.0 # [m]
-
- # set obstacle positions
- ox, oy = [], []
- for i in range(-10, 60):
- ox.append(float(i))
- oy.append(-10.0)
- for i in range(-10, 60):
- ox.append(60.0)
- oy.append(float(i))
- for i in range(-10, 61):
- ox.append(float(i))
- oy.append(60.0)
- for i in range(-10, 61):
- ox.append(-10.0)
- oy.append(float(i))
- for i in range(-10, 40):
- ox.append(20.0)
- oy.append(float(i))
- for i in range(0, 40):
- ox.append(40.0)
- oy.append(60.0 - i)
-
- if show_animation: # pragma: no cover
- plt.plot(ox, oy, ".k")
- plt.plot(sx, sy, "og")
- plt.plot(gx, gy, "xb")
- plt.grid(True)
- plt.axis("equal")
-
- bfs = BreadthFirstSearchPlanner(ox, oy, grid_size, robot_radius)
- rx, ry = bfs.planning(sx, sy, gx, gy)
-
- if show_animation: # pragma: no cover
- plt.plot(rx, ry, "-r")
- plt.pause(0.01)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/BugPlanning/bug.py b/PathPlanning/BugPlanning/bug.py
deleted file mode 100644
index 34890cb55a9..00000000000
--- a/PathPlanning/BugPlanning/bug.py
+++ /dev/null
@@ -1,333 +0,0 @@
-"""
-Bug Planning
-author: Sarim Mehdi(muhammadsarim.mehdi@studio.unibo.it)
-Source: https://web.archive.org/web/20201103052224/https://sites.google.com/site/ece452bugalgorithms/
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-show_animation = True
-
-
-class BugPlanner:
- def __init__(self, start_x, start_y, goal_x, goal_y, obs_x, obs_y):
- self.goal_x = goal_x
- self.goal_y = goal_y
- self.obs_x = obs_x
- self.obs_y = obs_y
- self.r_x = [start_x]
- self.r_y = [start_y]
- self.out_x = []
- self.out_y = []
- for o_x, o_y in zip(obs_x, obs_y):
- for add_x, add_y in zip([1, 0, -1, -1, -1, 0, 1, 1],
- [1, 1, 1, 0, -1, -1, -1, 0]):
- cand_x, cand_y = o_x+add_x, o_y+add_y
- valid_point = True
- for _x, _y in zip(obs_x, obs_y):
- if cand_x == _x and cand_y == _y:
- valid_point = False
- break
- if valid_point:
- self.out_x.append(cand_x), self.out_y.append(cand_y)
-
- def mov_normal(self):
- return self.r_x[-1] + np.sign(self.goal_x - self.r_x[-1]), \
- self.r_y[-1] + np.sign(self.goal_y - self.r_y[-1])
-
- def mov_to_next_obs(self, visited_x, visited_y):
- for add_x, add_y in zip([1, 0, -1, 0], [0, 1, 0, -1]):
- c_x, c_y = self.r_x[-1] + add_x, self.r_y[-1] + add_y
- for _x, _y in zip(self.out_x, self.out_y):
- use_pt = True
- if c_x == _x and c_y == _y:
- for v_x, v_y in zip(visited_x, visited_y):
- if c_x == v_x and c_y == v_y:
- use_pt = False
- break
- if use_pt:
- return c_x, c_y, False
- if not use_pt:
- break
- return self.r_x[-1], self.r_y[-1], True
-
- def bug0(self):
- """
- Greedy algorithm where you move towards goal
- until you hit an obstacle. Then you go around it
- (pick an arbitrary direction), until it is possible
- for you to start moving towards goal in a greedy manner again
- """
- mov_dir = 'normal'
- cand_x, cand_y = -np.inf, -np.inf
- if show_animation:
- plt.plot(self.obs_x, self.obs_y, ".k")
- plt.plot(self.r_x[-1], self.r_y[-1], "og")
- plt.plot(self.goal_x, self.goal_y, "xb")
- plt.plot(self.out_x, self.out_y, ".")
- plt.grid(True)
- plt.title('BUG 0')
-
- for x_ob, y_ob in zip(self.out_x, self.out_y):
- if self.r_x[-1] == x_ob and self.r_y[-1] == y_ob:
- mov_dir = 'obs'
- break
-
- visited_x, visited_y = [], []
- while True:
- if self.r_x[-1] == self.goal_x and \
- self.r_y[-1] == self.goal_y:
- break
- if mov_dir == 'normal':
- cand_x, cand_y = self.mov_normal()
- if mov_dir == 'obs':
- cand_x, cand_y, _ = self.mov_to_next_obs(visited_x, visited_y)
- if mov_dir == 'normal':
- found_boundary = False
- for x_ob, y_ob in zip(self.out_x, self.out_y):
- if cand_x == x_ob and cand_y == y_ob:
- self.r_x.append(cand_x), self.r_y.append(cand_y)
- visited_x[:], visited_y[:] = [], []
- visited_x.append(cand_x), visited_y.append(cand_y)
- mov_dir = 'obs'
- found_boundary = True
- break
- if not found_boundary:
- self.r_x.append(cand_x), self.r_y.append(cand_y)
- elif mov_dir == 'obs':
- can_go_normal = True
- for x_ob, y_ob in zip(self.obs_x, self.obs_y):
- if self.mov_normal()[0] == x_ob and \
- self.mov_normal()[1] == y_ob:
- can_go_normal = False
- break
- if can_go_normal:
- mov_dir = 'normal'
- else:
- self.r_x.append(cand_x), self.r_y.append(cand_y)
- visited_x.append(cand_x), visited_y.append(cand_y)
- if show_animation:
- plt.plot(self.r_x, self.r_y, "-r")
- plt.pause(0.001)
- if show_animation:
- plt.show()
-
- def bug1(self):
- """
- Move towards goal in a greedy manner.
- When you hit an obstacle, you go around it and
- back to where you hit the obstacle initially.
- Then, you go to the point on the obstacle that is
- closest to your goal and you start moving towards
- goal in a greedy manner from that new point.
- """
- mov_dir = 'normal'
- cand_x, cand_y = -np.inf, -np.inf
- exit_x, exit_y = -np.inf, -np.inf
- dist = np.inf
- back_to_start = False
- second_round = False
- if show_animation:
- plt.plot(self.obs_x, self.obs_y, ".k")
- plt.plot(self.r_x[-1], self.r_y[-1], "og")
- plt.plot(self.goal_x, self.goal_y, "xb")
- plt.plot(self.out_x, self.out_y, ".")
- plt.grid(True)
- plt.title('BUG 1')
-
- for xob, yob in zip(self.out_x, self.out_y):
- if self.r_x[-1] == xob and self.r_y[-1] == yob:
- mov_dir = 'obs'
- break
-
- visited_x, visited_y = [], []
- while True:
- if self.r_x[-1] == self.goal_x and \
- self.r_y[-1] == self.goal_y:
- break
- if mov_dir == 'normal':
- cand_x, cand_y = self.mov_normal()
- if mov_dir == 'obs':
- cand_x, cand_y, back_to_start = \
- self.mov_to_next_obs(visited_x, visited_y)
- if mov_dir == 'normal':
- found_boundary = False
- for x_ob, y_ob in zip(self.out_x, self.out_y):
- if cand_x == x_ob and cand_y == y_ob:
- self.r_x.append(cand_x), self.r_y.append(cand_y)
- visited_x[:], visited_y[:] = [], []
- visited_x.append(cand_x), visited_y.append(cand_y)
- mov_dir = 'obs'
- dist = np.inf
- back_to_start = False
- second_round = False
- found_boundary = True
- break
- if not found_boundary:
- self.r_x.append(cand_x), self.r_y.append(cand_y)
- elif mov_dir == 'obs':
- d = np.linalg.norm(np.array([cand_x, cand_y] -
- np.array([self.goal_x,
- self.goal_y])))
- if d < dist and not second_round:
- exit_x, exit_y = cand_x, cand_y
- dist = d
- if back_to_start and not second_round:
- second_round = True
- del self.r_x[-len(visited_x):]
- del self.r_y[-len(visited_y):]
- visited_x[:], visited_y[:] = [], []
- self.r_x.append(cand_x), self.r_y.append(cand_y)
- visited_x.append(cand_x), visited_y.append(cand_y)
- if cand_x == exit_x and \
- cand_y == exit_y and \
- second_round:
- mov_dir = 'normal'
- if show_animation:
- plt.plot(self.r_x, self.r_y, "-r")
- plt.pause(0.001)
- if show_animation:
- plt.show()
-
- def bug2(self):
- """
- Move towards goal in a greedy manner.
- When you hit an obstacle, you go around it and
- keep track of your distance from the goal.
- If the distance from your goal was decreasing before
- and now it starts increasing, that means the current
- point is probably the closest point to the
- goal (this may or may not be true because the algorithm
- doesn't explore the entire boundary around the obstacle).
- So, you depart from this point and continue towards the
- goal in a greedy manner
- """
- mov_dir = 'normal'
- cand_x, cand_y = -np.inf, -np.inf
- if show_animation:
- plt.plot(self.obs_x, self.obs_y, ".k")
- plt.plot(self.r_x[-1], self.r_y[-1], "og")
- plt.plot(self.goal_x, self.goal_y, "xb")
- plt.plot(self.out_x, self.out_y, ".")
-
- straight_x, straight_y = [self.r_x[-1]], [self.r_y[-1]]
- hit_x, hit_y = [], []
- while True:
- if straight_x[-1] == self.goal_x and \
- straight_y[-1] == self.goal_y:
- break
- c_x = straight_x[-1] + np.sign(self.goal_x - straight_x[-1])
- c_y = straight_y[-1] + np.sign(self.goal_y - straight_y[-1])
- for x_ob, y_ob in zip(self.out_x, self.out_y):
- if c_x == x_ob and c_y == y_ob:
- hit_x.append(c_x), hit_y.append(c_y)
- break
- straight_x.append(c_x), straight_y.append(c_y)
- if show_animation:
- plt.plot(straight_x, straight_y, ",")
- plt.plot(hit_x, hit_y, "d")
- plt.grid(True)
- plt.title('BUG 2')
-
- for x_ob, y_ob in zip(self.out_x, self.out_y):
- if self.r_x[-1] == x_ob and self.r_y[-1] == y_ob:
- mov_dir = 'obs'
- break
-
- visited_x, visited_y = [], []
- while True:
- if self.r_x[-1] == self.goal_x \
- and self.r_y[-1] == self.goal_y:
- break
- if mov_dir == 'normal':
- cand_x, cand_y = self.mov_normal()
- if mov_dir == 'obs':
- cand_x, cand_y, _ = self.mov_to_next_obs(visited_x, visited_y)
- if mov_dir == 'normal':
- found_boundary = False
- for x_ob, y_ob in zip(self.out_x, self.out_y):
- if cand_x == x_ob and cand_y == y_ob:
- self.r_x.append(cand_x), self.r_y.append(cand_y)
- visited_x[:], visited_y[:] = [], []
- visited_x.append(cand_x), visited_y.append(cand_y)
- del hit_x[0]
- del hit_y[0]
- mov_dir = 'obs'
- found_boundary = True
- break
- if not found_boundary:
- self.r_x.append(cand_x), self.r_y.append(cand_y)
- elif mov_dir == 'obs':
- self.r_x.append(cand_x), self.r_y.append(cand_y)
- visited_x.append(cand_x), visited_y.append(cand_y)
- for i_x, i_y in zip(range(len(hit_x)), range(len(hit_y))):
- if cand_x == hit_x[i_x] and cand_y == hit_y[i_y]:
- del hit_x[i_x]
- del hit_y[i_y]
- mov_dir = 'normal'
- break
- if show_animation:
- plt.plot(self.r_x, self.r_y, "-r")
- plt.pause(0.001)
- if show_animation:
- plt.show()
-
-
-def main(bug_0, bug_1, bug_2):
- # set obstacle positions
- o_x, o_y = [], []
-
- s_x = 0.0
- s_y = 0.0
- g_x = 167.0
- g_y = 50.0
-
- for i in range(20, 40):
- for j in range(20, 40):
- o_x.append(i)
- o_y.append(j)
-
- for i in range(60, 100):
- for j in range(40, 80):
- o_x.append(i)
- o_y.append(j)
-
- for i in range(120, 140):
- for j in range(80, 100):
- o_x.append(i)
- o_y.append(j)
-
- for i in range(80, 140):
- for j in range(0, 20):
- o_x.append(i)
- o_y.append(j)
-
- for i in range(0, 20):
- for j in range(60, 100):
- o_x.append(i)
- o_y.append(j)
-
- for i in range(20, 40):
- for j in range(80, 100):
- o_x.append(i)
- o_y.append(j)
-
- for i in range(120, 160):
- for j in range(40, 60):
- o_x.append(i)
- o_y.append(j)
-
- if bug_0:
- my_Bug = BugPlanner(s_x, s_y, g_x, g_y, o_x, o_y)
- my_Bug.bug0()
- if bug_1:
- my_Bug = BugPlanner(s_x, s_y, g_x, g_y, o_x, o_y)
- my_Bug.bug1()
- if bug_2:
- my_Bug = BugPlanner(s_x, s_y, g_x, g_y, o_x, o_y)
- my_Bug.bug2()
-
-
-if __name__ == '__main__':
- main(bug_0=True, bug_1=False, bug_2=False)
diff --git a/PathPlanning/Catmull_RomSplinePath/blending_functions.py b/PathPlanning/Catmull_RomSplinePath/blending_functions.py
deleted file mode 100644
index f3ef5dd3238..00000000000
--- a/PathPlanning/Catmull_RomSplinePath/blending_functions.py
+++ /dev/null
@@ -1,34 +0,0 @@
-import numpy as np
-import matplotlib.pyplot as plt
-
-def blending_function_1(t):
- return -t + 2*t**2 - t**3
-
-def blending_function_2(t):
- return 2 - 5*t**2 + 3*t**3
-
-def blending_function_3(t):
- return t + 4*t**2 - 3*t**3
-
-def blending_function_4(t):
- return -t**2 + t**3
-
-def plot_blending_functions():
- t = np.linspace(0, 1, 100)
-
- plt.plot(t, blending_function_1(t), label='b1')
- plt.plot(t, blending_function_2(t), label='b2')
- plt.plot(t, blending_function_3(t), label='b3')
- plt.plot(t, blending_function_4(t), label='b4')
-
- plt.title("Catmull-Rom Blending Functions")
- plt.xlabel("t")
- plt.ylabel("Value")
- plt.legend()
- plt.grid(True)
- plt.axhline(y=0, color='k', linestyle='--')
- plt.axvline(x=0, color='k', linestyle='--')
- plt.show()
-
-if __name__ == "__main__":
- plot_blending_functions()
\ No newline at end of file
diff --git a/PathPlanning/Catmull_RomSplinePath/catmull_rom_spline_path.py b/PathPlanning/Catmull_RomSplinePath/catmull_rom_spline_path.py
deleted file mode 100644
index 79916330c9b..00000000000
--- a/PathPlanning/Catmull_RomSplinePath/catmull_rom_spline_path.py
+++ /dev/null
@@ -1,86 +0,0 @@
-"""
-Path Planner with Catmull-Rom Spline
-Author: Surabhi Gupta (@this_is_surabhi)
-Source: http://graphics.cs.cmu.edu/nsp/course/15-462/Fall04/assts/catmullRom.pdf
-"""
-
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-def catmull_rom_point(t, p0, p1, p2, p3):
- """
- Parameters
- ----------
- t : float
- Parameter value (0 <= t <= 1) (0 <= t <= 1)
- p0, p1, p2, p3 : np.ndarray
- Control points for the spline segment
-
- Returns
- -------
- np.ndarray
- Calculated point on the spline
- """
- return 0.5 * ((2 * p1) +
- (-p0 + p2) * t +
- (2 * p0 - 5 * p1 + 4 * p2 - p3) * t**2 +
- (-p0 + 3 * p1 - 3 * p2 + p3) * t**3)
-
-
-def catmull_rom_spline(control_points, num_points):
- """
- Parameters
- ----------
- control_points : list
- List of control points
- num_points : int
- Number of points to generate on the spline
-
- Returns
- -------
- tuple
- x and y coordinates of the spline points
- """
- t_vals = np.linspace(0, 1, num_points)
- spline_points = []
-
- control_points = np.array(control_points)
-
- for i in range(len(control_points) - 1):
- if i == 0:
- p1, p2, p3 = control_points[i:i+3]
- p0 = p1
- elif i == len(control_points) - 2:
- p0, p1, p2 = control_points[i-1:i+2]
- p3 = p2
- else:
- p0, p1, p2, p3 = control_points[i-1:i+3]
-
- for t in t_vals:
- point = catmull_rom_point(t, p0, p1, p2, p3)
- spline_points.append(point)
-
- return np.array(spline_points).T
-
-
-def main():
- print(__file__ + " start!!")
-
- way_points = [[-1.0, -2.0], [1.0, -1.0], [3.0, -2.0], [4.0, -1.0], [3.0, 1.0], [1.0, 2.0], [0.0, 2.0]]
- n_course_point = 100
- spline_x, spline_y = catmull_rom_spline(way_points, n_course_point)
-
- plt.plot(spline_x,spline_y, '-r', label="Catmull-Rom Spline Path")
- plt.plot(np.array(way_points).T[0], np.array(way_points).T[1], '-og', label="Way points")
- plt.title("Catmull-Rom Spline Path")
- plt.grid(True)
- plt.legend()
- plt.axis("equal")
- plt.show()
-
-if __name__ == '__main__':
- main()
\ No newline at end of file
diff --git a/PathPlanning/ClosedLoopRRTStar/closed_loop_rrt_star_car.py b/PathPlanning/ClosedLoopRRTStar/closed_loop_rrt_star_car.py
deleted file mode 100644
index 01ab8349a9c..00000000000
--- a/PathPlanning/ClosedLoopRRTStar/closed_loop_rrt_star_car.py
+++ /dev/null
@@ -1,216 +0,0 @@
-"""
-
-Path planning Sample Code with Closed loop RRT for car like robot.
-
-author: AtsushiSakai(@Atsushi_twi)
-
-"""
-import matplotlib.pyplot as plt
-import numpy as np
-
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from ClosedLoopRRTStar import pure_pursuit
-from ClosedLoopRRTStar import unicycle_model
-from ReedsSheppPath import reeds_shepp_path_planning
-from RRTStarReedsShepp.rrt_star_reeds_shepp import RRTStarReedsShepp
-
-show_animation = True
-
-
-class ClosedLoopRRTStar(RRTStarReedsShepp):
- """
- Class for Closed loop RRT star planning
- """
-
- def __init__(self, start, goal, obstacle_list, rand_area,
- max_iter=200,
- connect_circle_dist=50.0,
- robot_radius=0.0
- ):
- super().__init__(start, goal, obstacle_list, rand_area,
- max_iter=max_iter,
- connect_circle_dist=connect_circle_dist,
- robot_radius=robot_radius
- )
-
- self.target_speed = 10.0 / 3.6
- self.yaw_th = np.deg2rad(3.0)
- self.xy_th = 0.5
- self.invalid_travel_ratio = 5.0
-
- def planning(self, animation=True):
- """
- do planning
-
- animation: flag for animation on or off
- """
- # planning with RRTStarReedsShepp
- super().planning(animation=animation)
-
- # generate coruse
- path_indexs = self.get_goal_indexes()
-
- flag, x, y, yaw, v, t, a, d = self.search_best_feasible_path(
- path_indexs)
-
- return flag, x, y, yaw, v, t, a, d
-
- def search_best_feasible_path(self, path_indexs):
-
- print("Start search feasible path")
-
- best_time = float("inf")
-
- fx, fy, fyaw, fv, ft, fa, fd = None, None, None, None, None, None, None
-
- # pure pursuit tracking
- for ind in path_indexs:
- path = self.generate_final_course(ind)
-
- flag, x, y, yaw, v, t, a, d = self.check_tracking_path_is_feasible(
- path)
-
- if flag and best_time >= t[-1]:
- print("feasible path is found")
- best_time = t[-1]
- fx, fy, fyaw, fv, ft, fa, fd = x, y, yaw, v, t, a, d
-
- print("best time is")
- print(best_time)
-
- if fx:
- fx.append(self.end.x)
- fy.append(self.end.y)
- fyaw.append(self.end.yaw)
- return True, fx, fy, fyaw, fv, ft, fa, fd
-
- return False, None, None, None, None, None, None, None
-
- def check_tracking_path_is_feasible(self, path):
- cx = np.array([state[0] for state in path])[::-1]
- cy = np.array([state[1] for state in path])[::-1]
- cyaw = np.array([state[2] for state in path])[::-1]
-
- goal = [cx[-1], cy[-1], cyaw[-1]]
-
- cx, cy, cyaw = pure_pursuit.extend_path(cx, cy, cyaw)
-
- speed_profile = pure_pursuit.calc_speed_profile(
- cx, cy, cyaw, self.target_speed)
-
- t, x, y, yaw, v, a, d, find_goal = pure_pursuit.closed_loop_prediction(
- cx, cy, cyaw, speed_profile, goal)
- yaw = [reeds_shepp_path_planning.pi_2_pi(iyaw) for iyaw in yaw]
-
- if not find_goal:
- print("cannot reach goal")
-
- if abs(yaw[-1] - goal[2]) >= self.yaw_th * 10.0:
- print("final angle is bad")
- find_goal = False
-
- travel = unicycle_model.dt * sum(np.abs(v))
- origin_travel = sum(np.hypot(np.diff(cx), np.diff(cy)))
-
- if (travel / origin_travel) >= self.invalid_travel_ratio:
- print("path is too long")
- find_goal = False
-
- tmp_node = self.Node(x, y, 0)
- tmp_node.path_x = x
- tmp_node.path_y = y
- if not self.check_collision(
- tmp_node, self.obstacle_list, self.robot_radius):
- print("This path is collision")
- find_goal = False
-
- return find_goal, x, y, yaw, v, t, a, d
-
- def get_goal_indexes(self):
- goalinds = []
- for (i, node) in enumerate(self.node_list):
- if self.calc_dist_to_goal(node.x, node.y) <= self.xy_th:
- goalinds.append(i)
- print("OK XY TH num is")
- print(len(goalinds))
-
- # angle check
- fgoalinds = []
- for i in goalinds:
- if abs(self.node_list[i].yaw - self.end.yaw) <= self.yaw_th:
- fgoalinds.append(i)
- print("OK YAW TH num is")
- print(len(fgoalinds))
-
- return fgoalinds
-
-
-def main(gx=6.0, gy=7.0, gyaw=np.deg2rad(90.0), max_iter=100):
- print("Start" + __file__)
- # ====Search Path with RRT====
- obstacle_list = [
- (5, 5, 1),
- (4, 6, 1),
- (4, 8, 1),
- (4, 10, 1),
- (6, 5, 1),
- (7, 5, 1),
- (8, 6, 1),
- (8, 8, 1),
- (8, 10, 1)
- ] # [x,y,size(radius)]
-
- # Set Initial parameters
- start = [0.0, 0.0, np.deg2rad(0.0)]
- goal = [gx, gy, gyaw]
-
- closed_loop_rrt_star = ClosedLoopRRTStar(start, goal,
- obstacle_list,
- [-2.0, 20.0],
- max_iter=max_iter)
- flag, x, y, yaw, v, t, a, d = closed_loop_rrt_star.planning(
- animation=show_animation)
-
- if not flag:
- print("cannot find feasible path")
-
- # Draw final path
- if show_animation:
- closed_loop_rrt_star.draw_graph()
- plt.plot(x, y, '-r')
- plt.grid(True)
- plt.pause(0.001)
-
- plt.subplots(1)
- plt.plot(t, [np.rad2deg(iyaw) for iyaw in yaw[:-1]], '-r')
- plt.xlabel("time[s]")
- plt.ylabel("Yaw[deg]")
- plt.grid(True)
-
- plt.subplots(1)
- plt.plot(t, [iv * 3.6 for iv in v], '-r')
-
- plt.xlabel("time[s]")
- plt.ylabel("velocity[km/h]")
- plt.grid(True)
-
- plt.subplots(1)
- plt.plot(t, a, '-r')
- plt.xlabel("time[s]")
- plt.ylabel("accel[m/ss]")
- plt.grid(True)
-
- plt.subplots(1)
- plt.plot(t, [np.rad2deg(td) for td in d], '-r')
- plt.xlabel("time[s]")
- plt.ylabel("Steering angle[deg]")
- plt.grid(True)
-
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/ClosedLoopRRTStar/pure_pursuit.py b/PathPlanning/ClosedLoopRRTStar/pure_pursuit.py
deleted file mode 100644
index 982ebeca064..00000000000
--- a/PathPlanning/ClosedLoopRRTStar/pure_pursuit.py
+++ /dev/null
@@ -1,300 +0,0 @@
-"""
-
-Path tracking simulation with pure pursuit steering control and PID speed control.
-
-author: Atsushi Sakai
-
-"""
-import math
-
-import matplotlib.pyplot as plt
-import numpy as np
-
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from ClosedLoopRRTStar import unicycle_model
-
-Kp = 2.0 # speed propotional gain
-Lf = 0.5 # look-ahead distance
-T = 100.0 # max simulation time
-goal_dis = 0.5
-stop_speed = 0.5
-
-# animation = True
-animation = False
-
-
-def PIDControl(target, current):
- a = Kp * (target - current)
-
- if a > unicycle_model.accel_max:
- a = unicycle_model.accel_max
- elif a < -unicycle_model.accel_max:
- a = -unicycle_model.accel_max
-
- return a
-
-
-def pure_pursuit_control(state, cx, cy, pind):
-
- ind, dis = calc_target_index(state, cx, cy)
-
- if pind >= ind:
- ind = pind
-
- # print(parent_index, ind)
- if ind < len(cx):
- tx = cx[ind]
- ty = cy[ind]
- else:
- tx = cx[-1]
- ty = cy[-1]
- ind = len(cx) - 1
-
- alpha = math.atan2(ty - state.y, tx - state.x) - state.yaw
-
- if state.v <= 0.0: # back
- alpha = math.pi - alpha
-
- delta = math.atan2(2.0 * unicycle_model.L * math.sin(alpha) / Lf, 1.0)
-
- if delta > unicycle_model.steer_max:
- delta = unicycle_model.steer_max
- elif delta < - unicycle_model.steer_max:
- delta = -unicycle_model.steer_max
-
- return delta, ind, dis
-
-
-def calc_target_index(state, cx, cy):
- dx = [state.x - icx for icx in cx]
- dy = [state.y - icy for icy in cy]
-
- d = np.hypot(dx, dy)
- mindis = min(d)
-
- ind = np.argmin(d)
-
- L = 0.0
-
- while Lf > L and (ind + 1) < len(cx):
- dx = cx[ind + 1] - cx[ind]
- dy = cy[ind + 1] - cy[ind]
- L += math.hypot(dx, dy)
- ind += 1
-
- # print(mindis)
- return ind, mindis
-
-
-def closed_loop_prediction(cx, cy, cyaw, speed_profile, goal):
-
- state = unicycle_model.State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
-
- # lastIndex = len(cx) - 1
- time = 0.0
- x = [state.x]
- y = [state.y]
- yaw = [state.yaw]
- v = [state.v]
- t = [0.0]
- a = [0.0]
- d = [0.0]
- target_ind, mindis = calc_target_index(state, cx, cy)
- find_goal = False
-
- maxdis = 0.5
-
- while T >= time:
- di, target_ind, dis = pure_pursuit_control(state, cx, cy, target_ind)
-
- target_speed = speed_profile[target_ind]
- target_speed = target_speed * \
- (maxdis - min(dis, maxdis - 0.1)) / maxdis
-
- ai = PIDControl(target_speed, state.v)
- state = unicycle_model.update(state, ai, di)
-
- if abs(state.v) <= stop_speed and target_ind <= len(cx) - 2:
- target_ind += 1
-
- time = time + unicycle_model.dt
-
- # check goal
- dx = state.x - goal[0]
- dy = state.y - goal[1]
- if math.hypot(dx, dy) <= goal_dis:
- find_goal = True
- break
-
- x.append(state.x)
- y.append(state.y)
- yaw.append(state.yaw)
- v.append(state.v)
- t.append(time)
- a.append(ai)
- d.append(di)
-
- if target_ind % 1 == 0 and animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(cx, cy, "-r", label="course")
- plt.plot(x, y, "ob", label="trajectory")
- plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
- plt.axis("equal")
- plt.grid(True)
- plt.title("speed:" + str(round(state.v, 2))
- + "tind:" + str(target_ind))
- plt.pause(0.0001)
-
- else:
- print("Time out!!")
-
- return t, x, y, yaw, v, a, d, find_goal
-
-
-def set_stop_point(target_speed, cx, cy, cyaw):
- speed_profile = [target_speed] * len(cx)
- forward = True
-
- d = []
- is_back = False
-
- # Set stop point
- for i in range(len(cx) - 1):
- dx = cx[i + 1] - cx[i]
- dy = cy[i + 1] - cy[i]
- d.append(math.hypot(dx, dy))
- iyaw = cyaw[i]
- move_direction = math.atan2(dy, dx)
- is_back = abs(move_direction - iyaw) >= math.pi / 2.0
-
- if dx == 0.0 and dy == 0.0:
- continue
-
- if is_back:
- speed_profile[i] = - target_speed
- else:
- speed_profile[i] = target_speed
-
- if is_back and forward:
- speed_profile[i] = 0.0
- forward = False
- # plt.plot(cx[i], cy[i], "xb")
- # print(i_yaw, move_direction, dx, dy)
- elif not is_back and not forward:
- speed_profile[i] = 0.0
- forward = True
- # plt.plot(cx[i], cy[i], "xb")
- # print(i_yaw, move_direction, dx, dy)
- speed_profile[0] = 0.0
- if is_back:
- speed_profile[-1] = -stop_speed
- else:
- speed_profile[-1] = stop_speed
-
- d.append(d[-1])
-
- return speed_profile, d
-
-
-def calc_speed_profile(cx, cy, cyaw, target_speed):
-
- speed_profile, d = set_stop_point(target_speed, cx, cy, cyaw)
-
- if animation: # pragma: no cover
- plt.plot(speed_profile, "xb")
-
- return speed_profile
-
-
-def extend_path(cx, cy, cyaw):
-
- dl = 0.1
- dl_list = [dl] * (int(Lf / dl) + 1)
-
- move_direction = math.atan2(cy[-1] - cy[-3], cx[-1] - cx[-3])
- is_back = abs(move_direction - cyaw[-1]) >= math.pi / 2.0
-
- for idl in dl_list:
- if is_back:
- idl *= -1
- cx = np.append(cx, cx[-1] + idl * math.cos(cyaw[-1]))
- cy = np.append(cy, cy[-1] + idl * math.sin(cyaw[-1]))
- cyaw = np.append(cyaw, cyaw[-1])
-
- return cx, cy, cyaw
-
-
-def main(): # pragma: no cover
- # target course
- cx = np.arange(0, 50, 0.1)
- cy = [math.sin(ix / 5.0) * ix / 2.0 for ix in cx]
-
- target_speed = 5.0 / 3.6
-
- T = 15.0 # max simulation time
-
- state = unicycle_model.State(x=-0.0, y=-3.0, yaw=0.0, v=0.0)
- # state = unicycle_model.State(x=-1.0, y=-5.0, yaw=0.0, v=-30.0 / 3.6)
- # state = unicycle_model.State(x=10.0, y=5.0, yaw=0.0, v=-30.0 / 3.6)
- # state = unicycle_model.State(
- # x=3.0, y=5.0, yaw=np.deg2rad(-40.0), v=-10.0 / 3.6)
- # state = unicycle_model.State(
- # x=3.0, y=5.0, yaw=np.deg2rad(40.0), v=50.0 / 3.6)
-
- lastIndex = len(cx) - 1
- time = 0.0
- x = [state.x]
- y = [state.y]
- yaw = [state.yaw]
- v = [state.v]
- t = [0.0]
- target_ind, dis = calc_target_index(state, cx, cy)
-
- while T >= time and lastIndex > target_ind:
- ai = PIDControl(target_speed, state.v)
- di, target_ind, _ = pure_pursuit_control(state, cx, cy, target_ind)
- state = unicycle_model.update(state, ai, di)
-
- time = time + unicycle_model.dt
-
- x.append(state.x)
- y.append(state.y)
- yaw.append(state.yaw)
- v.append(state.v)
- t.append(time)
-
- # plt.cla()
- # plt.plot(cx, cy, ".r", label="course")
- # plt.plot(x, y, "-b", label="trajectory")
- # plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
- # plt.axis("equal")
- # plt.grid(True)
- # plt.pause(0.1)
- # input()
-
- plt.subplots(1)
- plt.plot(cx, cy, ".r", label="course")
- plt.plot(x, y, "-b", label="trajectory")
- plt.legend()
- plt.xlabel("x[m]")
- plt.ylabel("y[m]")
- plt.axis("equal")
- plt.grid(True)
-
- plt.subplots(1)
- plt.plot(t, [iv * 3.6 for iv in v], "-r")
- plt.xlabel("Time[s]")
- plt.ylabel("Speed[km/h]")
- plt.grid(True)
- plt.show()
-
-
-if __name__ == '__main__': # pragma: no cover
- print("Pure pursuit path tracking simulation start")
- main()
diff --git a/PathPlanning/ClosedLoopRRTStar/unicycle_model.py b/PathPlanning/ClosedLoopRRTStar/unicycle_model.py
deleted file mode 100644
index c05f76c84e3..00000000000
--- a/PathPlanning/ClosedLoopRRTStar/unicycle_model.py
+++ /dev/null
@@ -1,80 +0,0 @@
-"""
-
-Unicycle model class
-
-author Atsushi Sakai
-
-"""
-
-import math
-import numpy as np
-from utils.angle import angle_mod
-
-dt = 0.05 # [s]
-L = 0.9 # [m]
-steer_max = np.deg2rad(40.0)
-curvature_max = math.tan(steer_max) / L
-curvature_max = 1.0 / curvature_max + 1.0
-
-accel_max = 5.0
-
-
-class State:
-
- def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
- self.x = x
- self.y = y
- self.yaw = yaw
- self.v = v
-
-
-def update(state, a, delta):
-
- state.x = state.x + state.v * math.cos(state.yaw) * dt
- state.y = state.y + state.v * math.sin(state.yaw) * dt
- state.yaw = state.yaw + state.v / L * math.tan(delta) * dt
- state.yaw = pi_2_pi(state.yaw)
- state.v = state.v + a * dt
-
- return state
-
-
-def pi_2_pi(angle):
- return angle_mod(angle)
-
-
-if __name__ == '__main__': # pragma: no cover
- print("start unicycle simulation")
- import matplotlib.pyplot as plt
-
- T = 100
- a = [1.0] * T
- delta = [np.deg2rad(1.0)] * T
- # print(delta)
- # print(a, delta)
-
- state = State()
-
- x = []
- y = []
- yaw = []
- v = []
-
- for (ai, di) in zip(a, delta):
- state = update(state, ai, di)
-
- x.append(state.x)
- y.append(state.y)
- yaw.append(state.yaw)
- v.append(state.v)
-
- plt.subplots(1)
- plt.plot(x, y)
- plt.axis("equal")
- plt.grid(True)
-
- plt.subplots(1)
- plt.plot(v)
- plt.grid(True)
-
- plt.show()
diff --git a/PathPlanning/ClothoidPath/clothoid_path_planner.py b/PathPlanning/ClothoidPath/clothoid_path_planner.py
deleted file mode 100644
index 5e5fc6e9a37..00000000000
--- a/PathPlanning/ClothoidPath/clothoid_path_planner.py
+++ /dev/null
@@ -1,192 +0,0 @@
-"""
-Clothoid Path Planner
-Author: Daniel Ingram (daniel-s-ingram)
- Atsushi Sakai (AtsushiSakai)
-Reference paper: Fast and accurate G1 fitting of clothoid curves
-https://www.researchgate.net/publication/237062806
-"""
-
-from collections import namedtuple
-import matplotlib.pyplot as plt
-import numpy as np
-import scipy.integrate as integrate
-from scipy.optimize import fsolve
-from math import atan2, cos, hypot, pi, sin
-from matplotlib import animation
-
-Point = namedtuple("Point", ["x", "y"])
-
-show_animation = True
-
-
-def generate_clothoid_paths(start_point, start_yaw_list,
- goal_point, goal_yaw_list,
- n_path_points):
- """
- Generate clothoid path list. This function generate multiple clothoid paths
- from multiple orientations(yaw) at start points to multiple orientations
- (yaw) at goal point.
-
- :param start_point: Start point of the path
- :param start_yaw_list: Orientation list at start point in radian
- :param goal_point: Goal point of the path
- :param goal_yaw_list: Orientation list at goal point in radian
- :param n_path_points: number of path points
- :return: clothoid path list
- """
- clothoids = []
- for start_yaw in start_yaw_list:
- for goal_yaw in goal_yaw_list:
- clothoid = generate_clothoid_path(start_point, start_yaw,
- goal_point, goal_yaw,
- n_path_points)
- clothoids.append(clothoid)
- return clothoids
-
-
-def generate_clothoid_path(start_point, start_yaw,
- goal_point, goal_yaw, n_path_points):
- """
- Generate a clothoid path list.
-
- :param start_point: Start point of the path
- :param start_yaw: Orientation at start point in radian
- :param goal_point: Goal point of the path
- :param goal_yaw: Orientation at goal point in radian
- :param n_path_points: number of path points
- :return: a clothoid path
- """
- dx = goal_point.x - start_point.x
- dy = goal_point.y - start_point.y
- r = hypot(dx, dy)
-
- phi = atan2(dy, dx)
- phi1 = normalize_angle(start_yaw - phi)
- phi2 = normalize_angle(goal_yaw - phi)
- delta = phi2 - phi1
-
- try:
- # Step1: Solve g function
- A = solve_g_for_root(phi1, phi2, delta)
-
- # Step2: Calculate path parameters
- L = compute_path_length(r, phi1, delta, A)
- curvature = compute_curvature(delta, A, L)
- curvature_rate = compute_curvature_rate(A, L)
- except Exception as e:
- print(f"Failed to generate clothoid points: {e}")
- return None
-
- # Step3: Construct a path with Fresnel integral
- points = []
- for s in np.linspace(0, L, n_path_points):
- try:
- x = start_point.x + s * X(curvature_rate * s ** 2, curvature * s,
- start_yaw)
- y = start_point.y + s * Y(curvature_rate * s ** 2, curvature * s,
- start_yaw)
- points.append(Point(x, y))
- except Exception as e:
- print(f"Skipping failed clothoid point: {e}")
-
- return points
-
-
-def X(a, b, c):
- return integrate.quad(lambda t: cos((a/2)*t**2 + b*t + c), 0, 1)[0]
-
-
-def Y(a, b, c):
- return integrate.quad(lambda t: sin((a/2)*t**2 + b*t + c), 0, 1)[0]
-
-
-def solve_g_for_root(theta1, theta2, delta):
- initial_guess = 3*(theta1 + theta2)
- return fsolve(lambda A: Y(2*A, delta - A, theta1), [initial_guess])
-
-
-def compute_path_length(r, theta1, delta, A):
- return r / X(2*A, delta - A, theta1)
-
-
-def compute_curvature(delta, A, L):
- return (delta - A) / L
-
-
-def compute_curvature_rate(A, L):
- return 2 * A / (L**2)
-
-
-def normalize_angle(angle_rad):
- return (angle_rad + pi) % (2 * pi) - pi
-
-
-def get_axes_limits(clothoids):
- x_vals = [p.x for clothoid in clothoids for p in clothoid]
- y_vals = [p.y for clothoid in clothoids for p in clothoid]
-
- x_min = min(x_vals)
- x_max = max(x_vals)
- y_min = min(y_vals)
- y_max = max(y_vals)
-
- x_offset = 0.1*(x_max - x_min)
- y_offset = 0.1*(y_max - y_min)
-
- x_min = x_min - x_offset
- x_max = x_max + x_offset
- y_min = y_min - y_offset
- y_max = y_max + y_offset
-
- return x_min, x_max, y_min, y_max
-
-
-def draw_clothoids(start, goal, num_steps, clothoidal_paths,
- save_animation=False):
-
- fig = plt.figure(figsize=(10, 10))
- x_min, x_max, y_min, y_max = get_axes_limits(clothoidal_paths)
- axes = plt.axes(xlim=(x_min, x_max), ylim=(y_min, y_max))
-
- axes.plot(start.x, start.y, 'ro')
- axes.plot(goal.x, goal.y, 'ro')
- lines = [axes.plot([], [], 'b-')[0] for _ in range(len(clothoidal_paths))]
-
- def animate(i):
- for line, clothoid_path in zip(lines, clothoidal_paths):
- x = [p.x for p in clothoid_path[:i]]
- y = [p.y for p in clothoid_path[:i]]
- line.set_data(x, y)
-
- return lines
-
- anim = animation.FuncAnimation(
- fig,
- animate,
- frames=num_steps,
- interval=25,
- blit=True
- )
- if save_animation:
- anim.save('clothoid.gif', fps=30, writer="imagemagick")
- plt.show()
-
-
-def main():
- start_point = Point(0, 0)
- start_orientation_list = [0.0]
- goal_point = Point(10, 0)
- goal_orientation_list = np.linspace(-pi, pi, 75)
- num_path_points = 100
- clothoid_paths = generate_clothoid_paths(
- start_point, start_orientation_list,
- goal_point, goal_orientation_list,
- num_path_points)
- if show_animation:
- draw_clothoids(start_point, goal_point,
- num_path_points, clothoid_paths,
- save_animation=False)
-
-
-if __name__ == "__main__":
- main()
diff --git a/PathPlanning/CubicSpline/__init__.py b/PathPlanning/CubicSpline/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathPlanning/CubicSpline/cubic_spline_planner.py b/PathPlanning/CubicSpline/cubic_spline_planner.py
deleted file mode 100644
index 2391f67c393..00000000000
--- a/PathPlanning/CubicSpline/cubic_spline_planner.py
+++ /dev/null
@@ -1,455 +0,0 @@
-"""
-Cubic spline planner
-
-Author: Atsushi Sakai(@Atsushi_twi)
-
-"""
-import math
-import numpy as np
-import bisect
-
-
-class CubicSpline1D:
- """
- 1D Cubic Spline class
-
- Parameters
- ----------
- x : list
- x coordinates for data points. This x coordinates must be
- sorted
- in ascending order.
- y : list
- y coordinates for data points
-
- Examples
- --------
- You can interpolate 1D data points.
-
- >>> import numpy as np
- >>> import matplotlib.pyplot as plt
- >>> x = np.arange(5)
- >>> y = [1.7, -6, 5, 6.5, 0.0]
- >>> sp = CubicSpline1D(x, y)
- >>> xi = np.linspace(0.0, 5.0)
- >>> yi = [sp.calc_position(x) for x in xi]
- >>> plt.plot(x, y, "xb", label="Data points")
- >>> plt.plot(xi, yi , "r", label="Cubic spline interpolation")
- >>> plt.grid(True)
- >>> plt.legend()
- >>> plt.show()
-
- .. image:: cubic_spline_1d.png
-
- """
-
- def __init__(self, x, y):
-
- h = np.diff(x)
- if np.any(h < 0):
- raise ValueError("x coordinates must be sorted in ascending order")
-
- self.a, self.b, self.c, self.d = [], [], [], []
- self.x = x
- self.y = y
- self.nx = len(x) # dimension of x
-
- # calc coefficient a
- self.a = [iy for iy in y]
-
- # calc coefficient c
- A = self.__calc_A(h)
- B = self.__calc_B(h, self.a)
- self.c = np.linalg.solve(A, B)
-
- # calc spline coefficient b and d
- for i in range(self.nx - 1):
- d = (self.c[i + 1] - self.c[i]) / (3.0 * h[i])
- b = 1.0 / h[i] * (self.a[i + 1] - self.a[i]) \
- - h[i] / 3.0 * (2.0 * self.c[i] + self.c[i + 1])
- self.d.append(d)
- self.b.append(b)
-
- def calc_position(self, x):
- """
- Calc `y` position for given `x`.
-
- if `x` is outside the data point's `x` range, return None.
-
- Parameters
- ----------
- x : float
- x position to calculate y.
-
- Returns
- -------
- y : float
- y position for given x.
- """
- if x < self.x[0]:
- return None
- elif x > self.x[-1]:
- return None
-
- i = self.__search_index(x)
- dx = x - self.x[i]
- position = self.a[i] + self.b[i] * dx + \
- self.c[i] * dx ** 2.0 + self.d[i] * dx ** 3.0
-
- return position
-
- def calc_first_derivative(self, x):
- """
- Calc first derivative at given x.
-
- if x is outside the input x, return None
-
- Parameters
- ----------
- x : float
- x position to calculate first derivative.
-
- Returns
- -------
- dy : float
- first derivative for given x.
- """
-
- if x < self.x[0]:
- return None
- elif x > self.x[-1]:
- return None
-
- i = self.__search_index(x)
- dx = x - self.x[i]
- dy = self.b[i] + 2.0 * self.c[i] * dx + 3.0 * self.d[i] * dx ** 2.0
- return dy
-
- def calc_second_derivative(self, x):
- """
- Calc second derivative at given x.
-
- if x is outside the input x, return None
-
- Parameters
- ----------
- x : float
- x position to calculate second derivative.
-
- Returns
- -------
- ddy : float
- second derivative for given x.
- """
-
- if x < self.x[0]:
- return None
- elif x > self.x[-1]:
- return None
-
- i = self.__search_index(x)
- dx = x - self.x[i]
- ddy = 2.0 * self.c[i] + 6.0 * self.d[i] * dx
- return ddy
-
- def calc_third_derivative(self, x):
- """
- Calc third derivative at given x.
-
- if x is outside the input x, return None
-
- Parameters
- ----------
- x : float
- x position to calculate third derivative.
-
- Returns
- -------
- dddy : float
- third derivative for given x.
- """
- if x < self.x[0]:
- return None
- elif x > self.x[-1]:
- return None
-
- i = self.__search_index(x)
- dddy = 6.0 * self.d[i]
- return dddy
-
- def __search_index(self, x):
- """
- search data segment index
- """
- return bisect.bisect(self.x, x) - 1
-
- def __calc_A(self, h):
- """
- calc matrix A for spline coefficient c
- """
- A = np.zeros((self.nx, self.nx))
- A[0, 0] = 1.0
- for i in range(self.nx - 1):
- if i != (self.nx - 2):
- A[i + 1, i + 1] = 2.0 * (h[i] + h[i + 1])
- A[i + 1, i] = h[i]
- A[i, i + 1] = h[i]
-
- A[0, 1] = 0.0
- A[self.nx - 1, self.nx - 2] = 0.0
- A[self.nx - 1, self.nx - 1] = 1.0
- return A
-
- def __calc_B(self, h, a):
- """
- calc matrix B for spline coefficient c
- """
- B = np.zeros(self.nx)
- for i in range(self.nx - 2):
- B[i + 1] = 3.0 * (a[i + 2] - a[i + 1]) / h[i + 1]\
- - 3.0 * (a[i + 1] - a[i]) / h[i]
- return B
-
-
-class CubicSpline2D:
- """
- Cubic CubicSpline2D class
-
- Parameters
- ----------
- x : list
- x coordinates for data points.
- y : list
- y coordinates for data points.
-
- Examples
- --------
- You can interpolate a 2D data points.
-
- >>> import matplotlib.pyplot as plt
- >>> x = [-2.5, 0.0, 2.5, 5.0, 7.5, 3.0, -1.0]
- >>> y = [0.7, -6, 5, 6.5, 0.0, 5.0, -2.0]
- >>> ds = 0.1 # [m] distance of each interpolated points
- >>> sp = CubicSpline2D(x, y)
- >>> s = np.arange(0, sp.s[-1], ds)
- >>> rx, ry, ryaw, rk = [], [], [], []
- >>> for i_s in s:
- ... ix, iy = sp.calc_position(i_s)
- ... rx.append(ix)
- ... ry.append(iy)
- ... ryaw.append(sp.calc_yaw(i_s))
- ... rk.append(sp.calc_curvature(i_s))
- >>> plt.subplots(1)
- >>> plt.plot(x, y, "xb", label="Data points")
- >>> plt.plot(rx, ry, "-r", label="Cubic spline path")
- >>> plt.grid(True)
- >>> plt.axis("equal")
- >>> plt.xlabel("x[m]")
- >>> plt.ylabel("y[m]")
- >>> plt.legend()
- >>> plt.show()
-
- .. image:: cubic_spline_2d_path.png
-
- >>> plt.subplots(1)
- >>> plt.plot(s, [np.rad2deg(iyaw) for iyaw in ryaw], "-r", label="yaw")
- >>> plt.grid(True)
- >>> plt.legend()
- >>> plt.xlabel("line length[m]")
- >>> plt.ylabel("yaw angle[deg]")
-
- .. image:: cubic_spline_2d_yaw.png
-
- >>> plt.subplots(1)
- >>> plt.plot(s, rk, "-r", label="curvature")
- >>> plt.grid(True)
- >>> plt.legend()
- >>> plt.xlabel("line length[m]")
- >>> plt.ylabel("curvature [1/m]")
-
- .. image:: cubic_spline_2d_curvature.png
- """
-
- def __init__(self, x, y):
- self.s = self.__calc_s(x, y)
- self.sx = CubicSpline1D(self.s, x)
- self.sy = CubicSpline1D(self.s, y)
-
- def __calc_s(self, x, y):
- dx = np.diff(x)
- dy = np.diff(y)
- self.ds = np.hypot(dx, dy)
- s = [0]
- s.extend(np.cumsum(self.ds))
- return s
-
- def calc_position(self, s):
- """
- calc position
-
- Parameters
- ----------
- s : float
- distance from the start point. if `s` is outside the data point's
- range, return None.
-
- Returns
- -------
- x : float
- x position for given s.
- y : float
- y position for given s.
- """
- x = self.sx.calc_position(s)
- y = self.sy.calc_position(s)
-
- return x, y
-
- def calc_curvature(self, s):
- """
- calc curvature
-
- Parameters
- ----------
- s : float
- distance from the start point. if `s` is outside the data point's
- range, return None.
-
- Returns
- -------
- k : float
- curvature for given s.
- """
- dx = self.sx.calc_first_derivative(s)
- ddx = self.sx.calc_second_derivative(s)
- dy = self.sy.calc_first_derivative(s)
- ddy = self.sy.calc_second_derivative(s)
- k = (ddy * dx - ddx * dy) / ((dx ** 2 + dy ** 2)**(3 / 2))
- return k
-
- def calc_curvature_rate(self, s):
- """
- calc curvature rate
-
- Parameters
- ----------
- s : float
- distance from the start point. if `s` is outside the data point's
- range, return None.
-
- Returns
- -------
- k : float
- curvature rate for given s.
- """
- dx = self.sx.calc_first_derivative(s)
- dy = self.sy.calc_first_derivative(s)
- ddx = self.sx.calc_second_derivative(s)
- ddy = self.sy.calc_second_derivative(s)
- dddx = self.sx.calc_third_derivative(s)
- dddy = self.sy.calc_third_derivative(s)
- a = dx * ddy - dy * ddx
- b = dx * dddy - dy * dddx
- c = dx * ddx + dy * ddy
- d = dx * dx + dy * dy
- return (b * d - 3.0 * a * c) / (d * d * d)
-
- def calc_yaw(self, s):
- """
- calc yaw
-
- Parameters
- ----------
- s : float
- distance from the start point. if `s` is outside the data point's
- range, return None.
-
- Returns
- -------
- yaw : float
- yaw angle (tangent vector) for given s.
- """
- dx = self.sx.calc_first_derivative(s)
- dy = self.sy.calc_first_derivative(s)
- yaw = math.atan2(dy, dx)
- return yaw
-
-
-def calc_spline_course(x, y, ds=0.1):
- sp = CubicSpline2D(x, y)
- s = list(np.arange(0, sp.s[-1], ds))
-
- rx, ry, ryaw, rk = [], [], [], []
- for i_s in s:
- ix, iy = sp.calc_position(i_s)
- rx.append(ix)
- ry.append(iy)
- ryaw.append(sp.calc_yaw(i_s))
- rk.append(sp.calc_curvature(i_s))
-
- return rx, ry, ryaw, rk, s
-
-
-def main_1d():
- print("CubicSpline1D test")
- import matplotlib.pyplot as plt
- x = np.arange(5)
- y = [1.7, -6, 5, 6.5, 0.0]
- sp = CubicSpline1D(x, y)
- xi = np.linspace(0.0, 5.0)
-
- plt.plot(x, y, "xb", label="Data points")
- plt.plot(xi, [sp.calc_position(x) for x in xi], "r",
- label="Cubic spline interpolation")
- plt.grid(True)
- plt.legend()
- plt.show()
-
-
-def main_2d(): # pragma: no cover
- print("CubicSpline1D 2D test")
- import matplotlib.pyplot as plt
- x = [-2.5, 0.0, 2.5, 5.0, 7.5, 3.0, -1.0]
- y = [0.7, -6, 5, 6.5, 0.0, 5.0, -2.0]
- ds = 0.1 # [m] distance of each interpolated points
-
- sp = CubicSpline2D(x, y)
- s = np.arange(0, sp.s[-1], ds)
-
- rx, ry, ryaw, rk = [], [], [], []
- for i_s in s:
- ix, iy = sp.calc_position(i_s)
- rx.append(ix)
- ry.append(iy)
- ryaw.append(sp.calc_yaw(i_s))
- rk.append(sp.calc_curvature(i_s))
-
- plt.subplots(1)
- plt.plot(x, y, "xb", label="Data points")
- plt.plot(rx, ry, "-r", label="Cubic spline path")
- plt.grid(True)
- plt.axis("equal")
- plt.xlabel("x[m]")
- plt.ylabel("y[m]")
- plt.legend()
-
- plt.subplots(1)
- plt.plot(s, [np.rad2deg(iyaw) for iyaw in ryaw], "-r", label="yaw")
- plt.grid(True)
- plt.legend()
- plt.xlabel("line length[m]")
- plt.ylabel("yaw angle[deg]")
-
- plt.subplots(1)
- plt.plot(s, rk, "-r", label="curvature")
- plt.grid(True)
- plt.legend()
- plt.xlabel("line length[m]")
- plt.ylabel("curvature [1/m]")
-
- plt.show()
-
-
-if __name__ == '__main__':
- # main_1d()
- main_2d()
diff --git a/PathPlanning/CubicSpline/spline_continuity.py b/PathPlanning/CubicSpline/spline_continuity.py
deleted file mode 100644
index ea85b37f7ce..00000000000
--- a/PathPlanning/CubicSpline/spline_continuity.py
+++ /dev/null
@@ -1,55 +0,0 @@
-
-import numpy as np
-import matplotlib.pyplot as plt
-from scipy import interpolate
-
-
-class Spline2D:
-
- def __init__(self, x, y, kind="cubic"):
- self.s = self.__calc_s(x, y)
- self.sx = interpolate.interp1d(self.s, x, kind=kind)
- self.sy = interpolate.interp1d(self.s, y, kind=kind)
-
- def __calc_s(self, x, y):
- self.ds = np.hypot(np.diff(x), np.diff(y))
- s = [0.0]
- s.extend(np.cumsum(self.ds))
- return s
-
- def calc_position(self, s):
- x = self.sx(s)
- y = self.sy(s)
- return x, y
-
-
-def main():
- x = [-2.5, 0.0, 2.5, 5.0, 7.5, 3.0, -1.0]
- y = [0.7, -6, -5, -3.5, 0.0, 5.0, -2.0]
- ds = 0.1 # [m] distance of each interpolated points
-
- plt.subplots(1)
- plt.plot(x, y, "xb", label="Data points")
-
- for (kind, label) in [("linear", "C0 (Linear spline)"),
- ("quadratic", "C0 & C1 (Quadratic spline)"),
- ("cubic", "C0 & C1 & C2 (Cubic spline)")]:
- rx, ry = [], []
- sp = Spline2D(x, y, kind=kind)
- s = np.arange(0, sp.s[-1], ds)
- for i_s in s:
- ix, iy = sp.calc_position(i_s)
- rx.append(ix)
- ry.append(iy)
- plt.plot(rx, ry, "-", label=label)
-
- plt.grid(True)
- plt.axis("equal")
- plt.xlabel("x[m]")
- plt.ylabel("y[m]")
- plt.legend()
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/DStar/dstar.py b/PathPlanning/DStar/dstar.py
deleted file mode 100644
index b62b939f542..00000000000
--- a/PathPlanning/DStar/dstar.py
+++ /dev/null
@@ -1,253 +0,0 @@
-"""
-
-D* grid planning
-
-author: Nirnay Roy
-
-See Wikipedia article (https://en.wikipedia.org/wiki/D*)
-
-"""
-import math
-
-
-from sys import maxsize
-
-import matplotlib.pyplot as plt
-
-show_animation = True
-
-
-class State:
-
- def __init__(self, x, y):
- self.x = x
- self.y = y
- self.parent = None
- self.state = "."
- self.t = "new" # tag for state
- self.h = 0
- self.k = 0
-
- def cost(self, state):
- if self.state == "#" or state.state == "#":
- return maxsize
-
- return math.sqrt(math.pow((self.x - state.x), 2) +
- math.pow((self.y - state.y), 2))
-
- def set_state(self, state):
- """
- .: new
- #: obstacle
- e: oparent of current state
- *: closed state
- s: current state
- """
- if state not in ["s", ".", "#", "e", "*"]:
- return
- self.state = state
-
-
-class Map:
-
- def __init__(self, row, col):
- self.row = row
- self.col = col
- self.map = self.init_map()
-
- def init_map(self):
- map_list = []
- for i in range(self.row):
- tmp = []
- for j in range(self.col):
- tmp.append(State(i, j))
- map_list.append(tmp)
- return map_list
-
- def get_neighbors(self, state):
- state_list = []
- for i in [-1, 0, 1]:
- for j in [-1, 0, 1]:
- if i == 0 and j == 0:
- continue
- if state.x + i < 0 or state.x + i >= self.row:
- continue
- if state.y + j < 0 or state.y + j >= self.col:
- continue
- state_list.append(self.map[state.x + i][state.y + j])
- return state_list
-
- def set_obstacle(self, point_list):
- for x, y in point_list:
- if x < 0 or x >= self.row or y < 0 or y >= self.col:
- continue
-
- self.map[x][y].set_state("#")
-
-
-class Dstar:
- def __init__(self, maps):
- self.map = maps
- self.open_list = set()
-
- def process_state(self):
- x = self.min_state()
-
- if x is None:
- return -1
-
- k_old = self.get_kmin()
- self.remove(x)
-
- if k_old < x.h:
- for y in self.map.get_neighbors(x):
- if y.h <= k_old and x.h > y.h + x.cost(y):
- x.parent = y
- x.h = y.h + x.cost(y)
- if k_old == x.h:
- for y in self.map.get_neighbors(x):
- if y.t == "new" or y.parent == x and y.h != x.h + x.cost(y) \
- or y.parent != x and y.h > x.h + x.cost(y):
- y.parent = x
- self.insert(y, x.h + x.cost(y))
- else:
- for y in self.map.get_neighbors(x):
- if y.t == "new" or y.parent == x and y.h != x.h + x.cost(y):
- y.parent = x
- self.insert(y, x.h + x.cost(y))
- else:
- if y.parent != x and y.h > x.h + x.cost(y):
- self.insert(x, x.h)
- else:
- if y.parent != x and x.h > y.h + x.cost(y) \
- and y.t == "close" and y.h > k_old:
- self.insert(y, y.h)
- return self.get_kmin()
-
- def min_state(self):
- if not self.open_list:
- return None
- min_state = min(self.open_list, key=lambda x: x.k)
- return min_state
-
- def get_kmin(self):
- if not self.open_list:
- return -1
- k_min = min([x.k for x in self.open_list])
- return k_min
-
- def insert(self, state, h_new):
- if state.t == "new":
- state.k = h_new
- elif state.t == "open":
- state.k = min(state.k, h_new)
- elif state.t == "close":
- state.k = min(state.h, h_new)
- state.h = h_new
- state.t = "open"
- self.open_list.add(state)
-
- def remove(self, state):
- if state.t == "open":
- state.t = "close"
- self.open_list.remove(state)
-
- def modify_cost(self, x):
- if x.t == "close":
- self.insert(x, x.parent.h + x.cost(x.parent))
-
- def run(self, start, end):
-
- rx = []
- ry = []
-
- self.insert(end, 0.0)
-
- while True:
- self.process_state()
- if start.t == "close":
- break
-
- start.set_state("s")
- s = start
- s = s.parent
- s.set_state("e")
- tmp = start
-
- AddNewObstacle(self.map) # add new obstacle after the first search finished
-
- while tmp != end:
- tmp.set_state("*")
- rx.append(tmp.x)
- ry.append(tmp.y)
- if show_animation:
- plt.plot(rx, ry, "-r")
- plt.pause(0.01)
- if tmp.parent.state == "#":
- self.modify(tmp)
- continue
- tmp = tmp.parent
- tmp.set_state("e")
-
- return rx, ry
-
- def modify(self, state):
- self.modify_cost(state)
- while True:
- k_min = self.process_state()
- if k_min >= state.h:
- break
-
-def AddNewObstacle(map:Map):
- ox, oy = [], []
- for i in range(5, 21):
- ox.append(i)
- oy.append(40)
- map.set_obstacle([(i, j) for i, j in zip(ox, oy)])
- if show_animation:
- plt.pause(0.001)
- plt.plot(ox, oy, ".g")
-
-def main():
- m = Map(100, 100)
- ox, oy = [], []
- for i in range(-10, 60):
- ox.append(i)
- oy.append(-10)
- for i in range(-10, 60):
- ox.append(60)
- oy.append(i)
- for i in range(-10, 61):
- ox.append(i)
- oy.append(60)
- for i in range(-10, 61):
- ox.append(-10)
- oy.append(i)
- for i in range(-10, 40):
- ox.append(20)
- oy.append(i)
- for i in range(0, 40):
- ox.append(40)
- oy.append(60 - i)
- m.set_obstacle([(i, j) for i, j in zip(ox, oy)])
-
- start = [10, 10]
- goal = [50, 50]
- if show_animation:
- plt.plot(ox, oy, ".k")
- plt.plot(start[0], start[1], "og")
- plt.plot(goal[0], goal[1], "xb")
- plt.axis("equal")
-
- start = m.map[start[0]][start[1]]
- end = m.map[goal[0]][goal[1]]
- dstar = Dstar(m)
- rx, ry = dstar.run(start, end)
-
- if show_animation:
- plt.plot(rx, ry, "-r")
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/DStarLite/d_star_lite.py b/PathPlanning/DStarLite/d_star_lite.py
deleted file mode 100644
index f099530173f..00000000000
--- a/PathPlanning/DStarLite/d_star_lite.py
+++ /dev/null
@@ -1,427 +0,0 @@
-"""
-D* Lite grid planning
-author: vss2sn (28676655+vss2sn@users.noreply.github.com)
-Link to papers:
-D* Lite (Link: http://idm-lab.org/bib/abstracts/papers/aaai02b.pdf)
-Improved Fast Replanning for Robot Navigation in Unknown Terrain
-(Link: http://www.cs.cmu.edu/~maxim/files/dlite_icra02.pdf)
-Implemented maintaining similarity with the pseudocode for understanding.
-Code can be significantly optimized by using a priority queue for U, etc.
-Avoiding additional imports based on repository philosophy.
-"""
-import math
-import matplotlib.pyplot as plt
-import random
-import numpy as np
-
-show_animation = True
-pause_time = 0.001
-p_create_random_obstacle = 0
-
-
-class Node:
- def __init__(self, x: int = 0, y: int = 0, cost: float = 0.0):
- self.x = x
- self.y = y
- self.cost = cost
-
-
-def add_coordinates(node1: Node, node2: Node):
- new_node = Node()
- new_node.x = node1.x + node2.x
- new_node.y = node1.y + node2.y
- new_node.cost = node1.cost + node2.cost
- return new_node
-
-
-def compare_coordinates(node1: Node, node2: Node):
- return node1.x == node2.x and node1.y == node2.y
-
-
-class DStarLite:
-
- # Please adjust the heuristic function (h) if you change the list of
- # possible motions
- motions = [
- Node(1, 0, 1),
- Node(0, 1, 1),
- Node(-1, 0, 1),
- Node(0, -1, 1),
- Node(1, 1, math.sqrt(2)),
- Node(1, -1, math.sqrt(2)),
- Node(-1, 1, math.sqrt(2)),
- Node(-1, -1, math.sqrt(2))
- ]
-
- def __init__(self, ox: list, oy: list):
- # Ensure that within the algorithm implementation all node coordinates
- # are indices in the grid and extend
- # from 0 to abs(<axis>_max - <axis>_min)
- self.x_min_world = int(min(ox))
- self.y_min_world = int(min(oy))
- self.x_max = int(abs(max(ox) - self.x_min_world))
- self.y_max = int(abs(max(oy) - self.y_min_world))
- self.obstacles = [Node(x - self.x_min_world, y - self.y_min_world)
- for x, y in zip(ox, oy)]
- self.obstacles_xy = np.array(
- [[obstacle.x, obstacle.y] for obstacle in self.obstacles]
- )
- self.start = Node(0, 0)
- self.goal = Node(0, 0)
- self.U = list() # type: ignore
- self.km = 0.0
- self.kold = 0.0
- self.rhs = self.create_grid(float("inf"))
- self.g = self.create_grid(float("inf"))
- self.detected_obstacles_xy = np.empty((0, 2))
- self.xy = np.empty((0, 2))
- if show_animation:
- self.detected_obstacles_for_plotting_x = list() # type: ignore
- self.detected_obstacles_for_plotting_y = list() # type: ignore
- self.initialized = False
-
- def create_grid(self, val: float):
- return np.full((self.x_max, self.y_max), val)
-
- def is_obstacle(self, node: Node):
- x = np.array([node.x])
- y = np.array([node.y])
- obstacle_x_equal = self.obstacles_xy[:, 0] == x
- obstacle_y_equal = self.obstacles_xy[:, 1] == y
- is_in_obstacles = (obstacle_x_equal & obstacle_y_equal).any()
-
- is_in_detected_obstacles = False
- if self.detected_obstacles_xy.shape[0] > 0:
- is_x_equal = self.detected_obstacles_xy[:, 0] == x
- is_y_equal = self.detected_obstacles_xy[:, 1] == y
- is_in_detected_obstacles = (is_x_equal & is_y_equal).any()
-
- return is_in_obstacles or is_in_detected_obstacles
-
- def c(self, node1: Node, node2: Node):
- if self.is_obstacle(node2):
- # Attempting to move from or to an obstacle
- return math.inf
- new_node = Node(node1.x-node2.x, node1.y-node2.y)
- detected_motion = list(filter(lambda motion:
- compare_coordinates(motion, new_node),
- self.motions))
- return detected_motion[0].cost
-
- def h(self, s: Node):
- # Cannot use the 2nd euclidean norm as this might sometimes generate
- # heuristics that overestimate the cost, making them inadmissible,
- # due to rounding errors etc (when combined with calculate_key)
- # To be admissible heuristic should
- # never overestimate the cost of a move
- # hence not using the line below
- # return math.hypot(self.start.x - s.x, self.start.y - s.y)
-
- # Below is the same as 1; modify if you modify the cost of each move in
- # motion
- # return max(abs(self.start.x - s.x), abs(self.start.y - s.y))
- return 1
-
- def calculate_key(self, s: Node):
- return (min(self.g[s.x][s.y], self.rhs[s.x][s.y]) + self.h(s)
- + self.km, min(self.g[s.x][s.y], self.rhs[s.x][s.y]))
-
- def is_valid(self, node: Node):
- if 0 <= node.x < self.x_max and 0 <= node.y < self.y_max:
- return True
- return False
-
- def get_neighbours(self, u: Node):
- return [add_coordinates(u, motion) for motion in self.motions
- if self.is_valid(add_coordinates(u, motion))]
-
- def pred(self, u: Node):
- # Grid, so each vertex is connected to the ones around it
- return self.get_neighbours(u)
-
- def succ(self, u: Node):
- # Grid, so each vertex is connected to the ones around it
- return self.get_neighbours(u)
-
- def initialize(self, start: Node, goal: Node):
- self.start.x = start.x - self.x_min_world
- self.start.y = start.y - self.y_min_world
- self.goal.x = goal.x - self.x_min_world
- self.goal.y = goal.y - self.y_min_world
- if not self.initialized:
- self.initialized = True
- print('Initializing')
- self.U = list() # Would normally be a priority queue
- self.km = 0.0
- self.rhs = self.create_grid(math.inf)
- self.g = self.create_grid(math.inf)
- self.rhs[self.goal.x][self.goal.y] = 0
- self.U.append((self.goal, self.calculate_key(self.goal)))
- self.detected_obstacles_xy = np.empty((0, 2))
-
- def update_vertex(self, u: Node):
- if not compare_coordinates(u, self.goal):
- self.rhs[u.x][u.y] = min([self.c(u, sprime) +
- self.g[sprime.x][sprime.y]
- for sprime in self.succ(u)])
- if any([compare_coordinates(u, node) for node, key in self.U]):
- self.U = [(node, key) for node, key in self.U
- if not compare_coordinates(node, u)]
- self.U.sort(key=lambda x: x[1])
- if self.g[u.x][u.y] != self.rhs[u.x][u.y]:
- self.U.append((u, self.calculate_key(u)))
- self.U.sort(key=lambda x: x[1])
-
- def compare_keys(self, key_pair1: tuple[float, float],
- key_pair2: tuple[float, float]):
- return key_pair1[0] < key_pair2[0] or \
- (key_pair1[0] == key_pair2[0] and key_pair1[1] < key_pair2[1])
-
- def compute_shortest_path(self):
- self.U.sort(key=lambda x: x[1])
- has_elements = len(self.U) > 0
- start_key_not_updated = self.compare_keys(
- self.U[0][1], self.calculate_key(self.start)
- )
- rhs_not_equal_to_g = self.rhs[self.start.x][self.start.y] != \
- self.g[self.start.x][self.start.y]
- while has_elements and start_key_not_updated or rhs_not_equal_to_g:
- self.kold = self.U[0][1]
- u = self.U[0][0]
- self.U.pop(0)
- if self.compare_keys(self.kold, self.calculate_key(u)):
- self.U.append((u, self.calculate_key(u)))
- self.U.sort(key=lambda x: x[1])
- elif (self.g[u.x, u.y] > self.rhs[u.x, u.y]).any():
- self.g[u.x, u.y] = self.rhs[u.x, u.y]
- for s in self.pred(u):
- self.update_vertex(s)
- else:
- self.g[u.x, u.y] = math.inf
- for s in self.pred(u) + [u]:
- self.update_vertex(s)
- self.U.sort(key=lambda x: x[1])
- start_key_not_updated = self.compare_keys(
- self.U[0][1], self.calculate_key(self.start)
- )
- rhs_not_equal_to_g = self.rhs[self.start.x][self.start.y] != \
- self.g[self.start.x][self.start.y]
-
- def detect_changes(self):
- changed_vertices = list()
- if len(self.spoofed_obstacles) > 0:
- for spoofed_obstacle in self.spoofed_obstacles[0]:
- if compare_coordinates(spoofed_obstacle, self.start) or \
- compare_coordinates(spoofed_obstacle, self.goal):
- continue
- changed_vertices.append(spoofed_obstacle)
- self.detected_obstacles_xy = np.concatenate(
- (
- self.detected_obstacles_xy,
- [[spoofed_obstacle.x, spoofed_obstacle.y]]
- )
- )
- if show_animation:
- self.detected_obstacles_for_plotting_x.append(
- spoofed_obstacle.x + self.x_min_world)
- self.detected_obstacles_for_plotting_y.append(
- spoofed_obstacle.y + self.y_min_world)
- plt.plot(self.detected_obstacles_for_plotting_x,
- self.detected_obstacles_for_plotting_y, ".k")
- plt.pause(pause_time)
- self.spoofed_obstacles.pop(0)
-
- # Allows random generation of obstacles
- random.seed()
- if random.random() > 1 - p_create_random_obstacle:
- x = random.randint(0, self.x_max - 1)
- y = random.randint(0, self.y_max - 1)
- new_obs = Node(x, y)
- if compare_coordinates(new_obs, self.start) or \
- compare_coordinates(new_obs, self.goal):
- return changed_vertices
- changed_vertices.append(Node(x, y))
- self.detected_obstacles_xy = np.concatenate(
- (
- self.detected_obstacles_xy,
- [[x, y]]
- )
- )
- if show_animation:
- self.detected_obstacles_for_plotting_x.append(x +
- self.x_min_world)
- self.detected_obstacles_for_plotting_y.append(y +
- self.y_min_world)
- plt.plot(self.detected_obstacles_for_plotting_x,
- self.detected_obstacles_for_plotting_y, ".k")
- plt.pause(pause_time)
- return changed_vertices
-
- def compute_current_path(self):
- path = list()
- current_point = Node(self.start.x, self.start.y)
- while not compare_coordinates(current_point, self.goal):
- path.append(current_point)
- current_point = min(self.succ(current_point),
- key=lambda sprime:
- self.c(current_point, sprime) +
- self.g[sprime.x][sprime.y])
- path.append(self.goal)
- return path
-
- def compare_paths(self, path1: list, path2: list):
- if len(path1) != len(path2):
- return False
- for node1, node2 in zip(path1, path2):
- if not compare_coordinates(node1, node2):
- return False
- return True
-
- def display_path(self, path: list, colour: str, alpha: float = 1.0):
- px = [(node.x + self.x_min_world) for node in path]
- py = [(node.y + self.y_min_world) for node in path]
- drawing = plt.plot(px, py, colour, alpha=alpha)
- plt.pause(pause_time)
- return drawing
-
- def main(self, start: Node, goal: Node,
- spoofed_ox: list, spoofed_oy: list):
- self.spoofed_obstacles = [[Node(x - self.x_min_world,
- y - self.y_min_world)
- for x, y in zip(rowx, rowy)]
- for rowx, rowy in zip(spoofed_ox, spoofed_oy)
- ]
- pathx = []
- pathy = []
- self.initialize(start, goal)
- last = self.start
- self.compute_shortest_path()
- pathx.append(self.start.x + self.x_min_world)
- pathy.append(self.start.y + self.y_min_world)
-
- if show_animation:
- current_path = self.compute_current_path()
- previous_path = current_path.copy()
- previous_path_image = self.display_path(previous_path, ".c",
- alpha=0.3)
- current_path_image = self.display_path(current_path, ".c")
-
- while not compare_coordinates(self.goal, self.start):
- if self.g[self.start.x][self.start.y] == math.inf:
- print("No path possible")
- return False, pathx, pathy
- self.start = min(self.succ(self.start),
- key=lambda sprime:
- self.c(self.start, sprime) +
- self.g[sprime.x][sprime.y])
- pathx.append(self.start.x + self.x_min_world)
- pathy.append(self.start.y + self.y_min_world)
- if show_animation:
- current_path.pop(0)
- plt.plot(pathx, pathy, "-r")
- plt.pause(pause_time)
- changed_vertices = self.detect_changes()
- if len(changed_vertices) != 0:
- print("New obstacle detected")
- self.km += self.h(last)
- last = self.start
- for u in changed_vertices:
- if compare_coordinates(u, self.start):
- continue
- self.rhs[u.x][u.y] = math.inf
- self.g[u.x][u.y] = math.inf
- self.update_vertex(u)
- self.compute_shortest_path()
-
- if show_animation:
- new_path = self.compute_current_path()
- if not self.compare_paths(current_path, new_path):
- current_path_image[0].remove()
- previous_path_image[0].remove()
- previous_path = current_path.copy()
- current_path = new_path.copy()
- previous_path_image = self.display_path(previous_path,
- ".c",
- alpha=0.3)
- current_path_image = self.display_path(current_path,
- ".c")
- plt.pause(pause_time)
- print("Path found")
- return True, pathx, pathy
-
-
-def main():
-
- # start and goal position
- sx = 10 # [m]
- sy = 10 # [m]
- gx = 50 # [m]
- gy = 50 # [m]
-
- # set obstacle positions
- ox, oy = [], []
- for i in range(-10, 60):
- ox.append(i)
- oy.append(-10.0)
- for i in range(-10, 60):
- ox.append(60.0)
- oy.append(i)
- for i in range(-10, 61):
- ox.append(i)
- oy.append(60.0)
- for i in range(-10, 61):
- ox.append(-10.0)
- oy.append(i)
- for i in range(-10, 40):
- ox.append(20.0)
- oy.append(i)
- for i in range(0, 40):
- ox.append(40.0)
- oy.append(60.0 - i)
-
- if show_animation:
- plt.plot(ox, oy, ".k")
- plt.plot(sx, sy, "og")
- plt.plot(gx, gy, "xb")
- plt.grid(True)
- plt.axis("equal")
- label_column = ['Start', 'Goal', 'Path taken',
- 'Current computed path', 'Previous computed path',
- 'Obstacles']
- columns = [plt.plot([], [], symbol, color=colour, alpha=alpha)[0]
- for symbol, colour, alpha in [['o', 'g', 1],
- ['x', 'b', 1],
- ['-', 'r', 1],
- ['.', 'c', 1],
- ['.', 'c', 0.3],
- ['.', 'k', 1]]]
- plt.legend(columns, label_column, bbox_to_anchor=(1, 1), title="Key:",
- fontsize="xx-small")
- plt.plot()
- plt.pause(pause_time)
-
- # Obstacles discovered at time = row
- # time = 1, obstacles discovered at (0, 2), (9, 2), (4, 0)
- # time = 2, obstacles discovered at (0, 1), (7, 7)
- # ...
- # when the spoofed obstacles are:
- # spoofed_ox = [[0, 9, 4], [0, 7], [], [], [], [], [], [5]]
- # spoofed_oy = [[2, 2, 0], [1, 7], [], [], [], [], [], [4]]
-
- # Reroute
- # spoofed_ox = [[], [], [], [], [], [], [], [40 for _ in range(10, 21)]]
- # spoofed_oy = [[], [], [], [], [], [], [], [i for i in range(10, 21)]]
-
- # Obstacles that demostrate large rerouting
- spoofed_ox = [[], [], [],
- [i for i in range(0, 21)] + [0 for _ in range(0, 20)]]
- spoofed_oy = [[], [], [],
- [20 for _ in range(0, 21)] + [i for i in range(0, 20)]]
-
- dstarlite = DStarLite(ox, oy)
- dstarlite.main(Node(x=sx, y=sy), Node(x=gx, y=gy),
- spoofed_ox=spoofed_ox, spoofed_oy=spoofed_oy)
-
-
-if __name__ == "__main__":
- main()
diff --git a/PathPlanning/DepthFirstSearch/depth_first_search.py b/PathPlanning/DepthFirstSearch/depth_first_search.py
deleted file mode 100644
index 6922b8cbadc..00000000000
--- a/PathPlanning/DepthFirstSearch/depth_first_search.py
+++ /dev/null
@@ -1,255 +0,0 @@
-"""
-
-Depth-First grid planning
-
-author: Erwin Lejeune (@spida_rwin)
-
-See Wikipedia article (https://en.wikipedia.org/wiki/Depth-first_search)
-
-"""
-
-import math
-
-import matplotlib.pyplot as plt
-
-show_animation = True
-
-
-class DepthFirstSearchPlanner:
-
- def __init__(self, ox, oy, reso, rr):
- """
- Initialize grid map for Depth-First planning
-
- ox: x position list of Obstacles [m]
- oy: y position list of Obstacles [m]
- resolution: grid resolution [m]
- rr: robot radius[m]
- """
-
- self.reso = reso
- self.rr = rr
- self.calc_obstacle_map(ox, oy)
- self.motion = self.get_motion_model()
-
- class Node:
- def __init__(self, x, y, cost, parent_index, parent):
- self.x = x # index of grid
- self.y = y # index of grid
- self.cost = cost
- self.parent_index = parent_index
- self.parent = parent
-
- def __str__(self):
- return str(self.x) + "," + str(self.y) + "," + str(
- self.cost) + "," + str(self.parent_index)
-
- def planning(self, sx, sy, gx, gy):
- """
- Depth First search
-
- input:
- s_x: start x position [m]
- s_y: start y position [m]
- gx: goal x position [m]
- gy: goal y position [m]
-
- output:
- rx: x position list of the final path
- ry: y position list of the final path
- """
-
- nstart = self.Node(self.calc_xyindex(sx, self.minx),
- self.calc_xyindex(sy, self.miny), 0.0, -1, None)
- ngoal = self.Node(self.calc_xyindex(gx, self.minx),
- self.calc_xyindex(gy, self.miny), 0.0, -1, None)
-
- open_set, closed_set = dict(), dict()
- open_set[self.calc_grid_index(nstart)] = nstart
-
- while True:
- if len(open_set) == 0:
- print("Open set is empty..")
- break
-
- current = open_set.pop(list(open_set.keys())[-1])
- c_id = self.calc_grid_index(current)
-
- # show graph
- if show_animation: # pragma: no cover
- plt.plot(self.calc_grid_position(current.x, self.minx),
- self.calc_grid_position(current.y, self.miny), "xc")
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event:
- [exit(0) if event.key == 'escape'
- else None])
- plt.pause(0.01)
-
- if current.x == ngoal.x and current.y == ngoal.y:
- print("Find goal")
- ngoal.parent_index = current.parent_index
- ngoal.cost = current.cost
- break
-
- # expand_grid search grid based on motion model
- for i, _ in enumerate(self.motion):
- node = self.Node(current.x + self.motion[i][0],
- current.y + self.motion[i][1],
- current.cost + self.motion[i][2], c_id, None)
- n_id = self.calc_grid_index(node)
-
- # If the node is not safe, do nothing
- if not self.verify_node(node):
- continue
-
- if n_id not in closed_set:
- open_set[n_id] = node
- closed_set[n_id] = node
- node.parent = current
-
- rx, ry = self.calc_final_path(ngoal, closed_set)
- return rx, ry
-
- def calc_final_path(self, ngoal, closedset):
- # generate final course
- rx, ry = [self.calc_grid_position(ngoal.x, self.minx)], [
- self.calc_grid_position(ngoal.y, self.miny)]
- n = closedset[ngoal.parent_index]
- while n is not None:
- rx.append(self.calc_grid_position(n.x, self.minx))
- ry.append(self.calc_grid_position(n.y, self.miny))
- n = n.parent
-
- return rx, ry
-
- def calc_grid_position(self, index, minp):
- """
- calc grid position
-
- :param index:
- :param minp:
- :return:
- """
- pos = index * self.reso + minp
- return pos
-
- def calc_xyindex(self, position, min_pos):
- return round((position - min_pos) / self.reso)
-
- def calc_grid_index(self, node):
- return (node.y - self.miny) * self.xwidth + (node.x - self.minx)
-
- def verify_node(self, node):
- px = self.calc_grid_position(node.x, self.minx)
- py = self.calc_grid_position(node.y, self.miny)
-
- if px < self.minx:
- return False
- elif py < self.miny:
- return False
- elif px >= self.maxx:
- return False
- elif py >= self.maxy:
- return False
-
- # collision check
- if self.obmap[node.x][node.y]:
- return False
-
- return True
-
- def calc_obstacle_map(self, ox, oy):
-
- self.minx = round(min(ox))
- self.miny = round(min(oy))
- self.maxx = round(max(ox))
- self.maxy = round(max(oy))
- print("min_x:", self.minx)
- print("min_y:", self.miny)
- print("max_x:", self.maxx)
- print("max_y:", self.maxy)
-
- self.xwidth = round((self.maxx - self.minx) / self.reso)
- self.ywidth = round((self.maxy - self.miny) / self.reso)
- print("x_width:", self.xwidth)
- print("y_width:", self.ywidth)
-
- # obstacle map generation
- self.obmap = [[False for _ in range(self.ywidth)]
- for _ in range(self.xwidth)]
- for ix in range(self.xwidth):
- x = self.calc_grid_position(ix, self.minx)
- for iy in range(self.ywidth):
- y = self.calc_grid_position(iy, self.miny)
- for iox, ioy in zip(ox, oy):
- d = math.hypot(iox - x, ioy - y)
- if d <= self.rr:
- self.obmap[ix][iy] = True
- break
-
- @staticmethod
- def get_motion_model():
- # dx, dy, cost
- motion = [[1, 0, 1],
- [0, 1, 1],
- [-1, 0, 1],
- [0, -1, 1],
- [-1, -1, math.sqrt(2)],
- [-1, 1, math.sqrt(2)],
- [1, -1, math.sqrt(2)],
- [1, 1, math.sqrt(2)]]
-
- return motion
-
-
-def main():
- print(__file__ + " start!!")
-
- # start and goal position
- sx = 10.0 # [m]
- sy = 10.0 # [m]
- gx = 50.0 # [m]
- gy = 50.0 # [m]
- grid_size = 2.0 # [m]
- robot_radius = 1.0 # [m]
-
- # set obstacle positions
- ox, oy = [], []
- for i in range(-10, 60):
- ox.append(i)
- oy.append(-10.0)
- for i in range(-10, 60):
- ox.append(60.0)
- oy.append(i)
- for i in range(-10, 61):
- ox.append(i)
- oy.append(60.0)
- for i in range(-10, 61):
- ox.append(-10.0)
- oy.append(i)
- for i in range(-10, 40):
- ox.append(20.0)
- oy.append(i)
- for i in range(0, 40):
- ox.append(40.0)
- oy.append(60.0 - i)
-
- if show_animation: # pragma: no cover
- plt.plot(ox, oy, ".k")
- plt.plot(sx, sy, "og")
- plt.plot(gx, gy, "xb")
- plt.grid(True)
- plt.axis("equal")
-
- dfs = DepthFirstSearchPlanner(ox, oy, grid_size, robot_radius)
- rx, ry = dfs.planning(sx, sy, gx, gy)
-
- if show_animation: # pragma: no cover
- plt.plot(rx, ry, "-r")
- plt.pause(0.01)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/Dijkstra/dijkstra.py b/PathPlanning/Dijkstra/dijkstra.py
deleted file mode 100644
index 8a585e4b182..00000000000
--- a/PathPlanning/Dijkstra/dijkstra.py
+++ /dev/null
@@ -1,259 +0,0 @@
-"""
-
-Grid based Dijkstra planning
-
-author: Atsushi Sakai(@Atsushi_twi)
-
-"""
-
-import matplotlib.pyplot as plt
-import math
-
-show_animation = True
-
-
-class Dijkstra:
-
- def __init__(self, ox, oy, resolution, robot_radius):
- """
- Initialize map for a star planning
-
- ox: x position list of Obstacles [m]
- oy: y position list of Obstacles [m]
- resolution: grid resolution [m]
- rr: robot radius[m]
- """
-
- self.min_x = None
- self.min_y = None
- self.max_x = None
- self.max_y = None
- self.x_width = None
- self.y_width = None
- self.obstacle_map = None
-
- self.resolution = resolution
- self.robot_radius = robot_radius
- self.calc_obstacle_map(ox, oy)
- self.motion = self.get_motion_model()
-
- class Node:
- def __init__(self, x, y, cost, parent_index):
- self.x = x # index of grid
- self.y = y # index of grid
- self.cost = cost
- self.parent_index = parent_index # index of previous Node
-
- def __str__(self):
- return str(self.x) + "," + str(self.y) + "," + str(
- self.cost) + "," + str(self.parent_index)
-
- def planning(self, sx, sy, gx, gy):
- """
- dijkstra path search
-
- input:
- s_x: start x position [m]
- s_y: start y position [m]
- gx: goal x position [m]
- gx: goal x position [m]
-
- output:
- rx: x position list of the final path
- ry: y position list of the final path
- """
-
- start_node = self.Node(self.calc_xy_index(sx, self.min_x),
- self.calc_xy_index(sy, self.min_y), 0.0, -1)
- goal_node = self.Node(self.calc_xy_index(gx, self.min_x),
- self.calc_xy_index(gy, self.min_y), 0.0, -1)
-
- open_set, closed_set = dict(), dict()
- open_set[self.calc_index(start_node)] = start_node
-
- while True:
- c_id = min(open_set, key=lambda o: open_set[o].cost)
- current = open_set[c_id]
-
- # show graph
- if show_animation: # pragma: no cover
- plt.plot(self.calc_position(current.x, self.min_x),
- self.calc_position(current.y, self.min_y), "xc")
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if len(closed_set.keys()) % 10 == 0:
- plt.pause(0.001)
-
- if current.x == goal_node.x and current.y == goal_node.y:
- print("Find goal")
- goal_node.parent_index = current.parent_index
- goal_node.cost = current.cost
- break
-
- # Remove the item from the open set
- del open_set[c_id]
-
- # Add it to the closed set
- closed_set[c_id] = current
-
- # expand search grid based on motion model
- for move_x, move_y, move_cost in self.motion:
- node = self.Node(current.x + move_x,
- current.y + move_y,
- current.cost + move_cost, c_id)
- n_id = self.calc_index(node)
-
- if n_id in closed_set:
- continue
-
- if not self.verify_node(node):
- continue
-
- if n_id not in open_set:
- open_set[n_id] = node # Discover a new node
- else:
- if open_set[n_id].cost >= node.cost:
- # This path is the best until now. record it!
- open_set[n_id] = node
-
- rx, ry = self.calc_final_path(goal_node, closed_set)
-
- return rx, ry
-
- def calc_final_path(self, goal_node, closed_set):
- # generate final course
- rx, ry = [self.calc_position(goal_node.x, self.min_x)], [
- self.calc_position(goal_node.y, self.min_y)]
- parent_index = goal_node.parent_index
- while parent_index != -1:
- n = closed_set[parent_index]
- rx.append(self.calc_position(n.x, self.min_x))
- ry.append(self.calc_position(n.y, self.min_y))
- parent_index = n.parent_index
-
- return rx, ry
-
- def calc_position(self, index, minp):
- pos = index * self.resolution + minp
- return pos
-
- def calc_xy_index(self, position, minp):
- return round((position - minp) / self.resolution)
-
- def calc_index(self, node):
- return (node.y - self.min_y) * self.x_width + (node.x - self.min_x)
-
- def verify_node(self, node):
- px = self.calc_position(node.x, self.min_x)
- py = self.calc_position(node.y, self.min_y)
-
- if px < self.min_x:
- return False
- if py < self.min_y:
- return False
- if px >= self.max_x:
- return False
- if py >= self.max_y:
- return False
-
- if self.obstacle_map[node.x][node.y]:
- return False
-
- return True
-
- def calc_obstacle_map(self, ox, oy):
-
- self.min_x = round(min(ox))
- self.min_y = round(min(oy))
- self.max_x = round(max(ox))
- self.max_y = round(max(oy))
- print("min_x:", self.min_x)
- print("min_y:", self.min_y)
- print("max_x:", self.max_x)
- print("max_y:", self.max_y)
-
- self.x_width = round((self.max_x - self.min_x) / self.resolution)
- self.y_width = round((self.max_y - self.min_y) / self.resolution)
- print("x_width:", self.x_width)
- print("y_width:", self.y_width)
-
- # obstacle map generation
- self.obstacle_map = [[False for _ in range(self.y_width)]
- for _ in range(self.x_width)]
- for ix in range(self.x_width):
- x = self.calc_position(ix, self.min_x)
- for iy in range(self.y_width):
- y = self.calc_position(iy, self.min_y)
- for iox, ioy in zip(ox, oy):
- d = math.hypot(iox - x, ioy - y)
- if d <= self.robot_radius:
- self.obstacle_map[ix][iy] = True
- break
-
- @staticmethod
- def get_motion_model():
- # dx, dy, cost
- motion = [[1, 0, 1],
- [0, 1, 1],
- [-1, 0, 1],
- [0, -1, 1],
- [-1, -1, math.sqrt(2)],
- [-1, 1, math.sqrt(2)],
- [1, -1, math.sqrt(2)],
- [1, 1, math.sqrt(2)]]
-
- return motion
-
-
-def main():
- print(__file__ + " start!!")
-
- # start and goal position
- sx = -5.0 # [m]
- sy = -5.0 # [m]
- gx = 50.0 # [m]
- gy = 50.0 # [m]
- grid_size = 2.0 # [m]
- robot_radius = 1.0 # [m]
-
- # set obstacle positions
- ox, oy = [], []
- for i in range(-10, 60):
- ox.append(float(i))
- oy.append(-10.0)
- for i in range(-10, 60):
- ox.append(60.0)
- oy.append(float(i))
- for i in range(-10, 61):
- ox.append(float(i))
- oy.append(60.0)
- for i in range(-10, 61):
- ox.append(-10.0)
- oy.append(float(i))
- for i in range(-10, 40):
- ox.append(20.0)
- oy.append(float(i))
- for i in range(0, 40):
- ox.append(40.0)
- oy.append(60.0 - i)
-
- if show_animation: # pragma: no cover
- plt.plot(ox, oy, ".k")
- plt.plot(sx, sy, "og")
- plt.plot(gx, gy, "xb")
- plt.grid(True)
- plt.axis("equal")
-
- dijkstra = Dijkstra(ox, oy, grid_size, robot_radius)
- rx, ry = dijkstra.planning(sx, sy, gx, gy)
-
- if show_animation: # pragma: no cover
- plt.plot(rx, ry, "-r")
- plt.pause(0.01)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/DubinsPath/__init__.py b/PathPlanning/DubinsPath/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathPlanning/DubinsPath/dubins_path_planner.py b/PathPlanning/DubinsPath/dubins_path_planner.py
deleted file mode 100644
index a7e8a100cc3..00000000000
--- a/PathPlanning/DubinsPath/dubins_path_planner.py
+++ /dev/null
@@ -1,317 +0,0 @@
-"""
-
-Dubins path planner sample code
-
-author Atsushi Sakai(@Atsushi_twi)
-
-"""
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-from math import sin, cos, atan2, sqrt, acos, pi, hypot
-import numpy as np
-from utils.angle import angle_mod, rot_mat_2d
-
-show_animation = True
-
-
-def plan_dubins_path(s_x, s_y, s_yaw, g_x, g_y, g_yaw, curvature,
- step_size=0.1, selected_types=None):
- """
- Plan dubins path
-
- Parameters
- ----------
- s_x : float
- x position of the start point [m]
- s_y : float
- y position of the start point [m]
- s_yaw : float
- yaw angle of the start point [rad]
- g_x : float
- x position of the goal point [m]
- g_y : float
- y position of the end point [m]
- g_yaw : float
- yaw angle of the end point [rad]
- curvature : float
- curvature for curve [1/m]
- step_size : float (optional)
- step size between two path points [m]. Default is 0.1
- selected_types : a list of string or None
- selected path planning types. If None, all types are used for
- path planning, and minimum path length result is returned.
- You can select used path plannings types by a string list.
- e.g.: ["RSL", "RSR"]
-
- Returns
- -------
- x_list: array
- x positions of the path
- y_list: array
- y positions of the path
- yaw_list: array
- yaw angles of the path
- modes: array
- mode list of the path
- lengths: array
- arrow_length list of the path segments.
-
- Examples
- --------
- You can generate a dubins path.
-
- >>> start_x = 1.0 # [m]
- >>> start_y = 1.0 # [m]
- >>> start_yaw = np.deg2rad(45.0) # [rad]
- >>> end_x = -3.0 # [m]
- >>> end_y = -3.0 # [m]
- >>> end_yaw = np.deg2rad(-45.0) # [rad]
- >>> curvature = 1.0
- >>> path_x, path_y, path_yaw, mode, _ = plan_dubins_path(
- start_x, start_y, start_yaw, end_x, end_y, end_yaw, curvature)
- >>> plt.plot(path_x, path_y, label="final course " + "".join(mode))
- >>> plot_arrow(start_x, start_y, start_yaw)
- >>> plot_arrow(end_x, end_y, end_yaw)
- >>> plt.legend()
- >>> plt.grid(True)
- >>> plt.axis("equal")
- >>> plt.show()
-
- .. image:: dubins_path.jpg
- """
- if selected_types is None:
- planning_funcs = _PATH_TYPE_MAP.values()
- else:
- planning_funcs = [_PATH_TYPE_MAP[ptype] for ptype in selected_types]
-
- # calculate local goal x, y, yaw
- l_rot = rot_mat_2d(s_yaw)
- le_xy = np.stack([g_x - s_x, g_y - s_y]).T @ l_rot
- local_goal_x = le_xy[0]
- local_goal_y = le_xy[1]
- local_goal_yaw = g_yaw - s_yaw
-
- lp_x, lp_y, lp_yaw, modes, lengths = _dubins_path_planning_from_origin(
- local_goal_x, local_goal_y, local_goal_yaw, curvature, step_size,
- planning_funcs)
-
- # Convert a local coordinate path to the global coordinate
- rot = rot_mat_2d(-s_yaw)
- converted_xy = np.stack([lp_x, lp_y]).T @ rot
- x_list = converted_xy[:, 0] + s_x
- y_list = converted_xy[:, 1] + s_y
- yaw_list = angle_mod(np.array(lp_yaw) + s_yaw)
-
- return x_list, y_list, yaw_list, modes, lengths
-
-
-def _mod2pi(theta):
- return angle_mod(theta, zero_2_2pi=True)
-
-
-def _calc_trig_funcs(alpha, beta):
- sin_a = sin(alpha)
- sin_b = sin(beta)
- cos_a = cos(alpha)
- cos_b = cos(beta)
- cos_ab = cos(alpha - beta)
- return sin_a, sin_b, cos_a, cos_b, cos_ab
-
-
-def _LSL(alpha, beta, d):
- sin_a, sin_b, cos_a, cos_b, cos_ab = _calc_trig_funcs(alpha, beta)
- mode = ["L", "S", "L"]
- p_squared = 2 + d ** 2 - (2 * cos_ab) + (2 * d * (sin_a - sin_b))
- if p_squared < 0: # invalid configuration
- return None, None, None, mode
- tmp = atan2((cos_b - cos_a), d + sin_a - sin_b)
- d1 = _mod2pi(-alpha + tmp)
- d2 = sqrt(p_squared)
- d3 = _mod2pi(beta - tmp)
- return d1, d2, d3, mode
-
-
-def _RSR(alpha, beta, d):
- sin_a, sin_b, cos_a, cos_b, cos_ab = _calc_trig_funcs(alpha, beta)
- mode = ["R", "S", "R"]
- p_squared = 2 + d ** 2 - (2 * cos_ab) + (2 * d * (sin_b - sin_a))
- if p_squared < 0:
- return None, None, None, mode
- tmp = atan2((cos_a - cos_b), d - sin_a + sin_b)
- d1 = _mod2pi(alpha - tmp)
- d2 = sqrt(p_squared)
- d3 = _mod2pi(-beta + tmp)
- return d1, d2, d3, mode
-
-
-def _LSR(alpha, beta, d):
- sin_a, sin_b, cos_a, cos_b, cos_ab = _calc_trig_funcs(alpha, beta)
- p_squared = -2 + d ** 2 + (2 * cos_ab) + (2 * d * (sin_a + sin_b))
- mode = ["L", "S", "R"]
- if p_squared < 0:
- return None, None, None, mode
- d1 = sqrt(p_squared)
- tmp = atan2((-cos_a - cos_b), (d + sin_a + sin_b)) - atan2(-2.0, d1)
- d2 = _mod2pi(-alpha + tmp)
- d3 = _mod2pi(-_mod2pi(beta) + tmp)
- return d2, d1, d3, mode
-
-
-def _RSL(alpha, beta, d):
- sin_a, sin_b, cos_a, cos_b, cos_ab = _calc_trig_funcs(alpha, beta)
- p_squared = d ** 2 - 2 + (2 * cos_ab) - (2 * d * (sin_a + sin_b))
- mode = ["R", "S", "L"]
- if p_squared < 0:
- return None, None, None, mode
- d1 = sqrt(p_squared)
- tmp = atan2((cos_a + cos_b), (d - sin_a - sin_b)) - atan2(2.0, d1)
- d2 = _mod2pi(alpha - tmp)
- d3 = _mod2pi(beta - tmp)
- return d2, d1, d3, mode
-
-
-def _RLR(alpha, beta, d):
- sin_a, sin_b, cos_a, cos_b, cos_ab = _calc_trig_funcs(alpha, beta)
- mode = ["R", "L", "R"]
- tmp = (6.0 - d ** 2 + 2.0 * cos_ab + 2.0 * d * (sin_a - sin_b)) / 8.0
- if abs(tmp) > 1.0:
- return None, None, None, mode
- d2 = _mod2pi(2 * pi - acos(tmp))
- d1 = _mod2pi(alpha - atan2(cos_a - cos_b, d - sin_a + sin_b) + d2 / 2.0)
- d3 = _mod2pi(alpha - beta - d1 + d2)
- return d1, d2, d3, mode
-
-
-def _LRL(alpha, beta, d):
- sin_a, sin_b, cos_a, cos_b, cos_ab = _calc_trig_funcs(alpha, beta)
- mode = ["L", "R", "L"]
- tmp = (6.0 - d ** 2 + 2.0 * cos_ab + 2.0 * d * (- sin_a + sin_b)) / 8.0
- if abs(tmp) > 1.0:
- return None, None, None, mode
- d2 = _mod2pi(2 * pi - acos(tmp))
- d1 = _mod2pi(-alpha - atan2(cos_a - cos_b, d + sin_a - sin_b) + d2 / 2.0)
- d3 = _mod2pi(_mod2pi(beta) - alpha - d1 + _mod2pi(d2))
- return d1, d2, d3, mode
-
-
-_PATH_TYPE_MAP = {"LSL": _LSL, "RSR": _RSR, "LSR": _LSR, "RSL": _RSL,
- "RLR": _RLR, "LRL": _LRL, }
-
-
-def _dubins_path_planning_from_origin(end_x, end_y, end_yaw, curvature,
- step_size, planning_funcs):
- dx = end_x
- dy = end_y
- d = hypot(dx, dy) * curvature
-
- theta = _mod2pi(atan2(dy, dx))
- alpha = _mod2pi(-theta)
- beta = _mod2pi(end_yaw - theta)
-
- best_cost = float("inf")
- b_d1, b_d2, b_d3, b_mode = None, None, None, None
-
- for planner in planning_funcs:
- d1, d2, d3, mode = planner(alpha, beta, d)
- if d1 is None:
- continue
-
- cost = (abs(d1) + abs(d2) + abs(d3))
- if best_cost > cost: # Select minimum length one.
- b_d1, b_d2, b_d3, b_mode, best_cost = d1, d2, d3, mode, cost
-
- lengths = [b_d1, b_d2, b_d3]
- x_list, y_list, yaw_list = _generate_local_course(lengths, b_mode,
- curvature, step_size)
-
- lengths = [length / curvature for length in lengths]
-
- return x_list, y_list, yaw_list, b_mode, lengths
-
-
-def _interpolate(length, mode, max_curvature, origin_x, origin_y,
- origin_yaw, path_x, path_y, path_yaw):
- if mode == "S":
- path_x.append(origin_x + length / max_curvature * cos(origin_yaw))
- path_y.append(origin_y + length / max_curvature * sin(origin_yaw))
- path_yaw.append(origin_yaw)
- else: # curve
- ldx = sin(length) / max_curvature
- ldy = 0.0
- if mode == "L": # left turn
- ldy = (1.0 - cos(length)) / max_curvature
- elif mode == "R": # right turn
- ldy = (1.0 - cos(length)) / -max_curvature
- gdx = cos(-origin_yaw) * ldx + sin(-origin_yaw) * ldy
- gdy = -sin(-origin_yaw) * ldx + cos(-origin_yaw) * ldy
- path_x.append(origin_x + gdx)
- path_y.append(origin_y + gdy)
-
- if mode == "L": # left turn
- path_yaw.append(origin_yaw + length)
- elif mode == "R": # right turn
- path_yaw.append(origin_yaw - length)
-
- return path_x, path_y, path_yaw
-
-
-def _generate_local_course(lengths, modes, max_curvature, step_size):
- p_x, p_y, p_yaw = [0.0], [0.0], [0.0]
-
- for (mode, length) in zip(modes, lengths):
- if length == 0.0:
- continue
-
- # set origin state
- origin_x, origin_y, origin_yaw = p_x[-1], p_y[-1], p_yaw[-1]
-
- current_length = step_size
- while abs(current_length + step_size) <= abs(length):
- p_x, p_y, p_yaw = _interpolate(current_length, mode, max_curvature,
- origin_x, origin_y, origin_yaw,
- p_x, p_y, p_yaw)
- current_length += step_size
-
- p_x, p_y, p_yaw = _interpolate(length, mode, max_curvature, origin_x,
- origin_y, origin_yaw, p_x, p_y, p_yaw)
-
- return p_x, p_y, p_yaw
-
-
-def main():
- print("Dubins path planner sample start!!")
- import matplotlib.pyplot as plt
- from utils.plot import plot_arrow
-
- start_x = 1.0 # [m]
- start_y = 1.0 # [m]
- start_yaw = np.deg2rad(45.0) # [rad]
-
- end_x = -3.0 # [m]
- end_y = -3.0 # [m]
- end_yaw = np.deg2rad(-45.0) # [rad]
-
- curvature = 1.0
-
- path_x, path_y, path_yaw, mode, lengths = plan_dubins_path(start_x,
- start_y,
- start_yaw,
- end_x,
- end_y,
- end_yaw,
- curvature)
-
- if show_animation:
- plt.plot(path_x, path_y, label="".join(mode))
- plot_arrow(start_x, start_y, start_yaw)
- plot_arrow(end_x, end_y, end_yaw)
- plt.legend()
- plt.grid(True)
- plt.axis("equal")
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/DynamicMovementPrimitives/dynamic_movement_primitives.py b/PathPlanning/DynamicMovementPrimitives/dynamic_movement_primitives.py
deleted file mode 100644
index 9ccd18b7c23..00000000000
--- a/PathPlanning/DynamicMovementPrimitives/dynamic_movement_primitives.py
+++ /dev/null
@@ -1,260 +0,0 @@
-"""
-Author: Jonathan Schwartz (github.com/SchwartzCode)
-
-This code provides a simple implementation of Dynamic Movement
-Primitives, which is an approach to learning curves by modelling
-them as a weighted sum of gaussian distributions. This approach
-can be used to dampen noise in a curve, and can also be used to
-stretch a curve by adjusting its start and end points.
-
-More information on Dynamic Movement Primitives available at:
-https://arxiv.org/abs/2102.03861
-https://www.frontiersin.org/journals/computational-neuroscience/articles/10.3389/fncom.2013.00138/full
-
-"""
-
-
-from matplotlib import pyplot as plt
-import numpy as np
-
-
-class DMP:
-
- def __init__(self, training_data, data_period, K=156.25, B=25):
- """
- Arguments:
- training_data - input data of form [N, dim]
- data_period - amount of time training data covers
- K and B - spring and damper constants to define
- DMP behavior
- """
-
- self.K = K # virtual spring constant
- self.B = B # virtual damper coefficient
-
- self.timesteps = training_data.shape[0]
- self.dt = data_period / self.timesteps
-
- self.weights = None # weights used to generate DMP trajectories
-
- self.T_orig = data_period
-
- self.training_data = training_data
- self.find_basis_functions_weights(training_data, data_period)
-
- def find_basis_functions_weights(self, training_data, data_period,
- num_weights=10):
- """
- Arguments:
- data [(steps x spacial dim) np array] - data to replicate with DMP
- data_period [float] - time duration of data
- """
-
- if not isinstance(training_data, np.ndarray):
- print("Warning: you should input training data as an np.ndarray")
- elif training_data.shape[0] < training_data.shape[1]:
- print("Warning: you probably need to transpose your training data")
-
- dt = data_period / len(training_data)
-
- init_state = training_data[0]
- goal_state = training_data[-1]
-
- # means (C) and std devs (H) of gaussian basis functions
- C = np.linspace(0, 1, num_weights)
- H = (0.65*(1./(num_weights-1))**2)
-
- for dim, _ in enumerate(training_data[0]):
-
- dimension_data = training_data[:, dim]
-
- q0 = init_state[dim]
- g = goal_state[dim]
-
- q = q0
- qd_last = 0
-
- phi_vals = []
- f_vals = []
-
- for i, _ in enumerate(dimension_data):
- if i + 1 == len(dimension_data):
- qd = 0
- else:
- qd = (dimension_data[i+1] - dimension_data[i]) / dt
-
- phi = [np.exp(-0.5 * ((i * dt / data_period) - c)**2 / H)
- for c in C]
- phi = phi/np.sum(phi)
-
- qdd = (qd - qd_last)/dt
-
- f = (qdd * data_period**2 - self.K * (g - q) + self.B * qd
- * data_period) / (g - q0)
-
- phi_vals.append(phi)
- f_vals.append(f)
-
- qd_last = qd
- q += qd * dt
-
- phi_vals = np.asarray(phi_vals)
- f_vals = np.asarray(f_vals)
-
- w = np.linalg.lstsq(phi_vals, f_vals, rcond=None)
-
- if self.weights is None:
- self.weights = np.asarray(w[0])
- else:
- self.weights = np.vstack([self.weights, w[0]])
-
- def recreate_trajectory(self, init_state, goal_state, T):
- """
- init_state - initial state/position
- goal_state - goal state/position
- T - amount of time to travel q0 -> g
- """
-
- nrBasis = len(self.weights[0]) # number of gaussian basis functions
-
- # means (C) and std devs (H) of gaussian basis functions
- C = np.linspace(0, 1, nrBasis)
- H = (0.65*(1./(nrBasis-1))**2)
-
- # initialize virtual system
- time = 0
-
- q = init_state
- dimensions = self.weights.shape[0]
- qd = np.zeros(dimensions)
-
- positions = np.array([])
- for k in range(self.timesteps):
- time = time + self.dt
-
- qdd = np.zeros(dimensions)
-
- for dim in range(dimensions):
-
- if time <= T:
- phi = [np.exp(-0.5 * ((time / T) - c)**2 / H) for c in C]
- phi = phi / np.sum(phi)
- f = np.dot(phi, self.weights[dim])
- else:
- f = 0
-
- # simulate dynamics
- qdd[dim] = (self.K*(goal_state[dim] - q[dim])/T**2
- - self.B*qd[dim]/T
- + (goal_state[dim] - init_state[dim])*f/T**2)
-
- qd = qd + qdd * self.dt
- q = q + qd * self.dt
-
- if positions.size == 0:
- positions = q
- else:
- positions = np.vstack([positions, q])
-
- t = np.arange(0, self.timesteps * self.dt, self.dt)
- return t, positions
-
- @staticmethod
- def dist_between(p1, p2):
- return np.linalg.norm(p1 - p2)
-
- def view_trajectory(self, path, title=None, demo=False):
-
- path = np.asarray(path)
-
- plt.cla()
- plt.plot(self.training_data[:, 0], self.training_data[:, 1],
- label="Training Data")
- plt.plot(path[:, 0], path[:, 1],
- linewidth=2, label="DMP Approximation")
-
- plt.xlabel("X Position")
- plt.ylabel("Y Position")
- plt.legend()
-
- if title is not None:
- plt.title(title)
-
- if demo:
- plt.xlim([-0.5, 5])
- plt.ylim([-2, 2])
- plt.draw()
- plt.pause(0.02)
- else:
- plt.show()
-
- def show_DMP_purpose(self):
- """
- This function conveys the purpose of DMPs:
- to capture a trajectory and be able to stretch
- and squeeze it in terms of start and stop position
- or time
- """
-
- q0_orig = self.training_data[0]
- g_orig = self.training_data[-1]
- T_orig = self.T_orig
-
- data_range = (np.amax(self.training_data[:, 0])
- - np.amin(self.training_data[:, 0])) / 4
-
- q0_right = q0_orig + np.array([data_range, 0])
- q0_up = q0_orig + np.array([0, data_range/2])
- g_left = g_orig - np.array([data_range, 0])
- g_down = g_orig - np.array([0, data_range/2])
-
- q0_vals = np.vstack([np.linspace(q0_orig, q0_right, 20),
- np.linspace(q0_orig, q0_up, 20)])
- g_vals = np.vstack([np.linspace(g_orig, g_left, 20),
- np.linspace(g_orig, g_down, 20)])
- T_vals = np.linspace(T_orig, 2*T_orig, 20)
-
- for new_q0_value in q0_vals:
- plot_title = (f"Initial Position = [{round(new_q0_value[0], 2)},"
- f" {round(new_q0_value[1], 2)}]")
-
- _, path = self.recreate_trajectory(new_q0_value, g_orig, T_orig)
- self.view_trajectory(path, title=plot_title, demo=True)
-
- for new_g_value in g_vals:
- plot_title = (f"Goal Position = [{round(new_g_value[0], 2)},"
- f" {round(new_g_value[1], 2)}]")
-
- _, path = self.recreate_trajectory(q0_orig, new_g_value, T_orig)
- self.view_trajectory(path, title=plot_title, demo=True)
-
- for new_T_value in T_vals:
- plot_title = f"Period = {round(new_T_value, 2)} [sec]"
-
- _, path = self.recreate_trajectory(q0_orig, g_orig, new_T_value)
- self.view_trajectory(path, title=plot_title, demo=True)
-
-
-def example_DMP():
- """
- Creates a noisy trajectory, fits weights to it, and then adjusts the
- trajectory by moving its start position, goal position, or period
- """
- t = np.arange(0, 3*np.pi/2, 0.01)
- t1 = np.arange(3*np.pi/2, 2*np.pi, 0.01)[:-1]
- t2 = np.arange(0, np.pi/2, 0.01)[:-1]
- t3 = np.arange(np.pi, 3*np.pi/2, 0.01)
- data_x = t + 0.02*np.random.rand(t.shape[0])
- data_y = np.concatenate([np.cos(t1) + 0.1*np.random.rand(t1.shape[0]),
- np.cos(t2) + 0.1*np.random.rand(t2.shape[0]),
- np.sin(t3) + 0.1*np.random.rand(t3.shape[0])])
- training_data = np.vstack([data_x, data_y]).T
-
- period = 3*np.pi/2
- DMP_controller = DMP(training_data, period)
-
- DMP_controller.show_DMP_purpose()
-
-
-if __name__ == '__main__':
- example_DMP()
diff --git a/PathPlanning/DynamicWindowApproach/dynamic_window_approach.py b/PathPlanning/DynamicWindowApproach/dynamic_window_approach.py
deleted file mode 100644
index 8664ec1745a..00000000000
--- a/PathPlanning/DynamicWindowApproach/dynamic_window_approach.py
+++ /dev/null
@@ -1,308 +0,0 @@
-"""
-
-Mobile robot motion planning sample with Dynamic Window Approach
-
-author: Atsushi Sakai (@Atsushi_twi), Göktuğ Karakaşlı
-
-"""
-
-import math
-from enum import Enum
-
-import matplotlib.pyplot as plt
-import numpy as np
-
-show_animation = True
-
-
-def dwa_control(x, config, goal, ob):
- """
- Dynamic Window Approach control
- """
- dw = calc_dynamic_window(x, config)
-
- u, trajectory = calc_control_and_trajectory(x, dw, config, goal, ob)
-
- return u, trajectory
-
-
-class RobotType(Enum):
- circle = 0
- rectangle = 1
-
-
-class Config:
- """
- simulation parameter class
- """
-
- def __init__(self):
- # robot parameter
- self.max_speed = 1.0 # [m/s]
- self.min_speed = -0.5 # [m/s]
- self.max_yaw_rate = 40.0 * math.pi / 180.0 # [rad/s]
- self.max_accel = 0.2 # [m/ss]
- self.max_delta_yaw_rate = 40.0 * math.pi / 180.0 # [rad/ss]
- self.v_resolution = 0.01 # [m/s]
- self.yaw_rate_resolution = 0.1 * math.pi / 180.0 # [rad/s]
- self.dt = 0.1 # [s] Time tick for motion prediction
- self.predict_time = 3.0 # [s]
- self.to_goal_cost_gain = 0.15
- self.speed_cost_gain = 1.0
- self.obstacle_cost_gain = 1.0
- self.robot_stuck_flag_cons = 0.001 # constant to prevent robot stucked
- self.robot_type = RobotType.circle
-
- # if robot_type == RobotType.circle
- # Also used to check if goal is reached in both types
- self.robot_radius = 1.0 # [m] for collision check
-
- # if robot_type == RobotType.rectangle
- self.robot_width = 0.5 # [m] for collision check
- self.robot_length = 1.2 # [m] for collision check
- # obstacles [x(m) y(m), ....]
- self.ob = np.array([[-1, -1],
- [0, 2],
- [4.0, 2.0],
- [5.0, 4.0],
- [5.0, 5.0],
- [5.0, 6.0],
- [5.0, 9.0],
- [8.0, 9.0],
- [7.0, 9.0],
- [8.0, 10.0],
- [9.0, 11.0],
- [12.0, 13.0],
- [12.0, 12.0],
- [15.0, 15.0],
- [13.0, 13.0]
- ])
-
- @property
- def robot_type(self):
- return self._robot_type
-
- @robot_type.setter
- def robot_type(self, value):
- if not isinstance(value, RobotType):
- raise TypeError("robot_type must be an instance of RobotType")
- self._robot_type = value
-
-
-config = Config()
-
-
-def motion(x, u, dt):
- """
- motion model
- """
-
- x[2] += u[1] * dt
- x[0] += u[0] * math.cos(x[2]) * dt
- x[1] += u[0] * math.sin(x[2]) * dt
- x[3] = u[0]
- x[4] = u[1]
-
- return x
-
-
-def calc_dynamic_window(x, config):
- """
- calculation dynamic window based on current state x
- """
-
- # Dynamic window from robot specification
- Vs = [config.min_speed, config.max_speed,
- -config.max_yaw_rate, config.max_yaw_rate]
-
- # Dynamic window from motion model
- Vd = [x[3] - config.max_accel * config.dt,
- x[3] + config.max_accel * config.dt,
- x[4] - config.max_delta_yaw_rate * config.dt,
- x[4] + config.max_delta_yaw_rate * config.dt]
-
- # [v_min, v_max, yaw_rate_min, yaw_rate_max]
- dw = [max(Vs[0], Vd[0]), min(Vs[1], Vd[1]),
- max(Vs[2], Vd[2]), min(Vs[3], Vd[3])]
-
- return dw
-
-
-def predict_trajectory(x_init, v, y, config):
- """
- predict trajectory with an input
- """
-
- x = np.array(x_init)
- trajectory = np.array(x)
- time = 0
- while time <= config.predict_time:
- x = motion(x, [v, y], config.dt)
- trajectory = np.vstack((trajectory, x))
- time += config.dt
-
- return trajectory
-
-
-def calc_control_and_trajectory(x, dw, config, goal, ob):
- """
- calculation final input with dynamic window
- """
-
- x_init = x[:]
- min_cost = float("inf")
- best_u = [0.0, 0.0]
- best_trajectory = np.array([x])
-
- # evaluate all trajectory with sampled input in dynamic window
- for v in np.arange(dw[0], dw[1], config.v_resolution):
- for y in np.arange(dw[2], dw[3], config.yaw_rate_resolution):
-
- trajectory = predict_trajectory(x_init, v, y, config)
- # calc cost
- to_goal_cost = config.to_goal_cost_gain * calc_to_goal_cost(trajectory, goal)
- speed_cost = config.speed_cost_gain * (config.max_speed - trajectory[-1, 3])
- ob_cost = config.obstacle_cost_gain * calc_obstacle_cost(trajectory, ob, config)
-
- final_cost = to_goal_cost + speed_cost + ob_cost
-
- # search minimum trajectory
- if min_cost >= final_cost:
- min_cost = final_cost
- best_u = [v, y]
- best_trajectory = trajectory
- if abs(best_u[0]) < config.robot_stuck_flag_cons \
- and abs(x[3]) < config.robot_stuck_flag_cons:
- # to ensure the robot do not get stuck in
- # best v=0 m/s (in front of an obstacle) and
- # best omega=0 rad/s (heading to the goal with
- # angle difference of 0)
- best_u[1] = -config.max_delta_yaw_rate
- return best_u, best_trajectory
-
-
-def calc_obstacle_cost(trajectory, ob, config):
- """
- calc obstacle cost inf: collision
- """
- ox = ob[:, 0]
- oy = ob[:, 1]
- dx = trajectory[:, 0] - ox[:, None]
- dy = trajectory[:, 1] - oy[:, None]
- r = np.hypot(dx, dy)
-
- if config.robot_type == RobotType.rectangle:
- yaw = trajectory[:, 2]
- rot = np.array([[np.cos(yaw), -np.sin(yaw)], [np.sin(yaw), np.cos(yaw)]])
- rot = np.transpose(rot, [2, 0, 1])
- local_ob = ob[:, None] - trajectory[:, 0:2]
- local_ob = local_ob.reshape(-1, local_ob.shape[-1])
- local_ob = np.array([local_ob @ x for x in rot])
- local_ob = local_ob.reshape(-1, local_ob.shape[-1])
- upper_check = local_ob[:, 0] <= config.robot_length / 2
- right_check = local_ob[:, 1] <= config.robot_width / 2
- bottom_check = local_ob[:, 0] >= -config.robot_length / 2
- left_check = local_ob[:, 1] >= -config.robot_width / 2
- if (np.logical_and(np.logical_and(upper_check, right_check),
- np.logical_and(bottom_check, left_check))).any():
- return float("Inf")
- elif config.robot_type == RobotType.circle:
- if np.array(r <= config.robot_radius).any():
- return float("Inf")
-
- min_r = np.min(r)
- return 1.0 / min_r # OK
-
-
-def calc_to_goal_cost(trajectory, goal):
- """
- calc to goal cost with angle difference
- """
-
- dx = goal[0] - trajectory[-1, 0]
- dy = goal[1] - trajectory[-1, 1]
- error_angle = math.atan2(dy, dx)
- cost_angle = error_angle - trajectory[-1, 2]
- cost = abs(math.atan2(math.sin(cost_angle), math.cos(cost_angle)))
-
- return cost
-
-
-def plot_arrow(x, y, yaw, length=0.5, width=0.1): # pragma: no cover
- plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),
- head_length=width, head_width=width)
- plt.plot(x, y)
-
-
-def plot_robot(x, y, yaw, config): # pragma: no cover
- if config.robot_type == RobotType.rectangle:
- outline = np.array([[-config.robot_length / 2, config.robot_length / 2,
- (config.robot_length / 2), -config.robot_length / 2,
- -config.robot_length / 2],
- [config.robot_width / 2, config.robot_width / 2,
- - config.robot_width / 2, -config.robot_width / 2,
- config.robot_width / 2]])
- Rot1 = np.array([[math.cos(yaw), math.sin(yaw)],
- [-math.sin(yaw), math.cos(yaw)]])
- outline = (outline.T.dot(Rot1)).T
- outline[0, :] += x
- outline[1, :] += y
- plt.plot(np.array(outline[0, :]).flatten(),
- np.array(outline[1, :]).flatten(), "-k")
- elif config.robot_type == RobotType.circle:
- circle = plt.Circle((x, y), config.robot_radius, color="b")
- plt.gcf().gca().add_artist(circle)
- out_x, out_y = (np.array([x, y]) +
- np.array([np.cos(yaw), np.sin(yaw)]) * config.robot_radius)
- plt.plot([x, out_x], [y, out_y], "-k")
-
-
-def main(gx=10.0, gy=10.0, robot_type=RobotType.circle):
- print(__file__ + " start!!")
- # initial state [x(m), y(m), yaw(rad), v(m/s), omega(rad/s)]
- x = np.array([0.0, 0.0, math.pi / 8.0, 0.0, 0.0])
- # goal position [x(m), y(m)]
- goal = np.array([gx, gy])
-
- # input [forward speed, yaw_rate]
-
- config.robot_type = robot_type
- trajectory = np.array(x)
- ob = config.ob
- while True:
- u, predicted_trajectory = dwa_control(x, config, goal, ob)
- x = motion(x, u, config.dt) # simulate robot
- trajectory = np.vstack((trajectory, x)) # store state history
-
- if show_animation:
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(predicted_trajectory[:, 0], predicted_trajectory[:, 1], "-g")
- plt.plot(x[0], x[1], "xr")
- plt.plot(goal[0], goal[1], "xb")
- plt.plot(ob[:, 0], ob[:, 1], "ok")
- plot_robot(x[0], x[1], x[2], config)
- plot_arrow(x[0], x[1], x[2])
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.0001)
-
- # check reaching goal
- dist_to_goal = math.hypot(x[0] - goal[0], x[1] - goal[1])
- if dist_to_goal <= config.robot_radius:
- print("Goal!!")
- break
-
- print("Done")
- if show_animation:
- plt.plot(trajectory[:, 0], trajectory[:, 1], "-r")
- plt.pause(0.0001)
- plt.show()
-
-
-if __name__ == '__main__':
- main(robot_type=RobotType.rectangle)
- # main(robot_type=RobotType.circle)
diff --git a/PathPlanning/ElasticBands/elastic_bands.py b/PathPlanning/ElasticBands/elastic_bands.py
deleted file mode 100644
index 785f822d141..00000000000
--- a/PathPlanning/ElasticBands/elastic_bands.py
+++ /dev/null
@@ -1,300 +0,0 @@
-"""
-Elastic Bands
-
-author: Wang Zheng (@Aglargil)
-
-Ref:
-
-- [Elastic Bands: Connecting Path Planning and Control]
-(http://www8.cs.umu.se/research/ifor/dl/Control/elastic%20bands.pdf)
-"""
-
-import numpy as np
-import sys
-import pathlib
-import matplotlib.pyplot as plt
-from matplotlib.patches import Circle
-
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-from Mapping.DistanceMap.distance_map import compute_sdf_scipy
-
-# Elastic Bands Params
-MAX_BUBBLE_RADIUS = 100
-MIN_BUBBLE_RADIUS = 10
-RHO0 = 20.0 # Maximum distance for applying repulsive force
-KC = 0.05 # Contraction force gain
-KR = -0.1 # Repulsive force gain
-LAMBDA = 0.7 # Overlap constraint factor
-STEP_SIZE = 3.0 # Step size for calculating gradient
-
-# Visualization Params
-ENABLE_PLOT = True
-# ENABLE_INTERACTIVE is True allows user to add obstacles by left clicking
-# and add path points by right clicking and start planning by middle clicking
-ENABLE_INTERACTIVE = False
-# ENABLE_SAVE_DATA is True allows saving the path and obstacles which added
-# by user in interactive mode to file
-ENABLE_SAVE_DATA = False
-MAX_ITER = 50
-
-
-class Bubble:
- def __init__(self, position, radius):
- self.pos = np.array(position) # Bubble center coordinates [x, y]
- self.radius = radius # Safety distance radius ρ(b)
- if self.radius > MAX_BUBBLE_RADIUS:
- self.radius = MAX_BUBBLE_RADIUS
- if self.radius < MIN_BUBBLE_RADIUS:
- self.radius = MIN_BUBBLE_RADIUS
-
-
-class ElasticBands:
- def __init__(
- self,
- initial_path,
- obstacles,
- rho0=RHO0,
- kc=KC,
- kr=KR,
- lambda_=LAMBDA,
- step_size=STEP_SIZE,
- ):
- self.distance_map = compute_sdf_scipy(obstacles)
- self.bubbles = [
- Bubble(p, self.compute_rho(p)) for p in initial_path
- ] # Initialize bubble chain
- self.kc = kc # Contraction force gain
- self.kr = kr # Repulsive force gain
- self.rho0 = rho0 # Maximum distance for applying repulsive force
- self.lambda_ = lambda_ # Overlap constraint factor
- self.step_size = step_size # Step size for calculating gradient
- self._maintain_overlap()
-
- def compute_rho(self, position):
- """Compute the distance field value at the position"""
- return self.distance_map[int(position[0]), int(position[1])]
-
- def contraction_force(self, i):
- """Calculate internal contraction force for the i-th bubble"""
- if i == 0 or i == len(self.bubbles) - 1:
- return np.zeros(2)
-
- prev = self.bubbles[i - 1].pos
- next_ = self.bubbles[i + 1].pos
- current = self.bubbles[i].pos
-
- # f_c = kc * ( (prev-current)/|prev-current| + (next-current)/|next-current| )
- dir_prev = (prev - current) / (np.linalg.norm(prev - current) + 1e-6)
- dir_next = (next_ - current) / (np.linalg.norm(next_ - current) + 1e-6)
- return self.kc * (dir_prev + dir_next)
-
- def repulsive_force(self, i):
- """Calculate external repulsive force for the i-th bubble"""
- h = self.step_size # Step size
- b = self.bubbles[i].pos
- rho = self.bubbles[i].radius
-
- if rho >= self.rho0:
- return np.zeros(2)
-
- # Finite difference approximation of the gradient ∂ρ/∂b
- dx = np.array([h, 0])
- dy = np.array([0, h])
- grad_x = (self.compute_rho(b - dx) - self.compute_rho(b + dx)) / (2 * h)
- grad_y = (self.compute_rho(b - dy) - self.compute_rho(b + dy)) / (2 * h)
- grad = np.array([grad_x, grad_y])
-
- return self.kr * (self.rho0 - rho) * grad
-
- def update_bubbles(self):
- """Update bubble positions"""
- new_bubbles = []
- for i in range(len(self.bubbles)):
- if i == 0 or i == len(self.bubbles) - 1:
- new_bubbles.append(self.bubbles[i]) # Fixed start and end points
- continue
-
- f_total = self.contraction_force(i) + self.repulsive_force(i)
- v = self.bubbles[i - 1].pos - self.bubbles[i + 1].pos
-
- # Remove tangential component
- f_star = f_total - f_total * v * v / (np.linalg.norm(v) ** 2 + 1e-6)
-
- alpha = self.bubbles[i].radius # Adaptive step size
- new_pos = self.bubbles[i].pos + alpha * f_star
- new_pos = np.clip(new_pos, 0, 499)
- new_radius = self.compute_rho(new_pos)
-
- # Update bubble and maintain overlap constraint
- new_bubble = Bubble(new_pos, new_radius)
- new_bubbles.append(new_bubble)
-
- self.bubbles = new_bubbles
- self._maintain_overlap()
-
- def _maintain_overlap(self):
- """Maintain bubble chain continuity (simplified insertion/deletion mechanism)"""
- # Insert bubbles
- i = 0
- while i < len(self.bubbles) - 1:
- bi, bj = self.bubbles[i], self.bubbles[i + 1]
- dist = np.linalg.norm(bi.pos - bj.pos)
- if dist > self.lambda_ * (bi.radius + bj.radius):
- new_pos = (bi.pos + bj.pos) / 2
- rho = self.compute_rho(
- new_pos
- ) # Calculate new radius using environment model
- self.bubbles.insert(i + 1, Bubble(new_pos, rho))
- i += 2 # Skip the processed region
- else:
- i += 1
-
- # Delete redundant bubbles
- i = 1
- while i < len(self.bubbles) - 1:
- prev = self.bubbles[i - 1]
- next_ = self.bubbles[i + 1]
- dist = np.linalg.norm(prev.pos - next_.pos)
- if dist <= self.lambda_ * (prev.radius + next_.radius):
- del self.bubbles[i] # Delete if redundant
- else:
- i += 1
-
-
-class ElasticBandsVisualizer:
- def __init__(self):
- self.obstacles = np.zeros((500, 500))
- self.obstacles_points = []
- self.path_points = []
- self.elastic_band = None
- self.running = True
-
- if ENABLE_PLOT:
- self.fig, self.ax = plt.subplots(figsize=(8, 8))
- self.fig.canvas.mpl_connect("close_event", self.on_close)
- self.ax.set_xlim(0, 500)
- self.ax.set_ylim(0, 500)
-
- if ENABLE_INTERACTIVE:
- self.path_points = [] # Add a list to store path points
- # Connect mouse events
- self.fig.canvas.mpl_connect("button_press_event", self.on_click)
- else:
- self.path_points = np.load(pathlib.Path(__file__).parent / "path.npy")
- self.obstacles_points = np.load(
- pathlib.Path(__file__).parent / "obstacles.npy"
- )
- for x, y in self.obstacles_points:
- self.add_obstacle(x, y)
- self.plan_path()
-
- self.plot_background()
-
- def on_close(self, event):
- """Handle window close event"""
- self.running = False
- plt.close("all") # Close all figure windows
-
- def plot_background(self):
- """Plot the background grid"""
- if not ENABLE_PLOT or not self.running:
- return
-
- self.ax.cla()
- self.ax.set_xlim(0, 500)
- self.ax.set_ylim(0, 500)
- self.ax.grid(True)
-
- if ENABLE_INTERACTIVE:
- self.ax.set_title(
- "Elastic Bands Path Planning\n"
- "Left click: Add obstacles\n"
- "Right click: Add path points\n"
- "Middle click: Start planning",
- pad=20,
- )
- else:
- self.ax.set_title("Elastic Bands Path Planning", pad=20)
-
- if self.path_points:
- self.ax.plot(
- [p[0] for p in self.path_points],
- [p[1] for p in self.path_points],
- "yo",
- markersize=8,
- )
-
- self.ax.imshow(self.obstacles.T, origin="lower", cmap="binary", alpha=0.8)
- self.ax.plot([], [], color="black", label="obstacles")
- if self.elastic_band is not None:
- path = [b.pos.tolist() for b in self.elastic_band.bubbles]
- path = np.array(path)
- self.ax.plot(path[:, 0], path[:, 1], "b-", linewidth=2, label="path")
-
- for bubble in self.elastic_band.bubbles:
- circle = Circle(
- bubble.pos, bubble.radius, fill=False, color="g", alpha=0.3
- )
- self.ax.add_patch(circle)
- self.ax.plot(bubble.pos[0], bubble.pos[1], "bo", markersize=10)
- self.ax.plot([], [], color="green", label="bubbles")
-
- self.ax.legend(loc="upper right")
- plt.draw()
- plt.pause(0.01)
-
- def add_obstacle(self, x, y):
- """Add an obstacle at the given coordinates"""
- size = 30 # Side length of the square
- half_size = size // 2
- x_start = max(0, x - half_size)
- x_end = min(self.obstacles.shape[0], x + half_size)
- y_start = max(0, y - half_size)
- y_end = min(self.obstacles.shape[1], y + half_size)
- self.obstacles[x_start:x_end, y_start:y_end] = 1
-
- def on_click(self, event):
- """Handle mouse click events"""
- if event.inaxes != self.ax:
- return
-
- x, y = int(event.xdata), int(event.ydata)
-
- if event.button == 1: # Left click to add obstacles
- self.add_obstacle(x, y)
- self.obstacles_points.append([x, y])
-
- elif event.button == 3: # Right click to add path points
- self.path_points.append([x, y])
-
- elif event.button == 2: # Middle click to end path input and start planning
- if len(self.path_points) >= 2:
- if ENABLE_SAVE_DATA:
- np.save(
- pathlib.Path(__file__).parent / "path.npy", self.path_points
- )
- np.save(
- pathlib.Path(__file__).parent / "obstacles.npy",
- self.obstacles_points,
- )
- self.plan_path()
-
- self.plot_background()
-
- def plan_path(self):
- """Plan the path"""
-
- initial_path = self.path_points
- # Create an elastic band object and optimize
- self.elastic_band = ElasticBands(initial_path, self.obstacles)
- for _ in range(MAX_ITER):
- self.elastic_band.update_bubbles()
- self.path_points = [b.pos for b in self.elastic_band.bubbles]
- self.plot_background()
-
-
-if __name__ == "__main__":
- _ = ElasticBandsVisualizer()
- if ENABLE_PLOT:
- plt.show(block=True)
diff --git a/PathPlanning/ElasticBands/obstacles.npy b/PathPlanning/ElasticBands/obstacles.npy
deleted file mode 100644
index af4376afcf0..00000000000
Binary files a/PathPlanning/ElasticBands/obstacles.npy and /dev/null differ
diff --git a/PathPlanning/ElasticBands/path.npy b/PathPlanning/ElasticBands/path.npy
deleted file mode 100644
index be7c253d650..00000000000
Binary files a/PathPlanning/ElasticBands/path.npy and /dev/null differ
diff --git a/PathPlanning/Eta3SplinePath/eta3_spline_path.py b/PathPlanning/Eta3SplinePath/eta3_spline_path.py
deleted file mode 100644
index dc07d3c84b9..00000000000
--- a/PathPlanning/Eta3SplinePath/eta3_spline_path.py
+++ /dev/null
@@ -1,361 +0,0 @@
-"""
-
-eta^3 polynomials planner
-
-author: Joe Dinius, Ph.D (https://jwdinius.github.io)
- Atsushi Sakai (@Atsushi_twi)
-
-Ref:
-- [eta^3-Splines for the Smooth Path Generation of Wheeled Mobile Robots]
-(https://ieeexplore.ieee.org/document/4339545/)
-
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-from scipy.integrate import quad
-
-# NOTE: *_pose is a 3-array:
-# 0 - x coord, 1 - y coord, 2 - orientation angle \theta
-
-show_animation = True
-
-
-class Eta3Path(object):
- """
- Eta3Path
-
- input
- segments: a list of `Eta3PathSegment` instances
- defining a continuous path
- """
-
- def __init__(self, segments):
- # ensure input has the correct form
- assert(isinstance(segments, list) and isinstance(
- segments[0], Eta3PathSegment))
- # ensure that each segment begins from the previous segment's end (continuity)
- for r, s in zip(segments[:-1], segments[1:]):
- assert(np.array_equal(r.end_pose, s.start_pose))
- self.segments = segments
-
- def calc_path_point(self, u):
- """
- Eta3Path::calc_path_point
-
- input
- normalized interpolation point along path object, 0 <= u <= len(self.segments)
- returns
- 2d (x,y) position vector
- """
-
- assert(0 <= u <= len(self.segments))
- if np.isclose(u, len(self.segments)):
- segment_idx = len(self.segments) - 1
- u = 1.
- else:
- segment_idx = int(np.floor(u))
- u -= segment_idx
- return self.segments[segment_idx].calc_point(u)
-
-
-class Eta3PathSegment(object):
- """
- Eta3PathSegment - constructs an eta^3 path segment based on desired
- shaping, eta, and curvature vector, kappa. If either, or both,
- of eta and kappa are not set during initialization,
- they will default to zeros.
-
- input
- start_pose - starting pose array (x, y, \theta)
- end_pose - ending pose array (x, y, \theta)
- eta - shaping parameters, default=None
- kappa - curvature parameters, default=None
- """
-
- def __init__(self, start_pose, end_pose, eta=None, kappa=None):
- # make sure inputs are of the correct size
- assert(len(start_pose) == 3 and len(start_pose) == len(end_pose))
- self.start_pose = start_pose
- self.end_pose = end_pose
- # if no eta is passed, initialize it to array of zeros
- if not eta:
- eta = np.zeros((6,))
- else:
- # make sure that eta has correct size
- assert(len(eta) == 6)
- # if no kappa is passed, initialize to array of zeros
- if not kappa:
- kappa = np.zeros((4,))
- else:
- assert(len(kappa) == 4)
- # set up angle cosines and sines for simpler computations below
- ca = np.cos(start_pose[2])
- sa = np.sin(start_pose[2])
- cb = np.cos(end_pose[2])
- sb = np.sin(end_pose[2])
- # 2 dimensions (x,y) x 8 coefficients per dimension
- self.coeffs = np.empty((2, 8))
- # constant terms (u^0)
- self.coeffs[0, 0] = start_pose[0]
- self.coeffs[1, 0] = start_pose[1]
- # linear (u^1)
- self.coeffs[0, 1] = eta[0] * ca
- self.coeffs[1, 1] = eta[0] * sa
- # quadratic (u^2)
- self.coeffs[0, 2] = 1. / 2 * eta[2] * \
- ca - 1. / 2 * eta[0]**2 * kappa[0] * sa
- self.coeffs[1, 2] = 1. / 2 * eta[2] * \
- sa + 1. / 2 * eta[0]**2 * kappa[0] * ca
- # cubic (u^3)
- self.coeffs[0, 3] = 1. / 6 * eta[4] * ca - 1. / 6 * \
- (eta[0]**3 * kappa[1] + 3. * eta[0] * eta[2] * kappa[0]) * sa
- self.coeffs[1, 3] = 1. / 6 * eta[4] * sa + 1. / 6 * \
- (eta[0]**3 * kappa[1] + 3. * eta[0] * eta[2] * kappa[0]) * ca
- # quartic (u^4)
- tmp1 = 35. * (end_pose[0] - start_pose[0])
- tmp2 = (20. * eta[0] + 5 * eta[2] + 2. / 3 * eta[4]) * ca
- tmp3 = (5. * eta[0] ** 2 * kappa[0] + 2. / 3 * eta[0] ** 3 * kappa[1]
- + 2. * eta[0] * eta[2] * kappa[0]) * sa
- tmp4 = (15. * eta[1] - 5. / 2 * eta[3] + 1. / 6 * eta[5]) * cb
- tmp5 = (5. / 2 * eta[1] ** 2 * kappa[2] - 1. / 6 * eta[1] ** 3 *
- kappa[3] - 1. / 2 * eta[1] * eta[3] * kappa[2]) * sb
- self.coeffs[0, 4] = tmp1 - tmp2 + tmp3 - tmp4 - tmp5
- tmp1 = 35. * (end_pose[1] - start_pose[1])
- tmp2 = (20. * eta[0] + 5. * eta[2] + 2. / 3 * eta[4]) * sa
- tmp3 = (5. * eta[0] ** 2 * kappa[0] + 2. / 3 * eta[0] ** 3 * kappa[1]
- + 2. * eta[0] * eta[2] * kappa[0]) * ca
- tmp4 = (15. * eta[1] - 5. / 2 * eta[3] + 1. / 6 * eta[5]) * sb
- tmp5 = (5. / 2 * eta[1] ** 2 * kappa[2] - 1. / 6 * eta[1] ** 3 *
- kappa[3] - 1. / 2 * eta[1] * eta[3] * kappa[2]) * cb
- self.coeffs[1, 4] = tmp1 - tmp2 - tmp3 - tmp4 + tmp5
- # quintic (u^5)
- tmp1 = -84. * (end_pose[0] - start_pose[0])
- tmp2 = (45. * eta[0] + 10. * eta[2] + eta[4]) * ca
- tmp3 = (10. * eta[0] ** 2 * kappa[0] + eta[0] ** 3 * kappa[1] + 3. *
- eta[0] * eta[2] * kappa[0]) * sa
- tmp4 = (39. * eta[1] - 7. * eta[3] + 1. / 2 * eta[5]) * cb
- tmp5 = + (7. * eta[1] ** 2 * kappa[2] - 1. / 2 * eta[1] ** 3 * kappa[3]
- - 3. / 2 * eta[1] * eta[3] * kappa[2]) * sb
- self.coeffs[0, 5] = tmp1 + tmp2 - tmp3 + tmp4 + tmp5
- tmp1 = -84. * (end_pose[1] - start_pose[1])
- tmp2 = (45. * eta[0] + 10. * eta[2] + eta[4]) * sa
- tmp3 = (10. * eta[0] ** 2 * kappa[0] + eta[0] ** 3 * kappa[1] + 3. *
- eta[0] * eta[2] * kappa[0]) * ca
- tmp4 = (39. * eta[1] - 7. * eta[3] + 1. / 2 * eta[5]) * sb
- tmp5 = - (7. * eta[1] ** 2 * kappa[2] - 1. / 2 * eta[1] ** 3 * kappa[3]
- - 3. / 2 * eta[1] * eta[3] * kappa[2]) * cb
- self.coeffs[1, 5] = tmp1 + tmp2 + tmp3 + tmp4 + tmp5
- # sextic (u^6)
- tmp1 = 70. * (end_pose[0] - start_pose[0])
- tmp2 = (36. * eta[0] + 15. / 2 * eta[2] + 2. / 3 * eta[4]) * ca
- tmp3 = + (15. / 2 * eta[0] ** 2 * kappa[0] + 2. / 3 * eta[0] ** 3 *
- kappa[1] + 2. * eta[0] * eta[2] * kappa[0]) * sa
- tmp4 = (34. * eta[1] - 13. / 2 * eta[3] + 1. / 2 * eta[5]) * cb
- tmp5 = - (13. / 2 * eta[1] ** 2 * kappa[2] - 1. / 2 * eta[1] ** 3 *
- kappa[3] - 3. / 2 * eta[1] * eta[3] * kappa[2]) * sb
- self.coeffs[0, 6] = tmp1 - tmp2 + tmp3 - tmp4 + tmp5
- tmp1 = 70. * (end_pose[1] - start_pose[1])
- tmp2 = - (36. * eta[0] + 15. / 2 * eta[2] + 2. / 3 * eta[4]) * sa
- tmp3 = - (15. / 2 * eta[0] ** 2 * kappa[0] + 2. / 3 * eta[0] ** 3 *
- kappa[1] + 2. * eta[0] * eta[2] * kappa[0]) * ca
- tmp4 = - (34. * eta[1] - 13. / 2 * eta[3] + 1. / 2 * eta[5]) * sb
- tmp5 = + (13. / 2 * eta[1] ** 2 * kappa[2] - 1. / 2 * eta[1] ** 3 *
- kappa[3] - 3. / 2 * eta[1] * eta[3] * kappa[2]) * cb
- self.coeffs[1, 6] = tmp1 + tmp2 + tmp3 + tmp4 + tmp5
- # septic (u^7)
- tmp1 = -20. * (end_pose[0] - start_pose[0])
- tmp2 = (10. * eta[0] + 2. * eta[2] + 1. / 6 * eta[4]) * ca
- tmp3 = - (2. * eta[0] ** 2 * kappa[0] + 1. / 6 * eta[0] ** 3 * kappa[1]
- + 1. / 2 * eta[0] * eta[2] * kappa[0]) * sa
- tmp4 = (10. * eta[1] - 2. * eta[3] + 1. / 6 * eta[5]) * cb
- tmp5 = (2. * eta[1] ** 2 * kappa[2] - 1. / 6 * eta[1] ** 3 * kappa[3]
- - 1. / 2 * eta[1] * eta[3] * kappa[2]) * sb
- self.coeffs[0, 7] = tmp1 + tmp2 + tmp3 + tmp4 + tmp5
-
- tmp1 = -20. * (end_pose[1] - start_pose[1])
- tmp2 = (10. * eta[0] + 2. * eta[2] + 1. / 6 * eta[4]) * sa
- tmp3 = (2. * eta[0] ** 2 * kappa[0] + 1. / 6 * eta[0] ** 3 * kappa[1]
- + 1. / 2 * eta[0] * eta[2] * kappa[0]) * ca
- tmp4 = (10. * eta[1] - 2. * eta[3] + 1. / 6 * eta[5]) * sb
- tmp5 = - (2. * eta[1] ** 2 * kappa[2] - 1. / 6 * eta[1] ** 3 * kappa[3]
- - 1. / 2 * eta[1] * eta[3] * kappa[2]) * cb
- self.coeffs[1, 7] = tmp1 + tmp2 + tmp3 + tmp4 + tmp5
- self.s_dot = lambda u: max(np.linalg.norm(
- self.coeffs[:, 1:].dot(np.array(
- [1, 2. * u, 3. * u**2, 4. * u**3,
- 5. * u**4, 6. * u**5, 7. * u**6]))), 1e-6)
- self.f_length = lambda ue: quad(lambda u: self.s_dot(u), 0, ue)
- self.segment_length = self.f_length(1)[0]
-
- def calc_point(self, u):
- """
- Eta3PathSegment::calc_point
-
- input
- u - parametric representation of a point along the segment, 0 <= u <= 1
- returns
- (x,y) of point along the segment
- """
- assert(0 <= u <= 1)
- return self.coeffs.dot(np.array([1, u, u**2, u**3, u**4, u**5, u**6, u**7]))
-
- def calc_deriv(self, u, order=1):
- """
- Eta3PathSegment::calc_deriv
-
- input
- u - parametric representation of a point along the segment, 0 <= u <= 1
- returns
- (d^nx/du^n,d^ny/du^n) of point along the segment, for 0 < n <= 2
- """
-
- assert(0 <= u <= 1)
- assert(0 < order <= 2)
- if order == 1:
- return self.coeffs[:, 1:].dot(np.array([1, 2. * u, 3. * u**2, 4. * u**3, 5. * u**4, 6. * u**5, 7. * u**6]))
-
- return self.coeffs[:, 2:].dot(np.array([2, 6. * u, 12. * u**2, 20. * u**3, 30. * u**4, 42. * u**5]))
-
-
-def test1():
-
- for i in range(10):
- path_segments = []
- # segment 1: lane-change curve
- start_pose = [0, 0, 0]
- end_pose = [4, 3.0, 0]
- # NOTE: The ordering on kappa is [kappa_A, kappad_A, kappa_B, kappad_B], with kappad_* being the curvature derivative
- kappa = [0, 0, 0, 0]
- eta = [i, i, 0, 0, 0, 0]
- path_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- path = Eta3Path(path_segments)
-
- # interpolate at several points along the path
- ui = np.linspace(0, len(path_segments), 1001)
- pos = np.empty((2, ui.size))
- for j, u in enumerate(ui):
- pos[:, j] = path.calc_path_point(u)
-
- if show_animation:
- # plot the path
- plt.plot(pos[0, :], pos[1, :])
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.pause(1.0)
-
- if show_animation:
- plt.close("all")
-
-
-def test2():
-
- for i in range(10):
- path_segments = []
- # segment 1: lane-change curve
- start_pose = [0, 0, 0]
- end_pose = [4, 3.0, 0]
- # NOTE: The ordering on kappa is [kappa_A, kappad_A, kappa_B, kappad_B], with kappad_* being the curvature derivative
- kappa = [0, 0, 0, 0]
- eta = [0, 0, (i - 5) * 20, (5 - i) * 20, 0, 0]
- path_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- path = Eta3Path(path_segments)
-
- # interpolate at several points along the path
- ui = np.linspace(0, len(path_segments), 1001)
- pos = np.empty((2, ui.size))
- for j, u in enumerate(ui):
- pos[:, j] = path.calc_path_point(u)
-
- if show_animation:
- # plot the path
- plt.plot(pos[0, :], pos[1, :])
- plt.pause(1.0)
-
- if show_animation:
- plt.close("all")
-
-
-def test3():
- path_segments = []
-
- # segment 1: lane-change curve
- start_pose = [0, 0, 0]
- end_pose = [4, 1.5, 0]
- # NOTE: The ordering on kappa is [kappa_A, kappad_A, kappa_B, kappad_B], with kappad_* being the curvature derivative
- kappa = [0, 0, 0, 0]
- eta = [4.27, 4.27, 0, 0, 0, 0]
- path_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- # segment 2: line segment
- start_pose = [4, 1.5, 0]
- end_pose = [5.5, 1.5, 0]
- kappa = [0, 0, 0, 0]
- eta = [0, 0, 0, 0, 0, 0]
- path_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- # segment 3: cubic spiral
- start_pose = [5.5, 1.5, 0]
- end_pose = [7.4377, 1.8235, 0.6667]
- kappa = [0, 0, 1, 1]
- eta = [1.88, 1.88, 0, 0, 0, 0]
- path_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- # segment 4: generic twirl arc
- start_pose = [7.4377, 1.8235, 0.6667]
- end_pose = [7.8, 4.3, 1.8]
- kappa = [1, 1, 0.5, 0]
- eta = [7, 10, 10, -10, 4, 4]
- path_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- # segment 5: circular arc
- start_pose = [7.8, 4.3, 1.8]
- end_pose = [5.4581, 5.8064, 3.3416]
- kappa = [0.5, 0, 0.5, 0]
- eta = [2.98, 2.98, 0, 0, 0, 0]
- path_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- # construct the whole path
- path = Eta3Path(path_segments)
-
- # interpolate at several points along the path
- ui = np.linspace(0, len(path_segments), 1001)
- pos = np.empty((2, ui.size))
- for i, u in enumerate(ui):
- pos[:, i] = path.calc_path_point(u)
-
- # plot the path
-
- if show_animation:
- plt.figure('Path from Reference')
- plt.plot(pos[0, :], pos[1, :])
- plt.xlabel('x')
- plt.ylabel('y')
- plt.title('Path')
- plt.pause(1.0)
-
- plt.show()
-
-
-def main():
- """
- recreate path from reference (see Table 1)
- """
- test1()
- test2()
- test3()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/Eta3SplineTrajectory/eta3_spline_trajectory.py b/PathPlanning/Eta3SplineTrajectory/eta3_spline_trajectory.py
deleted file mode 100644
index a73797dacb9..00000000000
--- a/PathPlanning/Eta3SplineTrajectory/eta3_spline_trajectory.py
+++ /dev/null
@@ -1,456 +0,0 @@
-"""
-
-eta^3 polynomials trajectory planner
-
-author: Joe Dinius, Ph.D (https://jwdinius.github.io)
- Atsushi Sakai (@Atsushi_twi)
-
-Refs:
-- https://jwdinius.github.io/blog/2018/eta3traj/
-- [eta^3-Splines for the Smooth Path Generation of Wheeled Mobile Robots]
-(https://ieeexplore.ieee.org/document/4339545/)
-
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-from matplotlib.collections import LineCollection
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from Eta3SplinePath.eta3_spline_path import Eta3Path, Eta3PathSegment
-
-show_animation = True
-
-
-class MaxVelocityNotReached(Exception):
- def __init__(self, actual_vel, max_vel):
- self.message = f'Actual velocity {actual_vel} does not equal desired max velocity {max_vel}!'
-
-
-class eta3_trajectory(Eta3Path):
- """
- eta3_trajectory
-
- input
- segments: list of `eta3_trajectory_segment` instances defining a continuous trajectory
- """
-
- def __init__(self, segments, max_vel, v0=0.0, a0=0.0, max_accel=2.0, max_jerk=5.0):
- # ensure that all inputs obey the assumptions of the model
- assert max_vel > 0 and v0 >= 0 and a0 >= 0 and max_accel > 0 and max_jerk > 0 \
- and a0 <= max_accel and v0 <= max_vel
- super(__class__, self).__init__(segments=segments)
- self.total_length = sum([s.segment_length for s in self.segments])
- self.max_vel = float(max_vel)
- self.v0 = float(v0)
- self.a0 = float(a0)
- self.max_accel = float(max_accel)
- self.max_jerk = float(max_jerk)
- length_array = np.array([s.segment_length for s in self.segments])
- # add a zero to the beginning for finding the correct segment_id
- self.cum_lengths = np.concatenate(
- (np.array([0]), np.cumsum(length_array)))
- # compute velocity profile on top of the path
- self.velocity_profile()
- self.ui_prev = 0
- self.prev_seg_id = 0
-
- def velocity_profile(self):
- r""" /~~~~~----------------\
- / \
- / \
- / \
- / \
- (v=v0, a=a0) ~~~~~ \
- \
- \ ~~~~~ (vf=0, af=0)
- pos.|pos.|neg.| cruise at |neg.| neg. |neg.
- max |max.|max.| max. |max.| max. |max.
- jerk|acc.|jerk| velocity |jerk| acc. |jerk
- index 0 1 2 3 (optional) 4 5 6
- """
- # delta_a: accel change from initial position to end of maximal jerk section
- delta_a = self.max_accel - self.a0
- # t_s1: time of traversal of maximal jerk section
- t_s1 = delta_a / self.max_jerk
- # v_s1: velocity at the end of the maximal jerk section
- v_s1 = self.v0 + self.a0 * t_s1 + self.max_jerk * t_s1**2 / 2.
- # s_s1: length of the maximal jerk section
- s_s1 = self.v0 * t_s1 + self.a0 * t_s1**2 / 2. + self.max_jerk * t_s1**3 / 6.
- # t_sf: time of traversal of final section, which is also maximal jerk, but has final velocity 0
- t_sf = self.max_accel / self.max_jerk
- # v_sf: velocity at beginning of final section
- v_sf = self.max_jerk * t_sf**2 / 2.
- # s_sf: length of final section
- s_sf = self.max_jerk * t_sf**3 / 6.
- # solve for the maximum achievable velocity based on the kinematic limits imposed by max_accel and max_jerk
- # this leads to a quadratic equation in v_max: a*v_max**2 + b*v_max + c = 0
- a = 1 / self.max_accel
- b = 3. * self.max_accel / (2. * self.max_jerk) + v_s1 / self.max_accel - (
- self.max_accel**2 / self.max_jerk + v_s1) / self.max_accel
- c = s_s1 + s_sf - self.total_length - 7. * self.max_accel**3 / (3. * self.max_jerk**2) \
- - v_s1 * (self.max_accel / self.max_jerk + v_s1 / self.max_accel) \
- + (self.max_accel**2 / self.max_jerk + v_s1 /
- self.max_accel)**2 / (2. * self.max_accel)
- v_max = (-b + np.sqrt(b**2 - 4. * a * c)) / (2. * a)
-
- # v_max represents the maximum velocity that could be attained if there was no cruise period
- # (i.e. driving at constant speed without accelerating or jerking)
- # if this velocity is less than our desired max velocity, the max velocity needs to be updated
- if self.max_vel > v_max:
- # when this condition is tripped, there will be no cruise period (s_cruise=0)
- self.max_vel = v_max
-
- # setup arrays to store values at END of trajectory sections
- self.times = np.zeros((7,))
- self.vels = np.zeros((7,))
- self.seg_lengths = np.zeros((7,))
-
- # Section 0: max jerk up to max acceleration
- self.times[0] = t_s1
- self.vels[0] = v_s1
- self.seg_lengths[0] = s_s1
-
- # Section 1: accelerate at max_accel
- index = 1
- # compute change in velocity over the section
- delta_v = (self.max_vel - self.max_jerk * (self.max_accel /
- self.max_jerk)**2 / 2.) - self.vels[index - 1]
- self.times[index] = delta_v / self.max_accel
- self.vels[index] = self.vels[index - 1] + \
- self.max_accel * self.times[index]
- self.seg_lengths[index] = self.vels[index - 1] * \
- self.times[index] + self.max_accel * self.times[index]**2 / 2.
-
- # Section 2: decrease acceleration (down to 0) until max speed is hit
- index = 2
- self.times[index] = self.max_accel / self.max_jerk
- self.vels[index] = self.vels[index - 1] + self.max_accel * self.times[index] \
- - self.max_jerk * self.times[index]**2 / 2.
-
- # as a check, the velocity at the end of the section should be self.max_vel
- if not np.isclose(self.vels[index], self.max_vel):
- raise MaxVelocityNotReached(self.vels[index], self.max_vel)
-
- self.seg_lengths[index] = self.vels[index - 1] * self.times[index] + self.max_accel * self.times[index]**2 / 2. \
- - self.max_jerk * self.times[index]**3 / 6.
-
- # Section 3: will be done last
-
- # Section 4: apply min jerk until min acceleration is hit
- index = 4
- self.times[index] = self.max_accel / self.max_jerk
- self.vels[index] = self.max_vel - \
- self.max_jerk * self.times[index]**2 / 2.
- self.seg_lengths[index] = self.max_vel * self.times[index] - \
- self.max_jerk * self.times[index]**3 / 6.
-
- # Section 5: continue deceleration at max rate
- index = 5
- # compute velocity change over sections
- delta_v = self.vels[index - 1] - v_sf
- self.times[index] = delta_v / self.max_accel
- self.vels[index] = self.vels[index - 1] - \
- self.max_accel * self.times[index]
- self.seg_lengths[index] = self.vels[index - 1] * \
- self.times[index] - self.max_accel * self.times[index]**2 / 2.
-
- # Section 6(final): max jerk to get to zero velocity and zero acceleration simultaneously
- index = 6
- self.times[index] = t_sf
- self.vels[index] = self.vels[index - 1] - self.max_jerk * t_sf**2 / 2.
-
- try:
- assert np.isclose(self.vels[index], 0)
- except AssertionError as e:
- print(f'The final velocity {self.vels[index]} is not zero')
- raise e
-
- self.seg_lengths[index] = s_sf
-
- if self.seg_lengths.sum() < self.total_length:
- index = 3
- # the length of the cruise section is whatever length hasn't already been accounted for
- # NOTE: the total array self.seg_lengths is summed because the entry for the cruise segment is
- # initialized to 0!
- self.seg_lengths[index] = self.total_length - \
- self.seg_lengths.sum()
- self.vels[index] = self.max_vel
- self.times[index] = self.seg_lengths[index] / self.max_vel
-
- # make sure that all of the times are positive, otherwise the kinematic limits
- # chosen cannot be enforced on the path
- assert(np.all(self.times >= 0))
- self.total_time = self.times.sum()
-
- def get_interp_param(self, seg_id, s, ui, tol=0.001):
- def f(u):
- return self.segments[seg_id].f_length(u)[0] - s
-
- def fprime(u):
- return self.segments[seg_id].s_dot(u)
- while (0 <= ui <= 1) and abs(f(ui)) > tol:
- ui -= f(ui) / fprime(ui)
- ui = max(0, min(ui, 1))
- return ui
-
- def calc_traj_point(self, time):
- # compute velocity at time
- if time <= self.times[0]:
- linear_velocity = self.v0 + self.max_jerk * time**2 / 2.
- s = self.v0 * time + self.max_jerk * time**3 / 6
- linear_accel = self.max_jerk * time
- elif time <= self.times[:2].sum():
- delta_t = time - self.times[0]
- linear_velocity = self.vels[0] + self.max_accel * delta_t
- s = self.seg_lengths[0] + self.vels[0] * \
- delta_t + self.max_accel * delta_t**2 / 2.
- linear_accel = self.max_accel
- elif time <= self.times[:3].sum():
- delta_t = time - self.times[:2].sum()
- linear_velocity = self.vels[1] + self.max_accel * \
- delta_t - self.max_jerk * delta_t**2 / 2.
- s = self.seg_lengths[:2].sum() + self.vels[1] * delta_t + self.max_accel * delta_t**2 / 2. \
- - self.max_jerk * delta_t**3 / 6.
- linear_accel = self.max_accel - self.max_jerk * delta_t
- elif time <= self.times[:4].sum():
- delta_t = time - self.times[:3].sum()
- linear_velocity = self.vels[3]
- s = self.seg_lengths[:3].sum() + self.vels[3] * delta_t
- linear_accel = 0.
- elif time <= self.times[:5].sum():
- delta_t = time - self.times[:4].sum()
- linear_velocity = self.vels[3] - self.max_jerk * delta_t**2 / 2.
- s = self.seg_lengths[:4].sum() + self.vels[3] * \
- delta_t - self.max_jerk * delta_t**3 / 6.
- linear_accel = -self.max_jerk * delta_t
- elif time <= self.times[:-1].sum():
- delta_t = time - self.times[:5].sum()
- linear_velocity = self.vels[4] - self.max_accel * delta_t
- s = self.seg_lengths[:5].sum() + self.vels[4] * \
- delta_t - self.max_accel * delta_t**2 / 2.
- linear_accel = -self.max_accel
- elif time < self.times.sum():
- delta_t = time - self.times[:-1].sum()
- linear_velocity = self.vels[5] - self.max_accel * \
- delta_t + self.max_jerk * delta_t**2 / 2.
- s = self.seg_lengths[:-1].sum() + self.vels[5] * delta_t - self.max_accel * delta_t**2 / 2. \
- + self.max_jerk * delta_t**3 / 6.
- linear_accel = -self.max_accel + self.max_jerk * delta_t
- else:
- linear_velocity = 0.
- s = self.total_length
- linear_accel = 0.
- seg_id = np.max(np.argwhere(self.cum_lengths <= s))
-
- # will happen at the end of the segment
- if seg_id == len(self.segments):
- seg_id -= 1
- ui = 1
- else:
- # compute interpolation parameter using length from current segment's starting point
- curr_segment_length = s - self.cum_lengths[seg_id]
- ui = self.get_interp_param(
- seg_id=seg_id, s=curr_segment_length, ui=self.ui_prev)
-
- if not seg_id == self.prev_seg_id:
- self.ui_prev = 0
- else:
- self.ui_prev = ui
-
- self.prev_seg_id = seg_id
- # compute angular velocity of current point= (ydd*xd - xdd*yd) / (xd**2 + yd**2)
- d = self.segments[seg_id].calc_deriv(ui, order=1)
- dd = self.segments[seg_id].calc_deriv(ui, order=2)
- # su - the rate of change of arclength wrt u
- su = self.segments[seg_id].s_dot(ui)
- if not np.isclose(su, 0.) and not np.isclose(linear_velocity, 0.):
- # ut - time-derivative of interpolation parameter u
- ut = linear_velocity / su
- # utt - time-derivative of ut
- utt = linear_accel / su - \
- (d[0] * dd[0] + d[1] * dd[1]) / su**2 * ut
- xt = d[0] * ut
- yt = d[1] * ut
- xtt = dd[0] * ut**2 + d[0] * utt
- ytt = dd[1] * ut**2 + d[1] * utt
- angular_velocity = (ytt * xt - xtt * yt) / linear_velocity**2
- else:
- angular_velocity = 0.
-
- # combine path point with orientation and velocities
- pos = self.segments[seg_id].calc_point(ui)
- state = np.array([pos[0], pos[1], np.arctan2(
- d[1], d[0]), linear_velocity, angular_velocity])
- return state
-
-
-def test1(max_vel=0.5):
-
- for i in range(10):
- trajectory_segments = []
- # segment 1: lane-change curve
- start_pose = [0, 0, 0]
- end_pose = [4, 3.0, 0]
- # NOTE: The ordering on kappa is [kappa_A, kappad_A, kappa_B, kappad_B], with kappad_* being the curvature derivative
- kappa = [0, 0, 0, 0]
- eta = [i, i, 0, 0, 0, 0]
- trajectory_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- traj = eta3_trajectory(trajectory_segments,
- max_vel=max_vel, max_accel=0.5)
-
- # interpolate at several points along the path
- times = np.linspace(0, traj.total_time, 101)
- state = np.empty((5, times.size))
- for j, t in enumerate(times):
- state[:, j] = traj.calc_traj_point(t)
-
- if show_animation: # pragma: no cover
- # plot the path
- plt.plot(state[0, :], state[1, :])
- plt.pause(1.0)
-
- plt.show()
- if show_animation:
- plt.close("all")
-
-
-def test2(max_vel=0.5):
-
- for i in range(10):
- trajectory_segments = []
- # segment 1: lane-change curve
- start_pose = [0, 0, 0]
- end_pose = [4, 3.0, 0]
- # NOTE: The ordering on kappa is [kappa_A, kappad_A, kappa_B, kappad_B], with kappad_* being the curvature derivative
- kappa = [0, 0, 0, 0]
- # NOTE: INTEGRATOR ERROR EXPLODES WHEN eta[:1] IS ZERO!
- # was: eta = [0, 0, (i - 5) * 20, (5 - i) * 20, 0, 0], now is:
- eta = [0.1, 0.1, (i - 5) * 20, (5 - i) * 20, 0, 0]
- trajectory_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- traj = eta3_trajectory(trajectory_segments,
- max_vel=max_vel, max_accel=0.5)
-
- # interpolate at several points along the path
- times = np.linspace(0, traj.total_time, 101)
- state = np.empty((5, times.size))
- for j, t in enumerate(times):
- state[:, j] = traj.calc_traj_point(t)
-
- if show_animation:
- # plot the path
- plt.plot(state[0, :], state[1, :])
- plt.pause(1.0)
-
- plt.show()
- if show_animation:
- plt.close("all")
-
-
-def test3(max_vel=2.0):
- trajectory_segments = []
-
- # segment 1: lane-change curve
- start_pose = [0, 0, 0]
- end_pose = [4, 1.5, 0]
- # NOTE: The ordering on kappa is [kappa_A, kappad_A, kappa_B, kappad_B], with kappad_* being the curvature derivative
- kappa = [0, 0, 0, 0]
- eta = [4.27, 4.27, 0, 0, 0, 0]
- trajectory_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- # segment 2: line segment
- start_pose = [4, 1.5, 0]
- end_pose = [5.5, 1.5, 0]
- kappa = [0, 0, 0, 0]
- # NOTE: INTEGRATOR ERROR EXPLODES WHEN eta[:1] IS ZERO!
- # was: eta = [0, 0, 0, 0, 0, 0], now is:
- eta = [0.5, 0.5, 0, 0, 0, 0]
- trajectory_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- # segment 3: cubic spiral
- start_pose = [5.5, 1.5, 0]
- end_pose = [7.4377, 1.8235, 0.6667]
- kappa = [0, 0, 1, 1]
- eta = [1.88, 1.88, 0, 0, 0, 0]
- trajectory_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- # segment 4: generic twirl arc
- start_pose = [7.4377, 1.8235, 0.6667]
- end_pose = [7.8, 4.3, 1.8]
- kappa = [1, 1, 0.5, 0]
- eta = [7, 10, 10, -10, 4, 4]
- trajectory_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- # segment 5: circular arc
- start_pose = [7.8, 4.3, 1.8]
- end_pose = [5.4581, 5.8064, 3.3416]
- kappa = [0.5, 0, 0.5, 0]
- eta = [2.98, 2.98, 0, 0, 0, 0]
- trajectory_segments.append(Eta3PathSegment(
- start_pose=start_pose, end_pose=end_pose, eta=eta, kappa=kappa))
-
- # construct the whole path
- traj = eta3_trajectory(trajectory_segments,
- max_vel=max_vel, max_accel=0.5, max_jerk=1)
-
- # interpolate at several points along the path
- times = np.linspace(0, traj.total_time, 1001)
- state = np.empty((5, times.size))
- for i, t in enumerate(times):
- state[:, i] = traj.calc_traj_point(t)
-
- # plot the path
-
- if show_animation:
- fig, ax = plt.subplots()
- x, y = state[0, :], state[1, :]
- points = np.array([x, y]).T.reshape(-1, 1, 2)
- segs = np.concatenate([points[:-1], points[1:]], axis=1)
- lc = LineCollection(segs, cmap=plt.get_cmap('inferno'))
- ax.set_xlim(np.min(x) - 1, np.max(x) + 1)
- ax.set_ylim(np.min(y) - 1, np.max(y) + 1)
- lc.set_array(state[3, :])
- lc.set_linewidth(3)
- ax.add_collection(lc)
- axcb = fig.colorbar(lc)
- axcb.set_label('velocity(m/s)')
- ax.set_title('Trajectory')
- plt.xlabel('x')
- plt.ylabel('y')
- plt.pause(1.0)
-
- fig1, ax1 = plt.subplots()
- ax1.plot(times, state[3, :], 'b-')
- ax1.set_xlabel('time(s)')
- ax1.set_ylabel('velocity(m/s)', color='b')
- ax1.tick_params('y', colors='b')
- ax1.set_title('Control')
- ax2 = ax1.twinx()
- ax2.plot(times, state[4, :], 'r-')
- ax2.set_ylabel('angular velocity(rad/s)', color='r')
- ax2.tick_params('y', colors='r')
- fig.tight_layout()
- plt.show()
-
-
-def main():
- """
- recreate path from reference (see Table 1)
- """
- # test1()
- # test2()
- test3()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/FlowField/flowfield.py b/PathPlanning/FlowField/flowfield.py
deleted file mode 100644
index e50430de3c2..00000000000
--- a/PathPlanning/FlowField/flowfield.py
+++ /dev/null
@@ -1,227 +0,0 @@
-"""
-flowfield pathfinding
-author: Sarim Mehdi (muhammadsarim.mehdi@studio.unibo.it)
-Source: https://leifnode.com/2013/12/flow-field-pathfinding/
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-show_animation = True
-
-
-def draw_horizontal_line(start_x, start_y, length, o_x, o_y, o_dict, path):
- for i in range(start_x, start_x + length):
- for j in range(start_y, start_y + 2):
- o_x.append(i)
- o_y.append(j)
- o_dict[(i, j)] = path
-
-
-def draw_vertical_line(start_x, start_y, length, o_x, o_y, o_dict, path):
- for i in range(start_x, start_x + 2):
- for j in range(start_y, start_y + length):
- o_x.append(i)
- o_y.append(j)
- o_dict[(i, j)] = path
-
-
-class FlowField:
- def __init__(self, obs_grid, goal_x, goal_y, start_x, start_y,
- limit_x, limit_y):
- self.start_pt = [start_x, start_y]
- self.goal_pt = [goal_x, goal_y]
- self.obs_grid = obs_grid
- self.limit_x, self.limit_y = limit_x, limit_y
- self.cost_field = {}
- self.integration_field = {}
- self.vector_field = {}
-
- def find_path(self):
- self.create_cost_field()
- self.create_integration_field()
- self.assign_vectors()
- self.follow_vectors()
-
- def create_cost_field(self):
- """Assign cost to each grid which defines the energy
- it would take to get there."""
- for i in range(self.limit_x):
- for j in range(self.limit_y):
- if self.obs_grid[(i, j)] == 'free':
- self.cost_field[(i, j)] = 1
- elif self.obs_grid[(i, j)] == 'medium':
- self.cost_field[(i, j)] = 7
- elif self.obs_grid[(i, j)] == 'hard':
- self.cost_field[(i, j)] = 20
- elif self.obs_grid[(i, j)] == 'obs':
- continue
-
- if [i, j] == self.goal_pt:
- self.cost_field[(i, j)] = 0
-
- def create_integration_field(self):
- """Start from the goal node and calculate the value
- of the integration field at each node. Start by
- assigning a value of infinity to every node except
- the goal node which is assigned a value of 0. Put the
- goal node in the open list and then get its neighbors
- (must not be obstacles). For each neighbor, the new
- cost is equal to the cost of the current node in the
- integration field (in the beginning, this will simply
- be the goal node) + the cost of the neighbor in the
- cost field + the extra cost (optional). The new cost
- is only assigned if it is less than the previously
- assigned cost of the node in the integration field and,
- when that happens, the neighbor is put on the open list.
- This process continues until the open list is empty."""
- for i in range(self.limit_x):
- for j in range(self.limit_y):
- if self.obs_grid[(i, j)] == 'obs':
- continue
- self.integration_field[(i, j)] = np.inf
- if [i, j] == self.goal_pt:
- self.integration_field[(i, j)] = 0
-
- open_list = [(self.goal_pt, 0)]
- while open_list:
- curr_pos, curr_cost = open_list[0]
- curr_x, curr_y = curr_pos
- for i in range(-1, 2):
- for j in range(-1, 2):
- x, y = curr_x + i, curr_y + j
- if self.obs_grid[(x, y)] == 'obs':
- continue
- if (i, j) in [(1, 0), (0, 1), (-1, 0), (0, -1)]:
- e_cost = 10
- else:
- e_cost = 14
- neighbor_energy = self.cost_field[(x, y)]
- neighbor_old_cost = self.integration_field[(x, y)]
- neighbor_new_cost = curr_cost + neighbor_energy + e_cost
- if neighbor_new_cost < neighbor_old_cost:
- self.integration_field[(x, y)] = neighbor_new_cost
- open_list.append(([x, y], neighbor_new_cost))
- del open_list[0]
-
- def assign_vectors(self):
- """For each node, assign a vector from itself to the node with
- the lowest cost in the integration field. An agent will simply
- follow this vector field to the goal"""
- for i in range(self.limit_x):
- for j in range(self.limit_y):
- if self.obs_grid[(i, j)] == 'obs':
- continue
- if [i, j] == self.goal_pt:
- self.vector_field[(i, j)] = (None, None)
- continue
- offset_list = [(i + a, j + b)
- for a in range(-1, 2)
- for b in range(-1, 2)]
- neighbor_list = [{'loc': pt,
- 'cost': self.integration_field[pt]}
- for pt in offset_list
- if self.obs_grid[pt] != 'obs']
- neighbor_list = sorted(neighbor_list, key=lambda x: x['cost'])
- best_neighbor = neighbor_list[0]['loc']
- self.vector_field[(i, j)] = best_neighbor
-
- def follow_vectors(self):
- curr_x, curr_y = self.start_pt
- while curr_x is not None and curr_y is not None:
- curr_x, curr_y = self.vector_field[(curr_x, curr_y)]
-
- if show_animation:
- plt.plot(curr_x, curr_y, "b*")
- plt.pause(0.001)
-
- if show_animation:
- plt.show()
-
-
-def main():
- # set obstacle positions
- obs_dict = {}
- for i in range(51):
- for j in range(51):
- obs_dict[(i, j)] = 'free'
- o_x, o_y, m_x, m_y, h_x, h_y = [], [], [], [], [], []
-
- s_x = 5.0
- s_y = 5.0
- g_x = 35.0
- g_y = 45.0
-
- # draw outer border of maze
- draw_vertical_line(0, 0, 50, o_x, o_y, obs_dict, 'obs')
- draw_vertical_line(48, 0, 50, o_x, o_y, obs_dict, 'obs')
- draw_horizontal_line(0, 0, 50, o_x, o_y, obs_dict, 'obs')
- draw_horizontal_line(0, 48, 50, o_x, o_y, obs_dict, 'obs')
-
- # draw inner walls
- all_x = [10, 10, 10, 15, 20, 20, 30, 30, 35, 30, 40, 45]
- all_y = [10, 30, 45, 20, 5, 40, 10, 40, 5, 40, 10, 25]
- all_len = [10, 10, 5, 10, 10, 5, 20, 10, 25, 10, 35, 15]
- for x, y, l in zip(all_x, all_y, all_len):
- draw_vertical_line(x, y, l, o_x, o_y, obs_dict, 'obs')
-
- all_x[:], all_y[:], all_len[:] = [], [], []
- all_x = [35, 40, 15, 10, 45, 20, 10, 15, 25, 45, 10, 30, 10, 40]
- all_y = [5, 10, 15, 20, 20, 25, 30, 35, 35, 35, 40, 40, 45, 45]
- all_len = [10, 5, 10, 10, 5, 5, 10, 5, 10, 5, 10, 5, 5, 5]
- for x, y, l in zip(all_x, all_y, all_len):
- draw_horizontal_line(x, y, l, o_x, o_y, obs_dict, 'obs')
-
- # Some points are assigned a slightly higher energy value in the cost
- # field. For example, if an agent wishes to go to a point, it might
- # encounter different kind of terrain like grass and dirt. Grass is
- # assigned medium difficulty of passage (color coded as green on the
- # map here). Dirt is assigned hard difficulty of passage (color coded
- # as brown here). Hence, this algorithm will take into account how
- # difficult it is to go through certain areas of a map when deciding
- # the shortest path.
-
- # draw paths that have medium difficulty (in terms of going through them)
- all_x[:], all_y[:], all_len[:] = [], [], []
- all_x = [10, 45]
- all_y = [22, 20]
- all_len = [8, 5]
- for x, y, l in zip(all_x, all_y, all_len):
- draw_vertical_line(x, y, l, m_x, m_y, obs_dict, 'medium')
-
- all_x[:], all_y[:], all_len[:] = [], [], []
- all_x = [20, 30, 42] + [47] * 5
- all_y = [35, 30, 38] + [37 + i for i in range(2)]
- all_len = [5, 7, 3] + [1] * 3
- for x, y, l in zip(all_x, all_y, all_len):
- draw_horizontal_line(x, y, l, m_x, m_y, obs_dict, 'medium')
-
- # draw paths that have hard difficulty (in terms of going through them)
- all_x[:], all_y[:], all_len[:] = [], [], []
- all_x = [15, 20, 35]
- all_y = [45, 20, 35]
- all_len = [3, 5, 7]
- for x, y, l in zip(all_x, all_y, all_len):
- draw_vertical_line(x, y, l, h_x, h_y, obs_dict, 'hard')
-
- all_x[:], all_y[:], all_len[:] = [], [], []
- all_x = [30] + [47] * 5
- all_y = [10] + [37 + i for i in range(2)]
- all_len = [5] + [1] * 3
- for x, y, l in zip(all_x, all_y, all_len):
- draw_horizontal_line(x, y, l, h_x, h_y, obs_dict, 'hard')
-
- if show_animation:
- plt.plot(o_x, o_y, "sr")
- plt.plot(m_x, m_y, "sg")
- plt.plot(h_x, h_y, "sy")
- plt.plot(s_x, s_y, "og")
- plt.plot(g_x, g_y, "o")
- plt.grid(True)
-
- flow_obj = FlowField(obs_dict, g_x, g_y, s_x, s_y, 50, 50)
- flow_obj.find_path()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/FrenetOptimalTrajectory/cartesian_frenet_converter.py b/PathPlanning/FrenetOptimalTrajectory/cartesian_frenet_converter.py
deleted file mode 100644
index 4cc8650c89a..00000000000
--- a/PathPlanning/FrenetOptimalTrajectory/cartesian_frenet_converter.py
+++ /dev/null
@@ -1,144 +0,0 @@
-"""
-
-A converter between Cartesian and Frenet coordinate systems
-
-author: Wang Zheng (@Aglargil)
-
-Ref:
-
-- [Optimal Trajectory Generation for Dynamic Street Scenarios in a Frenet Frame]
-(https://www.researchgate.net/profile/Moritz_Werling/publication/224156269_Optimal_Trajectory_Generation_for_Dynamic_Street_Scenarios_in_a_Frenet_Frame/links/54f749df0cf210398e9277af.pdf)
-
-"""
-
-import math
-
-
-class CartesianFrenetConverter:
- """
- A class for converting states between Cartesian and Frenet coordinate systems
- """
-
- @ staticmethod
- def cartesian_to_frenet(rs, rx, ry, rtheta, rkappa, rdkappa, x, y, v, a, theta, kappa):
- """
- Convert state from Cartesian coordinate to Frenet coordinate
-
- Parameters
- ----------
- rs: reference line s-coordinate
- rx, ry: reference point coordinates
- rtheta: reference point heading
- rkappa: reference point curvature
- rdkappa: reference point curvature rate
- x, y: current position
- v: velocity
- a: acceleration
- theta: heading angle
- kappa: curvature
-
- Returns
- -------
- s_condition: [s(t), s'(t), s''(t)]
- d_condition: [d(s), d'(s), d''(s)]
- """
- dx = x - rx
- dy = y - ry
-
- cos_theta_r = math.cos(rtheta)
- sin_theta_r = math.sin(rtheta)
-
- cross_rd_nd = cos_theta_r * dy - sin_theta_r * dx
- d = math.copysign(math.hypot(dx, dy), cross_rd_nd)
-
- delta_theta = theta - rtheta
- tan_delta_theta = math.tan(delta_theta)
- cos_delta_theta = math.cos(delta_theta)
-
- one_minus_kappa_r_d = 1 - rkappa * d
- d_dot = one_minus_kappa_r_d * tan_delta_theta
-
- kappa_r_d_prime = rdkappa * d + rkappa * d_dot
-
- d_ddot = (-kappa_r_d_prime * tan_delta_theta +
- one_minus_kappa_r_d / (cos_delta_theta * cos_delta_theta) *
- (kappa * one_minus_kappa_r_d / cos_delta_theta - rkappa))
-
- s = rs
- s_dot = v * cos_delta_theta / one_minus_kappa_r_d
-
- delta_theta_prime = one_minus_kappa_r_d / cos_delta_theta * kappa - rkappa
- s_ddot = (a * cos_delta_theta -
- s_dot * s_dot *
- (d_dot * delta_theta_prime - kappa_r_d_prime)) / one_minus_kappa_r_d
-
- return [s, s_dot, s_ddot], [d, d_dot, d_ddot]
-
- @ staticmethod
- def frenet_to_cartesian(rs, rx, ry, rtheta, rkappa, rdkappa, s_condition, d_condition):
- """
- Convert state from Frenet coordinate to Cartesian coordinate
-
- Parameters
- ----------
- rs: reference line s-coordinate
- rx, ry: reference point coordinates
- rtheta: reference point heading
- rkappa: reference point curvature
- rdkappa: reference point curvature rate
- s_condition: [s(t), s'(t), s''(t)]
- d_condition: [d(s), d'(s), d''(s)]
-
- Returns
- -------
- x, y: position
- theta: heading angle
- kappa: curvature
- v: velocity
- a: acceleration
- """
- if abs(rs - s_condition[0]) >= 1.0e-6:
- raise ValueError(
- "The reference point s and s_condition[0] don't match")
-
- cos_theta_r = math.cos(rtheta)
- sin_theta_r = math.sin(rtheta)
-
- x = rx - sin_theta_r * d_condition[0]
- y = ry + cos_theta_r * d_condition[0]
-
- one_minus_kappa_r_d = 1 - rkappa * d_condition[0]
-
- tan_delta_theta = d_condition[1] / one_minus_kappa_r_d
- delta_theta = math.atan2(d_condition[1], one_minus_kappa_r_d)
- cos_delta_theta = math.cos(delta_theta)
-
- theta = CartesianFrenetConverter.normalize_angle(delta_theta + rtheta)
-
- kappa_r_d_prime = rdkappa * d_condition[0] + rkappa * d_condition[1]
-
- kappa = (((d_condition[2] + kappa_r_d_prime * tan_delta_theta) *
- cos_delta_theta * cos_delta_theta) / one_minus_kappa_r_d + rkappa) * \
- cos_delta_theta / one_minus_kappa_r_d
-
- d_dot = d_condition[1] * s_condition[1]
- v = math.sqrt(one_minus_kappa_r_d * one_minus_kappa_r_d *
- s_condition[1] * s_condition[1] + d_dot * d_dot)
-
- delta_theta_prime = one_minus_kappa_r_d / cos_delta_theta * kappa - rkappa
-
- a = (s_condition[2] * one_minus_kappa_r_d / cos_delta_theta +
- s_condition[1] * s_condition[1] / cos_delta_theta *
- (d_condition[1] * delta_theta_prime - kappa_r_d_prime))
-
- return x, y, theta, kappa, v, a
-
- @ staticmethod
- def normalize_angle(angle):
- """
- Normalize angle to [-pi, pi]
- """
- a = math.fmod(angle + math.pi, 2.0 * math.pi)
- if a < 0.0:
- a += 2.0 * math.pi
- return a - math.pi
diff --git a/PathPlanning/FrenetOptimalTrajectory/frenet_optimal_trajectory.py b/PathPlanning/FrenetOptimalTrajectory/frenet_optimal_trajectory.py
deleted file mode 100644
index 248894c1c60..00000000000
--- a/PathPlanning/FrenetOptimalTrajectory/frenet_optimal_trajectory.py
+++ /dev/null
@@ -1,568 +0,0 @@
-"""
-
-Frenet optimal trajectory generator
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-Ref:
-
-- [Optimal Trajectory Generation for Dynamic Street Scenarios in a Frenet Frame]
-(https://www.researchgate.net/profile/Moritz_Werling/publication/224156269_Optimal_Trajectory_Generation_for_Dynamic_Street_Scenarios_in_a_Frenet_Frame/links/54f749df0cf210398e9277af.pdf)
-
-- [Optimal trajectory generation for dynamic street scenarios in a Frenet Frame]
-(https://www.youtube.com/watch?v=Cj6tAQe7UCY)
-
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-import copy
-import sys
-import pathlib
-
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from QuinticPolynomialsPlanner.quintic_polynomials_planner import QuinticPolynomial
-from CubicSpline import cubic_spline_planner
-
-from enum import Enum, auto
-from FrenetOptimalTrajectory.cartesian_frenet_converter import (
- CartesianFrenetConverter,
-)
-
-
-class LateralMovement(Enum):
- HIGH_SPEED = auto()
- LOW_SPEED = auto()
-
-
-class LongitudinalMovement(Enum):
- MERGING_AND_STOPPING = auto()
- VELOCITY_KEEPING = auto()
-
-
-# Default Parameters
-
-LATERAL_MOVEMENT = LateralMovement.HIGH_SPEED
-LONGITUDINAL_MOVEMENT = LongitudinalMovement.VELOCITY_KEEPING
-
-MAX_SPEED = 50.0 / 3.6 # maximum speed [m/s]
-MAX_ACCEL = 5.0 # maximum acceleration [m/ss]
-MAX_CURVATURE = 1.0 # maximum curvature [1/m]
-DT = 0.2 # time tick [s]
-MAX_T = 5.0 # max prediction time [m]
-MIN_T = 4.0 # min prediction time [m]
-N_S_SAMPLE = 1 # sampling number of target speed
-
-# cost weights
-K_J = 0.1
-K_T = 0.1
-K_S_DOT = 1.0
-K_D = 1.0
-K_S = 1.0
-K_LAT = 1.0
-K_LON = 1.0
-
-SIM_LOOP = 500
-show_animation = True
-
-
-if LATERAL_MOVEMENT == LateralMovement.LOW_SPEED:
- MAX_ROAD_WIDTH = 1.0 # maximum road width [m]
- D_ROAD_W = 0.2 # road width sampling length [m]
- TARGET_SPEED = 3.0 / 3.6 # maximum speed [m/s]
- D_T_S = 0.5 / 3.6 # target speed sampling length [m/s]
- # Waypoints
- WX = [0.0, 2.0, 4.0, 6.0, 8.0, 10.0]
- WY = [0.0, 0.0, 1.0, 0.0, -1.0, -2.0]
- OBSTACLES = np.array([[3.0, 1.0], [5.0, -0.0], [6.0, 0.5], [8.0, -1.5]])
- ROBOT_RADIUS = 0.5 # robot radius [m]
-
- # Initial state parameters
- INITIAL_SPEED = 1.0 / 3.6 # current speed [m/s]
- INITIAL_ACCEL = 0.0 # current acceleration [m/ss]
- INITIAL_LAT_POSITION = 0.5 # current lateral position [m]
- INITIAL_LAT_SPEED = 0.0 # current lateral speed [m/s]
- INITIAL_LAT_ACCELERATION = 0.0 # current lateral acceleration [m/s]
- INITIAL_COURSE_POSITION = 0.0 # current course position
-
- ANIMATION_AREA = 5.0 # Animation area length [m]
-
- STOP_S = 4.0 # Merge and stop distance [m]
- D_S = 0.3 # Stop point sampling length [m]
- N_STOP_S_SAMPLE = 3 # Stop point sampling number
-else:
- MAX_ROAD_WIDTH = 7.0 # maximum road width [m]
- D_ROAD_W = 1.0 # road width sampling length [m]
- TARGET_SPEED = 30.0 / 3.6 # target speed [m/s]
- D_T_S = 5.0 / 3.6 # target speed sampling length [m/s]
- # Waypoints
- WX = [0.0, 10.0, 20.5, 35.0, 70.5]
- WY = [0.0, -6.0, 5.0, 6.5, 0.0]
- # Obstacle list
- OBSTACLES = np.array(
- [[20.0, 10.0], [30.0, 6.0], [30.0, 8.0], [35.0, 8.0], [50.0, 3.0]]
- )
- ROBOT_RADIUS = 2.0 # robot radius [m]
-
- # Initial state parameters
- INITIAL_SPEED = 10.0 / 3.6 # current speed [m/s]
- INITIAL_ACCEL = 0.0 # current acceleration [m/ss]
- INITIAL_LAT_POSITION = 2.0 # current lateral position [m]
- INITIAL_LAT_SPEED = 0.0 # current lateral speed [m/s]
- INITIAL_LAT_ACCELERATION = 0.0 # current lateral acceleration [m/s]
- INITIAL_COURSE_POSITION = 0.0 # current course position
-
- ANIMATION_AREA = 20.0 # Animation area length [m]
- STOP_S = 25.0 # Merge and stop distance [m]
- D_S = 2 # Stop point sampling length [m]
- N_STOP_S_SAMPLE = 4 # Stop point sampling number
-
-
-class LateralMovementStrategy:
- def calc_lateral_trajectory(self, fp, di, c_d, c_d_d, c_d_dd, Ti):
- """
- Calculate the lateral trajectory
- """
- raise NotImplementedError("calc_lateral_trajectory not implemented")
-
- def calc_cartesian_parameters(self, fp, csp):
- """
- Calculate the cartesian parameters (x, y, yaw, curvature, v, a)
- """
- raise NotImplementedError("calc_cartesian_parameters not implemented")
-
-
-class HighSpeedLateralMovementStrategy(LateralMovementStrategy):
- def calc_lateral_trajectory(self, fp, di, c_d, c_d_d, c_d_dd, Ti):
- tp = copy.deepcopy(fp)
- s0_d = fp.s_d[0]
- s0_dd = fp.s_dd[0]
- # d'(t) = d'(s) * s'(t)
- # d''(t) = d''(s) * s'(t)^2 + d'(s) * s''(t)
- lat_qp = QuinticPolynomial(
- c_d, c_d_d * s0_d, c_d_dd * s0_d**2 + c_d_d * s0_dd, di, 0.0, 0.0, Ti
- )
-
- tp.d = []
- tp.d_d = []
- tp.d_dd = []
- tp.d_ddd = []
-
- # Calculate all derivatives in a single loop to reduce iterations
- for i in range(len(fp.t)):
- t = fp.t[i]
- s_d = fp.s_d[i]
- s_dd = fp.s_dd[i]
-
- s_d_inv = 1.0 / (s_d + 1e-6) + 1e-6 # Avoid division by zero
- s_d_inv_sq = s_d_inv * s_d_inv # Square of inverse
-
- d = lat_qp.calc_point(t)
- d_d = lat_qp.calc_first_derivative(t)
- d_dd = lat_qp.calc_second_derivative(t)
- d_ddd = lat_qp.calc_third_derivative(t)
-
- tp.d.append(d)
- # d'(s) = d'(t) / s'(t)
- tp.d_d.append(d_d * s_d_inv)
- # d''(s) = (d''(t) - d'(s) * s''(t)) / s'(t)^2
- tp.d_dd.append((d_dd - tp.d_d[i] * s_dd) * s_d_inv_sq)
- tp.d_ddd.append(d_ddd)
-
- return tp
-
- def calc_cartesian_parameters(self, fp, csp):
- # calc global positions
- for i in range(len(fp.s)):
- ix, iy = csp.calc_position(fp.s[i])
- if ix is None:
- break
- i_yaw = csp.calc_yaw(fp.s[i])
- i_kappa = csp.calc_curvature(fp.s[i])
- i_dkappa = csp.calc_curvature_rate(fp.s[i])
- s_condition = [fp.s[i], fp.s_d[i], fp.s_dd[i]]
- d_condition = [
- fp.d[i],
- fp.d_d[i],
- fp.d_dd[i],
- ]
- x, y, theta, kappa, v, a = CartesianFrenetConverter.frenet_to_cartesian(
- fp.s[i], ix, iy, i_yaw, i_kappa, i_dkappa, s_condition, d_condition
- )
- fp.x.append(x)
- fp.y.append(y)
- fp.yaw.append(theta)
- fp.c.append(kappa)
- fp.v.append(v)
- fp.a.append(a)
- return fp
-
-
-class LowSpeedLateralMovementStrategy(LateralMovementStrategy):
- def calc_lateral_trajectory(self, fp, di, c_d, c_d_d, c_d_dd, Ti):
- s0 = fp.s[0]
- s1 = fp.s[-1]
- tp = copy.deepcopy(fp)
- # d = d(s), d_d = d'(s), d_dd = d''(s)
- # * shift s range from [s0, s1] to [0, s1 - s0]
- lat_qp = QuinticPolynomial(c_d, c_d_d, c_d_dd, di, 0.0, 0.0, s1 - s0)
-
- tp.d = [lat_qp.calc_point(s - s0) for s in fp.s]
- tp.d_d = [lat_qp.calc_first_derivative(s - s0) for s in fp.s]
- tp.d_dd = [lat_qp.calc_second_derivative(s - s0) for s in fp.s]
- tp.d_ddd = [lat_qp.calc_third_derivative(s - s0) for s in fp.s]
- return tp
-
- def calc_cartesian_parameters(self, fp, csp):
- # calc global positions
- for i in range(len(fp.s)):
- ix, iy = csp.calc_position(fp.s[i])
- if ix is None:
- break
- i_yaw = csp.calc_yaw(fp.s[i])
- i_kappa = csp.calc_curvature(fp.s[i])
- i_dkappa = csp.calc_curvature_rate(fp.s[i])
- s_condition = [fp.s[i], fp.s_d[i], fp.s_dd[i]]
- d_condition = [fp.d[i], fp.d_d[i], fp.d_dd[i]]
- x, y, theta, kappa, v, a = CartesianFrenetConverter.frenet_to_cartesian(
- fp.s[i], ix, iy, i_yaw, i_kappa, i_dkappa, s_condition, d_condition
- )
- fp.x.append(x)
- fp.y.append(y)
- fp.yaw.append(theta)
- fp.c.append(kappa)
- fp.v.append(v)
- fp.a.append(a)
- return fp
-
-
-class LongitudinalMovementStrategy:
- def calc_longitudinal_trajectory(self, c_speed, c_accel, Ti, s0):
- """
- Calculate the longitudinal trajectory
- """
- raise NotImplementedError("calc_longitudinal_trajectory not implemented")
-
- def get_d_arrange(self, s0):
- """
- Get the d sample range
- """
- raise NotImplementedError("get_d_arrange not implemented")
-
- def calc_destination_cost(self, fp):
- """
- Calculate the destination cost
- """
- raise NotImplementedError("calc_destination_cost not implemented")
-
-
-class VelocityKeepingLongitudinalMovementStrategy(LongitudinalMovementStrategy):
- def calc_longitudinal_trajectory(self, c_speed, c_accel, Ti, s0):
- fplist = []
- for tv in np.arange(
- TARGET_SPEED - D_T_S * N_S_SAMPLE, TARGET_SPEED + D_T_S * N_S_SAMPLE, D_T_S
- ):
- fp = FrenetPath()
- lon_qp = QuarticPolynomial(s0, c_speed, c_accel, tv, 0.0, Ti)
- fp.t = [t for t in np.arange(0.0, Ti, DT)]
- fp.s = [lon_qp.calc_point(t) for t in fp.t]
- fp.s_d = [lon_qp.calc_first_derivative(t) for t in fp.t]
- fp.s_dd = [lon_qp.calc_second_derivative(t) for t in fp.t]
- fp.s_ddd = [lon_qp.calc_third_derivative(t) for t in fp.t]
- fplist.append(fp)
- return fplist
-
- def get_d_arrange(self, s0):
- return np.arange(-MAX_ROAD_WIDTH, MAX_ROAD_WIDTH, D_ROAD_W)
-
- def calc_destination_cost(self, fp):
- ds = (TARGET_SPEED - fp.s_d[-1]) ** 2
- return K_S_DOT * ds
-
-
-class MergingAndStoppingLongitudinalMovementStrategy(LongitudinalMovementStrategy):
- def calc_longitudinal_trajectory(self, c_speed, c_accel, Ti, s0):
- if s0 >= STOP_S:
- return []
- fplist = []
- for s in np.arange(
- STOP_S - D_S * N_STOP_S_SAMPLE, STOP_S + D_S * N_STOP_S_SAMPLE, D_S
- ):
- fp = FrenetPath()
- lon_qp = QuinticPolynomial(s0, c_speed, c_accel, s, 0.0, 0.0, Ti)
- fp.t = [t for t in np.arange(0.0, Ti, DT)]
- fp.s = [lon_qp.calc_point(t) for t in fp.t]
- fp.s_d = [lon_qp.calc_first_derivative(t) for t in fp.t]
- fp.s_dd = [lon_qp.calc_second_derivative(t) for t in fp.t]
- fp.s_ddd = [lon_qp.calc_third_derivative(t) for t in fp.t]
- fplist.append(fp)
- return fplist
-
- def get_d_arrange(self, s0):
- # Only if s0 is less than STOP_S / 3, then we sample the road width
- if s0 < STOP_S / 3:
- return np.arange(-MAX_ROAD_WIDTH, MAX_ROAD_WIDTH, D_ROAD_W)
- else:
- return [0.0]
-
- def calc_destination_cost(self, fp):
- ds = (STOP_S - fp.s[-1]) ** 2
- return K_S * ds
-
-LATERAL_MOVEMENT_STRATEGY: LateralMovementStrategy
-LONGITUDINAL_MOVEMENT_STRATEGY: LongitudinalMovementStrategy
-
-if LATERAL_MOVEMENT == LateralMovement.HIGH_SPEED:
- LATERAL_MOVEMENT_STRATEGY = HighSpeedLateralMovementStrategy()
-else:
- LATERAL_MOVEMENT_STRATEGY = LowSpeedLateralMovementStrategy()
-
-if LONGITUDINAL_MOVEMENT == LongitudinalMovement.VELOCITY_KEEPING:
- LONGITUDINAL_MOVEMENT_STRATEGY = VelocityKeepingLongitudinalMovementStrategy()
-else:
- LONGITUDINAL_MOVEMENT_STRATEGY = MergingAndStoppingLongitudinalMovementStrategy()
-
-
-class QuarticPolynomial:
- def __init__(self, xs, vxs, axs, vxe, axe, time):
- # calc coefficient of quartic polynomial
-
- self.a0 = xs
- self.a1 = vxs
- self.a2 = axs / 2.0
-
- A = np.array([[3 * time**2, 4 * time**3], [6 * time, 12 * time**2]])
- b = np.array([vxe - self.a1 - 2 * self.a2 * time, axe - 2 * self.a2])
- x = np.linalg.solve(A, b)
-
- self.a3 = x[0]
- self.a4 = x[1]
-
- def calc_point(self, t):
- xt = self.a0 + self.a1 * t + self.a2 * t**2 + self.a3 * t**3 + self.a4 * t**4
-
- return xt
-
- def calc_first_derivative(self, t):
- xt = self.a1 + 2 * self.a2 * t + 3 * self.a3 * t**2 + 4 * self.a4 * t**3
-
- return xt
-
- def calc_second_derivative(self, t):
- xt = 2 * self.a2 + 6 * self.a3 * t + 12 * self.a4 * t**2
-
- return xt
-
- def calc_third_derivative(self, t):
- xt = 6 * self.a3 + 24 * self.a4 * t
-
- return xt
-
-
-class FrenetPath:
- def __init__(self):
- self.t = []
- self.d = []
- self.d_d = [] # d'(s)
- self.d_dd = [] # d''(s)
- self.d_ddd = [] # d'''(t) in low speed / d'''(s) in high speed
- self.s = []
- self.s_d = [] # s'(t)
- self.s_dd = [] # s''(t)
- self.s_ddd = [] # s'''(t)
- self.cf = 0.0
-
- self.x = []
- self.y = []
- self.yaw = []
- self.v = []
- self.a = []
- self.ds = []
- self.c = []
-
- def pop_front(self):
- self.x.pop(0)
- self.y.pop(0)
- self.yaw.pop(0)
- self.v.pop(0)
- self.a.pop(0)
- self.s.pop(0)
- self.s_d.pop(0)
- self.s_dd.pop(0)
- self.s_ddd.pop(0)
- self.d.pop(0)
- self.d_d.pop(0)
- self.d_dd.pop(0)
- self.d_ddd.pop(0)
-
-
-def calc_frenet_paths(c_s_d, c_s_dd, c_d, c_d_d, c_d_dd, s0):
- frenet_paths = []
-
- for Ti in np.arange(MIN_T, MAX_T, DT):
- lon_paths = LONGITUDINAL_MOVEMENT_STRATEGY.calc_longitudinal_trajectory(
- c_s_d, c_s_dd, Ti, s0
- )
-
- for fp in lon_paths:
- for di in LONGITUDINAL_MOVEMENT_STRATEGY.get_d_arrange(s0):
- tp = LATERAL_MOVEMENT_STRATEGY.calc_lateral_trajectory(
- fp, di, c_d, c_d_d, c_d_dd, Ti
- )
-
- Jp = sum(np.power(tp.d_ddd, 2)) # square of jerk
- Js = sum(np.power(tp.s_ddd, 2)) # square of jerk
-
- lat_cost = K_J * Jp + K_T * Ti + K_D * tp.d[-1] ** 2
- lon_cost = (
- K_J * Js
- + K_T * Ti
- + LONGITUDINAL_MOVEMENT_STRATEGY.calc_destination_cost(tp)
- )
- tp.cf = K_LAT * lat_cost + K_LON * lon_cost
- frenet_paths.append(tp)
-
- return frenet_paths
-
-
-def calc_global_paths(fplist, csp):
- return [
- LATERAL_MOVEMENT_STRATEGY.calc_cartesian_parameters(fp, csp) for fp in fplist
- ]
-
-
-def check_collision(fp, ob):
- for i in range(len(ob[:, 0])):
- d = [
- ((ix - ob[i, 0]) ** 2 + (iy - ob[i, 1]) ** 2)
- for (ix, iy) in zip(fp.x, fp.y)
- ]
-
- collision = any([di <= ROBOT_RADIUS**2 for di in d])
-
- if collision:
- return False
-
- return True
-
-
-def check_paths(fplist, ob):
- path_dict = {
- "max_speed_error": [],
- "max_accel_error": [],
- "max_curvature_error": [],
- "collision_error": [],
- "ok": [],
- }
- for i, _ in enumerate(fplist):
- if any([v > MAX_SPEED for v in fplist[i].v]): # Max speed check
- path_dict["max_speed_error"].append(fplist[i])
- elif any([abs(a) > MAX_ACCEL for a in fplist[i].a]): # Max accel check
- path_dict["max_accel_error"].append(fplist[i])
- elif any([abs(c) > MAX_CURVATURE for c in fplist[i].c]): # Max curvature check
- path_dict["max_curvature_error"].append(fplist[i])
- elif not check_collision(fplist[i], ob):
- path_dict["collision_error"].append(fplist[i])
- else:
- path_dict["ok"].append(fplist[i])
- return path_dict
-
-
-def frenet_optimal_planning(csp, s0, c_s_d, c_s_dd, c_d, c_d_d, c_d_dd, ob):
- fplist = calc_frenet_paths(c_s_d, c_s_dd, c_d, c_d_d, c_d_dd, s0)
- fplist = calc_global_paths(fplist, csp)
- fpdict = check_paths(fplist, ob)
-
- # find minimum cost path
- min_cost = float("inf")
- best_path = None
- for fp in fpdict["ok"]:
- if min_cost >= fp.cf:
- min_cost = fp.cf
- best_path = fp
-
- return [best_path, fpdict]
-
-
-def generate_target_course(x, y):
- csp = cubic_spline_planner.CubicSpline2D(x, y)
- s = np.arange(0, csp.s[-1], 0.1)
-
- rx, ry, ryaw, rk = [], [], [], []
- for i_s in s:
- ix, iy = csp.calc_position(i_s)
- rx.append(ix)
- ry.append(iy)
- ryaw.append(csp.calc_yaw(i_s))
- rk.append(csp.calc_curvature(i_s))
-
- return rx, ry, ryaw, rk, csp
-
-
-def main():
- print(__file__ + " start!!")
-
- tx, ty, tyaw, tc, csp = generate_target_course(WX, WY)
-
- # Initialize state using global parameters
- c_s_d = INITIAL_SPEED
- c_s_dd = INITIAL_ACCEL
- c_d = INITIAL_LAT_POSITION
- c_d_d = INITIAL_LAT_SPEED
- c_d_dd = INITIAL_LAT_ACCELERATION
- s0 = INITIAL_COURSE_POSITION
-
- area = ANIMATION_AREA
-
- last_path = None
-
- for i in range(SIM_LOOP):
- [path, fpdict] = frenet_optimal_planning(
- csp, s0, c_s_d, c_s_dd, c_d, c_d_d, c_d_dd, OBSTACLES
- )
-
- if path is None:
- path = copy.deepcopy(last_path)
- path.pop_front()
- if len(path.x) <= 1:
- print("Finish")
- break
-
- last_path = path
- s0 = path.s[1]
- c_d = path.d[1]
- c_d_d = path.d_d[1]
- c_d_dd = path.d_dd[1]
- c_s_d = path.s_d[1]
- c_s_dd = path.s_dd[1]
- if np.hypot(path.x[1] - tx[-1], path.y[1] - ty[-1]) <= 1.0:
- print("Goal")
- break
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- "key_release_event",
- lambda event: [exit(0) if event.key == "escape" else None],
- )
- plt.plot(tx, ty)
- plt.plot(OBSTACLES[:, 0], OBSTACLES[:, 1], "xk")
- plt.plot(path.x[1:], path.y[1:], "-or")
- plt.plot(path.x[1], path.y[1], "vc")
- plt.xlim(path.x[1] - area, path.x[1] + area)
- plt.ylim(path.y[1] - area, path.y[1] + area)
- plt.title("v[km/h]:" + str(path.v[1] * 3.6)[0:4])
- plt.grid(True)
- plt.pause(0.0001)
-
- print("Finish")
- if show_animation: # pragma: no cover
- plt.grid(True)
- plt.pause(0.0001)
- plt.show()
-
-
-if __name__ == "__main__":
- main()
diff --git a/PathPlanning/GreedyBestFirstSearch/greedy_best_first_search.py b/PathPlanning/GreedyBestFirstSearch/greedy_best_first_search.py
deleted file mode 100644
index b259beb8700..00000000000
--- a/PathPlanning/GreedyBestFirstSearch/greedy_best_first_search.py
+++ /dev/null
@@ -1,278 +0,0 @@
-"""
-
-Greedy Best-First grid planning
-
-author: Erwin Lejeune (@spida_rwin)
-
-See Wikipedia article (https://en.wikipedia.org/wiki/Best-first_search)
-
-"""
-
-import math
-
-import matplotlib.pyplot as plt
-
-show_animation = True
-
-
-class BestFirstSearchPlanner:
-
- def __init__(self, ox, oy, reso, rr):
- """
- Initialize grid map for greedy best-first planning
-
- ox: x position list of Obstacles [m]
- oy: y position list of Obstacles [m]
- resolution: grid resolution [m]
- rr: robot radius[m]
- """
-
- self.reso = reso
- self.rr = rr
- self.calc_obstacle_map(ox, oy)
- self.motion = self.get_motion_model()
-
- class Node:
- def __init__(self, x, y, cost, pind, parent):
- self.x = x # index of grid
- self.y = y # index of grid
- self.cost = cost
- self.pind = pind
- self.parent = parent
-
- def __str__(self):
- return str(self.x) + "," + str(self.y) + "," + str(
- self.cost) + "," + str(self.pind)
-
- def planning(self, sx, sy, gx, gy):
- """
- Greedy Best-First search
-
- input:
- s_x: start x position [m]
- s_y: start y position [m]
- gx: goal x position [m]
- gy: goal y position [m]
-
- output:
- rx: x position list of the final path
- ry: y position list of the final path
- """
-
- nstart = self.Node(self.calc_xyindex(sx, self.minx),
- self.calc_xyindex(sy, self.miny), 0.0, -1, None)
- ngoal = self.Node(self.calc_xyindex(gx, self.minx),
- self.calc_xyindex(gy, self.miny), 0.0, -1, None)
-
- open_set, closed_set = dict(), dict()
- open_set[self.calc_grid_index(nstart)] = nstart
-
- while True:
- if len(open_set) == 0:
- print("Open set is empty..")
- break
-
- c_id = min(
- open_set,
- key=lambda o: self.calc_heuristic(ngoal, open_set[o]))
-
- current = open_set[c_id]
-
- # show graph
- if show_animation: # pragma: no cover
- plt.plot(self.calc_grid_position(current.x, self.minx),
- self.calc_grid_position(current.y, self.miny), "xc")
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event:
- [exit(0)
- if event.key == 'escape'
- else None])
- if len(closed_set.keys()) % 10 == 0:
- plt.pause(0.001)
-
- # Remove the item from the open set
- del open_set[c_id]
-
- # Add it to the closed set
- closed_set[c_id] = current
-
- if current.x == ngoal.x and current.y == ngoal.y:
- print("Found goal")
- ngoal.pind = current.pind
- ngoal.cost = current.cost
- break
-
- # expand_grid search grid based on motion model
- for i, _ in enumerate(self.motion):
- node = self.Node(current.x + self.motion[i][0],
- current.y + self.motion[i][1],
- current.cost + self.motion[i][2],
- c_id, current)
-
- n_id = self.calc_grid_index(node)
-
- # If the node is not safe, do nothing
- if not self.verify_node(node):
- continue
-
- if n_id in closed_set:
- continue
-
- if n_id not in open_set:
- open_set[n_id] = node
- else:
- if open_set[n_id].cost > node.cost:
- open_set[n_id] = node
- closed_set[ngoal.pind] = current
- rx, ry = self.calc_final_path(ngoal, closed_set)
- return rx, ry
-
- def calc_final_path(self, ngoal, closedset):
- # generate final course
- rx, ry = [self.calc_grid_position(ngoal.x, self.minx)], [
- self.calc_grid_position(ngoal.y, self.miny)]
- n = closedset[ngoal.pind]
- while n is not None:
- rx.append(self.calc_grid_position(n.x, self.minx))
- ry.append(self.calc_grid_position(n.y, self.miny))
- n = n.parent
-
- return rx, ry
-
- @staticmethod
- def calc_heuristic(n1, n2):
- w = 1.0 # weight of heuristic
- d = w * math.hypot(n1.x - n2.x, n1.y - n2.y)
- return d
-
- def calc_grid_position(self, index, minp):
- """
- calc grid position
-
- :param index:
- :param minp:
- :return:
- """
- pos = index * self.reso + minp
- return pos
-
- def calc_xyindex(self, position, min_pos):
- return round((position - min_pos) / self.reso)
-
- def calc_grid_index(self, node):
- return (node.y - self.miny) * self.xwidth + (node.x - self.minx)
-
- def verify_node(self, node):
- px = self.calc_grid_position(node.x, self.minx)
- py = self.calc_grid_position(node.y, self.miny)
-
- if px < self.minx:
- return False
- elif py < self.miny:
- return False
- elif px >= self.maxx:
- return False
- elif py >= self.maxy:
- return False
-
- # collision check
- if self.obmap[node.x][node.y]:
- return False
-
- return True
-
- def calc_obstacle_map(self, ox, oy):
-
- self.minx = round(min(ox))
- self.miny = round(min(oy))
- self.maxx = round(max(ox))
- self.maxy = round(max(oy))
- print("min_x:", self.minx)
- print("min_y:", self.miny)
- print("max_x:", self.maxx)
- print("max_y:", self.maxy)
-
- self.xwidth = round((self.maxx - self.minx) / self.reso)
- self.ywidth = round((self.maxy - self.miny) / self.reso)
- print("x_width:", self.xwidth)
- print("y_width:", self.ywidth)
-
- # obstacle map generation
- self.obmap = [[False for _ in range(self.ywidth)]
- for _ in range(self.xwidth)]
- for ix in range(self.xwidth):
- x = self.calc_grid_position(ix, self.minx)
- for iy in range(self.ywidth):
- y = self.calc_grid_position(iy, self.miny)
- for iox, ioy in zip(ox, oy):
- d = math.hypot(iox - x, ioy - y)
- if d <= self.rr:
- self.obmap[ix][iy] = True
- break
-
- @staticmethod
- def get_motion_model():
- # dx, dy, cost
- motion = [[1, 0, 1],
- [0, 1, 1],
- [-1, 0, 1],
- [0, -1, 1],
- [-1, -1, math.sqrt(2)],
- [-1, 1, math.sqrt(2)],
- [1, -1, math.sqrt(2)],
- [1, 1, math.sqrt(2)]]
-
- return motion
-
-
-def main():
- print(__file__ + " start!!")
-
- # start and goal position
- sx = 10.0 # [m]
- sy = 10.0 # [m]
- gx = 50.0 # [m]
- gy = 50.0 # [m]
- grid_size = 2.0 # [m]
- robot_radius = 1.0 # [m]
-
- # set obstacle positions
- ox, oy = [], []
- for i in range(-10, 60):
- ox.append(i)
- oy.append(-10.0)
- for i in range(-10, 60):
- ox.append(60.0)
- oy.append(i)
- for i in range(-10, 61):
- ox.append(i)
- oy.append(60.0)
- for i in range(-10, 61):
- ox.append(-10.0)
- oy.append(i)
- for i in range(-10, 40):
- ox.append(20.0)
- oy.append(i)
- for i in range(0, 40):
- ox.append(40.0)
- oy.append(60.0 - i)
-
- if show_animation: # pragma: no cover
- plt.plot(ox, oy, ".k")
- plt.plot(sx, sy, "og")
- plt.plot(gx, gy, "xb")
- plt.grid(True)
- plt.axis("equal")
-
- greedybestfirst = BestFirstSearchPlanner(ox, oy, grid_size, robot_radius)
- rx, ry = greedybestfirst.planning(sx, sy, gx, gy)
-
- if show_animation: # pragma: no cover
- plt.plot(rx, ry, "-r")
- plt.pause(0.01)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/GridBasedSweepCPP/grid_based_sweep_coverage_path_planner.py b/PathPlanning/GridBasedSweepCPP/grid_based_sweep_coverage_path_planner.py
deleted file mode 100644
index 10ba98cd352..00000000000
--- a/PathPlanning/GridBasedSweepCPP/grid_based_sweep_coverage_path_planner.py
+++ /dev/null
@@ -1,321 +0,0 @@
-"""
-Grid based sweep planner
-
-author: Atsushi Sakai
-"""
-
-import math
-from enum import IntEnum
-import numpy as np
-import matplotlib.pyplot as plt
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-from utils.angle import rot_mat_2d
-from Mapping.grid_map_lib.grid_map_lib import GridMap, FloatGrid
-
-do_animation = True
-
-
-class SweepSearcher:
- class SweepDirection(IntEnum):
- UP = 1
- DOWN = -1
-
- class MovingDirection(IntEnum):
- RIGHT = 1
- LEFT = -1
-
- def __init__(self,
- moving_direction, sweep_direction, x_inds_goal_y, goal_y):
- self.moving_direction = moving_direction
- self.sweep_direction = sweep_direction
- self.turing_window = []
- self.update_turning_window()
- self.x_indexes_goal_y = x_inds_goal_y
- self.goal_y = goal_y
-
- def move_target_grid(self, c_x_index, c_y_index, grid_map):
- n_x_index = self.moving_direction + c_x_index
- n_y_index = c_y_index
-
- # found safe grid
- if not self.check_occupied(n_x_index, n_y_index, grid_map):
- return n_x_index, n_y_index
- else: # occupied
- next_c_x_index, next_c_y_index = self.find_safe_turning_grid(
- c_x_index, c_y_index, grid_map)
- if (next_c_x_index is None) and (next_c_y_index is None):
- # moving backward
- next_c_x_index = -self.moving_direction + c_x_index
- next_c_y_index = c_y_index
- if self.check_occupied(next_c_x_index, next_c_y_index, grid_map, FloatGrid(1.0)):
- # moved backward, but the grid is occupied by obstacle
- return None, None
- else:
- # keep moving until end
- while not self.check_occupied(next_c_x_index + self.moving_direction, next_c_y_index, grid_map):
- next_c_x_index += self.moving_direction
- self.swap_moving_direction()
- return next_c_x_index, next_c_y_index
-
- @staticmethod
- def check_occupied(c_x_index, c_y_index, grid_map, occupied_val=FloatGrid(0.5)):
- return grid_map.check_occupied_from_xy_index(c_x_index, c_y_index, occupied_val)
-
- def find_safe_turning_grid(self, c_x_index, c_y_index, grid_map):
-
- for (d_x_ind, d_y_ind) in self.turing_window:
-
- next_x_ind = d_x_ind + c_x_index
- next_y_ind = d_y_ind + c_y_index
-
- # found safe grid
- if not self.check_occupied(next_x_ind, next_y_ind, grid_map):
- return next_x_ind, next_y_ind
-
- return None, None
-
- def is_search_done(self, grid_map):
- for ix in self.x_indexes_goal_y:
- if not self.check_occupied(ix, self.goal_y, grid_map):
- return False
-
- # all lower grid is occupied
- return True
-
- def update_turning_window(self):
- # turning window definition
- # robot can move grid based on it.
- self.turing_window = [
- (self.moving_direction, 0.0),
- (self.moving_direction, self.sweep_direction),
- (0, self.sweep_direction),
- (-self.moving_direction, self.sweep_direction),
- ]
-
- def swap_moving_direction(self):
- self.moving_direction *= -1
- self.update_turning_window()
-
- def search_start_grid(self, grid_map):
- x_inds = []
- y_ind = 0
- if self.sweep_direction == self.SweepDirection.DOWN:
- x_inds, y_ind = search_free_grid_index_at_edge_y(
- grid_map, from_upper=True)
- elif self.sweep_direction == self.SweepDirection.UP:
- x_inds, y_ind = search_free_grid_index_at_edge_y(
- grid_map, from_upper=False)
-
- if self.moving_direction == self.MovingDirection.RIGHT:
- return min(x_inds), y_ind
- elif self.moving_direction == self.MovingDirection.LEFT:
- return max(x_inds), y_ind
-
- raise ValueError("self.moving direction is invalid ")
-
-
-def find_sweep_direction_and_start_position(ox, oy):
- # find sweep_direction
- max_dist = 0.0
- vec = [0.0, 0.0]
- sweep_start_pos = [0.0, 0.0]
- for i in range(len(ox) - 1):
- dx = ox[i + 1] - ox[i]
- dy = oy[i + 1] - oy[i]
- d = np.hypot(dx, dy)
-
- if d > max_dist:
- max_dist = d
- vec = [dx, dy]
- sweep_start_pos = [ox[i], oy[i]]
-
- return vec, sweep_start_pos
-
-
-def convert_grid_coordinate(ox, oy, sweep_vec, sweep_start_position):
- tx = [ix - sweep_start_position[0] for ix in ox]
- ty = [iy - sweep_start_position[1] for iy in oy]
- th = math.atan2(sweep_vec[1], sweep_vec[0])
- converted_xy = np.stack([tx, ty]).T @ rot_mat_2d(th)
-
- return converted_xy[:, 0], converted_xy[:, 1]
-
-
-def convert_global_coordinate(x, y, sweep_vec, sweep_start_position):
- th = math.atan2(sweep_vec[1], sweep_vec[0])
- converted_xy = np.stack([x, y]).T @ rot_mat_2d(-th)
- rx = [ix + sweep_start_position[0] for ix in converted_xy[:, 0]]
- ry = [iy + sweep_start_position[1] for iy in converted_xy[:, 1]]
- return rx, ry
-
-
-def search_free_grid_index_at_edge_y(grid_map, from_upper=False):
- y_index = None
- x_indexes = []
-
- if from_upper:
- x_range = range(grid_map.height)[::-1]
- y_range = range(grid_map.width)[::-1]
- else:
- x_range = range(grid_map.height)
- y_range = range(grid_map.width)
-
- for iy in x_range:
- for ix in y_range:
- if not SweepSearcher.check_occupied(ix, iy, grid_map):
- y_index = iy
- x_indexes.append(ix)
- if y_index:
- break
-
- return x_indexes, y_index
-
-
-def setup_grid_map(ox, oy, resolution, sweep_direction, offset_grid=10):
- width = math.ceil((max(ox) - min(ox)) / resolution) + offset_grid
- height = math.ceil((max(oy) - min(oy)) / resolution) + offset_grid
- center_x = (np.max(ox) + np.min(ox)) / 2.0
- center_y = (np.max(oy) + np.min(oy)) / 2.0
-
- grid_map = GridMap(width, height, resolution, center_x, center_y)
- grid_map.print_grid_map_info()
- grid_map.set_value_from_polygon(ox, oy, FloatGrid(1.0), inside=False)
- grid_map.expand_grid()
-
- x_inds_goal_y = []
- goal_y = 0
- if sweep_direction == SweepSearcher.SweepDirection.UP:
- x_inds_goal_y, goal_y = search_free_grid_index_at_edge_y(
- grid_map, from_upper=True)
- elif sweep_direction == SweepSearcher.SweepDirection.DOWN:
- x_inds_goal_y, goal_y = search_free_grid_index_at_edge_y(
- grid_map, from_upper=False)
-
- return grid_map, x_inds_goal_y, goal_y
-
-
-def sweep_path_search(sweep_searcher, grid_map, grid_search_animation=False):
- # search start grid
- c_x_index, c_y_index = sweep_searcher.search_start_grid(grid_map)
- if not grid_map.set_value_from_xy_index(c_x_index, c_y_index, FloatGrid(0.5)):
- print("Cannot find start grid")
- return [], []
-
- x, y = grid_map.calc_grid_central_xy_position_from_xy_index(c_x_index,
- c_y_index)
- px, py = [x], [y]
-
- fig, ax = None, None
- if grid_search_animation:
- fig, ax = plt.subplots()
- # for stopping simulation with the esc key.
- fig.canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
-
- while True:
- c_x_index, c_y_index = sweep_searcher.move_target_grid(c_x_index,
- c_y_index,
- grid_map)
-
- if sweep_searcher.is_search_done(grid_map) or (
- c_x_index is None or c_y_index is None):
- print("Done")
- break
-
- x, y = grid_map.calc_grid_central_xy_position_from_xy_index(
- c_x_index, c_y_index)
-
- px.append(x)
- py.append(y)
-
- grid_map.set_value_from_xy_index(c_x_index, c_y_index, FloatGrid(0.5))
-
- if grid_search_animation:
- grid_map.plot_grid_map(ax=ax)
- plt.pause(1.0)
-
- return px, py
-
-
-def planning(ox, oy, resolution,
- moving_direction=SweepSearcher.MovingDirection.RIGHT,
- sweeping_direction=SweepSearcher.SweepDirection.UP,
- ):
- sweep_vec, sweep_start_position = find_sweep_direction_and_start_position(
- ox, oy)
-
- rox, roy = convert_grid_coordinate(ox, oy, sweep_vec,
- sweep_start_position)
-
- grid_map, x_inds_goal_y, goal_y = setup_grid_map(rox, roy, resolution,
- sweeping_direction)
-
- sweep_searcher = SweepSearcher(moving_direction, sweeping_direction,
- x_inds_goal_y, goal_y)
-
- px, py = sweep_path_search(sweep_searcher, grid_map)
-
- rx, ry = convert_global_coordinate(px, py, sweep_vec,
- sweep_start_position)
-
- print("Path length:", len(rx))
-
- return rx, ry
-
-
-def planning_animation(ox, oy, resolution): # pragma: no cover
- px, py = planning(ox, oy, resolution)
-
- # animation
- if do_animation:
- for ipx, ipy in zip(px, py):
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(ox, oy, "-xb")
- plt.plot(px, py, "-r")
- plt.plot(ipx, ipy, "or")
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.1)
-
- plt.cla()
- plt.plot(ox, oy, "-xb")
- plt.plot(px, py, "-r")
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.1)
- plt.close()
-
-
-def main(): # pragma: no cover
- print("start!!")
-
- ox = [0.0, 20.0, 50.0, 100.0, 130.0, 40.0, 0.0]
- oy = [0.0, -20.0, 0.0, 30.0, 60.0, 80.0, 0.0]
- resolution = 5.0
- planning_animation(ox, oy, resolution)
-
- ox = [0.0, 50.0, 50.0, 0.0, 0.0]
- oy = [0.0, 0.0, 30.0, 30.0, 0.0]
- resolution = 1.3
- planning_animation(ox, oy, resolution)
-
- ox = [0.0, 20.0, 50.0, 200.0, 130.0, 40.0, 0.0]
- oy = [0.0, -80.0, 0.0, 30.0, 60.0, 80.0, 0.0]
- resolution = 5.0
- planning_animation(ox, oy, resolution)
-
- if do_animation:
- plt.show()
- print("done!!")
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/HybridAStar/__init__.py b/PathPlanning/HybridAStar/__init__.py
deleted file mode 100644
index 087dab646e1..00000000000
--- a/PathPlanning/HybridAStar/__init__.py
+++ /dev/null
@@ -1,4 +0,0 @@
-import os
-import sys
-
-sys.path.append(os.path.dirname(os.path.abspath(__file__)))
diff --git a/PathPlanning/HybridAStar/car.py b/PathPlanning/HybridAStar/car.py
deleted file mode 100644
index 959db740784..00000000000
--- a/PathPlanning/HybridAStar/car.py
+++ /dev/null
@@ -1,113 +0,0 @@
-"""
-
-Car model for Hybrid A* path planning
-
-author: Zheng Zh (@Zhengzh)
-
-"""
-
-import sys
-import pathlib
-root_dir = pathlib.Path(__file__).parent.parent.parent
-sys.path.append(str(root_dir))
-
-from math import cos, sin, tan, pi
-
-import matplotlib.pyplot as plt
-import numpy as np
-
-from utils.angle import rot_mat_2d
-
-WB = 3.0 # rear to front wheel
-W = 2.0 # width of car
-LF = 3.3 # distance from rear to vehicle front end
-LB = 1.0 # distance from rear to vehicle back end
-MAX_STEER = 0.6 # [rad] maximum steering angle
-
-BUBBLE_DIST = (LF - LB) / 2.0 # distance from rear to center of vehicle.
-BUBBLE_R = np.hypot((LF + LB) / 2.0, W / 2.0) # bubble radius
-
-# vehicle rectangle vertices
-VRX = [LF, LF, -LB, -LB, LF]
-VRY = [W / 2, -W / 2, -W / 2, W / 2, W / 2]
-
-
-def check_car_collision(x_list, y_list, yaw_list, ox, oy, kd_tree):
- for i_x, i_y, i_yaw in zip(x_list, y_list, yaw_list):
- cx = i_x + BUBBLE_DIST * cos(i_yaw)
- cy = i_y + BUBBLE_DIST * sin(i_yaw)
-
- ids = kd_tree.query_ball_point([cx, cy], BUBBLE_R)
-
- if not ids:
- continue
-
- if not rectangle_check(i_x, i_y, i_yaw,
- [ox[i] for i in ids], [oy[i] for i in ids]):
- return False # collision
-
- return True # no collision
-
-
-def rectangle_check(x, y, yaw, ox, oy):
- # transform obstacles to base link frame
- rot = rot_mat_2d(yaw)
- for iox, ioy in zip(ox, oy):
- tx = iox - x
- ty = ioy - y
- converted_xy = np.stack([tx, ty]).T @ rot
- rx, ry = converted_xy[0], converted_xy[1]
-
- if not (rx > LF or rx < -LB or ry > W / 2.0 or ry < -W / 2.0):
- return False # collision
-
- return True # no collision
-
-
-def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"):
- """Plot arrow."""
- if not isinstance(x, float):
- for (i_x, i_y, i_yaw) in zip(x, y, yaw):
- plot_arrow(i_x, i_y, i_yaw)
- else:
- plt.arrow(x, y, length * cos(yaw), length * sin(yaw),
- fc=fc, ec=ec, head_width=width, head_length=width, alpha=0.4)
-
-
-def plot_car(x, y, yaw):
- car_color = '-k'
- c, s = cos(yaw), sin(yaw)
- rot = rot_mat_2d(-yaw)
- car_outline_x, car_outline_y = [], []
- for rx, ry in zip(VRX, VRY):
- converted_xy = np.stack([rx, ry]).T @ rot
- car_outline_x.append(converted_xy[0]+x)
- car_outline_y.append(converted_xy[1]+y)
-
- arrow_x, arrow_y, arrow_yaw = c * 1.5 + x, s * 1.5 + y, yaw
- plot_arrow(arrow_x, arrow_y, arrow_yaw)
-
- plt.plot(car_outline_x, car_outline_y, car_color)
-
-
-def pi_2_pi(angle):
- return (angle + pi) % (2 * pi) - pi
-
-
-def move(x, y, yaw, distance, steer, L=WB):
- x += distance * cos(yaw)
- y += distance * sin(yaw)
- yaw = pi_2_pi(yaw + distance * tan(steer) / L) # distance/2
-
- return x, y, yaw
-
-
-def main():
- x, y, yaw = 0., 0., 1.
- plt.axis('equal')
- plot_car(x, y, yaw)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/HybridAStar/dynamic_programming_heuristic.py b/PathPlanning/HybridAStar/dynamic_programming_heuristic.py
deleted file mode 100644
index 09bcd556a69..00000000000
--- a/PathPlanning/HybridAStar/dynamic_programming_heuristic.py
+++ /dev/null
@@ -1,176 +0,0 @@
-"""
-
-A* grid based planning
-
-author: Nikos Kanargias (nkana@tee.gr)
-
-See Wikipedia article (https://en.wikipedia.org/wiki/A*_search_algorithm)
-
-"""
-
-import heapq
-import math
-
-import matplotlib.pyplot as plt
-
-show_animation = False
-
-
-class Node:
-
- def __init__(self, x, y, cost, parent_index):
- self.x = x
- self.y = y
- self.cost = cost
- self.parent_index = parent_index
-
- def __str__(self):
- return str(self.x) + "," + str(self.y) + "," + str(
- self.cost) + "," + str(self.parent_index)
-
-
-def calc_final_path(goal_node, closed_node_set, resolution):
- # generate final course
- rx, ry = [goal_node.x * resolution], [goal_node.y * resolution]
- parent_index = goal_node.parent_index
- while parent_index != -1:
- n = closed_node_set[parent_index]
- rx.append(n.x * resolution)
- ry.append(n.y * resolution)
- parent_index = n.parent_index
-
- return rx, ry
-
-
-def calc_distance_heuristic(gx, gy, ox, oy, resolution, rr):
- """
- gx: goal x position [m]
- gx: goal x position [m]
- ox: x position list of Obstacles [m]
- oy: y position list of Obstacles [m]
- resolution: grid resolution [m]
- rr: robot radius[m]
- """
-
- goal_node = Node(round(gx / resolution), round(gy / resolution), 0.0, -1)
- ox = [iox / resolution for iox in ox]
- oy = [ioy / resolution for ioy in oy]
-
- obstacle_map, min_x, min_y, max_x, max_y, x_w, y_w = calc_obstacle_map(
- ox, oy, resolution, rr)
-
- motion = get_motion_model()
-
- open_set, closed_set = dict(), dict()
- open_set[calc_index(goal_node, x_w, min_x, min_y)] = goal_node
- priority_queue = [(0, calc_index(goal_node, x_w, min_x, min_y))]
-
- while True:
- if not priority_queue:
- break
- cost, c_id = heapq.heappop(priority_queue)
- if c_id in open_set:
- current = open_set[c_id]
- closed_set[c_id] = current
- open_set.pop(c_id)
- else:
- continue
-
- # show graph
- if show_animation: # pragma: no cover
- plt.plot(current.x * resolution, current.y * resolution, "xc")
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if len(closed_set.keys()) % 10 == 0:
- plt.pause(0.001)
-
- # Remove the item from the open set
-
- # expand search grid based on motion model
- for i, _ in enumerate(motion):
- node = Node(current.x + motion[i][0],
- current.y + motion[i][1],
- current.cost + motion[i][2], c_id)
- n_id = calc_index(node, x_w, min_x, min_y)
-
- if n_id in closed_set:
- continue
-
- if not verify_node(node, obstacle_map, min_x, min_y, max_x, max_y):
- continue
-
- if n_id not in open_set:
- open_set[n_id] = node # Discover a new node
- heapq.heappush(
- priority_queue,
- (node.cost, calc_index(node, x_w, min_x, min_y)))
- else:
- if open_set[n_id].cost >= node.cost:
- # This path is the best until now. record it!
- open_set[n_id] = node
- heapq.heappush(
- priority_queue,
- (node.cost, calc_index(node, x_w, min_x, min_y)))
-
- return closed_set
-
-
-def verify_node(node, obstacle_map, min_x, min_y, max_x, max_y):
- if node.x < min_x:
- return False
- elif node.y < min_y:
- return False
- elif node.x >= max_x:
- return False
- elif node.y >= max_y:
- return False
-
- if obstacle_map[node.x][node.y]:
- return False
-
- return True
-
-
-def calc_obstacle_map(ox, oy, resolution, vr):
- min_x = round(min(ox))
- min_y = round(min(oy))
- max_x = round(max(ox))
- max_y = round(max(oy))
-
- x_width = round(max_x - min_x)
- y_width = round(max_y - min_y)
-
- # obstacle map generation
- obstacle_map = [[False for _ in range(y_width)] for _ in range(x_width)]
- for ix in range(x_width):
- x = ix + min_x
- for iy in range(y_width):
- y = iy + min_y
- # print(x, y)
- for iox, ioy in zip(ox, oy):
- d = math.hypot(iox - x, ioy - y)
- if d <= vr / resolution:
- obstacle_map[ix][iy] = True
- break
-
- return obstacle_map, min_x, min_y, max_x, max_y, x_width, y_width
-
-
-def calc_index(node, x_width, x_min, y_min):
- return (node.y - y_min) * x_width + (node.x - x_min)
-
-
-def get_motion_model():
- # dx, dy, cost
- motion = [[1, 0, 1],
- [0, 1, 1],
- [-1, 0, 1],
- [0, -1, 1],
- [-1, -1, math.sqrt(2)],
- [-1, 1, math.sqrt(2)],
- [1, -1, math.sqrt(2)],
- [1, 1, math.sqrt(2)]]
-
- return motion
diff --git a/PathPlanning/HybridAStar/hybrid_a_star.py b/PathPlanning/HybridAStar/hybrid_a_star.py
deleted file mode 100644
index 0fa04189c6c..00000000000
--- a/PathPlanning/HybridAStar/hybrid_a_star.py
+++ /dev/null
@@ -1,441 +0,0 @@
-"""
-
-Hybrid A* path planning
-
-author: Zheng Zh (@Zhengzh)
-
-"""
-
-import heapq
-import math
-import matplotlib.pyplot as plt
-import numpy as np
-from scipy.spatial import cKDTree
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from dynamic_programming_heuristic import calc_distance_heuristic
-from ReedsSheppPath import reeds_shepp_path_planning as rs
-from car import move, check_car_collision, MAX_STEER, WB, plot_car, BUBBLE_R
-
-XY_GRID_RESOLUTION = 2.0 # [m]
-YAW_GRID_RESOLUTION = np.deg2rad(15.0) # [rad]
-MOTION_RESOLUTION = 0.1 # [m] path interpolate resolution
-N_STEER = 20 # number of steer command
-
-SB_COST = 100.0 # switch back penalty cost
-BACK_COST = 5.0 # backward penalty cost
-STEER_CHANGE_COST = 5.0 # steer angle change penalty cost
-STEER_COST = 1.0 # steer angle change penalty cost
-H_COST = 5.0 # Heuristic cost
-
-show_animation = True
-
-
-class Node:
-
- def __init__(self, x_ind, y_ind, yaw_ind, direction,
- x_list, y_list, yaw_list, directions,
- steer=0.0, parent_index=None, cost=None):
- self.x_index = x_ind
- self.y_index = y_ind
- self.yaw_index = yaw_ind
- self.direction = direction
- self.x_list = x_list
- self.y_list = y_list
- self.yaw_list = yaw_list
- self.directions = directions
- self.steer = steer
- self.parent_index = parent_index
- self.cost = cost
-
-
-class Path:
-
- def __init__(self, x_list, y_list, yaw_list, direction_list, cost):
- self.x_list = x_list
- self.y_list = y_list
- self.yaw_list = yaw_list
- self.direction_list = direction_list
- self.cost = cost
-
-
-class Config:
-
- def __init__(self, ox, oy, xy_resolution, yaw_resolution):
- min_x_m = min(ox)
- min_y_m = min(oy)
- max_x_m = max(ox)
- max_y_m = max(oy)
-
- ox.append(min_x_m)
- oy.append(min_y_m)
- ox.append(max_x_m)
- oy.append(max_y_m)
-
- self.min_x = round(min_x_m / xy_resolution)
- self.min_y = round(min_y_m / xy_resolution)
- self.max_x = round(max_x_m / xy_resolution)
- self.max_y = round(max_y_m / xy_resolution)
-
- self.x_w = round(self.max_x - self.min_x)
- self.y_w = round(self.max_y - self.min_y)
-
- self.min_yaw = round(- math.pi / yaw_resolution) - 1
- self.max_yaw = round(math.pi / yaw_resolution)
- self.yaw_w = round(self.max_yaw - self.min_yaw)
-
-
-def calc_motion_inputs():
- for steer in np.concatenate((np.linspace(-MAX_STEER, MAX_STEER,
- N_STEER), [0.0])):
- for d in [1, -1]:
- yield [steer, d]
-
-
-def get_neighbors(current, config, ox, oy, kd_tree):
- for steer, d in calc_motion_inputs():
- node = calc_next_node(current, steer, d, config, ox, oy, kd_tree)
- if node and verify_index(node, config):
- yield node
-
-
-def calc_next_node(current, steer, direction, config, ox, oy, kd_tree):
- x, y, yaw = current.x_list[-1], current.y_list[-1], current.yaw_list[-1]
-
- arc_l = XY_GRID_RESOLUTION * 1.5
- x_list, y_list, yaw_list, direction_list = [], [], [], []
- for _ in np.arange(0, arc_l, MOTION_RESOLUTION):
- x, y, yaw = move(x, y, yaw, MOTION_RESOLUTION * direction, steer)
- x_list.append(x)
- y_list.append(y)
- yaw_list.append(yaw)
- direction_list.append(direction == 1)
-
- if not check_car_collision(x_list, y_list, yaw_list, ox, oy, kd_tree):
- return None
-
- d = direction == 1
- x_ind = round(x / XY_GRID_RESOLUTION)
- y_ind = round(y / XY_GRID_RESOLUTION)
- yaw_ind = round(yaw / YAW_GRID_RESOLUTION)
-
- added_cost = 0.0
-
- if d != current.direction:
- added_cost += SB_COST
-
- # steer penalty
- added_cost += STEER_COST * abs(steer)
-
- # steer change penalty
- added_cost += STEER_CHANGE_COST * abs(current.steer - steer)
-
- cost = current.cost + added_cost + arc_l
-
- node = Node(x_ind, y_ind, yaw_ind, d, x_list,
- y_list, yaw_list, direction_list,
- parent_index=calc_index(current, config),
- cost=cost, steer=steer)
-
- return node
-
-
-def is_same_grid(n1, n2):
- if n1.x_index == n2.x_index \
- and n1.y_index == n2.y_index \
- and n1.yaw_index == n2.yaw_index:
- return True
- return False
-
-
-def analytic_expansion(current, goal, ox, oy, kd_tree):
- start_x = current.x_list[-1]
- start_y = current.y_list[-1]
- start_yaw = current.yaw_list[-1]
-
- goal_x = goal.x_list[-1]
- goal_y = goal.y_list[-1]
- goal_yaw = goal.yaw_list[-1]
-
- max_curvature = math.tan(MAX_STEER) / WB
- paths = rs.calc_paths(start_x, start_y, start_yaw,
- goal_x, goal_y, goal_yaw,
- max_curvature, step_size=MOTION_RESOLUTION)
-
- if not paths:
- return None
-
- best_path, best = None, None
-
- for path in paths:
- if check_car_collision(path.x, path.y, path.yaw, ox, oy, kd_tree):
- cost = calc_rs_path_cost(path)
- if not best or best > cost:
- best = cost
- best_path = path
-
- return best_path
-
-
-def update_node_with_analytic_expansion(current, goal,
- c, ox, oy, kd_tree):
- path = analytic_expansion(current, goal, ox, oy, kd_tree)
-
- if path:
- if show_animation:
- plt.plot(path.x, path.y)
- f_x = path.x[1:]
- f_y = path.y[1:]
- f_yaw = path.yaw[1:]
-
- f_cost = current.cost + calc_rs_path_cost(path)
- f_parent_index = calc_index(current, c)
-
- fd = []
- for d in path.directions[1:]:
- fd.append(d >= 0)
-
- f_steer = 0.0
- f_path = Node(current.x_index, current.y_index, current.yaw_index,
- current.direction, f_x, f_y, f_yaw, fd,
- cost=f_cost, parent_index=f_parent_index, steer=f_steer)
- return True, f_path
-
- return False, None
-
-
-def calc_rs_path_cost(reed_shepp_path):
- cost = 0.0
- for length in reed_shepp_path.lengths:
- if length >= 0: # forward
- cost += length
- else: # back
- cost += abs(length) * BACK_COST
-
- # switch back penalty
- for i in range(len(reed_shepp_path.lengths) - 1):
- # switch back
- if reed_shepp_path.lengths[i] * reed_shepp_path.lengths[i + 1] < 0.0:
- cost += SB_COST
-
- # steer penalty
- for course_type in reed_shepp_path.ctypes:
- if course_type != "S": # curve
- cost += STEER_COST * abs(MAX_STEER)
-
- # ==steer change penalty
- # calc steer profile
- n_ctypes = len(reed_shepp_path.ctypes)
- u_list = [0.0] * n_ctypes
- for i in range(n_ctypes):
- if reed_shepp_path.ctypes[i] == "R":
- u_list[i] = - MAX_STEER
- elif reed_shepp_path.ctypes[i] == "L":
- u_list[i] = MAX_STEER
-
- for i in range(len(reed_shepp_path.ctypes) - 1):
- cost += STEER_CHANGE_COST * abs(u_list[i + 1] - u_list[i])
-
- return cost
-
-
-def hybrid_a_star_planning(start, goal, ox, oy, xy_resolution, yaw_resolution):
- """
- start: start node
- goal: goal node
- ox: x position list of Obstacles [m]
- oy: y position list of Obstacles [m]
- xy_resolution: grid resolution [m]
- yaw_resolution: yaw angle resolution [rad]
- """
-
- start[2], goal[2] = rs.pi_2_pi(start[2]), rs.pi_2_pi(goal[2])
- tox, toy = ox[:], oy[:]
-
- obstacle_kd_tree = cKDTree(np.vstack((tox, toy)).T)
-
- config = Config(tox, toy, xy_resolution, yaw_resolution)
-
- start_node = Node(round(start[0] / xy_resolution),
- round(start[1] / xy_resolution),
- round(start[2] / yaw_resolution), True,
- [start[0]], [start[1]], [start[2]], [True], cost=0)
- goal_node = Node(round(goal[0] / xy_resolution),
- round(goal[1] / xy_resolution),
- round(goal[2] / yaw_resolution), True,
- [goal[0]], [goal[1]], [goal[2]], [True])
-
- openList, closedList = {}, {}
-
- h_dp = calc_distance_heuristic(
- goal_node.x_list[-1], goal_node.y_list[-1],
- ox, oy, xy_resolution, BUBBLE_R)
-
- pq = []
- openList[calc_index(start_node, config)] = start_node
- heapq.heappush(pq, (calc_cost(start_node, h_dp, config),
- calc_index(start_node, config)))
- final_path = None
-
- while True:
- if not openList:
- print("Error: Cannot find path, No open set")
- return Path([], [], [], [], 0)
-
- cost, c_id = heapq.heappop(pq)
- if c_id in openList:
- current = openList.pop(c_id)
- closedList[c_id] = current
- else:
- continue
-
- if show_animation: # pragma: no cover
- plt.plot(current.x_list[-1], current.y_list[-1], "xc")
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if len(closedList.keys()) % 10 == 0:
- plt.pause(0.001)
-
- is_updated, final_path = update_node_with_analytic_expansion(
- current, goal_node, config, ox, oy, obstacle_kd_tree)
-
- if is_updated:
- print("path found")
- break
-
- for neighbor in get_neighbors(current, config, ox, oy,
- obstacle_kd_tree):
- neighbor_index = calc_index(neighbor, config)
- if neighbor_index in closedList:
- continue
- if neighbor_index not in openList \
- or openList[neighbor_index].cost > neighbor.cost:
- heapq.heappush(
- pq, (calc_cost(neighbor, h_dp, config),
- neighbor_index))
- openList[neighbor_index] = neighbor
-
- path = get_final_path(closedList, final_path)
- return path
-
-
-def calc_cost(n, h_dp, c):
- ind = (n.y_index - c.min_y) * c.x_w + (n.x_index - c.min_x)
- if ind not in h_dp:
- return n.cost + 999999999 # collision cost
- return n.cost + H_COST * h_dp[ind].cost
-
-
-def get_final_path(closed, goal_node):
- reversed_x, reversed_y, reversed_yaw = \
- list(reversed(goal_node.x_list)), list(reversed(goal_node.y_list)), \
- list(reversed(goal_node.yaw_list))
- direction = list(reversed(goal_node.directions))
- nid = goal_node.parent_index
- final_cost = goal_node.cost
-
- while nid:
- n = closed[nid]
- reversed_x.extend(list(reversed(n.x_list)))
- reversed_y.extend(list(reversed(n.y_list)))
- reversed_yaw.extend(list(reversed(n.yaw_list)))
- direction.extend(list(reversed(n.directions)))
-
- nid = n.parent_index
-
- reversed_x = list(reversed(reversed_x))
- reversed_y = list(reversed(reversed_y))
- reversed_yaw = list(reversed(reversed_yaw))
- direction = list(reversed(direction))
-
- # adjust first direction
- direction[0] = direction[1]
-
- path = Path(reversed_x, reversed_y, reversed_yaw, direction, final_cost)
-
- return path
-
-
-def verify_index(node, c):
- x_ind, y_ind = node.x_index, node.y_index
- if c.min_x <= x_ind <= c.max_x and c.min_y <= y_ind <= c.max_y:
- return True
-
- return False
-
-
-def calc_index(node, c):
- ind = (node.yaw_index - c.min_yaw) * c.x_w * c.y_w + \
- (node.y_index - c.min_y) * c.x_w + (node.x_index - c.min_x)
-
- if ind <= 0:
- print("Error(calc_index):", ind)
-
- return ind
-
-
-def main():
- print("Start Hybrid A* planning")
-
- ox, oy = [], []
-
- for i in range(60):
- ox.append(i)
- oy.append(0.0)
- for i in range(60):
- ox.append(60.0)
- oy.append(i)
- for i in range(61):
- ox.append(i)
- oy.append(60.0)
- for i in range(61):
- ox.append(0.0)
- oy.append(i)
- for i in range(40):
- ox.append(20.0)
- oy.append(i)
- for i in range(40):
- ox.append(40.0)
- oy.append(60.0 - i)
-
- # Set Initial parameters
- start = [10.0, 10.0, np.deg2rad(90.0)]
- goal = [50.0, 50.0, np.deg2rad(-90.0)]
-
- print("start : ", start)
- print("goal : ", goal)
-
- if show_animation:
- plt.plot(ox, oy, ".k")
- rs.plot_arrow(start[0], start[1], start[2], fc='g')
- rs.plot_arrow(goal[0], goal[1], goal[2])
-
- plt.grid(True)
- plt.axis("equal")
-
- path = hybrid_a_star_planning(
- start, goal, ox, oy, XY_GRID_RESOLUTION, YAW_GRID_RESOLUTION)
-
- x = path.x_list
- y = path.y_list
- yaw = path.yaw_list
-
- if show_animation:
- for i_x, i_y, i_yaw in zip(x, y, yaw):
- plt.cla()
- plt.plot(ox, oy, ".k")
- plt.plot(x, y, "-r", label="Hybrid A* path")
- plt.grid(True)
- plt.axis("equal")
- plot_car(i_x, i_y, i_yaw)
- plt.pause(0.0001)
-
- print(__file__ + " done!!")
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/InformedRRTStar/informed_rrt_star.py b/PathPlanning/InformedRRTStar/informed_rrt_star.py
deleted file mode 100644
index 0483949c996..00000000000
--- a/PathPlanning/InformedRRTStar/informed_rrt_star.py
+++ /dev/null
@@ -1,350 +0,0 @@
-"""
-Informed RRT* path planning
-
-author: Karan Chawla
- Atsushi Sakai(@Atsushi_twi)
-
-Reference: Informed RRT*: Optimal Sampling-based Path planning Focused via
-Direct Sampling of an Admissible Ellipsoidal Heuristic
-https://arxiv.org/pdf/1404.2334
-
-"""
-import sys
-import pathlib
-
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import copy
-import math
-import random
-
-import matplotlib.pyplot as plt
-import numpy as np
-
-from utils.angle import rot_mat_2d
-
-show_animation = True
-
-
-class InformedRRTStar:
-
- def __init__(self, start, goal, obstacle_list, rand_area, expand_dis=0.5,
- goal_sample_rate=10, max_iter=200):
-
- self.start = Node(start[0], start[1])
- self.goal = Node(goal[0], goal[1])
- self.min_rand = rand_area[0]
- self.max_rand = rand_area[1]
- self.expand_dis = expand_dis
- self.goal_sample_rate = goal_sample_rate
- self.max_iter = max_iter
- self.obstacle_list = obstacle_list
- self.node_list = None
-
- def informed_rrt_star_search(self, animation=True):
-
- self.node_list = [self.start]
- # max length we expect to find in our 'informed' sample space,
- # starts as infinite
- c_best = float('inf')
- solution_set = set()
- path = None
-
- # Computing the sampling space
- c_min = math.hypot(self.start.x - self.goal.x,
- self.start.y - self.goal.y)
- x_center = np.array([[(self.start.x + self.goal.x) / 2.0],
- [(self.start.y + self.goal.y) / 2.0], [0]])
- a1 = np.array([[(self.goal.x - self.start.x) / c_min],
- [(self.goal.y - self.start.y) / c_min], [0]])
-
- e_theta = math.atan2(a1[1, 0], a1[0, 0])
- # first column of identity matrix transposed
- id1_t = np.array([1.0, 0.0, 0.0]).reshape(1, 3)
- m = a1 @ id1_t
- u, s, vh = np.linalg.svd(m, True, True)
- c = u @ np.diag(
- [1.0, 1.0,
- np.linalg.det(u) * np.linalg.det(np.transpose(vh))]) @ vh
-
- for i in range(self.max_iter):
- # Sample space is defined by c_best
- # c_min is the minimum distance between the start point and
- # the goal x_center is the midpoint between the start and the
- # goal c_best changes when a new path is found
-
- rnd = self.informed_sample(c_best, c_min, x_center, c)
- n_ind = self.get_nearest_list_index(self.node_list, rnd)
- nearest_node = self.node_list[n_ind]
- # steer
- theta = math.atan2(rnd[1] - nearest_node.y,
- rnd[0] - nearest_node.x)
- new_node = self.get_new_node(theta, n_ind, nearest_node)
- d = self.line_cost(nearest_node, new_node)
-
- no_collision = self.check_collision(nearest_node, theta, d)
-
- if no_collision:
- near_inds = self.find_near_nodes(new_node)
- new_node = self.choose_parent(new_node, near_inds)
-
- self.node_list.append(new_node)
- self.rewire(new_node, near_inds)
-
- if self.is_near_goal(new_node):
- if self.check_segment_collision(new_node.x, new_node.y,
- self.goal.x, self.goal.y):
- solution_set.add(new_node)
- last_index = len(self.node_list) - 1
- temp_path = self.get_final_course(last_index)
- temp_path_len = self.get_path_len(temp_path)
- if temp_path_len < c_best:
- path = temp_path
- c_best = temp_path_len
- if animation:
- self.draw_graph(x_center=x_center, c_best=c_best, c_min=c_min,
- e_theta=e_theta, rnd=rnd)
-
- return path
-
- def choose_parent(self, new_node, near_inds):
- if len(near_inds) == 0:
- return new_node
-
- d_list = []
- for i in near_inds:
- dx = new_node.x - self.node_list[i].x
- dy = new_node.y - self.node_list[i].y
- d = math.hypot(dx, dy)
- theta = math.atan2(dy, dx)
- if self.check_collision(self.node_list[i], theta, d):
- d_list.append(self.node_list[i].cost + d)
- else:
- d_list.append(float('inf'))
-
- min_cost = min(d_list)
- min_ind = near_inds[d_list.index(min_cost)]
-
- if min_cost == float('inf'):
- print("min cost is inf")
- return new_node
-
- new_node.cost = min_cost
- new_node.parent = min_ind
-
- return new_node
-
- def find_near_nodes(self, new_node):
- n_node = len(self.node_list)
- r = 50.0 * math.sqrt(math.log(n_node) / n_node)
- d_list = [(node.x - new_node.x) ** 2 + (node.y - new_node.y) ** 2 for
- node in self.node_list]
- near_inds = [d_list.index(i) for i in d_list if i <= r ** 2]
- return near_inds
-
- def informed_sample(self, c_max, c_min, x_center, c):
- if c_max < float('inf'):
- r = [c_max / 2.0, math.sqrt(c_max ** 2 - c_min ** 2) / 2.0,
- math.sqrt(c_max ** 2 - c_min ** 2) / 2.0]
- rl = np.diag(r)
- x_ball = self.sample_unit_ball()
- rnd = np.dot(np.dot(c, rl), x_ball) + x_center
- rnd = [rnd[(0, 0)], rnd[(1, 0)]]
- else:
- rnd = self.sample_free_space()
-
- return rnd
-
- @staticmethod
- def sample_unit_ball():
- a = random.random()
- b = random.random()
-
- if b < a:
- a, b = b, a
-
- sample = (b * math.cos(2 * math.pi * a / b),
- b * math.sin(2 * math.pi * a / b))
- return np.array([[sample[0]], [sample[1]], [0]])
-
- def sample_free_space(self):
- if random.randint(0, 100) > self.goal_sample_rate:
- rnd = [random.uniform(self.min_rand, self.max_rand),
- random.uniform(self.min_rand, self.max_rand)]
- else:
- rnd = [self.goal.x, self.goal.y]
-
- return rnd
-
- @staticmethod
- def get_path_len(path):
- path_len = 0
- for i in range(1, len(path)):
- node1_x = path[i][0]
- node1_y = path[i][1]
- node2_x = path[i - 1][0]
- node2_y = path[i - 1][1]
- path_len += math.hypot(node1_x - node2_x, node1_y - node2_y)
-
- return path_len
-
- @staticmethod
- def line_cost(node1, node2):
- return math.hypot(node1.x - node2.x, node1.y - node2.y)
-
- @staticmethod
- def get_nearest_list_index(nodes, rnd):
- d_list = [(node.x - rnd[0]) ** 2 + (node.y - rnd[1]) ** 2 for node in
- nodes]
- min_index = d_list.index(min(d_list))
- return min_index
-
- def get_new_node(self, theta, n_ind, nearest_node):
- new_node = copy.deepcopy(nearest_node)
-
- new_node.x += self.expand_dis * math.cos(theta)
- new_node.y += self.expand_dis * math.sin(theta)
-
- new_node.cost += self.expand_dis
- new_node.parent = n_ind
- return new_node
-
- def is_near_goal(self, node):
- d = self.line_cost(node, self.goal)
- if d < self.expand_dis:
- return True
- return False
-
- def rewire(self, new_node, near_inds):
- n_node = len(self.node_list)
- for i in near_inds:
- near_node = self.node_list[i]
-
- d = math.hypot(near_node.x - new_node.x, near_node.y - new_node.y)
-
- s_cost = new_node.cost + d
-
- if near_node.cost > s_cost:
- theta = math.atan2(new_node.y - near_node.y,
- new_node.x - near_node.x)
- if self.check_collision(near_node, theta, d):
- near_node.parent = n_node - 1
- near_node.cost = s_cost
-
- @staticmethod
- def distance_squared_point_to_segment(v, w, p):
- # Return minimum distance between line segment vw and point p
- if np.array_equal(v, w):
- return (p - v).dot(p - v) # v == w case
- l2 = (w - v).dot(w - v) # i.e. |w-v|^2 - avoid a sqrt
- # Consider the line extending the segment,
- # parameterized as v + t (w - v).
- # We find projection of point p onto the line.
- # It falls where t = [(p-v) . (w-v)] / |w-v|^2
- # We clamp t from [0,1] to handle points outside the segment vw.
- t = max(0, min(1, (p - v).dot(w - v) / l2))
- projection = v + t * (w - v) # Projection falls on the segment
- return (p - projection).dot(p - projection)
-
- def check_segment_collision(self, x1, y1, x2, y2):
- for (ox, oy, size) in self.obstacle_list:
- dd = self.distance_squared_point_to_segment(
- np.array([x1, y1]), np.array([x2, y2]), np.array([ox, oy]))
- if dd <= size ** 2:
- return False # collision
- return True
-
- def check_collision(self, near_node, theta, d):
- tmp_node = copy.deepcopy(near_node)
- end_x = tmp_node.x + math.cos(theta) * d
- end_y = tmp_node.y + math.sin(theta) * d
- return self.check_segment_collision(tmp_node.x, tmp_node.y,
- end_x, end_y)
-
- def get_final_course(self, last_index):
- path = [[self.goal.x, self.goal.y]]
- while self.node_list[last_index].parent is not None:
- node = self.node_list[last_index]
- path.append([node.x, node.y])
- last_index = node.parent
- path.append([self.start.x, self.start.y])
- return path
-
- def draw_graph(self, x_center=None, c_best=None, c_min=None, e_theta=None,
- rnd=None):
- plt.clf()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event', lambda event:
- [exit(0) if event.key == 'escape' else None])
- if rnd is not None:
- plt.plot(rnd[0], rnd[1], "^k")
- if c_best != float('inf'):
- self.plot_ellipse(x_center, c_best, c_min, e_theta)
-
- for node in self.node_list:
- if node.parent is not None:
- if node.x or node.y is not None:
- plt.plot([node.x, self.node_list[node.parent].x],
- [node.y, self.node_list[node.parent].y], "-g")
-
- for (ox, oy, size) in self.obstacle_list:
- plt.plot(ox, oy, "ok", ms=30 * size)
-
- plt.plot(self.start.x, self.start.y, "xr")
- plt.plot(self.goal.x, self.goal.y, "xr")
- plt.axis([self.min_rand, self.max_rand, self.min_rand, self.max_rand])
- plt.grid(True)
- plt.pause(0.01)
-
- @staticmethod
- def plot_ellipse(x_center, c_best, c_min, e_theta): # pragma: no cover
-
- a = math.sqrt(c_best ** 2 - c_min ** 2) / 2.0
- b = c_best / 2.0
- angle = math.pi / 2.0 - e_theta
- cx = x_center[0]
- cy = x_center[1]
- t = np.arange(0, 2 * math.pi + 0.1, 0.1)
- x = [a * math.cos(it) for it in t]
- y = [b * math.sin(it) for it in t]
- fx = rot_mat_2d(-angle) @ np.array([x, y])
- px = np.array(fx[0, :] + cx).flatten()
- py = np.array(fx[1, :] + cy).flatten()
- plt.plot(cx, cy, "xc")
- plt.plot(px, py, "--c")
-
-
-class Node:
-
- def __init__(self, x, y):
- self.x = x
- self.y = y
- self.cost = 0.0
- self.parent = None
-
-
-def main():
- print("Start informed rrt star planning")
-
- # create obstacles
- obstacle_list = [(5, 5, 0.5), (9, 6, 1), (7, 5, 1), (1, 5, 1), (3, 6, 1),
- (7, 9, 1)]
-
- # Set params
- rrt = InformedRRTStar(start=[0, 0], goal=[5, 10], rand_area=[-2, 15],
- obstacle_list=obstacle_list)
- path = rrt.informed_rrt_star_search(animation=show_animation)
- print("Done!!")
-
- # Plot path
- if show_animation:
- rrt.draw_graph()
- plt.plot([x for (x, y) in path], [y for (x, y) in path], '-r')
- plt.grid(True)
- plt.pause(0.01)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/LQRPlanner/lqr_planner.py b/PathPlanning/LQRPlanner/lqr_planner.py
deleted file mode 100644
index 0f58f93ea39..00000000000
--- a/PathPlanning/LQRPlanner/lqr_planner.py
+++ /dev/null
@@ -1,146 +0,0 @@
-"""
-
-LQR local path planning
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import math
-import random
-
-import matplotlib.pyplot as plt
-import numpy as np
-import scipy.linalg as la
-
-SHOW_ANIMATION = True
-
-
-class LQRPlanner:
-
- def __init__(self):
- self.MAX_TIME = 100.0 # Maximum simulation time
- self.DT = 0.1 # Time tick
- self.GOAL_DIST = 0.1
- self.MAX_ITER = 150
- self.EPS = 0.01
-
- def lqr_planning(self, sx, sy, gx, gy, show_animation=True):
-
- rx, ry = [sx], [sy]
-
- x = np.array([sx - gx, sy - gy]).reshape(2, 1) # State vector
-
- # Linear system model
- A, B = self.get_system_model()
-
- found_path = False
-
- time = 0.0
- while time <= self.MAX_TIME:
- time += self.DT
-
- u = self.lqr_control(A, B, x)
-
- x = A @ x + B @ u
-
- rx.append(x[0, 0] + gx)
- ry.append(x[1, 0] + gy)
-
- d = math.hypot(gx - rx[-1], gy - ry[-1])
- if d <= self.GOAL_DIST:
- found_path = True
- break
-
- # animation
- if show_animation: # pragma: no cover
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(sx, sy, "or")
- plt.plot(gx, gy, "ob")
- plt.plot(rx, ry, "-r")
- plt.axis("equal")
- plt.pause(1.0)
-
- if not found_path:
- print("Cannot found path")
- return [], []
-
- return rx, ry
-
- def solve_dare(self, A, B, Q, R):
- """
- solve a discrete time_Algebraic Riccati equation (DARE)
- """
- X, Xn = Q, Q
-
- for i in range(self.MAX_ITER):
- Xn = A.T * X * A - A.T * X * B * \
- la.inv(R + B.T * X * B) * B.T * X * A + Q
- if (abs(Xn - X)).max() < self.EPS:
- break
- X = Xn
-
- return Xn
-
- def dlqr(self, A, B, Q, R):
- """Solve the discrete time lqr controller.
- x[k+1] = A x[k] + B u[k]
- cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
- # ref Bertsekas, p.151
- """
-
- # first, try to solve the ricatti equation
- X = self.solve_dare(A, B, Q, R)
-
- # compute the LQR gain
- K = la.inv(B.T @ X @ B + R) @ (B.T @ X @ A)
-
- eigValues = la.eigvals(A - B @ K)
-
- return K, X, eigValues
-
- def get_system_model(self):
-
- A = np.array([[self.DT, 1.0],
- [0.0, self.DT]])
- B = np.array([0.0, 1.0]).reshape(2, 1)
-
- return A, B
-
- def lqr_control(self, A, B, x):
-
- Kopt, X, ev = self.dlqr(A, B, np.eye(2), np.eye(1))
-
- u = -Kopt @ x
-
- return u
-
-
-def main():
- print(__file__ + " start!!")
-
- ntest = 10 # number of goal
- area = 100.0 # sampling area
-
- lqr_planner = LQRPlanner()
-
- for i in range(ntest):
- sx = 6.0
- sy = 6.0
- gx = random.uniform(-area, area)
- gy = random.uniform(-area, area)
-
- rx, ry = lqr_planner.lqr_planning(sx, sy, gx, gy, show_animation=SHOW_ANIMATION)
-
- if SHOW_ANIMATION: # pragma: no cover
- plt.plot(sx, sy, "or")
- plt.plot(gx, gy, "ob")
- plt.plot(rx, ry, "-r")
- plt.axis("equal")
- plt.pause(1.0)
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/LQRRRTStar/lqr_rrt_star.py b/PathPlanning/LQRRRTStar/lqr_rrt_star.py
deleted file mode 100644
index 0ed08123eab..00000000000
--- a/PathPlanning/LQRRRTStar/lqr_rrt_star.py
+++ /dev/null
@@ -1,241 +0,0 @@
-"""
-
-Path planning code with LQR RRT*
-
-author: AtsushiSakai(@Atsushi_twi)
-
-"""
-import copy
-import math
-import random
-import matplotlib.pyplot as plt
-import numpy as np
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from LQRPlanner.lqr_planner import LQRPlanner
-from RRTStar.rrt_star import RRTStar
-
-show_animation = True
-
-
-class LQRRRTStar(RRTStar):
- """
- Class for RRT star planning with LQR planning
- """
-
- def __init__(self, start, goal, obstacle_list, rand_area,
- goal_sample_rate=10,
- max_iter=200,
- connect_circle_dist=50.0,
- step_size=0.2,
- robot_radius=0.0,
- ):
- """
- Setting Parameter
-
- start:Start Position [x,y]
- goal:Goal Position [x,y]
- obstacleList:obstacle Positions [[x,y,size],...]
- randArea:Random Sampling Area [min,max]
- robot_radius: robot body modeled as circle with given radius
-
- """
- self.start = self.Node(start[0], start[1])
- self.end = self.Node(goal[0], goal[1])
- self.min_rand = rand_area[0]
- self.max_rand = rand_area[1]
- self.goal_sample_rate = goal_sample_rate
- self.max_iter = max_iter
- self.obstacle_list = obstacle_list
- self.connect_circle_dist = connect_circle_dist
-
- self.curvature = 1.0
- self.goal_xy_th = 0.5
- self.step_size = step_size
- self.robot_radius = robot_radius
-
- self.lqr_planner = LQRPlanner()
-
- def planning(self, animation=True, search_until_max_iter=True):
- """
- RRT Star planning
-
- animation: flag for animation on or off
- """
-
- self.node_list = [self.start]
- for i in range(self.max_iter):
- print("Iter:", i, ", number of nodes:", len(self.node_list))
- rnd = self.get_random_node()
- nearest_ind = self.get_nearest_node_index(self.node_list, rnd)
- new_node = self.steer(self.node_list[nearest_ind], rnd)
-
- if self.check_collision(
- new_node, self.obstacle_list, self.robot_radius):
- near_indexes = self.find_near_nodes(new_node)
- new_node = self.choose_parent(new_node, near_indexes)
- if new_node:
- self.node_list.append(new_node)
- self.rewire(new_node, near_indexes)
-
- if animation and i % 5 == 0:
- self.draw_graph(rnd)
-
- if (not search_until_max_iter) and new_node: # check reaching the goal
- last_index = self.search_best_goal_node()
- if last_index:
- return self.generate_final_course(last_index)
-
- print("reached max iteration")
-
- last_index = self.search_best_goal_node()
- if last_index:
- return self.generate_final_course(last_index)
- else:
- print("Cannot find path")
-
- return None
-
- def draw_graph(self, rnd=None):
- plt.clf()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if rnd is not None:
- plt.plot(rnd.x, rnd.y, "^k")
- for node in self.node_list:
- if node.parent:
- plt.plot(node.path_x, node.path_y, "-g")
-
- for (ox, oy, size) in self.obstacle_list:
- plt.plot(ox, oy, "ok", ms=30 * size)
-
- plt.plot(self.start.x, self.start.y, "xr")
- plt.plot(self.end.x, self.end.y, "xr")
- plt.axis([-2, 15, -2, 15])
- plt.grid(True)
- plt.pause(0.01)
-
- def search_best_goal_node(self):
- dist_to_goal_list = [self.calc_dist_to_goal(n.x, n.y) for n in self.node_list]
- goal_inds = [dist_to_goal_list.index(i) for i in dist_to_goal_list if i <= self.goal_xy_th]
-
- if not goal_inds:
- return None
-
- min_cost = min([self.node_list[i].cost for i in goal_inds])
- for i in goal_inds:
- if self.node_list[i].cost == min_cost:
- return i
-
- return None
-
- def calc_new_cost(self, from_node, to_node):
-
- wx, wy = self.lqr_planner.lqr_planning(
- from_node.x, from_node.y, to_node.x, to_node.y, show_animation=False)
-
- px, py, course_lengths = self.sample_path(wx, wy, self.step_size)
-
- if not course_lengths:
- return float("inf")
-
- return from_node.cost + sum(course_lengths)
-
- def get_random_node(self):
-
- if random.randint(0, 100) > self.goal_sample_rate:
- rnd = self.Node(random.uniform(self.min_rand, self.max_rand),
- random.uniform(self.min_rand, self.max_rand)
- )
- else: # goal point sampling
- rnd = self.Node(self.end.x, self.end.y)
-
- return rnd
-
- def generate_final_course(self, goal_index):
- print("final")
- path = [[self.end.x, self.end.y]]
- node = self.node_list[goal_index]
- while node.parent:
- for (ix, iy) in zip(reversed(node.path_x), reversed(node.path_y)):
- path.append([ix, iy])
- node = node.parent
- path.append([self.start.x, self.start.y])
- return path
-
- def sample_path(self, wx, wy, step):
-
- px, py, clen = [], [], []
-
- for i in range(len(wx) - 1):
-
- for t in np.arange(0.0, 1.0, step):
- px.append(t * wx[i + 1] + (1.0 - t) * wx[i])
- py.append(t * wy[i + 1] + (1.0 - t) * wy[i])
-
- dx = np.diff(px)
- dy = np.diff(py)
-
- clen = [math.hypot(idx, idy) for (idx, idy) in zip(dx, dy)]
-
- return px, py, clen
-
- def steer(self, from_node, to_node):
-
- wx, wy = self.lqr_planner.lqr_planning(
- from_node.x, from_node.y, to_node.x, to_node.y, show_animation=False)
-
- px, py, course_lens = self.sample_path(wx, wy, self.step_size)
-
- if px is None:
- return None
-
- newNode = copy.deepcopy(from_node)
- newNode.x = px[-1]
- newNode.y = py[-1]
- newNode.path_x = px
- newNode.path_y = py
- newNode.cost += sum([abs(c) for c in course_lens])
- newNode.parent = from_node
-
- return newNode
-
-
-def main(maxIter=200):
- print("Start " + __file__)
-
- # ====Search Path with RRT====
- obstacleList = [
- (5, 5, 1),
- (4, 6, 1),
- (4, 7.5, 1),
- (4, 9, 1),
- (6, 5, 1),
- (7, 5, 1)
- ] # [x,y,size]
-
- # Set Initial parameters
- start = [0.0, 0.0]
- goal = [6.0, 7.0]
-
- lqr_rrt_star = LQRRRTStar(start, goal,
- obstacleList,
- [-2.0, 15.0])
- path = lqr_rrt_star.planning(animation=show_animation)
-
- # Draw final path
- if show_animation: # pragma: no cover
- lqr_rrt_star.draw_graph()
- plt.plot([x for (x, y) in path], [y for (x, y) in path], '-r')
- plt.grid(True)
- plt.pause(0.001)
- plt.show()
-
- print("Done")
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/ModelPredictiveTrajectoryGenerator/__init__.py b/PathPlanning/ModelPredictiveTrajectoryGenerator/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathPlanning/ModelPredictiveTrajectoryGenerator/lookup_table_generator.py b/PathPlanning/ModelPredictiveTrajectoryGenerator/lookup_table_generator.py
deleted file mode 100644
index 4c3b32f2807..00000000000
--- a/PathPlanning/ModelPredictiveTrajectoryGenerator/lookup_table_generator.py
+++ /dev/null
@@ -1,110 +0,0 @@
-"""
-
-Lookup Table generation for model predictive trajectory generator
-
-author: Atsushi Sakai
-
-"""
-import sys
-import pathlib
-path_planning_dir = pathlib.Path(__file__).parent.parent
-sys.path.append(str(path_planning_dir))
-
-from matplotlib import pyplot as plt
-import numpy as np
-import math
-
-from ModelPredictiveTrajectoryGenerator import trajectory_generator,\
- motion_model
-
-
-def calc_states_list(max_yaw=np.deg2rad(-30.0)):
-
- x = np.arange(10.0, 30.0, 5.0)
- y = np.arange(0.0, 20.0, 2.0)
- yaw = np.arange(-max_yaw, max_yaw, max_yaw)
-
- states = []
- for iyaw in yaw:
- for iy in y:
- for ix in x:
- states.append([ix, iy, iyaw])
- print("n_state:", len(states))
-
- return states
-
-
-def search_nearest_one_from_lookup_table(tx, ty, tyaw, lookup_table):
- mind = float("inf")
- minid = -1
-
- for (i, table) in enumerate(lookup_table):
-
- dx = tx - table[0]
- dy = ty - table[1]
- dyaw = tyaw - table[2]
- d = math.sqrt(dx ** 2 + dy ** 2 + dyaw ** 2)
- if d <= mind:
- minid = i
- mind = d
-
- # print(minid)
-
- return lookup_table[minid]
-
-
-def save_lookup_table(file_name, table):
- np.savetxt(file_name, np.array(table),
- fmt='%s', delimiter=",", header="x,y,yaw,s,km,kf", comments="")
-
- print("lookup table file is saved as " + file_name)
-
-
-def generate_lookup_table():
- states = calc_states_list(max_yaw=np.deg2rad(-30.0))
- k0 = 0.0
-
- # x, y, yaw, s, km, kf
- lookup_table = [[1.0, 0.0, 0.0, 1.0, 0.0, 0.0]]
-
- for state in states:
- best_p = search_nearest_one_from_lookup_table(
- state[0], state[1], state[2], lookup_table)
-
- target = motion_model.State(x=state[0], y=state[1], yaw=state[2])
- init_p = np.array(
- [np.hypot(state[0], state[1]), best_p[4], best_p[5]]).reshape(3, 1)
-
- x, y, yaw, p = trajectory_generator.optimize_trajectory(target,
- k0, init_p)
-
- if x is not None:
- print("find good path")
- lookup_table.append(
- [x[-1], y[-1], yaw[-1], float(p[0, 0]), float(p[1, 0]), float(p[2, 0])])
-
- print("finish lookup table generation")
-
- save_lookup_table("lookup_table.csv", lookup_table)
-
- for table in lookup_table:
- x_c, y_c, yaw_c = motion_model.generate_trajectory(
- table[3], table[4], table[5], k0)
- plt.plot(x_c, y_c, "-r")
- x_c, y_c, yaw_c = motion_model.generate_trajectory(
- table[3], -table[4], -table[5], k0)
- plt.plot(x_c, y_c, "-r")
-
- plt.grid(True)
- plt.axis("equal")
- plt.show()
-
- print("Done")
-
-
-def main():
- generate_lookup_table()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/ModelPredictiveTrajectoryGenerator/motion_model.py b/PathPlanning/ModelPredictiveTrajectoryGenerator/motion_model.py
deleted file mode 100644
index 5ef6d2e23f1..00000000000
--- a/PathPlanning/ModelPredictiveTrajectoryGenerator/motion_model.py
+++ /dev/null
@@ -1,95 +0,0 @@
-import math
-import numpy as np
-from scipy.interpolate import interp1d
-from utils.angle import angle_mod
-
-# motion parameter
-L = 1.0 # wheel base
-ds = 0.1 # course distance
-v = 10.0 / 3.6 # velocity [m/s]
-
-
-class State:
-
- def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
- self.x = x
- self.y = y
- self.yaw = yaw
- self.v = v
-
-
-def pi_2_pi(angle):
- return angle_mod(angle)
-
-
-def update(state, v, delta, dt, L):
- state.v = v
- state.x = state.x + state.v * math.cos(state.yaw) * dt
- state.y = state.y + state.v * math.sin(state.yaw) * dt
- state.yaw = state.yaw + state.v / L * math.tan(delta) * dt
- state.yaw = pi_2_pi(state.yaw)
-
- return state
-
-
-def generate_trajectory(s, km, kf, k0):
- n = s / ds
- time = s / v # [s]
-
- if isinstance(time, type(np.array([]))):
- time = time[0]
- if isinstance(km, type(np.array([]))):
- km = km[0]
- if isinstance(kf, type(np.array([]))):
- kf = kf[0]
-
- tk = np.array([0.0, time / 2.0, time])
- kk = np.array([k0, km, kf])
- t = np.arange(0.0, time, time / n)
- fkp = interp1d(tk, kk, kind="quadratic")
- kp = [fkp(ti) for ti in t]
- dt = float(time / n)
-
- # plt.plot(t, kp)
- # plt.show()
-
- state = State()
- x, y, yaw = [state.x], [state.y], [state.yaw]
-
- for ikp in kp:
- state = update(state, v, ikp, dt, L)
- x.append(state.x)
- y.append(state.y)
- yaw.append(state.yaw)
-
- return x, y, yaw
-
-
-def generate_last_state(s, km, kf, k0):
- n = s / ds
- time = s / v # [s]
-
- if isinstance(n, type(np.array([]))):
- n = n[0]
- if isinstance(time, type(np.array([]))):
- time = time[0]
- if isinstance(km, type(np.array([]))):
- km = km[0]
- if isinstance(kf, type(np.array([]))):
- kf = kf[0]
-
- tk = np.array([0.0, time / 2.0, time])
- kk = np.array([k0, km, kf])
- t = np.arange(0.0, time, time / n)
- fkp = interp1d(tk, kk, kind="quadratic")
- kp = [fkp(ti) for ti in t]
- dt = time / n
-
- # plt.plot(t, kp)
- # plt.show()
-
- state = State()
-
- _ = [update(state, v, ikp, dt, L) for ikp in kp]
-
- return state.x, state.y, state.yaw
diff --git a/PathPlanning/ModelPredictiveTrajectoryGenerator/trajectory_generator.py b/PathPlanning/ModelPredictiveTrajectoryGenerator/trajectory_generator.py
deleted file mode 100644
index 6084fc1a074..00000000000
--- a/PathPlanning/ModelPredictiveTrajectoryGenerator/trajectory_generator.py
+++ /dev/null
@@ -1,162 +0,0 @@
-"""
-
-Model trajectory generator
-
-author: Atsushi Sakai(@Atsushi_twi)
-
-"""
-
-import math
-import matplotlib.pyplot as plt
-import numpy as np
-import sys
-import pathlib
-path_planning_dir = pathlib.Path(__file__).parent.parent
-sys.path.append(str(path_planning_dir))
-
-import ModelPredictiveTrajectoryGenerator.motion_model as motion_model
-
-# optimization parameter
-max_iter = 100
-h: np.ndarray = np.array([0.5, 0.02, 0.02]).T # parameter sampling distance
-cost_th = 0.1
-
-show_animation = True
-
-
-def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"): # pragma: no cover
- """
- Plot arrow
- """
- plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),
- fc=fc, ec=ec, head_width=width, head_length=width)
- plt.plot(x, y)
- plt.plot(0, 0)
-
-
-def calc_diff(target, x, y, yaw):
- d = np.array([target.x - x[-1],
- target.y - y[-1],
- motion_model.pi_2_pi(target.yaw - yaw[-1])])
-
- return d
-
-
-def calc_j(target, p, h, k0):
- xp, yp, yawp = motion_model.generate_last_state(
- p[0, 0] + h[0], p[1, 0], p[2, 0], k0)
- dp = calc_diff(target, [xp], [yp], [yawp])
- xn, yn, yawn = motion_model.generate_last_state(
- p[0, 0] - h[0], p[1, 0], p[2, 0], k0)
- dn = calc_diff(target, [xn], [yn], [yawn])
- d1 = np.array((dp - dn) / (2.0 * h[0])).reshape(3, 1)
-
- xp, yp, yawp = motion_model.generate_last_state(
- p[0, 0], p[1, 0] + h[1], p[2, 0], k0)
- dp = calc_diff(target, [xp], [yp], [yawp])
- xn, yn, yawn = motion_model.generate_last_state(
- p[0, 0], p[1, 0] - h[1], p[2, 0], k0)
- dn = calc_diff(target, [xn], [yn], [yawn])
- d2 = np.array((dp - dn) / (2.0 * h[1])).reshape(3, 1)
-
- xp, yp, yawp = motion_model.generate_last_state(
- p[0, 0], p[1, 0], p[2, 0] + h[2], k0)
- dp = calc_diff(target, [xp], [yp], [yawp])
- xn, yn, yawn = motion_model.generate_last_state(
- p[0, 0], p[1, 0], p[2, 0] - h[2], k0)
- dn = calc_diff(target, [xn], [yn], [yawn])
- d3 = np.array((dp - dn) / (2.0 * h[2])).reshape(3, 1)
-
- J = np.hstack((d1, d2, d3))
-
- return J
-
-
-def selection_learning_param(dp, p, k0, target):
- mincost = float("inf")
- mina = 1.0
- maxa = 2.0
- da = 0.5
-
- for a in np.arange(mina, maxa, da):
- tp = p + a * dp
- xc, yc, yawc = motion_model.generate_last_state(
- tp[0], tp[1], tp[2], k0)
- dc = calc_diff(target, [xc], [yc], [yawc])
- cost = np.linalg.norm(dc)
-
- if cost <= mincost and a != 0.0:
- mina = a
- mincost = cost
-
- # print(mincost, mina)
- # input()
-
- return mina
-
-
-def show_trajectory(target, xc, yc): # pragma: no cover
- plt.clf()
- plot_arrow(target.x, target.y, target.yaw)
- plt.plot(xc, yc, "-r")
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.1)
-
-
-def optimize_trajectory(target, k0, p):
- for i in range(max_iter):
- xc, yc, yawc = motion_model.generate_trajectory(p[0, 0], p[1, 0], p[2, 0], k0)
- dc = np.array(calc_diff(target, xc, yc, yawc)).reshape(3, 1)
-
- cost = np.linalg.norm(dc)
- if cost <= cost_th:
- print("path is ok cost is:" + str(cost))
- break
-
- J = calc_j(target, p, h, k0)
- try:
- dp = - np.linalg.inv(J) @ dc
- except np.linalg.linalg.LinAlgError:
- print("cannot calc path LinAlgError")
- xc, yc, yawc, p = None, None, None, None
- break
- alpha = selection_learning_param(dp, p, k0, target)
-
- p += alpha * np.array(dp)
- # print(p.T)
-
- if show_animation: # pragma: no cover
- show_trajectory(target, xc, yc)
- else:
- xc, yc, yawc, p = None, None, None, None
- print("cannot calc path")
-
- return xc, yc, yawc, p
-
-
-def optimize_trajectory_demo(): # pragma: no cover
-
- # target = motion_model.State(x=5.0, y=2.0, yaw=np.deg2rad(00.0))
- target = motion_model.State(x=5.0, y=2.0, yaw=np.deg2rad(90.0))
- k0 = 0.0
-
- init_p = np.array([6.0, 0.0, 0.0]).reshape(3, 1)
-
- x, y, yaw, p = optimize_trajectory(target, k0, init_p)
-
- if show_animation:
- show_trajectory(target, x, y)
- plot_arrow(target.x, target.y, target.yaw)
- plt.axis("equal")
- plt.grid(True)
- plt.show()
-
-
-def main(): # pragma: no cover
- print(__file__ + " start!!")
- optimize_trajectory_demo()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/PotentialFieldPlanning/potential_field_planning.py b/PathPlanning/PotentialFieldPlanning/potential_field_planning.py
deleted file mode 100644
index 8f136b5ee3f..00000000000
--- a/PathPlanning/PotentialFieldPlanning/potential_field_planning.py
+++ /dev/null
@@ -1,199 +0,0 @@
-"""
-
-Potential Field based path planner
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-Ref:
-https://www.cs.cmu.edu/~motionplanning/lecture/Chap4-Potential-Field_howie.pdf
-
-"""
-
-from collections import deque
-import numpy as np
-import matplotlib.pyplot as plt
-
-# Parameters
-KP = 5.0 # attractive potential gain
-ETA = 100.0 # repulsive potential gain
-AREA_WIDTH = 30.0 # potential area width [m]
-# the number of previous positions used to check oscillations
-OSCILLATIONS_DETECTION_LENGTH = 3
-
-show_animation = True
-
-
-def calc_potential_field(gx, gy, ox, oy, reso, rr, sx, sy):
- minx = min(min(ox), sx, gx) - AREA_WIDTH / 2.0
- miny = min(min(oy), sy, gy) - AREA_WIDTH / 2.0
- maxx = max(max(ox), sx, gx) + AREA_WIDTH / 2.0
- maxy = max(max(oy), sy, gy) + AREA_WIDTH / 2.0
- xw = int(round((maxx - minx) / reso))
- yw = int(round((maxy - miny) / reso))
-
- # calc each potential
- pmap = [[0.0 for i in range(yw)] for i in range(xw)]
-
- for ix in range(xw):
- x = ix * reso + minx
-
- for iy in range(yw):
- y = iy * reso + miny
- ug = calc_attractive_potential(x, y, gx, gy)
- uo = calc_repulsive_potential(x, y, ox, oy, rr)
- uf = ug + uo
- pmap[ix][iy] = uf
-
- return pmap, minx, miny
-
-
-def calc_attractive_potential(x, y, gx, gy):
- return 0.5 * KP * np.hypot(x - gx, y - gy)
-
-
-def calc_repulsive_potential(x, y, ox, oy, rr):
- # search nearest obstacle
- minid = -1
- dmin = float("inf")
- for i, _ in enumerate(ox):
- d = np.hypot(x - ox[i], y - oy[i])
- if dmin >= d:
- dmin = d
- minid = i
-
- # calc repulsive potential
- dq = np.hypot(x - ox[minid], y - oy[minid])
-
- if dq <= rr:
- if dq <= 0.1:
- dq = 0.1
-
- return 0.5 * ETA * (1.0 / dq - 1.0 / rr) ** 2
- else:
- return 0.0
-
-
-def get_motion_model():
- # dx, dy
- motion = [[1, 0],
- [0, 1],
- [-1, 0],
- [0, -1],
- [-1, -1],
- [-1, 1],
- [1, -1],
- [1, 1]]
-
- return motion
-
-
-def oscillations_detection(previous_ids, ix, iy):
- previous_ids.append((ix, iy))
-
- if (len(previous_ids) > OSCILLATIONS_DETECTION_LENGTH):
- previous_ids.popleft()
-
- # check if contains any duplicates by copying into a set
- previous_ids_set = set()
- for index in previous_ids:
- if index in previous_ids_set:
- return True
- else:
- previous_ids_set.add(index)
- return False
-
-
-def potential_field_planning(sx, sy, gx, gy, ox, oy, reso, rr):
-
- # calc potential field
- pmap, minx, miny = calc_potential_field(gx, gy, ox, oy, reso, rr, sx, sy)
-
- # search path
- d = np.hypot(sx - gx, sy - gy)
- ix = round((sx - minx) / reso)
- iy = round((sy - miny) / reso)
- gix = round((gx - minx) / reso)
- giy = round((gy - miny) / reso)
-
- if show_animation:
- draw_heatmap(pmap)
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(ix, iy, "*k")
- plt.plot(gix, giy, "*m")
-
- rx, ry = [sx], [sy]
- motion = get_motion_model()
- previous_ids = deque()
-
- while d >= reso:
- minp = float("inf")
- minix, miniy = -1, -1
- for i, _ in enumerate(motion):
- inx = int(ix + motion[i][0])
- iny = int(iy + motion[i][1])
- if inx >= len(pmap) or iny >= len(pmap[0]) or inx < 0 or iny < 0:
- p = float("inf") # outside area
- print("outside potential!")
- else:
- p = pmap[inx][iny]
- if minp > p:
- minp = p
- minix = inx
- miniy = iny
- ix = minix
- iy = miniy
- xp = ix * reso + minx
- yp = iy * reso + miny
- d = np.hypot(gx - xp, gy - yp)
- rx.append(xp)
- ry.append(yp)
-
- if (oscillations_detection(previous_ids, ix, iy)):
- print("Oscillation detected at ({},{})!".format(ix, iy))
- break
-
- if show_animation:
- plt.plot(ix, iy, ".r")
- plt.pause(0.01)
-
- print("Goal!!")
-
- return rx, ry
-
-
-def draw_heatmap(data):
- data = np.array(data).T
- plt.pcolor(data, vmax=100.0, cmap=plt.cm.Blues)
-
-
-def main():
- print("potential_field_planning start")
-
- sx = 0.0 # start x position [m]
- sy = 10.0 # start y positon [m]
- gx = 30.0 # goal x position [m]
- gy = 30.0 # goal y position [m]
- grid_size = 0.5 # potential grid size [m]
- robot_radius = 5.0 # robot radius [m]
-
- ox = [15.0, 5.0, 20.0, 25.0] # obstacle x position list [m]
- oy = [25.0, 15.0, 26.0, 25.0] # obstacle y position list [m]
-
- if show_animation:
- plt.grid(True)
- plt.axis("equal")
-
- # path generation
- _, _ = potential_field_planning(
- sx, sy, gx, gy, ox, oy, grid_size, robot_radius)
-
- if show_animation:
- plt.show()
-
-
-if __name__ == '__main__':
- print(__file__ + " start!!")
- main()
- print(__file__ + " Done!!")
diff --git a/PathPlanning/ProbabilisticRoadMap/probabilistic_road_map.py b/PathPlanning/ProbabilisticRoadMap/probabilistic_road_map.py
deleted file mode 100644
index 8bacfd5d199..00000000000
--- a/PathPlanning/ProbabilisticRoadMap/probabilistic_road_map.py
+++ /dev/null
@@ -1,312 +0,0 @@
-"""
-
-Probabilistic Road Map (PRM) Planner
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import math
-import numpy as np
-import matplotlib.pyplot as plt
-from scipy.spatial import KDTree
-
-# parameter
-N_SAMPLE = 500 # number of sample_points
-N_KNN = 10 # number of edge from one sampled point
-MAX_EDGE_LEN = 30.0 # [m] Maximum edge length
-
-show_animation = True
-
-
-class Node:
- """
- Node class for dijkstra search
- """
-
- def __init__(self, x, y, cost, parent_index):
- self.x = x
- self.y = y
- self.cost = cost
- self.parent_index = parent_index
-
- def __str__(self):
- return str(self.x) + "," + str(self.y) + "," +\
- str(self.cost) + "," + str(self.parent_index)
-
-
-def prm_planning(start_x, start_y, goal_x, goal_y,
- obstacle_x_list, obstacle_y_list, robot_radius, *, rng=None):
- """
- Run probabilistic road map planning
-
- :param start_x: start x position
- :param start_y: start y position
- :param goal_x: goal x position
- :param goal_y: goal y position
- :param obstacle_x_list: obstacle x positions
- :param obstacle_y_list: obstacle y positions
- :param robot_radius: robot radius
- :param rng: (Optional) Random generator
- :return:
- """
- obstacle_kd_tree = KDTree(np.vstack((obstacle_x_list, obstacle_y_list)).T)
-
- sample_x, sample_y = sample_points(start_x, start_y, goal_x, goal_y,
- robot_radius,
- obstacle_x_list, obstacle_y_list,
- obstacle_kd_tree, rng)
- if show_animation:
- plt.plot(sample_x, sample_y, ".b")
-
- road_map = generate_road_map(sample_x, sample_y,
- robot_radius, obstacle_kd_tree)
-
- rx, ry = dijkstra_planning(
- start_x, start_y, goal_x, goal_y, road_map, sample_x, sample_y)
-
- return rx, ry
-
-
-def is_collision(sx, sy, gx, gy, rr, obstacle_kd_tree):
- x = sx
- y = sy
- dx = gx - sx
- dy = gy - sy
- yaw = math.atan2(gy - sy, gx - sx)
- d = math.hypot(dx, dy)
-
- if d >= MAX_EDGE_LEN:
- return True
-
- D = rr
- n_step = round(d / D)
-
- for i in range(n_step):
- dist, _ = obstacle_kd_tree.query([x, y])
- if dist <= rr:
- return True # collision
- x += D * math.cos(yaw)
- y += D * math.sin(yaw)
-
- # goal point check
- dist, _ = obstacle_kd_tree.query([gx, gy])
- if dist <= rr:
- return True # collision
-
- return False # OK
-
-
-def generate_road_map(sample_x, sample_y, rr, obstacle_kd_tree):
- """
- Road map generation
-
- sample_x: [m] x positions of sampled points
- sample_y: [m] y positions of sampled points
- robot_radius: Robot Radius[m]
- obstacle_kd_tree: KDTree object of obstacles
- """
-
- road_map = []
- n_sample = len(sample_x)
- sample_kd_tree = KDTree(np.vstack((sample_x, sample_y)).T)
-
- for (i, ix, iy) in zip(range(n_sample), sample_x, sample_y):
-
- dists, indexes = sample_kd_tree.query([ix, iy], k=n_sample)
- edge_id = []
-
- for ii in range(1, len(indexes)):
- nx = sample_x[indexes[ii]]
- ny = sample_y[indexes[ii]]
-
- if not is_collision(ix, iy, nx, ny, rr, obstacle_kd_tree):
- edge_id.append(indexes[ii])
-
- if len(edge_id) >= N_KNN:
- break
-
- road_map.append(edge_id)
-
- # plot_road_map(road_map, sample_x, sample_y)
-
- return road_map
-
-
-def dijkstra_planning(sx, sy, gx, gy, road_map, sample_x, sample_y):
- """
- s_x: start x position [m]
- s_y: start y position [m]
- goal_x: goal x position [m]
- goal_y: goal y position [m]
- obstacle_x_list: x position list of Obstacles [m]
- obstacle_y_list: y position list of Obstacles [m]
- robot_radius: robot radius [m]
- road_map: ??? [m]
- sample_x: ??? [m]
- sample_y: ??? [m]
-
- @return: Two lists of path coordinates ([x1, x2, ...], [y1, y2, ...]), empty list when no path was found
- """
-
- start_node = Node(sx, sy, 0.0, -1)
- goal_node = Node(gx, gy, 0.0, -1)
-
- open_set, closed_set = dict(), dict()
- open_set[len(road_map) - 2] = start_node
-
- path_found = True
-
- while True:
- if not open_set:
- print("Cannot find path")
- path_found = False
- break
-
- c_id = min(open_set, key=lambda o: open_set[o].cost)
- current = open_set[c_id]
-
- # show graph
- if show_animation and len(closed_set.keys()) % 2 == 0:
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(current.x, current.y, "xg")
- plt.pause(0.001)
-
- if c_id == (len(road_map) - 1):
- print("goal is found!")
- goal_node.parent_index = current.parent_index
- goal_node.cost = current.cost
- break
-
- # Remove the item from the open set
- del open_set[c_id]
- # Add it to the closed set
- closed_set[c_id] = current
-
- # expand search grid based on motion model
- for i in range(len(road_map[c_id])):
- n_id = road_map[c_id][i]
- dx = sample_x[n_id] - current.x
- dy = sample_y[n_id] - current.y
- d = math.hypot(dx, dy)
- node = Node(sample_x[n_id], sample_y[n_id],
- current.cost + d, c_id)
-
- if n_id in closed_set:
- continue
- # Otherwise if it is already in the open set
- if n_id in open_set:
- if open_set[n_id].cost > node.cost:
- open_set[n_id].cost = node.cost
- open_set[n_id].parent_index = c_id
- else:
- open_set[n_id] = node
-
- if path_found is False:
- return [], []
-
- # generate final course
- rx, ry = [goal_node.x], [goal_node.y]
- parent_index = goal_node.parent_index
- while parent_index != -1:
- n = closed_set[parent_index]
- rx.append(n.x)
- ry.append(n.y)
- parent_index = n.parent_index
-
- return rx, ry
-
-
-def plot_road_map(road_map, sample_x, sample_y): # pragma: no cover
-
- for i, _ in enumerate(road_map):
- for ii in range(len(road_map[i])):
- ind = road_map[i][ii]
-
- plt.plot([sample_x[i], sample_x[ind]],
- [sample_y[i], sample_y[ind]], "-k")
-
-
-def sample_points(sx, sy, gx, gy, rr, ox, oy, obstacle_kd_tree, rng):
- max_x = max(ox)
- max_y = max(oy)
- min_x = min(ox)
- min_y = min(oy)
-
- sample_x, sample_y = [], []
-
- if rng is None:
- rng = np.random.default_rng()
-
- while len(sample_x) <= N_SAMPLE:
- tx = (rng.random() * (max_x - min_x)) + min_x
- ty = (rng.random() * (max_y - min_y)) + min_y
-
- dist, index = obstacle_kd_tree.query([tx, ty])
-
- if dist >= rr:
- sample_x.append(tx)
- sample_y.append(ty)
-
- sample_x.append(sx)
- sample_y.append(sy)
- sample_x.append(gx)
- sample_y.append(gy)
-
- return sample_x, sample_y
-
-
-def main(rng=None):
- print(__file__ + " start!!")
-
- # start and goal position
- sx = 10.0 # [m]
- sy = 10.0 # [m]
- gx = 50.0 # [m]
- gy = 50.0 # [m]
- robot_size = 5.0 # [m]
-
- ox = []
- oy = []
-
- for i in range(60):
- ox.append(float(i))
- oy.append(0.0)
- for i in range(60):
- ox.append(60.0)
- oy.append(float(i))
- for i in range(61):
- ox.append(float(i))
- oy.append(60.0)
- for i in range(61):
- ox.append(0.0)
- oy.append(float(i))
- for i in range(40):
- ox.append(20.0)
- oy.append(float(i))
- for i in range(40):
- ox.append(40.0)
- oy.append(60.0 - i)
-
- if show_animation:
- plt.plot(ox, oy, ".k")
- plt.plot(sx, sy, "^r")
- plt.plot(gx, gy, "^c")
- plt.grid(True)
- plt.axis("equal")
-
- rx, ry = prm_planning(sx, sy, gx, gy, ox, oy, robot_size, rng=rng)
-
- assert rx, 'Cannot found path'
-
- if show_animation:
- plt.plot(rx, ry, "-r")
- plt.pause(0.001)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.py b/PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.py
deleted file mode 100644
index fdc181afab9..00000000000
--- a/PathPlanning/QuinticPolynomialsPlanner/quintic_polynomials_planner.py
+++ /dev/null
@@ -1,230 +0,0 @@
-"""
-
-Quintic Polynomials Planner
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-Ref:
-
-- [Local Path planning And Motion Control For Agv In Positioning](https://ieeexplore.ieee.org/document/637936/)
-
-"""
-
-import math
-
-import matplotlib.pyplot as plt
-import numpy as np
-
-# parameter
-MAX_T = 100.0 # maximum time to the goal [s]
-MIN_T = 5.0 # minimum time to the goal[s]
-
-show_animation = True
-
-
-class QuinticPolynomial:
-
- def __init__(self, xs, vxs, axs, xe, vxe, axe, time):
- # calc coefficient of quintic polynomial
- # See jupyter notebook document for derivation of this equation.
- self.a0 = xs
- self.a1 = vxs
- self.a2 = axs / 2.0
-
- A = np.array([[time ** 3, time ** 4, time ** 5],
- [3 * time ** 2, 4 * time ** 3, 5 * time ** 4],
- [6 * time, 12 * time ** 2, 20 * time ** 3]])
- b = np.array([xe - self.a0 - self.a1 * time - self.a2 * time ** 2,
- vxe - self.a1 - 2 * self.a2 * time,
- axe - 2 * self.a2])
- x = np.linalg.solve(A, b)
-
- self.a3 = x[0]
- self.a4 = x[1]
- self.a5 = x[2]
-
- def calc_point(self, t):
- xt = self.a0 + self.a1 * t + self.a2 * t ** 2 + \
- self.a3 * t ** 3 + self.a4 * t ** 4 + self.a5 * t ** 5
-
- return xt
-
- def calc_first_derivative(self, t):
- xt = self.a1 + 2 * self.a2 * t + \
- 3 * self.a3 * t ** 2 + 4 * self.a4 * t ** 3 + 5 * self.a5 * t ** 4
-
- return xt
-
- def calc_second_derivative(self, t):
- xt = 2 * self.a2 + 6 * self.a3 * t + 12 * self.a4 * t ** 2 + 20 * self.a5 * t ** 3
-
- return xt
-
- def calc_third_derivative(self, t):
- xt = 6 * self.a3 + 24 * self.a4 * t + 60 * self.a5 * t ** 2
-
- return xt
-
-
-def quintic_polynomials_planner(sx, sy, syaw, sv, sa, gx, gy, gyaw, gv, ga, max_accel, max_jerk, dt):
- """
- quintic polynomial planner
-
- input
- s_x: start x position [m]
- s_y: start y position [m]
- s_yaw: start yaw angle [rad]
- sa: start accel [m/ss]
- gx: goal x position [m]
- gy: goal y position [m]
- gyaw: goal yaw angle [rad]
- ga: goal accel [m/ss]
- max_accel: maximum accel [m/ss]
- max_jerk: maximum jerk [m/sss]
- dt: time tick [s]
-
- return
- time: time result
- rx: x position result list
- ry: y position result list
- ryaw: yaw angle result list
- rv: velocity result list
- ra: accel result list
-
- """
-
- vxs = sv * math.cos(syaw)
- vys = sv * math.sin(syaw)
- vxg = gv * math.cos(gyaw)
- vyg = gv * math.sin(gyaw)
-
- axs = sa * math.cos(syaw)
- ays = sa * math.sin(syaw)
- axg = ga * math.cos(gyaw)
- ayg = ga * math.sin(gyaw)
-
- time, rx, ry, ryaw, rv, ra, rj = [], [], [], [], [], [], []
-
- for T in np.arange(MIN_T, MAX_T, MIN_T):
- xqp = QuinticPolynomial(sx, vxs, axs, gx, vxg, axg, T)
- yqp = QuinticPolynomial(sy, vys, ays, gy, vyg, ayg, T)
-
- time, rx, ry, ryaw, rv, ra, rj = [], [], [], [], [], [], []
-
- for t in np.arange(0.0, T + dt, dt):
- time.append(t)
- rx.append(xqp.calc_point(t))
- ry.append(yqp.calc_point(t))
-
- vx = xqp.calc_first_derivative(t)
- vy = yqp.calc_first_derivative(t)
- v = np.hypot(vx, vy)
- yaw = math.atan2(vy, vx)
- rv.append(v)
- ryaw.append(yaw)
-
- ax = xqp.calc_second_derivative(t)
- ay = yqp.calc_second_derivative(t)
- a = np.hypot(ax, ay)
- if len(rv) >= 2 and rv[-1] - rv[-2] < 0.0:
- a *= -1
- ra.append(a)
-
- jx = xqp.calc_third_derivative(t)
- jy = yqp.calc_third_derivative(t)
- j = np.hypot(jx, jy)
- if len(ra) >= 2 and ra[-1] - ra[-2] < 0.0:
- j *= -1
- rj.append(j)
-
- if max([abs(i) for i in ra]) <= max_accel and max([abs(i) for i in rj]) <= max_jerk:
- print("find path!!")
- break
-
- if show_animation: # pragma: no cover
- for i, _ in enumerate(time):
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.grid(True)
- plt.axis("equal")
- plot_arrow(sx, sy, syaw)
- plot_arrow(gx, gy, gyaw)
- plot_arrow(rx[i], ry[i], ryaw[i])
- plt.title("Time[s]:" + str(time[i])[0:4] +
- " v[m/s]:" + str(rv[i])[0:4] +
- " a[m/ss]:" + str(ra[i])[0:4] +
- " jerk[m/sss]:" + str(rj[i])[0:4],
- )
- plt.pause(0.001)
-
- return time, rx, ry, ryaw, rv, ra, rj
-
-
-def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"): # pragma: no cover
- """
- Plot arrow
- """
-
- if not isinstance(x, float):
- for (ix, iy, iyaw) in zip(x, y, yaw):
- plot_arrow(ix, iy, iyaw)
- else:
- plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),
- fc=fc, ec=ec, head_width=width, head_length=width)
- plt.plot(x, y)
-
-
-def main():
- print(__file__ + " start!!")
-
- sx = 10.0 # start x position [m]
- sy = 10.0 # start y position [m]
- syaw = np.deg2rad(10.0) # start yaw angle [rad]
- sv = 1.0 # start speed [m/s]
- sa = 0.1 # start accel [m/ss]
- gx = 30.0 # goal x position [m]
- gy = -10.0 # goal y position [m]
- gyaw = np.deg2rad(20.0) # goal yaw angle [rad]
- gv = 1.0 # goal speed [m/s]
- ga = 0.1 # goal accel [m/ss]
- max_accel = 1.0 # max accel [m/ss]
- max_jerk = 0.5 # max jerk [m/sss]
- dt = 0.1 # time tick [s]
-
- time, x, y, yaw, v, a, j = quintic_polynomials_planner(
- sx, sy, syaw, sv, sa, gx, gy, gyaw, gv, ga, max_accel, max_jerk, dt)
-
- if show_animation: # pragma: no cover
- plt.plot(x, y, "-r")
-
- plt.subplots()
- plt.plot(time, [np.rad2deg(i) for i in yaw], "-r")
- plt.xlabel("Time[s]")
- plt.ylabel("Yaw[deg]")
- plt.grid(True)
-
- plt.subplots()
- plt.plot(time, v, "-r")
- plt.xlabel("Time[s]")
- plt.ylabel("Speed[m/s]")
- plt.grid(True)
-
- plt.subplots()
- plt.plot(time, a, "-r")
- plt.xlabel("Time[s]")
- plt.ylabel("accel[m/ss]")
- plt.grid(True)
-
- plt.subplots()
- plt.plot(time, j, "-r")
- plt.xlabel("Time[s]")
- plt.ylabel("jerk[m/sss]")
- plt.grid(True)
-
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/RRT/__init__.py b/PathPlanning/RRT/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathPlanning/RRT/rrt.py b/PathPlanning/RRT/rrt.py
deleted file mode 100644
index e6dd9b648b5..00000000000
--- a/PathPlanning/RRT/rrt.py
+++ /dev/null
@@ -1,291 +0,0 @@
-"""
-
-Path planning Sample Code with Randomized Rapidly-Exploring Random Trees (RRT)
-
-author: AtsushiSakai(@Atsushi_twi)
-
-"""
-
-import math
-import random
-
-import matplotlib.pyplot as plt
-import numpy as np
-
-show_animation = True
-
-
-class RRT:
- """
- Class for RRT planning
- """
-
- class Node:
- """
- RRT Node
- """
-
- def __init__(self, x, y):
- self.x = x
- self.y = y
- self.path_x = []
- self.path_y = []
- self.parent = None
-
- class AreaBounds:
-
- def __init__(self, area):
- self.xmin = float(area[0])
- self.xmax = float(area[1])
- self.ymin = float(area[2])
- self.ymax = float(area[3])
-
-
- def __init__(self,
- start,
- goal,
- obstacle_list,
- rand_area,
- expand_dis=3.0,
- path_resolution=0.5,
- goal_sample_rate=5,
- max_iter=500,
- play_area=None,
- robot_radius=0.0,
- ):
- """
- Setting Parameter
-
- start:Start Position [x,y]
- goal:Goal Position [x,y]
- obstacleList:obstacle Positions [[x,y,size],...]
- randArea:Random Sampling Area [min,max]
- play_area:stay inside this area [xmin,xmax,ymin,ymax]
- robot_radius: robot body modeled as circle with given radius
-
- """
- self.start = self.Node(start[0], start[1])
- self.end = self.Node(goal[0], goal[1])
- self.min_rand = rand_area[0]
- self.max_rand = rand_area[1]
- if play_area is not None:
- self.play_area = self.AreaBounds(play_area)
- else:
- self.play_area = None
- self.expand_dis = expand_dis
- self.path_resolution = path_resolution
- self.goal_sample_rate = goal_sample_rate
- self.max_iter = max_iter
- self.obstacle_list = obstacle_list
- self.node_list = []
- self.robot_radius = robot_radius
-
- def planning(self, animation=True):
- """
- rrt path planning
-
- animation: flag for animation on or off
- """
-
- self.node_list = [self.start]
- for i in range(self.max_iter):
- rnd_node = self.get_random_node()
- nearest_ind = self.get_nearest_node_index(self.node_list, rnd_node)
- nearest_node = self.node_list[nearest_ind]
-
- new_node = self.steer(nearest_node, rnd_node, self.expand_dis)
-
- if self.check_if_outside_play_area(new_node, self.play_area) and \
- self.check_collision(
- new_node, self.obstacle_list, self.robot_radius):
- self.node_list.append(new_node)
-
- if animation and i % 5 == 0:
- self.draw_graph(rnd_node)
-
- if self.calc_dist_to_goal(self.node_list[-1].x,
- self.node_list[-1].y) <= self.expand_dis:
- final_node = self.steer(self.node_list[-1], self.end,
- self.expand_dis)
- if self.check_collision(
- final_node, self.obstacle_list, self.robot_radius):
- return self.generate_final_course(len(self.node_list) - 1)
-
- if animation and i % 5:
- self.draw_graph(rnd_node)
-
- return None # cannot find path
-
- def steer(self, from_node, to_node, extend_length=float("inf")):
-
- new_node = self.Node(from_node.x, from_node.y)
- d, theta = self.calc_distance_and_angle(new_node, to_node)
-
- new_node.path_x = [new_node.x]
- new_node.path_y = [new_node.y]
-
- if extend_length > d:
- extend_length = d
-
- n_expand = math.floor(extend_length / self.path_resolution)
-
- for _ in range(n_expand):
- new_node.x += self.path_resolution * math.cos(theta)
- new_node.y += self.path_resolution * math.sin(theta)
- new_node.path_x.append(new_node.x)
- new_node.path_y.append(new_node.y)
-
- d, _ = self.calc_distance_and_angle(new_node, to_node)
- if d <= self.path_resolution:
- new_node.path_x.append(to_node.x)
- new_node.path_y.append(to_node.y)
- new_node.x = to_node.x
- new_node.y = to_node.y
-
- new_node.parent = from_node
-
- return new_node
-
- def generate_final_course(self, goal_ind):
- path = [[self.end.x, self.end.y]]
- node = self.node_list[goal_ind]
- while node.parent is not None:
- path.append([node.x, node.y])
- node = node.parent
- path.append([node.x, node.y])
-
- return path
-
- def calc_dist_to_goal(self, x, y):
- dx = x - self.end.x
- dy = y - self.end.y
- return math.hypot(dx, dy)
-
- def get_random_node(self):
- if random.randint(0, 100) > self.goal_sample_rate:
- rnd = self.Node(
- random.uniform(self.min_rand, self.max_rand),
- random.uniform(self.min_rand, self.max_rand))
- else: # goal point sampling
- rnd = self.Node(self.end.x, self.end.y)
- return rnd
-
- def draw_graph(self, rnd=None):
- plt.clf()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if rnd is not None:
- plt.plot(rnd.x, rnd.y, "^k")
- if self.robot_radius > 0.0:
- self.plot_circle(rnd.x, rnd.y, self.robot_radius, '-r')
- for node in self.node_list:
- if node.parent:
- plt.plot(node.path_x, node.path_y, "-g")
-
- for (ox, oy, size) in self.obstacle_list:
- self.plot_circle(ox, oy, size)
-
- if self.play_area is not None:
- plt.plot([self.play_area.xmin, self.play_area.xmax,
- self.play_area.xmax, self.play_area.xmin,
- self.play_area.xmin],
- [self.play_area.ymin, self.play_area.ymin,
- self.play_area.ymax, self.play_area.ymax,
- self.play_area.ymin],
- "-k")
-
- plt.plot(self.start.x, self.start.y, "xr")
- plt.plot(self.end.x, self.end.y, "xr")
- plt.axis("equal")
- plt.axis([self.min_rand, self.max_rand, self.min_rand, self.max_rand])
- plt.grid(True)
- plt.pause(0.01)
-
- @staticmethod
- def plot_circle(x, y, size, color="-b"): # pragma: no cover
- deg = list(range(0, 360, 5))
- deg.append(0)
- xl = [x + size * math.cos(np.deg2rad(d)) for d in deg]
- yl = [y + size * math.sin(np.deg2rad(d)) for d in deg]
- plt.plot(xl, yl, color)
-
- @staticmethod
- def get_nearest_node_index(node_list, rnd_node):
- dlist = [(node.x - rnd_node.x)**2 + (node.y - rnd_node.y)**2
- for node in node_list]
- minind = dlist.index(min(dlist))
-
- return minind
-
- @staticmethod
- def check_if_outside_play_area(node, play_area):
-
- if play_area is None:
- return True # no play_area was defined, every pos should be ok
-
- if node.x < play_area.xmin or node.x > play_area.xmax or \
- node.y < play_area.ymin or node.y > play_area.ymax:
- return False # outside - bad
- else:
- return True # inside - ok
-
- @staticmethod
- def check_collision(node, obstacleList, robot_radius):
-
- if node is None:
- return False
-
- for (ox, oy, size) in obstacleList:
- dx_list = [ox - x for x in node.path_x]
- dy_list = [oy - y for y in node.path_y]
- d_list = [dx * dx + dy * dy for (dx, dy) in zip(dx_list, dy_list)]
-
- if min(d_list) <= (size+robot_radius)**2:
- return False # collision
-
- return True # safe
-
- @staticmethod
- def calc_distance_and_angle(from_node, to_node):
- dx = to_node.x - from_node.x
- dy = to_node.y - from_node.y
- d = math.hypot(dx, dy)
- theta = math.atan2(dy, dx)
- return d, theta
-
-
-def main(gx=6.0, gy=10.0):
- print("start " + __file__)
-
- # ====Search Path with RRT====
- obstacleList = [(5, 5, 1), (3, 6, 2), (3, 8, 2), (3, 10, 2), (7, 5, 2),
- (9, 5, 2), (8, 10, 1)] # [x, y, radius]
- # Set Initial parameters
- rrt = RRT(
- start=[0, 0],
- goal=[gx, gy],
- rand_area=[-2, 15],
- obstacle_list=obstacleList,
- # play_area=[0, 10, 0, 14]
- robot_radius=0.8
- )
- path = rrt.planning(animation=show_animation)
-
- if path is None:
- print("Cannot find path")
- else:
- print("found path!!")
-
- # Draw final path
- if show_animation:
- rrt.draw_graph()
- plt.plot([x for (x, y) in path], [y for (x, y) in path], '-r')
- plt.grid(True)
- plt.pause(0.01) # Need for Mac
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/RRT/rrt_with_pathsmoothing.py b/PathPlanning/RRT/rrt_with_pathsmoothing.py
deleted file mode 100644
index 2ed6a366d15..00000000000
--- a/PathPlanning/RRT/rrt_with_pathsmoothing.py
+++ /dev/null
@@ -1,145 +0,0 @@
-"""
-
-Path planning Sample Code with RRT with path smoothing
-
-@author: AtsushiSakai(@Atsushi_twi)
-
-"""
-
-import math
-import random
-import matplotlib.pyplot as plt
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent))
-
-from rrt import RRT
-
-show_animation = True
-
-
-def get_path_length(path):
- le = 0
- for i in range(len(path) - 1):
- dx = path[i + 1][0] - path[i][0]
- dy = path[i + 1][1] - path[i][1]
- d = math.hypot(dx, dy)
- le += d
-
- return le
-
-
-def get_target_point(path, targetL):
- le = 0
- ti = 0
- lastPairLen = 0
- for i in range(len(path) - 1):
- dx = path[i + 1][0] - path[i][0]
- dy = path[i + 1][1] - path[i][1]
- d = math.hypot(dx, dy)
- le += d
- if le >= targetL:
- ti = i - 1
- lastPairLen = d
- break
-
- partRatio = (le - targetL) / lastPairLen
-
- x = path[ti][0] + (path[ti + 1][0] - path[ti][0]) * partRatio
- y = path[ti][1] + (path[ti + 1][1] - path[ti][1]) * partRatio
-
- return [x, y, ti]
-
-
-def line_collision_check(first, second, obstacleList):
- # Line Equation
-
- x1 = first[0]
- y1 = first[1]
- x2 = second[0]
- y2 = second[1]
-
- try:
- a = y2 - y1
- b = -(x2 - x1)
- c = y2 * (x2 - x1) - x2 * (y2 - y1)
- except ZeroDivisionError:
- return False
-
- for (ox, oy, size) in obstacleList:
- d = abs(a * ox + b * oy + c) / (math.hypot(a, b))
- if d <= size:
- return False
-
- return True # OK
-
-
-def path_smoothing(path, max_iter, obstacle_list):
- le = get_path_length(path)
-
- for i in range(max_iter):
- # Sample two points
- pickPoints = [random.uniform(0, le), random.uniform(0, le)]
- pickPoints.sort()
- first = get_target_point(path, pickPoints[0])
- second = get_target_point(path, pickPoints[1])
-
- if first[2] <= 0 or second[2] <= 0:
- continue
-
- if (second[2] + 1) > len(path):
- continue
-
- if second[2] == first[2]:
- continue
-
- # collision check
- if not line_collision_check(first, second, obstacle_list):
- continue
-
- # Create New path
- newPath = []
- newPath.extend(path[:first[2] + 1])
- newPath.append([first[0], first[1]])
- newPath.append([second[0], second[1]])
- newPath.extend(path[second[2] + 1:])
- path = newPath
- le = get_path_length(path)
-
- return path
-
-
-def main():
- # ====Search Path with RRT====
- # Parameter
- obstacleList = [
- (5, 5, 1),
- (3, 6, 2),
- (3, 8, 2),
- (3, 10, 2),
- (7, 5, 2),
- (9, 5, 2)
- ] # [x,y,size]
- rrt = RRT(start=[0, 0], goal=[6, 10],
- rand_area=[-2, 15], obstacle_list=obstacleList)
- path = rrt.planning(animation=show_animation)
-
- # Path smoothing
- maxIter = 1000
- smoothedPath = path_smoothing(path, maxIter, obstacleList)
-
- # Draw final path
- if show_animation:
- rrt.draw_graph()
- plt.plot([x for (x, y) in path], [y for (x, y) in path], '-r')
-
- plt.plot([x for (x, y) in smoothedPath], [
- y for (x, y) in smoothedPath], '-c')
-
- plt.grid(True)
- plt.pause(0.01) # Need for Mac
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/RRT/rrt_with_sobol_sampler.py b/PathPlanning/RRT/rrt_with_sobol_sampler.py
deleted file mode 100644
index 06e0c04c683..00000000000
--- a/PathPlanning/RRT/rrt_with_sobol_sampler.py
+++ /dev/null
@@ -1,278 +0,0 @@
-"""
-
-Path planning Sample Code with Randomized Rapidly-Exploring Random
-Trees with sobol low discrepancy sampler(RRTSobol).
-Sobol wiki https://en.wikipedia.org/wiki/Sobol_sequence
-
-The goal of low discrepancy samplers is to generate a sequence of points that
-optimizes a criterion called dispersion. Intuitively, the idea is to place
-samples to cover the exploration space in a way that makes the largest
-uncovered area be as small as possible. This generalizes of the idea of grid
-resolution. For a grid, the resolution may be selected by defining the step
-size for each axis. As the step size is decreased, the resolution increases.
-If a grid-based motion planning algorithm can increase the resolution
-arbitrarily, it becomes resolution complete. Dispersion can be considered as a
-powerful generalization of the notion of resolution.
-
-Taken from
-LaValle, Steven M. Planning algorithms. Cambridge university press, 2006.
-
-
-authors:
- First implementation AtsushiSakai(@Atsushi_twi)
- Sobol sampler Rafael A.
-Rojas (rafaelrojasmiliani@gmail.com)
-
-
-"""
-
-import math
-import random
-import sys
-import matplotlib.pyplot as plt
-import numpy as np
-
-from sobol import sobol_quasirand
-
-show_animation = True
-
-
-class RRTSobol:
- """
- Class for RRTSobol planning
- """
-
- class Node:
- """
- RRTSobol Node
- """
-
- def __init__(self, x, y):
- self.x = x
- self.y = y
- self.path_x = []
- self.path_y = []
- self.parent = None
-
- def __init__(self,
- start,
- goal,
- obstacle_list,
- rand_area,
- expand_dis=3.0,
- path_resolution=0.5,
- goal_sample_rate=5,
- max_iter=500,
- robot_radius=0.0):
- """
- Setting Parameter
-
- start:Start Position [x,y]
- goal:Goal Position [x,y]
- obstacle_list:obstacle Positions [[x,y,size],...]
- randArea:Random Sampling Area [min,max]
- robot_radius: robot body modeled as circle with given radius
-
- """
- self.start = self.Node(start[0], start[1])
- self.end = self.Node(goal[0], goal[1])
- self.min_rand = rand_area[0]
- self.max_rand = rand_area[1]
- self.expand_dis = expand_dis
- self.path_resolution = path_resolution
- self.goal_sample_rate = goal_sample_rate
- self.max_iter = max_iter
- self.obstacle_list = obstacle_list
- self.node_list = []
- self.sobol_inter_ = 0
- self.robot_radius = robot_radius
-
- def planning(self, animation=True):
- """
- rrt path planning
-
- animation: flag for animation on or off
- """
-
- self.node_list = [self.start]
- for i in range(self.max_iter):
- rnd_node = self.get_random_node()
- nearest_ind = self.get_nearest_node_index(self.node_list, rnd_node)
- nearest_node = self.node_list[nearest_ind]
-
- new_node = self.steer(nearest_node, rnd_node, self.expand_dis)
-
- if self.check_collision(
- new_node, self.obstacle_list, self.robot_radius):
- self.node_list.append(new_node)
-
- if animation and i % 5 == 0:
- self.draw_graph(rnd_node)
-
- if self.calc_dist_to_goal(self.node_list[-1].x,
- self.node_list[-1].y) <= self.expand_dis:
- final_node = self.steer(self.node_list[-1], self.end,
- self.expand_dis)
- if self.check_collision(
- final_node, self.obstacle_list, self.robot_radius):
- return self.generate_final_course(len(self.node_list) - 1)
-
- if animation and i % 5:
- self.draw_graph(rnd_node)
-
- return None # cannot find path
-
- def steer(self, from_node, to_node, extend_length=float("inf")):
-
- new_node = self.Node(from_node.x, from_node.y)
- d, theta = self.calc_distance_and_angle(new_node, to_node)
-
- new_node.path_x = [new_node.x]
- new_node.path_y = [new_node.y]
-
- if extend_length > d:
- extend_length = d
-
- n_expand = math.floor(extend_length / self.path_resolution)
-
- for _ in range(n_expand):
- new_node.x += self.path_resolution * math.cos(theta)
- new_node.y += self.path_resolution * math.sin(theta)
- new_node.path_x.append(new_node.x)
- new_node.path_y.append(new_node.y)
-
- d, _ = self.calc_distance_and_angle(new_node, to_node)
- if d <= self.path_resolution:
- new_node.path_x.append(to_node.x)
- new_node.path_y.append(to_node.y)
- new_node.x = to_node.x
- new_node.y = to_node.y
-
- new_node.parent = from_node
-
- return new_node
-
- def generate_final_course(self, goal_ind):
- path = [[self.end.x, self.end.y]]
- node = self.node_list[goal_ind]
- while node.parent is not None:
- path.append([node.x, node.y])
- node = node.parent
- path.append([node.x, node.y])
-
- return path
-
- def calc_dist_to_goal(self, x, y):
- dx = x - self.end.x
- dy = y - self.end.y
- return math.hypot(dx, dy)
-
- def get_random_node(self):
- if random.randint(0, 100) > self.goal_sample_rate:
- rand_coordinates, n = sobol_quasirand(2, self.sobol_inter_)
-
- rand_coordinates = self.min_rand + \
- rand_coordinates*(self.max_rand - self.min_rand)
- self.sobol_inter_ = n
- rnd = self.Node(*rand_coordinates)
-
- else: # goal point sampling
- rnd = self.Node(self.end.x, self.end.y)
- return rnd
-
- def draw_graph(self, rnd=None):
- plt.clf()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [sys.exit(0) if event.key == 'escape' else None])
- if rnd is not None:
- plt.plot(rnd.x, rnd.y, "^k")
- if self.robot_radius >= 0.0:
- self.plot_circle(rnd.x, rnd.y, self.robot_radius, '-r')
- for node in self.node_list:
- if node.parent:
- plt.plot(node.path_x, node.path_y, "-g")
-
- for (ox, oy, size) in self.obstacle_list:
- self.plot_circle(ox, oy, size)
-
- plt.plot(self.start.x, self.start.y, "xr")
- plt.plot(self.end.x, self.end.y, "xr")
- plt.axis("equal")
- plt.axis([-2, 15, -2, 15])
- plt.grid(True)
- plt.pause(0.01)
-
- @staticmethod
- def plot_circle(x, y, size, color="-b"): # pragma: no cover
- deg = list(range(0, 360, 5))
- deg.append(0)
- xl = [x + size * math.cos(np.deg2rad(d)) for d in deg]
- yl = [y + size * math.sin(np.deg2rad(d)) for d in deg]
- plt.plot(xl, yl, color)
-
- @staticmethod
- def get_nearest_node_index(node_list, rnd_node):
- dlist = [(node.x - rnd_node.x)**2 + (node.y - rnd_node.y)**2
- for node in node_list]
- minind = dlist.index(min(dlist))
-
- return minind
-
- @staticmethod
- def check_collision(node, obstacle_list, robot_radius):
-
- if node is None:
- return False
-
- for (ox, oy, size) in obstacle_list:
- dx_list = [ox - x for x in node.path_x]
- dy_list = [oy - y for y in node.path_y]
- d_list = [dx * dx + dy * dy for (dx, dy) in zip(dx_list, dy_list)]
-
- if min(d_list) <= (size+robot_radius)**2:
- return False # collision
-
- return True # safe
-
- @staticmethod
- def calc_distance_and_angle(from_node, to_node):
- dx = to_node.x - from_node.x
- dy = to_node.y - from_node.y
- d = math.hypot(dx, dy)
- theta = math.atan2(dy, dx)
- return d, theta
-
-
-def main(gx=6.0, gy=10.0):
- print("start " + __file__)
-
- # ====Search Path with RRTSobol====
- obstacle_list = [(5, 5, 1), (3, 6, 2), (3, 8, 2), (3, 10, 2), (7, 5, 2),
- (9, 5, 2), (8, 10, 1)] # [x, y, radius]
- # Set Initial parameters
- rrt = RRTSobol(
- start=[0, 0],
- goal=[gx, gy],
- rand_area=[-2, 15],
- obstacle_list=obstacle_list,
- robot_radius=0.8)
- path = rrt.planning(animation=show_animation)
-
- if path is None:
- print("Cannot find path")
- else:
- print("found path!!")
-
- # Draw final path
- if show_animation:
- rrt.draw_graph()
- plt.plot([x for (x, y) in path], [y for (x, y) in path], '-r')
- plt.grid(True)
- plt.pause(0.01) # Need for Mac
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/RRT/sobol/__init__.py b/PathPlanning/RRT/sobol/__init__.py
deleted file mode 100644
index c95ac8983b5..00000000000
--- a/PathPlanning/RRT/sobol/__init__.py
+++ /dev/null
@@ -1 +0,0 @@
-from .sobol import i4_sobol as sobol_quasirand
diff --git a/PathPlanning/RRT/sobol/sobol.py b/PathPlanning/RRT/sobol/sobol.py
deleted file mode 100644
index 520d686a1d3..00000000000
--- a/PathPlanning/RRT/sobol/sobol.py
+++ /dev/null
@@ -1,911 +0,0 @@
-"""
- Licensing:
- This code is distributed under the MIT license.
-
- Authors:
- Original FORTRAN77 version of i4_sobol by Bennett Fox.
- MATLAB version by John Burkardt.
- PYTHON version by Corrado Chisari
-
- Original Python version of is_prime by Corrado Chisari
-
- Original MATLAB versions of other functions by John Burkardt.
- PYTHON versions by Corrado Chisari
-
- Original code is available at
- https://people.sc.fsu.edu/~jburkardt/py_src/sobol/sobol.html
-
- Note: the i4 prefix means that the function takes a numeric argument or
- returns a number which is interpreted inside the function as a 4
- byte integer
- Note: the r4 prefix means that the function takes a numeric argument or
- returns a number which is interpreted inside the function as a 4
- byte float
-"""
-import math
-import sys
-import numpy as np
-
-atmost = None
-dim_max = None
-dim_num_save = None
-initialized = None
-lastq = None
-log_max = None
-maxcol = None
-poly = None
-recipd = None
-seed_save = None
-v = None
-
-
-def i4_bit_hi1(n):
- """
- I4_BIT_HI1 returns the position of the high 1 bit base 2 in an I4.
-
- Discussion:
-
- An I4 is an integer ( kind = 4 ) value.
-
- Example:
-
- N Binary Hi 1
- ---- -------- ----
- 0 0 0
- 1 1 1
- 2 10 2
- 3 11 2
- 4 100 3
- 5 101 3
- 6 110 3
- 7 111 3
- 8 1000 4
- 9 1001 4
- 10 1010 4
- 11 1011 4
- 12 1100 4
- 13 1101 4
- 14 1110 4
- 15 1111 4
- 16 10000 5
- 17 10001 5
- 1023 1111111111 10
- 1024 10000000000 11
- 1025 10000000001 11
-
- Licensing:
-
- This code is distributed under the GNU LGPL license.
-
- Modified:
-
- 26 October 2014
-
- Author:
-
- John Burkardt
-
- Parameters:
-
- Input, integer N, the integer to be measured.
- N should be nonnegative. If N is nonpositive, the function
- will always be 0.
-
- Output, integer BIT, the position of the highest bit.
-
- """
- i = n
- bit = 0
-
- while True:
-
- if i <= 0:
- break
-
- bit = bit + 1
- i = i // 2
-
- return bit
-
-
-def i4_bit_lo0(n):
- """
- I4_BIT_LO0 returns the position of the low 0 bit base 2 in an I4.
-
- Discussion:
-
- An I4 is an integer ( kind = 4 ) value.
-
- Example:
-
- N Binary Lo 0
- ---- -------- ----
- 0 0 1
- 1 1 2
- 2 10 1
- 3 11 3
- 4 100 1
- 5 101 2
- 6 110 1
- 7 111 4
- 8 1000 1
- 9 1001 2
- 10 1010 1
- 11 1011 3
- 12 1100 1
- 13 1101 2
- 14 1110 1
- 15 1111 5
- 16 10000 1
- 17 10001 2
- 1023 1111111111 11
- 1024 10000000000 1
- 1025 10000000001 2
-
- Licensing:
-
- This code is distributed under the GNU LGPL license.
-
- Modified:
-
- 08 February 2018
-
- Author:
-
- John Burkardt
-
- Parameters:
-
- Input, integer N, the integer to be measured.
- N should be nonnegative.
-
- Output, integer BIT, the position of the low 1 bit.
-
- """
- bit = 0
- i = n
-
- while True:
-
- bit = bit + 1
- i2 = i // 2
-
- if i == 2 * i2:
- break
-
- i = i2
-
- return bit
-
-
-def i4_sobol_generate(m, n, skip):
- """
-
-
- I4_SOBOL_GENERATE generates a Sobol dataset.
-
- Licensing:
-
- This code is distributed under the MIT license.
-
- Modified:
-
- 22 February 2011
-
- Author:
-
- Original MATLAB version by John Burkardt.
- PYTHON version by Corrado Chisari
-
- Parameters:
-
- Input, integer M, the spatial dimension.
-
- Input, integer N, the number of points to generate.
-
- Input, integer SKIP, the number of initial points to skip.
-
- Output, real R(M,N), the points.
-
- """
- r = np.zeros((m, n))
- for j in range(1, n + 1):
- seed = skip + j - 2
- [r[0:m, j - 1], seed] = i4_sobol(m, seed)
- return r
-
-
-def i4_sobol(dim_num, seed):
- """
-
-
- I4_SOBOL generates a new quasirandom Sobol vector with each call.
-
- Discussion:
-
- The routine adapts the ideas of Antonov and Saleev.
-
- Licensing:
-
- This code is distributed under the MIT license.
-
- Modified:
-
- 22 February 2011
-
- Author:
-
- Original FORTRAN77 version by Bennett Fox.
- MATLAB version by John Burkardt.
- PYTHON version by Corrado Chisari
-
- Reference:
-
- Antonov, Saleev,
- USSR Computational Mathematics and Mathematical Physics,
- olume 19, 19, pages 252 - 256.
-
- Paul Bratley, Bennett Fox,
- Algorithm 659:
- Implementing Sobol's Quasirandom Sequence Generator,
- ACM Transactions on Mathematical Software,
- Volume 14, Number 1, pages 88-100, 1988.
-
- Bennett Fox,
- Algorithm 647:
- Implementation and Relative Efficiency of Quasirandom
- Sequence Generators,
- ACM Transactions on Mathematical Software,
- Volume 12, Number 4, pages 362-376, 1986.
-
- Ilya Sobol,
- USSR Computational Mathematics and Mathematical Physics,
- Volume 16, pages 236-242, 1977.
-
- Ilya Sobol, Levitan,
- The Production of Points Uniformly Distributed in a Multidimensional
- Cube (in Russian),
- Preprint IPM Akad. Nauk SSSR,
- Number 40, Moscow 1976.
-
- Parameters:
-
- Input, integer DIM_NUM, the number of spatial dimensions.
- DIM_NUM must satisfy 1 <= DIM_NUM <= 40.
-
- Input/output, integer SEED, the "seed" for the sequence.
- This is essentially the index in the sequence of the quasirandom
- value to be generated. On output, SEED has been set to the
- appropriate next value, usually simply SEED+1.
- If SEED is less than 0 on input, it is treated as though it were 0.
- An input value of 0 requests the first (0-th) element of the sequence.
-
- Output, real QUASI(DIM_NUM), the next quasirandom vector.
-
- """
-
- global atmost
- global dim_max
- global dim_num_save
- global initialized
- global lastq
- global log_max
- global maxcol
- global poly
- global recipd
- global seed_save
- global v
-
- if not initialized or dim_num != dim_num_save:
- initialized = 1
- dim_max = 40
- dim_num_save = -1
- log_max = 30
- seed_save = -1
- #
- # Initialize (part of) V.
- #
- v = np.zeros((dim_max, log_max))
- v[0:40, 0] = np.transpose([
- 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
- 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
- ])
-
- v[2:40, 1] = np.transpose([
- 1, 3, 1, 3, 1, 3, 3, 1, 3, 1, 3, 1, 3, 1, 1, 3, 1, 3, 1, 3, 1, 3,
- 3, 1, 3, 1, 3, 1, 3, 1, 1, 3, 1, 3, 1, 3, 1, 3
- ])
-
- v[3:40, 2] = np.transpose([
- 7, 5, 1, 3, 3, 7, 5, 5, 7, 7, 1, 3, 3, 7, 5, 1, 1, 5, 3, 3, 1, 7,
- 5, 1, 3, 3, 7, 5, 1, 1, 5, 7, 7, 5, 1, 3, 3
- ])
-
- v[5:40, 3] = np.transpose([
- 1, 7, 9, 13, 11, 1, 3, 7, 9, 5, 13, 13, 11, 3, 15, 5, 3, 15, 7, 9,
- 13, 9, 1, 11, 7, 5, 15, 1, 15, 11, 5, 3, 1, 7, 9
- ])
-
- v[7:40, 4] = np.transpose([
- 9, 3, 27, 15, 29, 21, 23, 19, 11, 25, 7, 13, 17, 1, 25, 29, 3, 31,
- 11, 5, 23, 27, 19, 21, 5, 1, 17, 13, 7, 15, 9, 31, 9
- ])
-
- v[13:40, 5] = np.transpose([
- 37, 33, 7, 5, 11, 39, 63, 27, 17, 15, 23, 29, 3, 21, 13, 31, 25, 9,
- 49, 33, 19, 29, 11, 19, 27, 15, 25
- ])
-
- v[19:40, 6] = np.transpose([
- 13, 33, 115, 41, 79, 17, 29, 119, 75, 73, 105, 7, 59, 65, 21, 3,
- 113, 61, 89, 45, 107
- ])
-
- v[37:40, 7] = np.transpose([7, 23, 39])
- #
- # Set POLY.
- #
- poly = [
- 1, 3, 7, 11, 13, 19, 25, 37, 59, 47, 61, 55, 41, 67, 97, 91, 109,
- 103, 115, 131, 193, 137, 145, 143, 241, 157, 185, 167, 229, 171,
- 213, 191, 253, 203, 211, 239, 247, 285, 369, 299
- ]
-
- atmost = 2**log_max - 1
- #
- # Find the number of bits in ATMOST.
- #
- maxcol = i4_bit_hi1(atmost)
- #
- # Initialize row 1 of V.
- #
- v[0, 0:maxcol] = 1
-
- # Things to do only if the dimension changed.
-
- if dim_num != dim_num_save:
- #
- # Check parameters.
- #
- if (dim_num < 1 or dim_max < dim_num):
- print('I4_SOBOL - Fatal error!')
- print(' The spatial dimension DIM_NUM should satisfy:')
- print(f' 1 <= DIM_NUM <= {dim_max:d}')
- print(f' But this input value is DIM_NUM = {dim_num:d}')
- return None
-
- dim_num_save = dim_num
- #
- # Initialize the remaining rows of V.
- #
- for i in range(2, dim_num + 1):
- #
- # The bits of the integer POLY(I) gives the form of polynomial
- # I.
- #
- # Find the degree of polynomial I from binary encoding.
- #
- j = poly[i - 1]
- m = 0
- while True:
- j = math.floor(j / 2.)
- if (j <= 0):
- break
- m = m + 1
- #
- # Expand this bit pattern to separate components of the logical
- # array INCLUD.
- #
- j = poly[i - 1]
- includ = np.zeros(m)
- for k in range(m, 0, -1):
- j2 = math.floor(j / 2.)
- includ[k - 1] = (j != 2 * j2)
- j = j2
- #
- # Calculate the remaining elements of row I as explained
- # in Bratley and Fox, section 2.
- #
- for j in range(m + 1, maxcol + 1):
- newv = v[i - 1, j - m - 1]
- l_var = 1
- for k in range(1, m + 1):
- l_var = 2 * l_var
- if (includ[k - 1]):
- newv = np.bitwise_xor(
- int(newv), int(l_var * v[i - 1, j - k - 1]))
- v[i - 1, j - 1] = newv
-#
-# Multiply columns of V by appropriate power of 2.
-#
- l_var = 1
- for j in range(maxcol - 1, 0, -1):
- l_var = 2 * l_var
- v[0:dim_num, j - 1] = v[0:dim_num, j - 1] * l_var
-#
-# RECIPD is 1/(common denominator of the elements in V).
-#
- recipd = 1.0 / (2 * l_var)
- lastq = np.zeros(dim_num)
-
- seed = int(math.floor(seed))
-
- if (seed < 0):
- seed = 0
-
- if (seed == 0):
- l_var = 1
- lastq = np.zeros(dim_num)
-
- elif (seed == seed_save + 1):
- #
- # Find the position of the right-hand zero in SEED.
- #
- l_var = i4_bit_lo0(seed)
-
- elif seed <= seed_save:
-
- seed_save = 0
- lastq = np.zeros(dim_num)
-
- for seed_temp in range(int(seed_save), int(seed)):
- l_var = i4_bit_lo0(seed_temp)
- for i in range(1, dim_num + 1):
- lastq[i - 1] = np.bitwise_xor(
- int(lastq[i - 1]), int(v[i - 1, l_var - 1]))
-
- l_var = i4_bit_lo0(seed)
-
- elif (seed_save + 1 < seed):
-
- for seed_temp in range(int(seed_save + 1), int(seed)):
- l_var = i4_bit_lo0(seed_temp)
- for i in range(1, dim_num + 1):
- lastq[i - 1] = np.bitwise_xor(
- int(lastq[i - 1]), int(v[i - 1, l_var - 1]))
-
- l_var = i4_bit_lo0(seed)
-#
-# Check that the user is not calling too many times!
-#
- if maxcol < l_var:
- print('I4_SOBOL - Fatal error!')
- print(' Too many calls!')
- print(f' MAXCOL = {maxcol:d}\n')
- print(f' L = {l_var:d}\n')
- return None
-
-
-#
-# Calculate the new components of QUASI.
-#
- quasi = np.zeros(dim_num)
- for i in range(1, dim_num + 1):
- quasi[i - 1] = lastq[i - 1] * recipd
- lastq[i - 1] = np.bitwise_xor(
- int(lastq[i - 1]), int(v[i - 1, l_var - 1]))
-
- seed_save = seed
- seed = seed + 1
-
- return [quasi, seed]
-
-
-def i4_uniform_ab(a, b, seed):
- """
-
-
- I4_UNIFORM_AB returns a scaled pseudorandom I4.
-
- Discussion:
-
- The pseudorandom number will be scaled to be uniformly distributed
- between A and B.
-
- Licensing:
-
- This code is distributed under the GNU LGPL license.
-
- Modified:
-
- 05 April 2013
-
- Author:
-
- John Burkardt
-
- Reference:
-
- Paul Bratley, Bennett Fox, Linus Schrage,
- A Guide to Simulation,
- Second Edition,
- Springer, 1987,
- ISBN: 0387964673,
- LC: QA76.9.C65.B73.
-
- Bennett Fox,
- Algorithm 647:
- Implementation and Relative Efficiency of Quasirandom
- Sequence Generators,
- ACM Transactions on Mathematical Software,
- Volume 12, Number 4, December 1986, pages 362-376.
-
- Pierre L'Ecuyer,
- Random Number Generation,
- in Handbook of Simulation,
- edited by Jerry Banks,
- Wiley, 1998,
- ISBN: 0471134031,
- LC: T57.62.H37.
-
- Peter Lewis, Allen Goodman, James Miller,
- A Pseudo-Random Number Generator for the System/360,
- IBM Systems Journal,
- Volume 8, Number 2, 1969, pages 136-143.
-
- Parameters:
-
- Input, integer A, B, the minimum and maximum acceptable values.
-
- Input, integer SEED, a seed for the random number generator.
-
- Output, integer C, the randomly chosen integer.
-
- Output, integer SEED, the updated seed.
-
- """
-
- i4_huge = 2147483647
-
- seed = int(seed)
-
- seed = (seed % i4_huge)
-
- if seed < 0:
- seed = seed + i4_huge
-
- if seed == 0:
- print('')
- print('I4_UNIFORM_AB - Fatal error!')
- print(' Input SEED = 0!')
- sys.exit('I4_UNIFORM_AB - Fatal error!')
-
- k = (seed // 127773)
-
- seed = 167 * (seed - k * 127773) - k * 2836
-
- if seed < 0:
- seed = seed + i4_huge
-
- r = seed * 4.656612875E-10
- #
- # Scale R to lie between A-0.5 and B+0.5.
- #
- a = round(a)
- b = round(b)
-
- r = (1.0 - r) * (min(a, b) - 0.5) \
- + r * (max(a, b) + 0.5)
- #
- # Use rounding to convert R to an integer between A and B.
- #
- value = round(r)
-
- value = max(value, min(a, b))
- value = min(value, max(a, b))
- value = int(value)
-
- return value, seed
-
-
-def prime_ge(n):
- """
-
-
- PRIME_GE returns the smallest prime greater than or equal to N.
-
- Example:
-
- N PRIME_GE
-
- -10 2
- 1 2
- 2 2
- 3 3
- 4 5
- 5 5
- 6 7
- 7 7
- 8 11
- 9 11
- 10 11
-
- Licensing:
-
- This code is distributed under the MIT license.
-
- Modified:
-
- 22 February 2011
-
- Author:
-
- Original MATLAB version by John Burkardt.
- PYTHON version by Corrado Chisari
-
- Parameters:
-
- Input, integer N, the number to be bounded.
-
- Output, integer P, the smallest prime number that is greater
- than or equal to N.
-
- """
- p = max(math.ceil(n), 2)
- while not isprime(p):
- p = p + 1
-
- return p
-
-
-def isprime(n):
- """
-
-
- IS_PRIME returns True if N is a prime number, False otherwise
-
- Licensing:
-
- This code is distributed under the MIT license.
-
- Modified:
-
- 22 February 2011
-
- Author:
-
- Corrado Chisari
-
- Parameters:
-
- Input, integer N, the number to be checked.
-
- Output, boolean value, True or False
-
- """
- if n != int(n) or n < 1:
- return False
- p = 2
- while p < n:
- if n % p == 0:
- return False
- p += 1
-
- return True
-
-
-def r4_uniform_01(seed):
- """
-
-
- R4_UNIFORM_01 returns a unit pseudorandom R4.
-
- Discussion:
-
- This routine implements the recursion
-
- seed = 167 * seed mod ( 2^31 - 1 )
- r = seed / ( 2^31 - 1 )
-
- The integer arithmetic never requires more than 32 bits,
- including a sign bit.
-
- If the initial seed is 12345, then the first three computations are
-
- Input Output R4_UNIFORM_01
- SEED SEED
-
- 12345 207482415 0.096616
- 207482415 1790989824 0.833995
- 1790989824 2035175616 0.947702
-
- Licensing:
-
- This code is distributed under the GNU LGPL license.
-
- Modified:
-
- 04 April 2013
-
- Author:
-
- John Burkardt
-
- Reference:
-
- Paul Bratley, Bennett Fox, Linus Schrage,
- A Guide to Simulation,
- Second Edition,
- Springer, 1987,
- ISBN: 0387964673,
- LC: QA76.9.C65.B73.
-
- Bennett Fox,
- Algorithm 647:
- Implementation and Relative Efficiency of Quasirandom
- Sequence Generators,
- ACM Transactions on Mathematical Software,
- Volume 12, Number 4, December 1986, pages 362-376.
-
- Pierre L'Ecuyer,
- Random Number Generation,
- in Handbook of Simulation,
- edited by Jerry Banks,
- Wiley, 1998,
- ISBN: 0471134031,
- LC: T57.62.H37.
-
- Peter Lewis, Allen Goodman, James Miller,
- A Pseudo-Random Number Generator for the System/360,
- IBM Systems Journal,
- Volume 8, Number 2, 1969, pages 136-143.
-
- Parameters:
-
- Input, integer SEED, the integer "seed" used to generate
- the output random number. SEED should not be 0.
-
- Output, real R, a random value between 0 and 1.
-
- Output, integer SEED, the updated seed. This would
- normally be used as the input seed on the next call.
-
- """
-
- i4_huge = 2147483647
-
- if (seed == 0):
- print('')
- print('R4_UNIFORM_01 - Fatal error!')
- print(' Input SEED = 0!')
- sys.exit('R4_UNIFORM_01 - Fatal error!')
-
- seed = (seed % i4_huge)
-
- if seed < 0:
- seed = seed + i4_huge
-
- k = (seed // 127773)
-
- seed = 167 * (seed - k * 127773) - k * 2836
-
- if seed < 0:
- seed = seed + i4_huge
-
- r = seed * 4.656612875E-10
-
- return r, seed
-
-
-def r8mat_write(filename, m, n, a):
- """
-
-
- R8MAT_WRITE writes an R8MAT to a file.
-
- Licensing:
-
- This code is distributed under the GNU LGPL license.
-
- Modified:
-
- 12 October 2014
-
- Author:
-
- John Burkardt
-
- Parameters:
-
- Input, string FILENAME, the name of the output file.
-
- Input, integer M, the number of rows in A.
-
- Input, integer N, the number of columns in A.
-
- Input, real A(M,N), the matrix.
- """
-
- with open(filename, 'w') as output:
- for i in range(0, m):
- for j in range(0, n):
- s = f' {a[i, j]:g}'
- output.write(s)
- output.write('\n')
-
-
-def tau_sobol(dim_num):
- """
-
-
- TAU_SOBOL defines favorable starting seeds for Sobol sequences.
-
- Discussion:
-
- For spatial dimensions 1 through 13, this routine returns
- a "favorable" value TAU by which an appropriate starting point
- in the Sobol sequence can be determined.
-
- These starting points have the form N = 2**K, where
- for integration problems, it is desirable that
- TAU + DIM_NUM - 1 <= K
- while for optimization problems, it is desirable that
- TAU < K.
-
- Licensing:
-
- This code is distributed under the MIT license.
-
- Modified:
-
- 22 February 2011
-
- Author:
-
- Original FORTRAN77 version by Bennett Fox.
- MATLAB version by John Burkardt.
- PYTHON version by Corrado Chisari
-
- Reference:
-
- IA Antonov, VM Saleev,
- USSR Computational Mathematics and Mathematical Physics,
- Volume 19, 19, pages 252 - 256.
-
- Paul Bratley, Bennett Fox,
- Algorithm 659:
- Implementing Sobol's Quasirandom Sequence Generator,
- ACM Transactions on Mathematical Software,
- Volume 14, Number 1, pages 88-100, 1988.
-
- Bennett Fox,
- Algorithm 647:
- Implementation and Relative Efficiency of Quasirandom
- Sequence Generators,
- ACM Transactions on Mathematical Software,
- Volume 12, Number 4, pages 362-376, 1986.
-
- Stephen Joe, Frances Kuo
- Remark on Algorithm 659:
- Implementing Sobol's Quasirandom Sequence Generator,
- ACM Transactions on Mathematical Software,
- Volume 29, Number 1, pages 49-57, March 2003.
-
- Ilya Sobol,
- USSR Computational Mathematics and Mathematical Physics,
- Volume 16, pages 236-242, 1977.
-
- Ilya Sobol, YL Levitan,
- The Production of Points Uniformly Distributed in a Multidimensional
- Cube (in Russian),
- Preprint IPM Akad. Nauk SSSR,
- Number 40, Moscow 1976.
-
- Parameters:
-
- Input, integer DIM_NUM, the spatial dimension. Only values
- of 1 through 13 will result in useful responses.
-
- Output, integer TAU, the value TAU.
-
- """
- dim_max = 13
-
- tau_table = [0, 0, 1, 3, 5, 8, 11, 15, 19, 23, 27, 31, 35]
-
- if 1 <= dim_num <= dim_max:
- tau = tau_table[dim_num]
- else:
- tau = -1
-
- return tau
diff --git a/PathPlanning/RRTDubins/__init__.py b/PathPlanning/RRTDubins/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathPlanning/RRTDubins/rrt_dubins.py b/PathPlanning/RRTDubins/rrt_dubins.py
deleted file mode 100644
index f938419f359..00000000000
--- a/PathPlanning/RRTDubins/rrt_dubins.py
+++ /dev/null
@@ -1,238 +0,0 @@
-"""
-Path planning Sample Code with RRT with Dubins path
-
-author: AtsushiSakai(@Atsushi_twi)
-
-"""
-import copy
-import math
-import random
-import numpy as np
-import matplotlib.pyplot as plt
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent)) # root dir
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from RRT.rrt import RRT
-from DubinsPath import dubins_path_planner
-from utils.plot import plot_arrow
-
-show_animation = True
-
-
-class RRTDubins(RRT):
- """
- Class for RRT planning with Dubins path
- """
-
- class Node(RRT.Node):
- """
- RRT Node
- """
-
- def __init__(self, x, y, yaw):
- super().__init__(x, y)
- self.cost = 0
- self.yaw = yaw
- self.path_yaw = []
-
- def __init__(self, start, goal, obstacle_list, rand_area,
- goal_sample_rate=10,
- max_iter=200,
- robot_radius=0.0
- ):
- """
- Setting Parameter
-
- start:Start Position [x,y]
- goal:Goal Position [x,y]
- obstacleList:obstacle Positions [[x,y,size],...]
- randArea:Random Sampling Area [min,max]
- robot_radius: robot body modeled as circle with given radius
-
- """
- self.start = self.Node(start[0], start[1], start[2])
- self.end = self.Node(goal[0], goal[1], goal[2])
- self.min_rand = rand_area[0]
- self.max_rand = rand_area[1]
- self.goal_sample_rate = goal_sample_rate
- self.max_iter = max_iter
- self.obstacle_list = obstacle_list
-
- self.curvature = 1.0 # for dubins path
- self.goal_yaw_th = np.deg2rad(1.0)
- self.goal_xy_th = 0.5
- self.robot_radius = robot_radius
-
- def planning(self, animation=True, search_until_max_iter=True):
- """
- execute planning
-
- animation: flag for animation on or off
- """
-
- self.node_list = [self.start]
- for i in range(self.max_iter):
- print("Iter:", i, ", number of nodes:", len(self.node_list))
- rnd = self.get_random_node()
- nearest_ind = self.get_nearest_node_index(self.node_list, rnd)
- new_node = self.steer(self.node_list[nearest_ind], rnd)
-
- if self.check_collision(
- new_node, self.obstacle_list, self.robot_radius):
- self.node_list.append(new_node)
-
- if animation and i % 5 == 0:
- self.plot_start_goal_arrow()
- self.draw_graph(rnd)
-
- if (not search_until_max_iter) and new_node: # check reaching the goal
- last_index = self.search_best_goal_node()
- if last_index:
- return self.generate_final_course(last_index)
-
- print("reached max iteration")
-
- last_index = self.search_best_goal_node()
- if last_index:
- return self.generate_final_course(last_index)
- else:
- print("Cannot find path")
-
- return None
-
- def draw_graph(self, rnd=None): # pragma: no cover
- plt.clf()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if rnd is not None:
- plt.plot(rnd.x, rnd.y, "^k")
- for node in self.node_list:
- if node.parent:
- plt.plot(node.path_x, node.path_y, "-g")
-
- for (ox, oy, size) in self.obstacle_list:
- plt.plot(ox, oy, "ok", ms=30 * size)
-
- plt.plot(self.start.x, self.start.y, "xr")
- plt.plot(self.end.x, self.end.y, "xr")
- plt.axis([-2, 15, -2, 15])
- plt.grid(True)
- self.plot_start_goal_arrow()
- plt.pause(0.01)
-
- def plot_start_goal_arrow(self): # pragma: no cover
- plot_arrow(self.start.x, self.start.y, self.start.yaw)
- plot_arrow(self.end.x, self.end.y, self.end.yaw)
-
- def steer(self, from_node, to_node):
-
- px, py, pyaw, mode, course_lengths = \
- dubins_path_planner.plan_dubins_path(
- from_node.x, from_node.y, from_node.yaw,
- to_node.x, to_node.y, to_node.yaw, self.curvature)
-
- if len(px) <= 1: # cannot find a dubins path
- return None
-
- new_node = copy.deepcopy(from_node)
- new_node.x = px[-1]
- new_node.y = py[-1]
- new_node.yaw = pyaw[-1]
-
- new_node.path_x = px
- new_node.path_y = py
- new_node.path_yaw = pyaw
- new_node.cost += sum([abs(c) for c in course_lengths])
- new_node.parent = from_node
-
- return new_node
-
- def calc_new_cost(self, from_node, to_node):
-
- _, _, _, _, course_length = dubins_path_planner.plan_dubins_path(
- from_node.x, from_node.y, from_node.yaw,
- to_node.x, to_node.y, to_node.yaw, self.curvature)
-
- return from_node.cost + course_length
-
- def get_random_node(self):
-
- if random.randint(0, 100) > self.goal_sample_rate:
- rnd = self.Node(random.uniform(self.min_rand, self.max_rand),
- random.uniform(self.min_rand, self.max_rand),
- random.uniform(-math.pi, math.pi)
- )
- else: # goal point sampling
- rnd = self.Node(self.end.x, self.end.y, self.end.yaw)
-
- return rnd
-
- def search_best_goal_node(self):
-
- goal_indexes = []
- for (i, node) in enumerate(self.node_list):
- if self.calc_dist_to_goal(node.x, node.y) <= self.goal_xy_th:
- goal_indexes.append(i)
-
- # angle check
- final_goal_indexes = []
- for i in goal_indexes:
- if abs(self.node_list[i].yaw - self.end.yaw) <= self.goal_yaw_th:
- final_goal_indexes.append(i)
-
- if not final_goal_indexes:
- return None
-
- min_cost = min([self.node_list[i].cost for i in final_goal_indexes])
- for i in final_goal_indexes:
- if self.node_list[i].cost == min_cost:
- return i
-
- return None
-
- def generate_final_course(self, goal_index):
- print("final")
- path = [[self.end.x, self.end.y]]
- node = self.node_list[goal_index]
- while node.parent:
- for (ix, iy) in zip(reversed(node.path_x), reversed(node.path_y)):
- path.append([ix, iy])
- node = node.parent
- path.append([self.start.x, self.start.y])
- return path
-
-
-def main():
-
- print("Start " + __file__)
- # ====Search Path with RRT====
- obstacleList = [
- (5, 5, 1),
- (3, 6, 2),
- (3, 8, 2),
- (3, 10, 2),
- (7, 5, 2),
- (9, 5, 2)
- ] # [x,y,size(radius)]
-
- # Set Initial parameters
- start = [0.0, 0.0, np.deg2rad(0.0)]
- goal = [10.0, 10.0, np.deg2rad(0.0)]
-
- rrt_dubins = RRTDubins(start, goal, obstacleList, [-2.0, 15.0])
- path = rrt_dubins.planning(animation=show_animation)
-
- # Draw final path
- if show_animation: # pragma: no cover
- rrt_dubins.draw_graph()
- plt.plot([x for (x, y) in path], [y for (x, y) in path], '-r')
- plt.grid(True)
- plt.pause(0.001)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/RRTStar/__init__.py b/PathPlanning/RRTStar/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathPlanning/RRTStar/rrt_star.py b/PathPlanning/RRTStar/rrt_star.py
deleted file mode 100644
index dcb1a066eb3..00000000000
--- a/PathPlanning/RRTStar/rrt_star.py
+++ /dev/null
@@ -1,289 +0,0 @@
-"""
-
-Path planning Sample Code with RRT*
-
-author: Atsushi Sakai(@Atsushi_twi)
-
-"""
-
-import math
-import sys
-import matplotlib.pyplot as plt
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from RRT.rrt import RRT
-
-show_animation = True
-
-
-class RRTStar(RRT):
- """
- Class for RRT Star planning
- """
-
- class Node(RRT.Node):
- def __init__(self, x, y):
- super().__init__(x, y)
- self.cost = 0.0
-
- def __init__(self,
- start,
- goal,
- obstacle_list,
- rand_area,
- expand_dis=30.0,
- path_resolution=1.0,
- goal_sample_rate=20,
- max_iter=300,
- connect_circle_dist=50.0,
- search_until_max_iter=False,
- robot_radius=0.0):
- """
- Setting Parameter
-
- start:Start Position [x,y]
- goal:Goal Position [x,y]
- obstacleList:obstacle Positions [[x,y,size],...]
- randArea:Random Sampling Area [min,max]
-
- """
- super().__init__(start, goal, obstacle_list, rand_area, expand_dis,
- path_resolution, goal_sample_rate, max_iter,
- robot_radius=robot_radius)
- self.connect_circle_dist = connect_circle_dist
- self.goal_node = self.Node(goal[0], goal[1])
- self.search_until_max_iter = search_until_max_iter
- self.node_list = []
-
- def planning(self, animation=True):
- """
- rrt star path planning
-
- animation: flag for animation on or off .
- """
-
- self.node_list = [self.start]
- for i in range(self.max_iter):
- print("Iter:", i, ", number of nodes:", len(self.node_list))
- rnd = self.get_random_node()
- nearest_ind = self.get_nearest_node_index(self.node_list, rnd)
- new_node = self.steer(self.node_list[nearest_ind], rnd,
- self.expand_dis)
- near_node = self.node_list[nearest_ind]
- new_node.cost = near_node.cost + \
- math.hypot(new_node.x-near_node.x,
- new_node.y-near_node.y)
-
- if self.check_collision(
- new_node, self.obstacle_list, self.robot_radius):
- near_inds = self.find_near_nodes(new_node)
- node_with_updated_parent = self.choose_parent(
- new_node, near_inds)
- if node_with_updated_parent:
- self.rewire(node_with_updated_parent, near_inds)
- self.node_list.append(node_with_updated_parent)
- else:
- self.node_list.append(new_node)
-
- if animation:
- self.draw_graph(rnd)
-
- if ((not self.search_until_max_iter)
- and new_node): # if reaches goal
- last_index = self.search_best_goal_node()
- if last_index is not None:
- return self.generate_final_course(last_index)
-
- print("reached max iteration")
-
- last_index = self.search_best_goal_node()
- if last_index is not None:
- return self.generate_final_course(last_index)
-
- return None
-
- def choose_parent(self, new_node, near_inds):
- """
- Computes the cheapest point to new_node contained in the list
- near_inds and set such a node as the parent of new_node.
- Arguments:
- --------
- new_node, Node
- randomly generated node with a path from its neared point
- There are not coalitions between this node and th tree.
- near_inds: list
- Indices of indices of the nodes what are near to new_node
-
- Returns.
- ------
- Node, a copy of new_node
- """
- if not near_inds:
- return None
-
- # search nearest cost in near_inds
- costs = []
- for i in near_inds:
- near_node = self.node_list[i]
- t_node = self.steer(near_node, new_node)
- if t_node and self.check_collision(
- t_node, self.obstacle_list, self.robot_radius):
- costs.append(self.calc_new_cost(near_node, new_node))
- else:
- costs.append(float("inf")) # the cost of collision node
- min_cost = min(costs)
-
- if min_cost == float("inf"):
- print("There is no good path.(min_cost is inf)")
- return None
-
- min_ind = near_inds[costs.index(min_cost)]
- new_node = self.steer(self.node_list[min_ind], new_node)
- new_node.cost = min_cost
-
- return new_node
-
- def search_best_goal_node(self):
- dist_to_goal_list = [
- self.calc_dist_to_goal(n.x, n.y) for n in self.node_list
- ]
- goal_inds = [
- dist_to_goal_list.index(i) for i in dist_to_goal_list
- if i <= self.expand_dis
- ]
-
- safe_goal_inds = []
- for goal_ind in goal_inds:
- t_node = self.steer(self.node_list[goal_ind], self.goal_node)
- if self.check_collision(
- t_node, self.obstacle_list, self.robot_radius):
- safe_goal_inds.append(goal_ind)
-
- if not safe_goal_inds:
- return None
-
- safe_goal_costs = [self.node_list[i].cost +
- self.calc_dist_to_goal(self.node_list[i].x, self.node_list[i].y)
- for i in safe_goal_inds]
-
- min_cost = min(safe_goal_costs)
- for i, cost in zip(safe_goal_inds, safe_goal_costs):
- if cost == min_cost:
- return i
-
- return None
-
- def find_near_nodes(self, new_node):
- """
- 1) defines a ball centered on new_node
- 2) Returns all nodes of the three that are inside this ball
- Arguments:
- ---------
- new_node: Node
- new randomly generated node, without collisions between
- its nearest node
- Returns:
- -------
- list
- List with the indices of the nodes inside the ball of
- radius r
- """
- nnode = len(self.node_list) + 1
- r = self.connect_circle_dist * math.sqrt(math.log(nnode) / nnode)
- # if expand_dist exists, search vertices in a range no more than
- # expand_dist
- if hasattr(self, 'expand_dis'):
- r = min(r, self.expand_dis)
- dist_list = [(node.x - new_node.x)**2 + (node.y - new_node.y)**2
- for node in self.node_list]
- near_inds = [dist_list.index(i) for i in dist_list if i <= r**2]
- return near_inds
-
- def rewire(self, new_node, near_inds):
- """
- For each node in near_inds, this will check if it is cheaper to
- arrive to them from new_node.
- In such a case, this will re-assign the parent of the nodes in
- near_inds to new_node.
- Parameters:
- ----------
- new_node, Node
- Node randomly added which can be joined to the tree
-
- near_inds, list of uints
- A list of indices of the self.new_node which contains
- nodes within a circle of a given radius.
- Remark: parent is designated in choose_parent.
-
- """
- for i in near_inds:
- near_node = self.node_list[i]
- edge_node = self.steer(new_node, near_node)
- if not edge_node:
- continue
- edge_node.cost = self.calc_new_cost(new_node, near_node)
-
- no_collision = self.check_collision(
- edge_node, self.obstacle_list, self.robot_radius)
- improved_cost = near_node.cost > edge_node.cost
-
- if no_collision and improved_cost:
- for node in self.node_list:
- if node.parent == self.node_list[i]:
- node.parent = edge_node
- self.node_list[i] = edge_node
- self.propagate_cost_to_leaves(self.node_list[i])
-
- def calc_new_cost(self, from_node, to_node):
- d, _ = self.calc_distance_and_angle(from_node, to_node)
- return from_node.cost + d
-
- def propagate_cost_to_leaves(self, parent_node):
-
- for node in self.node_list:
- if node.parent == parent_node:
- node.cost = self.calc_new_cost(parent_node, node)
- self.propagate_cost_to_leaves(node)
-
-
-def main():
- print("Start " + __file__)
-
- # ====Search Path with RRT====
- obstacle_list = [
- (5, 5, 1),
- (3, 6, 2),
- (3, 8, 2),
- (3, 10, 2),
- (7, 5, 2),
- (9, 5, 2),
- (8, 10, 1),
- (6, 12, 1),
- ] # [x,y,size(radius)]
-
- # Set Initial parameters
- rrt_star = RRTStar(
- start=[0, 0],
- goal=[6, 10],
- rand_area=[-2, 15],
- obstacle_list=obstacle_list,
- expand_dis=1,
- robot_radius=0.8)
- path = rrt_star.planning(animation=show_animation)
-
- if path is None:
- print("Cannot find path")
- else:
- print("found path!!")
-
- # Draw final path
- if show_animation:
- rrt_star.draw_graph()
- plt.plot([x for (x, y) in path], [y for (x, y) in path], 'r--')
- plt.grid(True)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/RRTStarDubins/rrt_star_dubins.py b/PathPlanning/RRTStarDubins/rrt_star_dubins.py
deleted file mode 100644
index 7c52879b7c4..00000000000
--- a/PathPlanning/RRTStarDubins/rrt_star_dubins.py
+++ /dev/null
@@ -1,246 +0,0 @@
-"""
-Path planning Sample Code with RRT and Dubins path
-
-author: AtsushiSakai(@Atsushi_twi)
-
-"""
-import copy
-import math
-import random
-import matplotlib.pyplot as plt
-import numpy as np
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent)) # root dir
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from DubinsPath import dubins_path_planner
-from RRTStar.rrt_star import RRTStar
-from utils.plot import plot_arrow
-
-show_animation = True
-
-
-class RRTStarDubins(RRTStar):
- """
- Class for RRT star planning with Dubins path
- """
-
- class Node(RRTStar.Node):
- """
- RRT Node
- """
-
- def __init__(self, x, y, yaw):
- super().__init__(x, y)
- self.yaw = yaw
- self.path_yaw = []
-
- def __init__(self, start, goal, obstacle_list, rand_area,
- goal_sample_rate=10,
- max_iter=200,
- connect_circle_dist=50.0,
- robot_radius=0.0,
- ):
- """
- Setting Parameter
-
- start:Start Position [x,y]
- goal:Goal Position [x,y]
- obstacleList:obstacle Positions [[x,y,size],...]
- randArea:Random Sampling Area [min,max]
- robot_radius: robot body modeled as circle with given radius
-
- """
- self.start = self.Node(start[0], start[1], start[2])
- self.end = self.Node(goal[0], goal[1], goal[2])
- self.min_rand = rand_area[0]
- self.max_rand = rand_area[1]
- self.goal_sample_rate = goal_sample_rate
- self.max_iter = max_iter
- self.obstacle_list = obstacle_list
- self.connect_circle_dist = connect_circle_dist
-
- self.curvature = 1.0 # for dubins path
- self.goal_yaw_th = np.deg2rad(1.0)
- self.goal_xy_th = 0.5
- self.robot_radius = robot_radius
-
- def planning(self, animation=True, search_until_max_iter=True):
- """
- RRT Star planning
-
- animation: flag for animation on or off
- """
-
- self.node_list = [self.start]
- for i in range(self.max_iter):
- print("Iter:", i, ", number of nodes:", len(self.node_list))
- rnd = self.get_random_node()
- nearest_ind = self.get_nearest_node_index(self.node_list, rnd)
- new_node = self.steer(self.node_list[nearest_ind], rnd)
-
- if self.check_collision(
- new_node, self.obstacle_list, self.robot_radius):
- near_indexes = self.find_near_nodes(new_node)
- new_node = self.choose_parent(new_node, near_indexes)
- if new_node:
- self.node_list.append(new_node)
- self.rewire(new_node, near_indexes)
-
- if animation and i % 5 == 0:
- self.plot_start_goal_arrow()
- self.draw_graph(rnd)
-
- if (not search_until_max_iter) and new_node: # check reaching the goal
- last_index = self.search_best_goal_node()
- if last_index:
- return self.generate_final_course(last_index)
-
- print("reached max iteration")
-
- last_index = self.search_best_goal_node()
- if last_index:
- return self.generate_final_course(last_index)
- else:
- print("Cannot find path")
-
- return None
-
- def draw_graph(self, rnd=None):
- plt.clf()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if rnd is not None:
- plt.plot(rnd.x, rnd.y, "^k")
- for node in self.node_list:
- if node.parent:
- plt.plot(node.path_x, node.path_y, "-g")
-
- for (ox, oy, size) in self.obstacle_list:
- plt.plot(ox, oy, "ok", ms=30 * size)
-
- plt.plot(self.start.x, self.start.y, "xr")
- plt.plot(self.end.x, self.end.y, "xr")
- plt.axis([-2, 15, -2, 15])
- plt.grid(True)
- self.plot_start_goal_arrow()
- plt.pause(0.01)
-
- def plot_start_goal_arrow(self):
- plot_arrow(self.start.x, self.start.y, self.start.yaw)
- plot_arrow(self.end.x, self.end.y, self.end.yaw)
-
- def steer(self, from_node, to_node):
-
- px, py, pyaw, mode, course_lengths = \
- dubins_path_planner.plan_dubins_path(
- from_node.x, from_node.y, from_node.yaw,
- to_node.x, to_node.y, to_node.yaw, self.curvature)
-
- if len(px) <= 1: # cannot find a dubins path
- return None
-
- new_node = copy.deepcopy(from_node)
- new_node.x = px[-1]
- new_node.y = py[-1]
- new_node.yaw = pyaw[-1]
-
- new_node.path_x = px
- new_node.path_y = py
- new_node.path_yaw = pyaw
- new_node.cost += sum([abs(c) for c in course_lengths])
- new_node.parent = from_node
-
- return new_node
-
- def calc_new_cost(self, from_node, to_node):
-
- _, _, _, _, course_lengths = dubins_path_planner.plan_dubins_path(
- from_node.x, from_node.y, from_node.yaw,
- to_node.x, to_node.y, to_node.yaw, self.curvature)
-
- cost = sum([abs(c) for c in course_lengths])
-
- return from_node.cost + cost
-
- def get_random_node(self):
-
- if random.randint(0, 100) > self.goal_sample_rate:
- rnd = self.Node(random.uniform(self.min_rand, self.max_rand),
- random.uniform(self.min_rand, self.max_rand),
- random.uniform(-math.pi, math.pi)
- )
- else: # goal point sampling
- rnd = self.Node(self.end.x, self.end.y, self.end.yaw)
-
- return rnd
-
- def search_best_goal_node(self):
-
- goal_indexes = []
- for (i, node) in enumerate(self.node_list):
- if self.calc_dist_to_goal(node.x, node.y) <= self.goal_xy_th:
- goal_indexes.append(i)
-
- # angle check
- final_goal_indexes = []
- for i in goal_indexes:
- if abs(self.node_list[i].yaw - self.end.yaw) <= self.goal_yaw_th:
- final_goal_indexes.append(i)
-
- if not final_goal_indexes:
- return None
-
- min_cost = min([self.node_list[i].cost for i in final_goal_indexes])
- for i in final_goal_indexes:
- if self.node_list[i].cost == min_cost:
- return i
-
- return None
-
- def generate_final_course(self, goal_index):
- print("final")
- path = [[self.end.x, self.end.y]]
- node = self.node_list[goal_index]
- while node.parent:
- for (ix, iy) in zip(reversed(node.path_x), reversed(node.path_y)):
- path.append([ix, iy])
- node = node.parent
- path.append([self.start.x, self.start.y])
- return path
-
-
-def main():
- print("Start rrt star with dubins planning")
-
- # ====Search Path with RRT====
- obstacleList = [
- (5, 5, 1),
- (3, 6, 2),
- (3, 8, 2),
- (3, 10, 2),
- (7, 5, 2),
- (9, 5, 2)
- ] # [x,y,size(radius)]
-
- # Set Initial parameters
- start = [0.0, 0.0, np.deg2rad(0.0)]
- goal = [10.0, 10.0, np.deg2rad(0.0)]
-
- rrtstar_dubins = RRTStarDubins(start, goal, rand_area=[-2.0, 15.0], obstacle_list=obstacleList)
- path = rrtstar_dubins.planning(animation=show_animation)
-
- # Draw final path
- if show_animation: # pragma: no cover
- rrtstar_dubins.draw_graph()
- plt.plot([x for (x, y) in path], [y for (x, y) in path], '-r')
- plt.grid(True)
- plt.pause(0.001)
-
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/RRTStarReedsShepp/rrt_star_reeds_shepp.py b/PathPlanning/RRTStarReedsShepp/rrt_star_reeds_shepp.py
deleted file mode 100644
index c4c3e7c8a8f..00000000000
--- a/PathPlanning/RRTStarReedsShepp/rrt_star_reeds_shepp.py
+++ /dev/null
@@ -1,265 +0,0 @@
-"""
-
-Path planning Sample Code with RRT with Reeds-Shepp path
-
-author: AtsushiSakai(@Atsushi_twi)
-
-"""
-import copy
-import math
-import random
-import sys
-import pathlib
-import matplotlib.pyplot as plt
-import numpy as np
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from ReedsSheppPath import reeds_shepp_path_planning
-from RRTStar.rrt_star import RRTStar
-
-show_animation = True
-
-
-class RRTStarReedsShepp(RRTStar):
- """
- Class for RRT star planning with Reeds Shepp path
- """
-
- class Node(RRTStar.Node):
- """
- RRT Node
- """
-
- def __init__(self, x, y, yaw):
- super().__init__(x, y)
- self.yaw = yaw
- self.path_yaw = []
-
- def __init__(self, start, goal, obstacle_list, rand_area,
- max_iter=200, step_size=0.2,
- connect_circle_dist=50.0,
- robot_radius=0.0
- ):
- """
- Setting Parameter
-
- start:Start Position [x,y]
- goal:Goal Position [x,y]
- obstacleList:obstacle Positions [[x,y,size],...]
- randArea:Random Sampling Area [min,max]
- robot_radius: robot body modeled as circle with given radius
-
- """
- self.start = self.Node(start[0], start[1], start[2])
- self.end = self.Node(goal[0], goal[1], goal[2])
- self.min_rand = rand_area[0]
- self.max_rand = rand_area[1]
- self.max_iter = max_iter
- self.step_size = step_size
- self.obstacle_list = obstacle_list
- self.connect_circle_dist = connect_circle_dist
- self.robot_radius = robot_radius
-
- self.curvature = 1.0
- self.goal_yaw_th = np.deg2rad(1.0)
- self.goal_xy_th = 0.5
-
- def set_random_seed(self, seed):
- random.seed(seed)
-
- def planning(self, animation=True, search_until_max_iter=True):
- """
- planning
-
- animation: flag for animation on or off
- """
-
- self.node_list = [self.start]
- for i in range(self.max_iter):
- print("Iter:", i, ", number of nodes:", len(self.node_list))
- rnd = self.get_random_node()
- nearest_ind = self.get_nearest_node_index(self.node_list, rnd)
- new_node = self.steer(self.node_list[nearest_ind], rnd)
-
- if self.check_collision(
- new_node, self.obstacle_list, self.robot_radius):
- near_indexes = self.find_near_nodes(new_node)
- new_node = self.choose_parent(new_node, near_indexes)
- if new_node:
- self.node_list.append(new_node)
- self.rewire(new_node, near_indexes)
- self.try_goal_path(new_node)
-
- if animation and i % 5 == 0:
- self.plot_start_goal_arrow()
- self.draw_graph(rnd)
-
- if (not search_until_max_iter) and new_node: # check reaching the goal
- last_index = self.search_best_goal_node()
- if last_index:
- return self.generate_final_course(last_index)
-
- print("reached max iteration")
-
- last_index = self.search_best_goal_node()
- if last_index:
- return self.generate_final_course(last_index)
- else:
- print("Cannot find path")
-
- return None
-
- def try_goal_path(self, node):
-
- goal = self.Node(self.end.x, self.end.y, self.end.yaw)
-
- new_node = self.steer(node, goal)
- if new_node is None:
- return
-
- if self.check_collision(
- new_node, self.obstacle_list, self.robot_radius):
- self.node_list.append(new_node)
-
- def draw_graph(self, rnd=None):
- plt.clf()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if rnd is not None:
- plt.plot(rnd.x, rnd.y, "^k")
- for node in self.node_list:
- if node.parent:
- plt.plot(node.path_x, node.path_y, "-g")
-
- for (ox, oy, size) in self.obstacle_list:
- plt.plot(ox, oy, "ok", ms=30 * size)
-
- plt.plot(self.start.x, self.start.y, "xr")
- plt.plot(self.end.x, self.end.y, "xr")
- plt.axis([-2, 15, -2, 15])
- plt.grid(True)
- self.plot_start_goal_arrow()
- plt.pause(0.01)
-
- def plot_start_goal_arrow(self):
- reeds_shepp_path_planning.plot_arrow(
- self.start.x, self.start.y, self.start.yaw)
- reeds_shepp_path_planning.plot_arrow(
- self.end.x, self.end.y, self.end.yaw)
-
- def steer(self, from_node, to_node):
-
- px, py, pyaw, mode, course_lengths = reeds_shepp_path_planning.reeds_shepp_path_planning(
- from_node.x, from_node.y, from_node.yaw, to_node.x,
- to_node.y, to_node.yaw, self.curvature, self.step_size)
-
- if not px:
- return None
-
- new_node = copy.deepcopy(from_node)
- new_node.x = px[-1]
- new_node.y = py[-1]
- new_node.yaw = pyaw[-1]
-
- new_node.path_x = px
- new_node.path_y = py
- new_node.path_yaw = pyaw
- new_node.cost += sum([abs(l) for l in course_lengths])
- new_node.parent = from_node
-
- return new_node
-
- def calc_new_cost(self, from_node, to_node):
-
- _, _, _, _, course_lengths = reeds_shepp_path_planning.reeds_shepp_path_planning(
- from_node.x, from_node.y, from_node.yaw, to_node.x,
- to_node.y, to_node.yaw, self.curvature, self.step_size)
- if not course_lengths:
- return float("inf")
-
- return from_node.cost + sum([abs(l) for l in course_lengths])
-
- def get_random_node(self):
-
- rnd = self.Node(random.uniform(self.min_rand, self.max_rand),
- random.uniform(self.min_rand, self.max_rand),
- random.uniform(-math.pi, math.pi)
- )
-
- return rnd
-
- def search_best_goal_node(self):
-
- goal_indexes = []
- for (i, node) in enumerate(self.node_list):
- if self.calc_dist_to_goal(node.x, node.y) <= self.goal_xy_th:
- goal_indexes.append(i)
- print("goal_indexes:", len(goal_indexes))
-
- # angle check
- final_goal_indexes = []
- for i in goal_indexes:
- if abs(self.node_list[i].yaw - self.end.yaw) <= self.goal_yaw_th:
- final_goal_indexes.append(i)
-
- print("final_goal_indexes:", len(final_goal_indexes))
-
- if not final_goal_indexes:
- return None
-
- min_cost = min([self.node_list[i].cost for i in final_goal_indexes])
- print("min_cost:", min_cost)
- for i in final_goal_indexes:
- if self.node_list[i].cost == min_cost:
- return i
-
- return None
-
- def generate_final_course(self, goal_index):
- path = [[self.end.x, self.end.y, self.end.yaw]]
- node = self.node_list[goal_index]
- while node.parent:
- for (ix, iy, iyaw) in zip(reversed(node.path_x), reversed(node.path_y), reversed(node.path_yaw)):
- path.append([ix, iy, iyaw])
- node = node.parent
- path.append([self.start.x, self.start.y, self.start.yaw])
- return path
-
-
-def main(max_iter=100):
- print("Start " + __file__)
-
- # ====Search Path with RRT====
- obstacleList = [
- (5, 5, 1),
- (4, 6, 1),
- (4, 8, 1),
- (4, 10, 1),
- (6, 5, 1),
- (7, 5, 1),
- (8, 6, 1),
- (8, 8, 1),
- (8, 10, 1)
- ] # [x,y,size(radius)]
-
- # Set Initial parameters
- start = [0.0, 0.0, np.deg2rad(0.0)]
- goal = [6.0, 7.0, np.deg2rad(90.0)]
-
- rrt_star_reeds_shepp = RRTStarReedsShepp(start, goal,
- obstacleList,
- [-2.0, 15.0], max_iter=max_iter)
- path = rrt_star_reeds_shepp.planning(animation=show_animation)
-
- # Draw final path
- if path and show_animation: # pragma: no cover
- rrt_star_reeds_shepp.draw_graph()
- plt.plot([x for (x, y, yaw) in path], [y for (x, y, yaw) in path], '-r')
- plt.grid(True)
- plt.pause(0.001)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/ReedsSheppPath/reeds_shepp_path_planning.py b/PathPlanning/ReedsSheppPath/reeds_shepp_path_planning.py
deleted file mode 100644
index 618d1d99ba0..00000000000
--- a/PathPlanning/ReedsSheppPath/reeds_shepp_path_planning.py
+++ /dev/null
@@ -1,478 +0,0 @@
-"""
-
-Reeds Shepp path planner sample code
-
-author Atsushi Sakai(@Atsushi_twi)
-co-author Videh Patel(@videh25) : Added the missing RS paths
-
-"""
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import math
-
-import matplotlib.pyplot as plt
-import numpy as np
-from utils.angle import angle_mod
-
-show_animation = True
-
-
-class Path:
- """
- Path data container
- """
-
- def __init__(self):
- # course segment length (negative value is backward segment)
- self.lengths = []
- # course segment type char ("S": straight, "L": left, "R": right)
- self.ctypes = []
- self.L = 0.0 # Total lengths of the path
- self.x = [] # x positions
- self.y = [] # y positions
- self.yaw = [] # orientations [rad]
- self.directions = [] # directions (1:forward, -1:backward)
-
-
-def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"):
- if isinstance(x, list):
- for (ix, iy, iyaw) in zip(x, y, yaw):
- plot_arrow(ix, iy, iyaw)
- else:
- plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw), fc=fc,
- ec=ec, head_width=width, head_length=width)
- plt.plot(x, y)
-
-
-def pi_2_pi(x):
- return angle_mod(x)
-
-def mod2pi(x):
- # Be consistent with fmod in cplusplus here.
- v = np.mod(x, np.copysign(2.0 * math.pi, x))
- if v < -math.pi:
- v += 2.0 * math.pi
- else:
- if v > math.pi:
- v -= 2.0 * math.pi
- return v
-
-def set_path(paths, lengths, ctypes, step_size):
- path = Path()
- path.ctypes = ctypes
- path.lengths = lengths
- path.L = sum(np.abs(lengths))
-
- # check same path exist
- for i_path in paths:
- type_is_same = (i_path.ctypes == path.ctypes)
- length_is_close = (sum(np.abs(i_path.lengths)) - path.L) <= step_size
- if type_is_same and length_is_close:
- return paths # same path found, so do not insert path
-
- # check path is long enough
- if path.L <= step_size:
- return paths # too short, so do not insert path
-
- paths.append(path)
- return paths
-
-
-def polar(x, y):
- r = math.hypot(x, y)
- theta = math.atan2(y, x)
- return r, theta
-
-
-def left_straight_left(x, y, phi):
- u, t = polar(x - math.sin(phi), y - 1.0 + math.cos(phi))
- if 0.0 <= t <= math.pi:
- v = mod2pi(phi - t)
- if 0.0 <= v <= math.pi:
- return True, [t, u, v], ['L', 'S', 'L']
-
- return False, [], []
-
-
-def left_straight_right(x, y, phi):
- u1, t1 = polar(x + math.sin(phi), y - 1.0 - math.cos(phi))
- u1 = u1 ** 2
- if u1 >= 4.0:
- u = math.sqrt(u1 - 4.0)
- theta = math.atan2(2.0, u)
- t = mod2pi(t1 + theta)
- v = mod2pi(t - phi)
-
- if (t >= 0.0) and (v >= 0.0):
- return True, [t, u, v], ['L', 'S', 'R']
-
- return False, [], []
-
-
-def left_x_right_x_left(x, y, phi):
- zeta = x - math.sin(phi)
- eeta = y - 1 + math.cos(phi)
- u1, theta = polar(zeta, eeta)
-
- if u1 <= 4.0:
- A = math.acos(0.25 * u1)
- t = mod2pi(A + theta + math.pi/2)
- u = mod2pi(math.pi - 2 * A)
- v = mod2pi(phi - t - u)
- return True, [t, -u, v], ['L', 'R', 'L']
-
- return False, [], []
-
-
-def left_x_right_left(x, y, phi):
- zeta = x - math.sin(phi)
- eeta = y - 1 + math.cos(phi)
- u1, theta = polar(zeta, eeta)
-
- if u1 <= 4.0:
- A = math.acos(0.25 * u1)
- t = mod2pi(A + theta + math.pi/2)
- u = mod2pi(math.pi - 2*A)
- v = mod2pi(-phi + t + u)
- return True, [t, -u, -v], ['L', 'R', 'L']
-
- return False, [], []
-
-
-def left_right_x_left(x, y, phi):
- zeta = x - math.sin(phi)
- eeta = y - 1 + math.cos(phi)
- u1, theta = polar(zeta, eeta)
-
- if u1 <= 4.0:
- u = math.acos(1 - u1**2 * 0.125)
- A = math.asin(2 * math.sin(u) / u1)
- t = mod2pi(-A + theta + math.pi/2)
- v = mod2pi(t - u - phi)
- return True, [t, u, -v], ['L', 'R', 'L']
-
- return False, [], []
-
-
-def left_right_x_left_right(x, y, phi):
- zeta = x + math.sin(phi)
- eeta = y - 1 - math.cos(phi)
- u1, theta = polar(zeta, eeta)
-
- # Solutions refering to (2 < u1 <= 4) are considered sub-optimal in paper
- # Solutions do not exist for u1 > 4
- if u1 <= 2:
- A = math.acos((u1 + 2) * 0.25)
- t = mod2pi(theta + A + math.pi/2)
- u = mod2pi(A)
- v = mod2pi(phi - t + 2*u)
- if ((t >= 0) and (u >= 0) and (v >= 0)):
- return True, [t, u, -u, -v], ['L', 'R', 'L', 'R']
-
- return False, [], []
-
-
-def left_x_right_left_x_right(x, y, phi):
- zeta = x + math.sin(phi)
- eeta = y - 1 - math.cos(phi)
- u1, theta = polar(zeta, eeta)
- u2 = (20 - u1**2) / 16
-
- if (0 <= u2 <= 1):
- u = math.acos(u2)
- A = math.asin(2 * math.sin(u) / u1)
- t = mod2pi(theta + A + math.pi/2)
- v = mod2pi(t - phi)
- if (t >= 0) and (v >= 0):
- return True, [t, -u, -u, v], ['L', 'R', 'L', 'R']
-
- return False, [], []
-
-
-def left_x_right90_straight_left(x, y, phi):
- zeta = x - math.sin(phi)
- eeta = y - 1 + math.cos(phi)
- u1, theta = polar(zeta, eeta)
-
- if u1 >= 2.0:
- u = math.sqrt(u1**2 - 4) - 2
- A = math.atan2(2, math.sqrt(u1**2 - 4))
- t = mod2pi(theta + A + math.pi/2)
- v = mod2pi(t - phi + math.pi/2)
- if (t >= 0) and (v >= 0):
- return True, [t, -math.pi/2, -u, -v], ['L', 'R', 'S', 'L']
-
- return False, [], []
-
-
-def left_straight_right90_x_left(x, y, phi):
- zeta = x - math.sin(phi)
- eeta = y - 1 + math.cos(phi)
- u1, theta = polar(zeta, eeta)
-
- if u1 >= 2.0:
- u = math.sqrt(u1**2 - 4) - 2
- A = math.atan2(math.sqrt(u1**2 - 4), 2)
- t = mod2pi(theta - A + math.pi/2)
- v = mod2pi(t - phi - math.pi/2)
- if (t >= 0) and (v >= 0):
- return True, [t, u, math.pi/2, -v], ['L', 'S', 'R', 'L']
-
- return False, [], []
-
-
-def left_x_right90_straight_right(x, y, phi):
- zeta = x + math.sin(phi)
- eeta = y - 1 - math.cos(phi)
- u1, theta = polar(zeta, eeta)
-
- if u1 >= 2.0:
- t = mod2pi(theta + math.pi/2)
- u = u1 - 2
- v = mod2pi(phi - t - math.pi/2)
- if (t >= 0) and (v >= 0):
- return True, [t, -math.pi/2, -u, -v], ['L', 'R', 'S', 'R']
-
- return False, [], []
-
-
-def left_straight_left90_x_right(x, y, phi):
- zeta = x + math.sin(phi)
- eeta = y - 1 - math.cos(phi)
- u1, theta = polar(zeta, eeta)
-
- if u1 >= 2.0:
- t = mod2pi(theta)
- u = u1 - 2
- v = mod2pi(phi - t - math.pi/2)
- if (t >= 0) and (v >= 0):
- return True, [t, u, math.pi/2, -v], ['L', 'S', 'L', 'R']
-
- return False, [], []
-
-
-def left_x_right90_straight_left90_x_right(x, y, phi):
- zeta = x + math.sin(phi)
- eeta = y - 1 - math.cos(phi)
- u1, theta = polar(zeta, eeta)
-
- if u1 >= 4.0:
- u = math.sqrt(u1**2 - 4) - 4
- A = math.atan2(2, math.sqrt(u1**2 - 4))
- t = mod2pi(theta + A + math.pi/2)
- v = mod2pi(t - phi)
- if (t >= 0) and (v >= 0):
- return True, [t, -math.pi/2, -u, -math.pi/2, v], ['L', 'R', 'S', 'L', 'R']
-
- return False, [], []
-
-
-def timeflip(travel_distances):
- return [-x for x in travel_distances]
-
-
-def reflect(steering_directions):
- def switch_dir(dirn):
- if dirn == 'L':
- return 'R'
- elif dirn == 'R':
- return 'L'
- else:
- return 'S'
- return[switch_dir(dirn) for dirn in steering_directions]
-
-
-def generate_path(q0, q1, max_curvature, step_size):
- dx = q1[0] - q0[0]
- dy = q1[1] - q0[1]
- dth = q1[2] - q0[2]
- c = math.cos(q0[2])
- s = math.sin(q0[2])
- x = (c * dx + s * dy) * max_curvature
- y = (-s * dx + c * dy) * max_curvature
- step_size *= max_curvature
-
- paths = []
- path_functions = [left_straight_left, left_straight_right, # CSC
- left_x_right_x_left, left_x_right_left, left_right_x_left, # CCC
- left_right_x_left_right, left_x_right_left_x_right, # CCCC
- left_x_right90_straight_left, left_x_right90_straight_right, # CCSC
- left_straight_right90_x_left, left_straight_left90_x_right, # CSCC
- left_x_right90_straight_left90_x_right] # CCSCC
-
- for path_func in path_functions:
- flag, travel_distances, steering_dirns = path_func(x, y, dth)
- if flag:
- for distance in travel_distances:
- if (0.1*sum([abs(d) for d in travel_distances]) < abs(distance) < step_size):
- print("Step size too large for Reeds-Shepp paths.")
- return []
- paths = set_path(paths, travel_distances, steering_dirns, step_size)
-
- flag, travel_distances, steering_dirns = path_func(-x, y, -dth)
- if flag:
- for distance in travel_distances:
- if (0.1*sum([abs(d) for d in travel_distances]) < abs(distance) < step_size):
- print("Step size too large for Reeds-Shepp paths.")
- return []
- travel_distances = timeflip(travel_distances)
- paths = set_path(paths, travel_distances, steering_dirns, step_size)
-
- flag, travel_distances, steering_dirns = path_func(x, -y, -dth)
- if flag:
- for distance in travel_distances:
- if (0.1*sum([abs(d) for d in travel_distances]) < abs(distance) < step_size):
- print("Step size too large for Reeds-Shepp paths.")
- return []
- steering_dirns = reflect(steering_dirns)
- paths = set_path(paths, travel_distances, steering_dirns, step_size)
-
- flag, travel_distances, steering_dirns = path_func(-x, -y, dth)
- if flag:
- for distance in travel_distances:
- if (0.1*sum([abs(d) for d in travel_distances]) < abs(distance) < step_size):
- print("Step size too large for Reeds-Shepp paths.")
- return []
- travel_distances = timeflip(travel_distances)
- steering_dirns = reflect(steering_dirns)
- paths = set_path(paths, travel_distances, steering_dirns, step_size)
-
- return paths
-
-
-def calc_interpolate_dists_list(lengths, step_size):
- interpolate_dists_list = []
- for length in lengths:
- d_dist = step_size if length >= 0.0 else -step_size
- interp_dists = np.arange(0.0, length, d_dist)
- interp_dists = np.append(interp_dists, length)
- interpolate_dists_list.append(interp_dists)
-
- return interpolate_dists_list
-
-
-def generate_local_course(lengths, modes, max_curvature, step_size):
- interpolate_dists_list = calc_interpolate_dists_list(lengths, step_size * max_curvature)
-
- origin_x, origin_y, origin_yaw = 0.0, 0.0, 0.0
-
- xs, ys, yaws, directions = [], [], [], []
- for (interp_dists, mode, length) in zip(interpolate_dists_list, modes,
- lengths):
-
- for dist in interp_dists:
- x, y, yaw, direction = interpolate(dist, length, mode,
- max_curvature, origin_x,
- origin_y, origin_yaw)
- xs.append(x)
- ys.append(y)
- yaws.append(yaw)
- directions.append(direction)
- origin_x = xs[-1]
- origin_y = ys[-1]
- origin_yaw = yaws[-1]
-
- return xs, ys, yaws, directions
-
-
-def interpolate(dist, length, mode, max_curvature, origin_x, origin_y,
- origin_yaw):
- if mode == "S":
- x = origin_x + dist / max_curvature * math.cos(origin_yaw)
- y = origin_y + dist / max_curvature * math.sin(origin_yaw)
- yaw = origin_yaw
- else: # curve
- ldx = math.sin(dist) / max_curvature
- ldy = 0.0
- yaw = None
- if mode == "L": # left turn
- ldy = (1.0 - math.cos(dist)) / max_curvature
- yaw = origin_yaw + dist
- elif mode == "R": # right turn
- ldy = (1.0 - math.cos(dist)) / -max_curvature
- yaw = origin_yaw - dist
- gdx = math.cos(-origin_yaw) * ldx + math.sin(-origin_yaw) * ldy
- gdy = -math.sin(-origin_yaw) * ldx + math.cos(-origin_yaw) * ldy
- x = origin_x + gdx
- y = origin_y + gdy
-
- return x, y, yaw, 1 if length > 0.0 else -1
-
-
-def calc_paths(sx, sy, syaw, gx, gy, gyaw, maxc, step_size):
- q0 = [sx, sy, syaw]
- q1 = [gx, gy, gyaw]
-
- paths = generate_path(q0, q1, maxc, step_size)
- for path in paths:
- xs, ys, yaws, directions = generate_local_course(path.lengths,
- path.ctypes, maxc,
- step_size)
-
- # convert global coordinate
- path.x = [math.cos(-q0[2]) * ix + math.sin(-q0[2]) * iy + q0[0] for
- (ix, iy) in zip(xs, ys)]
- path.y = [-math.sin(-q0[2]) * ix + math.cos(-q0[2]) * iy + q0[1] for
- (ix, iy) in zip(xs, ys)]
- path.yaw = [pi_2_pi(yaw + q0[2]) for yaw in yaws]
- path.directions = directions
- path.lengths = [length / maxc for length in path.lengths]
- path.L = path.L / maxc
-
- return paths
-
-
-def reeds_shepp_path_planning(sx, sy, syaw, gx, gy, gyaw, maxc, step_size=0.2):
- paths = calc_paths(sx, sy, syaw, gx, gy, gyaw, maxc, step_size)
- if not paths:
- return None, None, None, None, None # could not generate any path
-
- # search minimum cost path
- best_path_index = paths.index(min(paths, key=lambda p: abs(p.L)))
- b_path = paths[best_path_index]
-
- return b_path.x, b_path.y, b_path.yaw, b_path.ctypes, b_path.lengths
-
-
-def main():
- print("Reeds Shepp path planner sample start!!")
-
- start_x = -1.0 # [m]
- start_y = -4.0 # [m]
- start_yaw = np.deg2rad(-20.0) # [rad]
-
- end_x = 5.0 # [m]
- end_y = 5.0 # [m]
- end_yaw = np.deg2rad(25.0) # [rad]
-
- curvature = 0.1
- step_size = 0.05
-
- xs, ys, yaws, modes, lengths = reeds_shepp_path_planning(start_x, start_y,
- start_yaw, end_x,
- end_y, end_yaw,
- curvature,
- step_size)
-
- if not xs:
- assert False, "No path"
-
- if show_animation: # pragma: no cover
- plt.cla()
- plt.plot(xs, ys, label="final course " + str(modes))
- print(f"{lengths=}")
-
- # plotting
- plot_arrow(start_x, start_y, start_yaw)
- plot_arrow(end_x, end_y, end_yaw)
-
- plt.legend()
- plt.grid(True)
- plt.axis("equal")
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/SpiralSpanningTreeCPP/map/test.png b/PathPlanning/SpiralSpanningTreeCPP/map/test.png
deleted file mode 100644
index 4abca0bf309..00000000000
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diff --git a/PathPlanning/SpiralSpanningTreeCPP/map/test_2.png b/PathPlanning/SpiralSpanningTreeCPP/map/test_2.png
deleted file mode 100644
index 0d27fa9f958..00000000000
Binary files a/PathPlanning/SpiralSpanningTreeCPP/map/test_2.png and /dev/null differ
diff --git a/PathPlanning/SpiralSpanningTreeCPP/map/test_3.png b/PathPlanning/SpiralSpanningTreeCPP/map/test_3.png
deleted file mode 100644
index 1a50b87ccff..00000000000
Binary files a/PathPlanning/SpiralSpanningTreeCPP/map/test_3.png and /dev/null differ
diff --git a/PathPlanning/SpiralSpanningTreeCPP/spiral_spanning_tree_coverage_path_planner.py b/PathPlanning/SpiralSpanningTreeCPP/spiral_spanning_tree_coverage_path_planner.py
deleted file mode 100644
index a8c513e6b16..00000000000
--- a/PathPlanning/SpiralSpanningTreeCPP/spiral_spanning_tree_coverage_path_planner.py
+++ /dev/null
@@ -1,313 +0,0 @@
-"""
-Spiral Spanning Tree Coverage Path Planner
-
-author: Todd Tang
-paper: Spiral-STC: An On-Line Coverage Algorithm of Grid Environments
- by a Mobile Robot - Gabriely et.al.
-link: https://ieeexplore.ieee.org/abstract/document/1013479
-"""
-
-import os
-import sys
-import math
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-do_animation = True
-
-
-class SpiralSpanningTreeCoveragePlanner:
- def __init__(self, occ_map):
- self.origin_map_height = occ_map.shape[0]
- self.origin_map_width = occ_map.shape[1]
-
- # original map resolution must be even
- if self.origin_map_height % 2 == 1 or self.origin_map_width % 2 == 1:
- sys.exit('original map width/height must be even \
- in grayscale .png format')
-
- self.occ_map = occ_map
- self.merged_map_height = self.origin_map_height // 2
- self.merged_map_width = self.origin_map_width // 2
-
- self.edge = []
-
- def plan(self, start):
- """plan
-
- performing Spiral Spanning Tree Coverage path planning
-
- :param start: the start node of Spiral Spanning Tree Coverage
- """
-
- visit_times = np.zeros(
- (self.merged_map_height, self.merged_map_width), dtype=int)
- visit_times[start[0]][start[1]] = 1
-
- # generate route by
- # recusively call perform_spanning_tree_coverage() from start node
- route = []
- self.perform_spanning_tree_coverage(start, visit_times, route)
-
- path = []
- # generate path from route
- for idx in range(len(route)-1):
- dp = abs(route[idx][0] - route[idx+1][0]) + \
- abs(route[idx][1] - route[idx+1][1])
- if dp == 0:
- # special handle for round-trip path
- path.append(self.get_round_trip_path(route[idx-1], route[idx]))
- elif dp == 1:
- path.append(self.move(route[idx], route[idx+1]))
- elif dp == 2:
- # special handle for non-adjacent route nodes
- mid_node = self.get_intermediate_node(route[idx], route[idx+1])
- path.append(self.move(route[idx], mid_node))
- path.append(self.move(mid_node, route[idx+1]))
- else:
- sys.exit('adjacent path node distance larger than 2')
-
- return self.edge, route, path
-
- def perform_spanning_tree_coverage(self, current_node, visit_times, route):
- """perform_spanning_tree_coverage
-
- recursive function for function <plan>
-
- :param current_node: current node
- """
-
- def is_valid_node(i, j):
- is_i_valid_bounded = 0 <= i < self.merged_map_height
- is_j_valid_bounded = 0 <= j < self.merged_map_width
- if is_i_valid_bounded and is_j_valid_bounded:
- # free only when the 4 sub-cells are all free
- return bool(
- self.occ_map[2*i][2*j]
- and self.occ_map[2*i+1][2*j]
- and self.occ_map[2*i][2*j+1]
- and self.occ_map[2*i+1][2*j+1])
-
- return False
-
- # counter-clockwise neighbor finding order
- order = [[1, 0], [0, 1], [-1, 0], [0, -1]]
-
- found = False
- route.append(current_node)
- for inc in order:
- ni, nj = current_node[0] + inc[0], current_node[1] + inc[1]
- if is_valid_node(ni, nj) and visit_times[ni][nj] == 0:
- neighbor_node = (ni, nj)
- self.edge.append((current_node, neighbor_node))
- found = True
- visit_times[ni][nj] += 1
- self.perform_spanning_tree_coverage(
- neighbor_node, visit_times, route)
-
- # backtrace route from node with neighbors all visited
- # to first node with unvisited neighbor
- if not found:
- has_node_with_unvisited_ngb = False
- for node in reversed(route):
- # drop nodes that have been visited twice
- if visit_times[node[0]][node[1]] == 2:
- continue
-
- visit_times[node[0]][node[1]] += 1
- route.append(node)
-
- for inc in order:
- ni, nj = node[0] + inc[0], node[1] + inc[1]
- if is_valid_node(ni, nj) and visit_times[ni][nj] == 0:
- has_node_with_unvisited_ngb = True
- break
-
- if has_node_with_unvisited_ngb:
- break
-
- return route
-
- def move(self, p, q):
- direction = self.get_vector_direction(p, q)
- # move east
- if direction == 'E':
- p = self.get_sub_node(p, 'SE')
- q = self.get_sub_node(q, 'SW')
- # move west
- elif direction == 'W':
- p = self.get_sub_node(p, 'NW')
- q = self.get_sub_node(q, 'NE')
- # move south
- elif direction == 'S':
- p = self.get_sub_node(p, 'SW')
- q = self.get_sub_node(q, 'NW')
- # move north
- elif direction == 'N':
- p = self.get_sub_node(p, 'NE')
- q = self.get_sub_node(q, 'SE')
- else:
- sys.exit('move direction error...')
- return [p, q]
-
- def get_round_trip_path(self, last, pivot):
- direction = self.get_vector_direction(last, pivot)
- if direction == 'E':
- return [self.get_sub_node(pivot, 'SE'),
- self.get_sub_node(pivot, 'NE')]
- elif direction == 'S':
- return [self.get_sub_node(pivot, 'SW'),
- self.get_sub_node(pivot, 'SE')]
- elif direction == 'W':
- return [self.get_sub_node(pivot, 'NW'),
- self.get_sub_node(pivot, 'SW')]
- elif direction == 'N':
- return [self.get_sub_node(pivot, 'NE'),
- self.get_sub_node(pivot, 'NW')]
- else:
- sys.exit('get_round_trip_path: last->pivot direction error.')
-
- def get_vector_direction(self, p, q):
- # east
- if p[0] == q[0] and p[1] < q[1]:
- return 'E'
- # west
- elif p[0] == q[0] and p[1] > q[1]:
- return 'W'
- # south
- elif p[0] < q[0] and p[1] == q[1]:
- return 'S'
- # north
- elif p[0] > q[0] and p[1] == q[1]:
- return 'N'
- else:
- sys.exit('get_vector_direction: Only E/W/S/N direction supported.')
-
- def get_sub_node(self, node, direction):
- if direction == 'SE':
- return [2*node[0]+1, 2*node[1]+1]
- elif direction == 'SW':
- return [2*node[0]+1, 2*node[1]]
- elif direction == 'NE':
- return [2*node[0], 2*node[1]+1]
- elif direction == 'NW':
- return [2*node[0], 2*node[1]]
- else:
- sys.exit('get_sub_node: sub-node direction error.')
-
- def get_interpolated_path(self, p, q):
- # direction p->q: southwest / northeast
- if (p[0] < q[0]) ^ (p[1] < q[1]):
- ipx = [p[0], p[0], q[0]]
- ipy = [p[1], q[1], q[1]]
- # direction p->q: southeast / northwest
- else:
- ipx = [p[0], q[0], q[0]]
- ipy = [p[1], p[1], q[1]]
- return ipx, ipy
-
- def get_intermediate_node(self, p, q):
- p_ngb, q_ngb = set(), set()
-
- for m, n in self.edge:
- if m == p:
- p_ngb.add(n)
- if n == p:
- p_ngb.add(m)
- if m == q:
- q_ngb.add(n)
- if n == q:
- q_ngb.add(m)
-
- itsc = p_ngb.intersection(q_ngb)
- if len(itsc) == 0:
- sys.exit('get_intermediate_node: \
- no intermediate node between', p, q)
- elif len(itsc) == 1:
- return list(itsc)[0]
- else:
- sys.exit('get_intermediate_node: \
- more than 1 intermediate node between', p, q)
-
- def visualize_path(self, edge, path, start):
- def coord_transform(p):
- return [2*p[1] + 0.5, 2*p[0] + 0.5]
-
- if do_animation:
- last = path[0][0]
- trajectory = [[last[1]], [last[0]]]
- for p, q in path:
- distance = math.hypot(p[0]-last[0], p[1]-last[1])
- if distance <= 1.0:
- trajectory[0].append(p[1])
- trajectory[1].append(p[0])
- else:
- ipx, ipy = self.get_interpolated_path(last, p)
- trajectory[0].extend(ipy)
- trajectory[1].extend(ipx)
-
- last = q
-
- trajectory[0].append(last[1])
- trajectory[1].append(last[0])
-
- for idx, state in enumerate(np.transpose(trajectory)):
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
-
- # draw spanning tree
- plt.imshow(self.occ_map, 'gray')
- for p, q in edge:
- p = coord_transform(p)
- q = coord_transform(q)
- plt.plot([p[0], q[0]], [p[1], q[1]], '-oc')
- sx, sy = coord_transform(start)
- plt.plot([sx], [sy], 'pr', markersize=10)
-
- # draw move path
- plt.plot(trajectory[0][:idx+1], trajectory[1][:idx+1], '-k')
- plt.plot(state[0], state[1], 'or')
- plt.axis('equal')
- plt.grid(True)
- plt.pause(0.01)
-
- else:
- # draw spanning tree
- plt.imshow(self.occ_map, 'gray')
- for p, q in edge:
- p = coord_transform(p)
- q = coord_transform(q)
- plt.plot([p[0], q[0]], [p[1], q[1]], '-oc')
- sx, sy = coord_transform(start)
- plt.plot([sx], [sy], 'pr', markersize=10)
-
- # draw move path
- last = path[0][0]
- for p, q in path:
- distance = math.hypot(p[0]-last[0], p[1]-last[1])
- if distance == 1.0:
- plt.plot([last[1], p[1]], [last[0], p[0]], '-k')
- else:
- ipx, ipy = self.get_interpolated_path(last, p)
- plt.plot(ipy, ipx, '-k')
- plt.arrow(p[1], p[0], q[1]-p[1], q[0]-p[0], head_width=0.2)
- last = q
-
- plt.show()
-
-
-def main():
- dir_path = os.path.dirname(os.path.realpath(__file__))
- img = plt.imread(os.path.join(dir_path, 'map', 'test_2.png'))
- STC_planner = SpiralSpanningTreeCoveragePlanner(img)
- start = (10, 0)
- edge, route, path = STC_planner.plan(start)
- STC_planner.visualize_path(edge, path, start)
-
-
-if __name__ == "__main__":
- main()
diff --git a/PathPlanning/StateLatticePlanner/__init__.py b/PathPlanning/StateLatticePlanner/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathPlanning/StateLatticePlanner/lookup_table.csv b/PathPlanning/StateLatticePlanner/lookup_table.csv
deleted file mode 100644
index 2c48a11a18b..00000000000
--- a/PathPlanning/StateLatticePlanner/lookup_table.csv
+++ /dev/null
@@ -1,82 +0,0 @@
-x,y,yaw,s,km,kf
-1.0,0.0,0.0,1.0,0.0,0.0
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-9.999999973554228,8.906672256498078e-05,-0.00024912926939091307,9.993250237275609,1.9794429093204823e-06,-0.00016167063578544257
-14.999999988951053,0.00030609885737583985,-9.259737492950393e-05,14.939586274030715,4.066161982234725e-06,-5.3230908443270726e-05
-19.999999963637627,0.0008196433029304879,-0.00010277758318455454,19.985770355960977,6.0902800817987275e-06,-5.581407356116362e-05
-24.999999906323,0.001558015443394581,-0.0001252423879458675,24.925430653319882,7.508303551937611e-06,-5.98269885073166e-05
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-9.974854017566281,5.998183884411291,0.01394025812352817,12.27808815775426,0.13163310345287574,-0.5111693653344966
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diff --git a/PathPlanning/StateLatticePlanner/state_lattice_planner.py b/PathPlanning/StateLatticePlanner/state_lattice_planner.py
deleted file mode 100644
index 7f8e725e0ac..00000000000
--- a/PathPlanning/StateLatticePlanner/state_lattice_planner.py
+++ /dev/null
@@ -1,343 +0,0 @@
-"""
-
-State lattice planner with model predictive trajectory generator
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-- plookuptable.csv is generated with this script:
-https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning
-/ModelPredictiveTrajectoryGenerator/lookup_table_generator.py
-
-Ref:
-
-- State Space Sampling of Feasible Motions for High-Performance Mobile Robot
-Navigation in Complex Environments
-https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf
-&doi=e2256b5b24137f89e473f01df288cb3aa72e56a0
-
-"""
-import sys
-import os
-from matplotlib import pyplot as plt
-import numpy as np
-import math
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-import ModelPredictiveTrajectoryGenerator.trajectory_generator as planner
-import ModelPredictiveTrajectoryGenerator.motion_model as motion_model
-
-TABLE_PATH = os.path.dirname(os.path.abspath(__file__)) + "/lookup_table.csv"
-
-show_animation = True
-
-
-def search_nearest_one_from_lookup_table(t_x, t_y, t_yaw, lookup_table):
- mind = float("inf")
- minid = -1
-
- for (i, table) in enumerate(lookup_table):
- dx = t_x - table[0]
- dy = t_y - table[1]
- dyaw = t_yaw - table[2]
- d = math.sqrt(dx ** 2 + dy ** 2 + dyaw ** 2)
- if d <= mind:
- minid = i
- mind = d
-
- return lookup_table[minid]
-
-
-def get_lookup_table(table_path):
- return np.loadtxt(table_path, delimiter=',', skiprows=1)
-
-
-def generate_path(target_states, k0):
- # x, y, yaw, s, km, kf
- lookup_table = get_lookup_table(TABLE_PATH)
- result = []
-
- for state in target_states:
- bestp = search_nearest_one_from_lookup_table(
- state[0], state[1], state[2], lookup_table)
-
- target = motion_model.State(x=state[0], y=state[1], yaw=state[2])
- init_p = np.array(
- [np.hypot(state[0], state[1]), bestp[4], bestp[5]]).reshape(3, 1)
-
- x, y, yaw, p = planner.optimize_trajectory(target, k0, init_p)
-
- if x is not None:
- print("find good path")
- result.append(
- [x[-1], y[-1], yaw[-1], float(p[0, 0]), float(p[1, 0]), float(p[2, 0])])
-
- print("finish path generation")
- return result
-
-
-def calc_uniform_polar_states(nxy, nh, d, a_min, a_max, p_min, p_max):
- """
-
- Parameters
- ----------
- nxy :
- number of position sampling
- nh :
- number of heading sampleing
- d :
- distance of terminal state
- a_min :
- position sampling min angle
- a_max :
- position sampling max angle
- p_min :
- heading sampling min angle
- p_max :
- heading sampling max angle
-
- Returns
- -------
-
- """
- angle_samples = [i / (nxy - 1) for i in range(nxy)]
- states = sample_states(angle_samples, a_min, a_max, d, p_max, p_min, nh)
-
- return states
-
-
-def calc_biased_polar_states(goal_angle, ns, nxy, nh, d, a_min, a_max, p_min, p_max):
- """
- calc biased state
-
- :param goal_angle: goal orientation for biased sampling
- :param ns: number of biased sampling
- :param nxy: number of position sampling
- :param nxy: number of position sampling
- :param nh: number of heading sampleing
- :param d: distance of terminal state
- :param a_min: position sampling min angle
- :param a_max: position sampling max angle
- :param p_min: heading sampling min angle
- :param p_max: heading sampling max angle
- :return: states list
- """
-
- asi = [a_min + (a_max - a_min) * i / (ns - 1) for i in range(ns - 1)]
- cnav = [math.pi - abs(i - goal_angle) for i in asi]
-
- cnav_sum = sum(cnav)
- cnav_max = max(cnav)
-
- # normalize
- cnav = [(cnav_max - cnav[i]) / (cnav_max * ns - cnav_sum)
- for i in range(ns - 1)]
-
- csumnav = np.cumsum(cnav)
- di = []
- li = 0
- for i in range(nxy):
- for ii in range(li, ns - 1):
- if ii / ns >= i / (nxy - 1):
- di.append(csumnav[ii])
- li = ii - 1
- break
-
- states = sample_states(di, a_min, a_max, d, p_max, p_min, nh)
-
- return states
-
-
-def calc_lane_states(l_center, l_heading, l_width, v_width, d, nxy):
- """
-
- calc lane states
-
- :param l_center: lane lateral position
- :param l_heading: lane heading
- :param l_width: lane width
- :param v_width: vehicle width
- :param d: longitudinal position
- :param nxy: sampling number
- :return: state list
- """
- xc = d
- yc = l_center
-
- states = []
- for i in range(nxy):
- delta = -0.5 * (l_width - v_width) + \
- (l_width - v_width) * i / (nxy - 1)
- xf = xc - delta * math.sin(l_heading)
- yf = yc + delta * math.cos(l_heading)
- yawf = l_heading
- states.append([xf, yf, yawf])
-
- return states
-
-
-def sample_states(angle_samples, a_min, a_max, d, p_max, p_min, nh):
- states = []
- for i in angle_samples:
- a = a_min + (a_max - a_min) * i
-
- for j in range(nh):
- xf = d * math.cos(a)
- yf = d * math.sin(a)
- if nh == 1:
- yawf = (p_max - p_min) / 2 + a
- else:
- yawf = p_min + (p_max - p_min) * j / (nh - 1) + a
- states.append([xf, yf, yawf])
-
- return states
-
-
-def uniform_terminal_state_sampling_test1():
- k0 = 0.0
- nxy = 5
- nh = 3
- d = 20
- a_min = - np.deg2rad(45.0)
- a_max = np.deg2rad(45.0)
- p_min = - np.deg2rad(45.0)
- p_max = np.deg2rad(45.0)
- states = calc_uniform_polar_states(nxy, nh, d, a_min, a_max, p_min, p_max)
- result = generate_path(states, k0)
-
- for table in result:
- xc, yc, yawc = motion_model.generate_trajectory(
- table[3], table[4], table[5], k0)
-
- if show_animation:
- plt.plot(xc, yc, "-r")
-
- if show_animation:
- plt.grid(True)
- plt.axis("equal")
- plt.show()
-
- print("Done")
-
-
-def uniform_terminal_state_sampling_test2():
- k0 = 0.1
- nxy = 6
- nh = 3
- d = 20
- a_min = - np.deg2rad(-10.0)
- a_max = np.deg2rad(45.0)
- p_min = - np.deg2rad(20.0)
- p_max = np.deg2rad(20.0)
- states = calc_uniform_polar_states(nxy, nh, d, a_min, a_max, p_min, p_max)
- result = generate_path(states, k0)
-
- for table in result:
- xc, yc, yawc = motion_model.generate_trajectory(
- table[3], table[4], table[5], k0)
-
- if show_animation:
- plt.plot(xc, yc, "-r")
-
- if show_animation:
- plt.grid(True)
- plt.axis("equal")
- plt.show()
-
- print("Done")
-
-
-def biased_terminal_state_sampling_test1():
- k0 = 0.0
- nxy = 30
- nh = 2
- d = 20
- a_min = np.deg2rad(-45.0)
- a_max = np.deg2rad(45.0)
- p_min = - np.deg2rad(20.0)
- p_max = np.deg2rad(20.0)
- ns = 100
- goal_angle = np.deg2rad(0.0)
- states = calc_biased_polar_states(
- goal_angle, ns, nxy, nh, d, a_min, a_max, p_min, p_max)
- result = generate_path(states, k0)
-
- for table in result:
- xc, yc, yawc = motion_model.generate_trajectory(
- table[3], table[4], table[5], k0)
- if show_animation:
- plt.plot(xc, yc, "-r")
-
- if show_animation:
- plt.grid(True)
- plt.axis("equal")
- plt.show()
-
-
-def biased_terminal_state_sampling_test2():
- k0 = 0.0
- nxy = 30
- nh = 1
- d = 20
- a_min = np.deg2rad(0.0)
- a_max = np.deg2rad(45.0)
- p_min = - np.deg2rad(20.0)
- p_max = np.deg2rad(20.0)
- ns = 100
- goal_angle = np.deg2rad(30.0)
- states = calc_biased_polar_states(
- goal_angle, ns, nxy, nh, d, a_min, a_max, p_min, p_max)
- result = generate_path(states, k0)
-
- for table in result:
- xc, yc, yawc = motion_model.generate_trajectory(
- table[3], table[4], table[5], k0)
-
- if show_animation:
- plt.plot(xc, yc, "-r")
-
- if show_animation:
- plt.grid(True)
- plt.axis("equal")
- plt.show()
-
-
-def lane_state_sampling_test1():
- k0 = 0.0
-
- l_center = 10.0
- l_heading = np.deg2rad(0.0)
- l_width = 3.0
- v_width = 1.0
- d = 10
- nxy = 5
- states = calc_lane_states(l_center, l_heading, l_width, v_width, d, nxy)
- result = generate_path(states, k0)
-
- if show_animation:
- plt.close("all")
-
- for table in result:
- x_c, y_c, yaw_c = motion_model.generate_trajectory(
- table[3], table[4], table[5], k0)
-
- if show_animation:
- plt.plot(x_c, y_c, "-r")
-
- if show_animation:
- plt.grid(True)
- plt.axis("equal")
- plt.show()
-
-
-def main():
- planner.show_animation = show_animation
- uniform_terminal_state_sampling_test1()
- uniform_terminal_state_sampling_test2()
- biased_terminal_state_sampling_test1()
- biased_terminal_state_sampling_test2()
- lane_state_sampling_test1()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/TimeBasedPathPlanning/GridWithDynamicObstacles.py b/PathPlanning/TimeBasedPathPlanning/GridWithDynamicObstacles.py
deleted file mode 100644
index 2a47023f8cd..00000000000
--- a/PathPlanning/TimeBasedPathPlanning/GridWithDynamicObstacles.py
+++ /dev/null
@@ -1,331 +0,0 @@
-"""
-This file implements a grid with a 3d reservation matrix with dimensions for x, y, and time. There
-is also infrastructure to generate dynamic obstacles that move around the grid. The obstacles' paths
-are stored in the reservation matrix on creation.
-"""
-import numpy as np
-import matplotlib.pyplot as plt
-from enum import Enum
-from dataclasses import dataclass
-
-@dataclass(order=True)
-class Position:
- x: int
- y: int
-
- def as_ndarray(self) -> np.ndarray:
- return np.array([self.x, self.y])
-
- def __add__(self, other):
- if isinstance(other, Position):
- return Position(self.x + other.x, self.y + other.y)
- raise NotImplementedError(
- f"Addition not supported for Position and {type(other)}"
- )
-
- def __sub__(self, other):
- if isinstance(other, Position):
- return Position(self.x - other.x, self.y - other.y)
- raise NotImplementedError(
- f"Subtraction not supported for Position and {type(other)}"
- )
-
- def __hash__(self):
- return hash((self.x, self.y))
-
-@dataclass
-class Interval:
- start_time: int
- end_time: int
-
-class ObstacleArrangement(Enum):
- # Random obstacle positions and movements
- RANDOM = 0
- # Obstacles start in a line in y at center of grid and move side-to-side in x
- ARRANGEMENT1 = 1
-
-"""
-Generates a 2d numpy array with lists for elements.
-"""
-def empty_2d_array_of_lists(x: int, y: int) -> np.ndarray:
- arr = np.empty((x, y), dtype=object)
- # assign each element individually - np.full creates references to the same list
- arr[:] = [[[] for _ in range(y)] for _ in range(x)]
- return arr
-
-class Grid:
- # Set in constructor
- grid_size: np.ndarray
- reservation_matrix: np.ndarray
- obstacle_paths: list[list[Position]] = []
- # Obstacles will never occupy these points. Useful to avoid impossible scenarios
- obstacle_avoid_points: list[Position] = []
-
- # Number of time steps in the simulation
- time_limit: int
-
- # Logging control
- verbose = False
-
- def __init__(
- self,
- grid_size: np.ndarray,
- num_obstacles: int = 40,
- obstacle_avoid_points: list[Position] = [],
- obstacle_arrangement: ObstacleArrangement = ObstacleArrangement.RANDOM,
- time_limit: int = 100,
- ):
- self.obstacle_avoid_points = obstacle_avoid_points
- self.time_limit = time_limit
- self.grid_size = grid_size
- self.reservation_matrix = np.zeros((grid_size[0], grid_size[1], self.time_limit))
-
- if num_obstacles > self.grid_size[0] * self.grid_size[1]:
- raise Exception("Number of obstacles is greater than grid size!")
-
- if obstacle_arrangement == ObstacleArrangement.RANDOM:
- self.obstacle_paths = self.generate_dynamic_obstacles(num_obstacles)
- elif obstacle_arrangement == ObstacleArrangement.ARRANGEMENT1:
- self.obstacle_paths = self.obstacle_arrangement_1(num_obstacles)
-
- for i, path in enumerate(self.obstacle_paths):
- obs_idx = i + 1 # avoid using 0 - that indicates free space in the grid
- for t, position in enumerate(path):
- # Reserve old & new position at this time step
- if t > 0:
- self.reservation_matrix[path[t - 1].x, path[t - 1].y, t] = obs_idx
- self.reservation_matrix[position.x, position.y, t] = obs_idx
-
- """
- Generate dynamic obstacles that move around the grid. Initial positions and movements are random
- """
- def generate_dynamic_obstacles(self, obs_count: int) -> list[list[Position]]:
- obstacle_paths = []
- for _ in range(0, obs_count):
- # Sample until a free starting space is found
- initial_position = self.sample_random_position()
- while not self.valid_obstacle_position(initial_position, 0):
- initial_position = self.sample_random_position()
-
- positions = [initial_position]
- if self.verbose:
- print("Obstacle initial position: ", initial_position)
-
- # Encourage obstacles to mostly stay in place - too much movement leads to chaotic planning scenarios
- # that are not fun to watch
- weights = [0.05, 0.05, 0.05, 0.05, 0.8]
- diffs = [
- Position(0, 1),
- Position(0, -1),
- Position(1, 0),
- Position(-1, 0),
- Position(0, 0),
- ]
-
- for t in range(1, self.time_limit - 1):
- sampled_indices = np.random.choice(
- len(diffs), size=5, replace=False, p=weights
- )
- rand_diffs = [diffs[i] for i in sampled_indices]
-
- valid_position = None
- for diff in rand_diffs:
- new_position = positions[-1] + diff
-
- if not self.valid_obstacle_position(new_position, t):
- continue
-
- valid_position = new_position
- break
-
- # Impossible situation for obstacle - stay in place
- # -> this can happen if the oaths of other obstacles this one
- if valid_position is None:
- valid_position = positions[-1]
-
- positions.append(valid_position)
-
- obstacle_paths.append(positions)
-
- return obstacle_paths
-
- """
- Generate a line of obstacles in y at the center of the grid that move side-to-side in x
- Bottom half start moving right, top half start moving left. If `obs_count` is less than the length of
- the grid, only the first `obs_count` obstacles will be generated.
- """
- def obstacle_arrangement_1(self, obs_count: int) -> list[list[Position]]:
- obstacle_paths = []
- half_grid_x = self.grid_size[0] // 2
- half_grid_y = self.grid_size[1] // 2
-
- for y_idx in range(0, min(obs_count, self.grid_size[1])):
- moving_right = y_idx < half_grid_y
- position = Position(half_grid_x, y_idx)
- path = [position]
-
- for t in range(1, self.time_limit - 1):
- # sit in place every other time step
- if t % 2 == 0:
- path.append(position)
- continue
-
- # first check if we should switch direction (at edge of grid)
- if (moving_right and position.x == self.grid_size[0] - 1) or (
- not moving_right and position.x == 0
- ):
- moving_right = not moving_right
- # step in direction
- position = Position(
- position.x + (1 if moving_right else -1), position.y
- )
- path.append(position)
-
- obstacle_paths.append(path)
-
- return obstacle_paths
-
- """
- Check if the given position is valid at time t
-
- input:
- position (Position): (x, y) position
- t (int): time step
-
- output:
- bool: True if position/time combination is valid, False otherwise
- """
- def valid_position(self, position: Position, t: int) -> bool:
- # Check if new position is in grid
- if not self.inside_grid_bounds(position):
- return False
-
- # Check if new position is not occupied at time t
- return self.reservation_matrix[position.x, position.y, t] == 0
-
- """
- Returns True if the given position is valid at time t and is not in the set of obstacle_avoid_points
- """
- def valid_obstacle_position(self, position: Position, t: int) -> bool:
- return (
- self.valid_position(position, t)
- and position not in self.obstacle_avoid_points
- )
-
- """
- Returns True if the given position is within the grid's boundaries
- """
- def inside_grid_bounds(self, position: Position) -> bool:
- return (
- position.x >= 0
- and position.x < self.grid_size[0]
- and position.y >= 0
- and position.y < self.grid_size[1]
- )
-
- """
- Sample a random position that is within the grid's boundaries
-
- output:
- Position: (x, y) position
- """
- def sample_random_position(self) -> Position:
- return Position(
- np.random.randint(0, self.grid_size[0]),
- np.random.randint(0, self.grid_size[1]),
- )
-
- """
- Returns a tuple of (x_positions, y_positions) of the obstacles at time t
- """
- def get_obstacle_positions_at_time(self, t: int) -> tuple[list[int], list[int]]:
- x_positions = []
- y_positions = []
- for obs_path in self.obstacle_paths:
- x_positions.append(obs_path[t].x)
- y_positions.append(obs_path[t].y)
- return (x_positions, y_positions)
-
- """
- Returns safe intervals for each cell.
- """
- def get_safe_intervals(self) -> np.ndarray:
- intervals = empty_2d_array_of_lists(self.grid_size[0], self.grid_size[1])
- for x in range(intervals.shape[0]):
- for y in range(intervals.shape[1]):
- intervals[x, y] = self.get_safe_intervals_at_cell(Position(x, y))
-
- return intervals
-
- """
- Generate the safe intervals for a given cell. The intervals will be in order of start time.
- ex: Interval (2, 3) will be before Interval (4, 5)
- """
- def get_safe_intervals_at_cell(self, cell: Position) -> list[Interval]:
- vals = self.reservation_matrix[cell.x, cell.y, :]
- # Find where the array is zero
- zero_mask = (vals == 0)
-
- # Identify transitions between zero and nonzero elements
- diff = np.diff(zero_mask.astype(int))
-
- # Start indices: where zeros begin (1 after a nonzero)
- start_indices = np.where(diff == 1)[0] + 1
-
- # End indices: where zeros stop (just before a nonzero)
- end_indices = np.where(diff == -1)[0]
-
- # Handle edge cases if the array starts or ends with zeros
- if zero_mask[0]: # If the first element is zero, add index 0 to start_indices
- start_indices = np.insert(start_indices, 0, 0)
- if zero_mask[-1]: # If the last element is zero, add the last index to end_indices
- end_indices = np.append(end_indices, len(vals) - 1)
-
- # Create pairs of (first zero, last zero)
- intervals = [Interval(int(start), int(end)) for start, end in zip(start_indices, end_indices)]
-
- # Remove intervals where a cell is only free for one time step. Those intervals not provide enough time to
- # move into and out of the cell each take 1 time step, and the cell is considered occupied during
- # both the time step when it is entering the cell, and the time step when it is leaving the cell.
- intervals = [interval for interval in intervals if interval.start_time != interval.end_time]
- return intervals
-
-show_animation = True
-
-
-def main():
- grid = Grid(
- np.array([11, 11]),
- num_obstacles=10,
- obstacle_arrangement=ObstacleArrangement.ARRANGEMENT1,
- )
-
- if not show_animation:
- return
-
- fig = plt.figure(figsize=(8, 7))
- ax = fig.add_subplot(
- autoscale_on=False,
- xlim=(0, grid.grid_size[0] - 1),
- ylim=(0, grid.grid_size[1] - 1),
- )
- ax.set_aspect("equal")
- ax.grid()
- ax.set_xticks(np.arange(0, 11, 1))
- ax.set_yticks(np.arange(0, 11, 1))
- (obs_points,) = ax.plot([], [], "ro", ms=15)
-
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- "key_release_event", lambda event: [exit(0) if event.key == "escape" else None]
- )
-
- for i in range(0, grid.time_limit - 1):
- obs_positions = grid.get_obstacle_positions_at_time(i)
- obs_points.set_data(obs_positions[0], obs_positions[1])
- plt.pause(0.2)
- plt.show()
-
-
-if __name__ == "__main__":
- main()
diff --git a/PathPlanning/TimeBasedPathPlanning/SafeInterval.py b/PathPlanning/TimeBasedPathPlanning/SafeInterval.py
deleted file mode 100644
index 7fea10c67fb..00000000000
--- a/PathPlanning/TimeBasedPathPlanning/SafeInterval.py
+++ /dev/null
@@ -1,303 +0,0 @@
-"""
-Safe interval path planner
- This script implements a safe-interval path planner for a 2d grid with dynamic obstacles. It is faster than
- SpaceTime A* because it reduces the number of redundant node expansions by pre-computing regions of adjacent
- time steps that are safe ("safe intervals") at each position. This allows the algorithm to skip expanding nodes
- that are in intervals that have already been visited earlier.
-
- Reference: https://www.cs.cmu.edu/~maxim/files/sipp_icra11.pdf
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-from PathPlanning.TimeBasedPathPlanning.GridWithDynamicObstacles import (
- Grid,
- Interval,
- ObstacleArrangement,
- Position,
- empty_2d_array_of_lists,
-)
-import heapq
-import random
-from dataclasses import dataclass
-from functools import total_ordering
-import time
-
-@dataclass()
-# Note: Total_ordering is used instead of adding `order=True` to the @dataclass decorator because
-# this class needs to override the __lt__ and __eq__ methods to ignore parent_index. The Parent
-# index and interval member variables are just used to track the path found by the algorithm,
-# and has no effect on the quality of a node.
-@total_ordering
-class Node:
- position: Position
- time: int
- heuristic: int
- parent_index: int
- interval: Interval
-
- """
- This is what is used to drive node expansion. The node with the lowest value is expanded next.
- This comparison prioritizes the node with the lowest cost-to-come (self.time) + cost-to-go (self.heuristic)
- """
- def __lt__(self, other: object):
- if not isinstance(other, Node):
- return NotImplementedError(f"Cannot compare Node with object of type: {type(other)}")
- return (self.time + self.heuristic) < (other.time + other.heuristic)
-
- """
- Equality only cares about position and time. Heuristic and interval will always be the same for a given
- (position, time) pairing, so they are not considered in equality.
- """
- def __eq__(self, other: object):
- if not isinstance(other, Node):
- return NotImplemented
- return self.position == other.position and self.time == other.time
-
-@dataclass
-class EntryTimeAndInterval:
- entry_time: int
- interval: Interval
-
-class NodePath:
- path: list[Node]
- positions_at_time: dict[int, Position] = {}
-
- def __init__(self, path: list[Node]):
- self.path = path
- for (i, node) in enumerate(path):
- if i > 0:
- # account for waiting in interval at previous node
- prev_node = path[i-1]
- for t in range(prev_node.time, node.time):
- self.positions_at_time[t] = prev_node.position
-
- self.positions_at_time[node.time] = node.position
-
- """
- Get the position of the path at a given time
- """
- def get_position(self, time: int) -> Position | None:
- return self.positions_at_time.get(time)
-
- """
- Time stamp of the last node in the path
- """
- def goal_reached_time(self) -> int:
- return self.path[-1].time
-
- def __repr__(self):
- repr_string = ""
- for i, node in enumerate(self.path):
- repr_string += f"{i}: {node}\n"
- return repr_string
-
-
-class SafeIntervalPathPlanner:
- grid: Grid
- start: Position
- goal: Position
-
- def __init__(self, grid: Grid, start: Position, goal: Position):
- self.grid = grid
- self.start = start
- self.goal = goal
-
- # Seed randomness for reproducibility
- RANDOM_SEED = 50
- random.seed(RANDOM_SEED)
- np.random.seed(RANDOM_SEED)
-
- """
- Generate a plan given the loaded problem statement. Raises an exception if it fails to find a path.
- Arguments:
- verbose (bool): set to True to print debug information
- """
- def plan(self, verbose: bool = False) -> NodePath:
-
- safe_intervals = self.grid.get_safe_intervals()
-
- open_set: list[Node] = []
- first_node_interval = safe_intervals[self.start.x, self.start.y][0]
- heapq.heappush(
- open_set, Node(self.start, 0, self.calculate_heuristic(self.start), -1, first_node_interval)
- )
-
- expanded_list: list[Node] = []
- visited_intervals = empty_2d_array_of_lists(self.grid.grid_size[0], self.grid.grid_size[1])
- while open_set:
- expanded_node: Node = heapq.heappop(open_set)
- if verbose:
- print("Expanded node:", expanded_node)
-
- if expanded_node.time + 1 >= self.grid.time_limit:
- if verbose:
- print(f"\tSkipping node that is past time limit: {expanded_node}")
- continue
-
- if expanded_node.position == self.goal:
- print(f"Found path to goal after {len(expanded_list)} expansions")
- path = []
- path_walker: Node = expanded_node
- while True:
- path.append(path_walker)
- if path_walker.parent_index == -1:
- break
- path_walker = expanded_list[path_walker.parent_index]
-
- # reverse path so it goes start -> goal
- path.reverse()
- return NodePath(path)
-
- expanded_idx = len(expanded_list)
- expanded_list.append(expanded_node)
- entry_time_and_node = EntryTimeAndInterval(expanded_node.time, expanded_node.interval)
- add_entry_to_visited_intervals_array(entry_time_and_node, visited_intervals, expanded_node)
-
- for child in self.generate_successors(expanded_node, expanded_idx, safe_intervals, visited_intervals):
- heapq.heappush(open_set, child)
-
- raise Exception("No path found")
-
- """
- Generate list of possible successors of the provided `parent_node` that are worth expanding
- """
- def generate_successors(
- self, parent_node: Node, parent_node_idx: int, intervals: np.ndarray, visited_intervals: np.ndarray
- ) -> list[Node]:
- new_nodes = []
- diffs = [
- Position(0, 0),
- Position(1, 0),
- Position(-1, 0),
- Position(0, 1),
- Position(0, -1),
- ]
- for diff in diffs:
- new_pos = parent_node.position + diff
- if not self.grid.inside_grid_bounds(new_pos):
- continue
-
- current_interval = parent_node.interval
-
- new_cell_intervals: list[Interval] = intervals[new_pos.x, new_pos.y]
- for interval in new_cell_intervals:
- # if interval starts after current ends, break
- # assumption: intervals are sorted by start time, so all future intervals will hit this condition as well
- if interval.start_time > current_interval.end_time:
- break
-
- # if interval ends before current starts, skip
- if interval.end_time < current_interval.start_time:
- continue
-
- # if we have already expanded a node in this interval with a <= starting time, skip
- better_node_expanded = False
- for visited in visited_intervals[new_pos.x, new_pos.y]:
- if interval == visited.interval and visited.entry_time <= parent_node.time + 1:
- better_node_expanded = True
- break
- if better_node_expanded:
- continue
-
- # We know there is a node worth expanding. Generate successor at the earliest possible time the
- # new interval can be entered
- for possible_t in range(max(parent_node.time + 1, interval.start_time), min(current_interval.end_time, interval.end_time)):
- if self.grid.valid_position(new_pos, possible_t):
- new_nodes.append(Node(
- new_pos,
- # entry is max of interval start and parent node time + 1 (get there as soon as possible)
- max(interval.start_time, parent_node.time + 1),
- self.calculate_heuristic(new_pos),
- parent_node_idx,
- interval,
- ))
- # break because all t's after this will make nodes with a higher cost, the same heuristic, and are in the same interval
- break
-
- return new_nodes
-
- """
- Calculate the heuristic for a given position - Manhattan distance to the goal
- """
- def calculate_heuristic(self, position) -> int:
- diff = self.goal - position
- return abs(diff.x) + abs(diff.y)
-
-
-"""
-Adds a new entry to the visited intervals array. If the entry is already present, the entry time is updated if the new
-entry time is better. Otherwise, the entry is added to `visited_intervals` at the position of `expanded_node`.
-"""
-def add_entry_to_visited_intervals_array(entry_time_and_interval: EntryTimeAndInterval, visited_intervals: np.ndarray, expanded_node: Node):
- # if entry is present, update entry time if better
- for existing_entry_and_interval in visited_intervals[expanded_node.position.x, expanded_node.position.y]:
- if existing_entry_and_interval.interval == entry_time_and_interval.interval:
- existing_entry_and_interval.entry_time = min(existing_entry_and_interval.entry_time, entry_time_and_interval.entry_time)
-
- # Otherwise, append
- visited_intervals[expanded_node.position.x, expanded_node.position.y].append(entry_time_and_interval)
-
-
-show_animation = True
-verbose = False
-
-def main():
- start = Position(1, 18)
- goal = Position(19, 19)
- grid_side_length = 21
-
- start_time = time.time()
-
- grid = Grid(
- np.array([grid_side_length, grid_side_length]),
- num_obstacles=250,
- obstacle_avoid_points=[start, goal],
- obstacle_arrangement=ObstacleArrangement.ARRANGEMENT1,
- # obstacle_arrangement=ObstacleArrangement.RANDOM,
- )
-
- planner = SafeIntervalPathPlanner(grid, start, goal)
- path = planner.plan(verbose)
- runtime = time.time() - start_time
- print(f"Planning took: {runtime:.5f} seconds")
-
- if verbose:
- print(f"Path: {path}")
-
- if not show_animation:
- return
-
- fig = plt.figure(figsize=(10, 7))
- ax = fig.add_subplot(
- autoscale_on=False,
- xlim=(0, grid.grid_size[0] - 1),
- ylim=(0, grid.grid_size[1] - 1),
- )
- ax.set_aspect("equal")
- ax.grid()
- ax.set_xticks(np.arange(0, grid_side_length, 1))
- ax.set_yticks(np.arange(0, grid_side_length, 1))
-
- (start_and_goal,) = ax.plot([], [], "mD", ms=15, label="Start and Goal")
- start_and_goal.set_data([start.x, goal.x], [start.y, goal.y])
- (obs_points,) = ax.plot([], [], "ro", ms=15, label="Obstacles")
- (path_points,) = ax.plot([], [], "bo", ms=10, label="Path Found")
- ax.legend(bbox_to_anchor=(1.05, 1))
-
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- "key_release_event", lambda event: [exit(0) if event.key == "escape" else None]
- )
-
- for i in range(0, path.goal_reached_time() + 1):
- obs_positions = grid.get_obstacle_positions_at_time(i)
- obs_points.set_data(obs_positions[0], obs_positions[1])
- path_position = path.get_position(i)
- path_points.set_data([path_position.x], [path_position.y])
- plt.pause(0.2)
- plt.show()
-
-
-if __name__ == "__main__":
- main()
diff --git a/PathPlanning/TimeBasedPathPlanning/SpaceTimeAStar.py b/PathPlanning/TimeBasedPathPlanning/SpaceTimeAStar.py
deleted file mode 100644
index c4e2802d372..00000000000
--- a/PathPlanning/TimeBasedPathPlanning/SpaceTimeAStar.py
+++ /dev/null
@@ -1,241 +0,0 @@
-"""
-Space-time A* Algorithm
- This script demonstrates the Space-time A* algorithm for path planning in a grid world with moving obstacles.
- This algorithm is different from normal 2D A* in one key way - the cost (often notated as g(n)) is
- the number of time steps it took to get to a given node, instead of the number of cells it has
- traversed. This ensures the path is time-optimal, while respecting any dynamic obstacles in the environment.
-
- Reference: https://www.davidsilver.uk/wp-content/uploads/2020/03/coop-path-AIWisdom.pdf
-"""
-
-import numpy as np
-import matplotlib.pyplot as plt
-from PathPlanning.TimeBasedPathPlanning.GridWithDynamicObstacles import (
- Grid,
- ObstacleArrangement,
- Position,
-)
-import heapq
-from collections.abc import Generator
-import random
-from dataclasses import dataclass
-from functools import total_ordering
-import time
-
-# Seed randomness for reproducibility
-RANDOM_SEED = 50
-random.seed(RANDOM_SEED)
-np.random.seed(RANDOM_SEED)
-
-@dataclass()
-# Note: Total_ordering is used instead of adding `order=True` to the @dataclass decorator because
-# this class needs to override the __lt__ and __eq__ methods to ignore parent_index. Parent
-# index is just used to track the path found by the algorithm, and has no effect on the quality
-# of a node.
-@total_ordering
-class Node:
- position: Position
- time: int
- heuristic: int
- parent_index: int
-
- """
- This is what is used to drive node expansion. The node with the lowest value is expanded next.
- This comparison prioritizes the node with the lowest cost-to-come (self.time) + cost-to-go (self.heuristic)
- """
- def __lt__(self, other: object):
- if not isinstance(other, Node):
- return NotImplementedError(f"Cannot compare Node with object of type: {type(other)}")
- return (self.time + self.heuristic) < (other.time + other.heuristic)
-
- """
- Note: cost and heuristic are not included in eq or hash, since they will always be the same
- for a given (position, time) pair. Including either cost or heuristic would be redundant.
- """
- def __eq__(self, other: object):
- if not isinstance(other, Node):
- return NotImplementedError(f"Cannot compare Node with object of type: {type(other)}")
- return self.position == other.position and self.time == other.time
-
- def __hash__(self):
- return hash((self.position, self.time))
-
-class NodePath:
- path: list[Node]
- positions_at_time: dict[int, Position] = {}
-
- def __init__(self, path: list[Node]):
- self.path = path
- for node in path:
- self.positions_at_time[node.time] = node.position
-
- """
- Get the position of the path at a given time
- """
- def get_position(self, time: int) -> Position | None:
- return self.positions_at_time.get(time)
-
- """
- Time stamp of the last node in the path
- """
- def goal_reached_time(self) -> int:
- return self.path[-1].time
-
- def __repr__(self):
- repr_string = ""
- for i, node in enumerate(self.path):
- repr_string += f"{i}: {node}\n"
- return repr_string
-
-
-class SpaceTimeAStar:
- grid: Grid
- start: Position
- goal: Position
- # Used to evaluate solutions
- expanded_node_count: int = -1
-
- def __init__(self, grid: Grid, start: Position, goal: Position):
- self.grid = grid
- self.start = start
- self.goal = goal
-
- def plan(self, verbose: bool = False) -> NodePath:
- open_set: list[Node] = []
- heapq.heappush(
- open_set, Node(self.start, 0, self.calculate_heuristic(self.start), -1)
- )
-
- expanded_list: list[Node] = []
- expanded_set: set[Node] = set()
- while open_set:
- expanded_node: Node = heapq.heappop(open_set)
- if verbose:
- print("Expanded node:", expanded_node)
-
- if expanded_node.time + 1 >= self.grid.time_limit:
- if verbose:
- print(f"\tSkipping node that is past time limit: {expanded_node}")
- continue
-
- if expanded_node.position == self.goal:
- print(f"Found path to goal after {len(expanded_list)} expansions")
- path = []
- path_walker: Node = expanded_node
- while True:
- path.append(path_walker)
- if path_walker.parent_index == -1:
- break
- path_walker = expanded_list[path_walker.parent_index]
-
- # reverse path so it goes start -> goal
- path.reverse()
- self.expanded_node_count = len(expanded_set)
- return NodePath(path)
-
- expanded_idx = len(expanded_list)
- expanded_list.append(expanded_node)
- expanded_set.add(expanded_node)
-
- for child in self.generate_successors(expanded_node, expanded_idx, verbose, expanded_set):
- heapq.heappush(open_set, child)
-
- raise Exception("No path found")
-
- """
- Generate possible successors of the provided `parent_node`
- """
- def generate_successors(
- self, parent_node: Node, parent_node_idx: int, verbose: bool, expanded_set: set[Node]
- ) -> Generator[Node, None, None]:
- diffs = [
- Position(0, 0),
- Position(1, 0),
- Position(-1, 0),
- Position(0, 1),
- Position(0, -1),
- ]
- for diff in diffs:
- new_pos = parent_node.position + diff
- new_node = Node(
- new_pos,
- parent_node.time + 1,
- self.calculate_heuristic(new_pos),
- parent_node_idx,
- )
-
- if new_node in expanded_set:
- continue
-
- if self.grid.valid_position(new_pos, parent_node.time + 1):
- if verbose:
- print("\tNew successor node: ", new_node)
- yield new_node
-
- def calculate_heuristic(self, position) -> int:
- diff = self.goal - position
- return abs(diff.x) + abs(diff.y)
-
-
-show_animation = True
-verbose = False
-
-def main():
- start = Position(1, 5)
- goal = Position(19, 19)
- grid_side_length = 21
-
- start_time = time.time()
-
- grid = Grid(
- np.array([grid_side_length, grid_side_length]),
- num_obstacles=40,
- obstacle_avoid_points=[start, goal],
- obstacle_arrangement=ObstacleArrangement.ARRANGEMENT1,
- )
-
- planner = SpaceTimeAStar(grid, start, goal)
- path = planner.plan(verbose)
-
- runtime = time.time() - start_time
- print(f"Planning took: {runtime:.5f} seconds")
-
- if verbose:
- print(f"Path: {path}")
-
- if not show_animation:
- return
-
- fig = plt.figure(figsize=(10, 7))
- ax = fig.add_subplot(
- autoscale_on=False,
- xlim=(0, grid.grid_size[0] - 1),
- ylim=(0, grid.grid_size[1] - 1),
- )
- ax.set_aspect("equal")
- ax.grid()
- ax.set_xticks(np.arange(0, grid_side_length, 1))
- ax.set_yticks(np.arange(0, grid_side_length, 1))
-
- (start_and_goal,) = ax.plot([], [], "mD", ms=15, label="Start and Goal")
- start_and_goal.set_data([start.x, goal.x], [start.y, goal.y])
- (obs_points,) = ax.plot([], [], "ro", ms=15, label="Obstacles")
- (path_points,) = ax.plot([], [], "bo", ms=10, label="Path Found")
- ax.legend(bbox_to_anchor=(1.05, 1))
-
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- "key_release_event", lambda event: [exit(0) if event.key == "escape" else None]
- )
-
- for i in range(0, path.goal_reached_time()):
- obs_positions = grid.get_obstacle_positions_at_time(i)
- obs_points.set_data(obs_positions[0], obs_positions[1])
- path_position = path.get_position(i)
- path_points.set_data([path_position.x], [path_position.y])
- plt.pause(0.2)
- plt.show()
-
-
-if __name__ == "__main__":
- main()
diff --git a/PathPlanning/TimeBasedPathPlanning/__init__.py b/PathPlanning/TimeBasedPathPlanning/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathPlanning/VisibilityRoadMap/__init__.py b/PathPlanning/VisibilityRoadMap/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathPlanning/VisibilityRoadMap/geometry.py b/PathPlanning/VisibilityRoadMap/geometry.py
deleted file mode 100644
index b15cdb8a43a..00000000000
--- a/PathPlanning/VisibilityRoadMap/geometry.py
+++ /dev/null
@@ -1,44 +0,0 @@
-class Geometry:
-
- class Point:
- def __init__(self, x, y):
- self.x = x
- self.y = y
-
- @staticmethod
- def is_seg_intersect(p1, q1, p2, q2):
-
- def on_segment(p, q, r):
- if ((q.x <= max(p.x, r.x)) and (q.x >= min(p.x, r.x)) and
- (q.y <= max(p.y, r.y)) and (q.y >= min(p.y, r.y))):
- return True
- return False
-
- def orientation(p, q, r):
- val = (float(q.y - p.y) * (r.x - q.x)) - (
- float(q.x - p.x) * (r.y - q.y))
- if val > 0:
- return 1
- if val < 0:
- return 2
- return 0
-
- # Find the 4 orientations required for
- # the general and special cases
- o1 = orientation(p1, q1, p2)
- o2 = orientation(p1, q1, q2)
- o3 = orientation(p2, q2, p1)
- o4 = orientation(p2, q2, q1)
-
- if (o1 != o2) and (o3 != o4):
- return True
- if (o1 == 0) and on_segment(p1, p2, q1):
- return True
- if (o2 == 0) and on_segment(p1, q2, q1):
- return True
- if (o3 == 0) and on_segment(p2, p1, q2):
- return True
- if (o4 == 0) and on_segment(p2, q1, q2):
- return True
-
- return False
diff --git a/PathPlanning/VisibilityRoadMap/visibility_road_map.py b/PathPlanning/VisibilityRoadMap/visibility_road_map.py
deleted file mode 100644
index 5f7ffadd16f..00000000000
--- a/PathPlanning/VisibilityRoadMap/visibility_road_map.py
+++ /dev/null
@@ -1,222 +0,0 @@
-"""
-
-Visibility Road Map Planner
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import sys
-import math
-import numpy as np
-import matplotlib.pyplot as plt
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from VisibilityRoadMap.geometry import Geometry
-from VoronoiRoadMap.dijkstra_search import DijkstraSearch
-
-show_animation = True
-
-
-class VisibilityRoadMap:
-
- def __init__(self, expand_distance, do_plot=False):
- self.expand_distance = expand_distance
- self.do_plot = do_plot
-
- def planning(self, start_x, start_y, goal_x, goal_y, obstacles):
-
- nodes = self.generate_visibility_nodes(start_x, start_y,
- goal_x, goal_y, obstacles)
-
- road_map_info = self.generate_road_map_info(nodes, obstacles)
-
- if self.do_plot:
- self.plot_road_map(nodes, road_map_info)
- plt.pause(1.0)
-
- rx, ry = DijkstraSearch(show_animation).search(
- start_x, start_y,
- goal_x, goal_y,
- [node.x for node in nodes],
- [node.y for node in nodes],
- road_map_info
- )
-
- return rx, ry
-
- def generate_visibility_nodes(self, start_x, start_y, goal_x, goal_y,
- obstacles):
-
- # add start and goal as nodes
- nodes = [DijkstraSearch.Node(start_x, start_y),
- DijkstraSearch.Node(goal_x, goal_y, 0, None)]
-
- # add vertexes in configuration space as nodes
- for obstacle in obstacles:
-
- cvx_list, cvy_list = self.calc_vertexes_in_configuration_space(
- obstacle.x_list, obstacle.y_list)
-
- for (vx, vy) in zip(cvx_list, cvy_list):
- nodes.append(DijkstraSearch.Node(vx, vy))
-
- if self.do_plot:
- for node in nodes:
- plt.plot(node.x, node.y, "xr")
-
- return nodes
-
- def calc_vertexes_in_configuration_space(self, x_list, y_list):
- x_list = x_list[0:-1]
- y_list = y_list[0:-1]
- cvx_list, cvy_list = [], []
-
- n_data = len(x_list)
-
- for index in range(n_data):
- offset_x, offset_y = self.calc_offset_xy(
- x_list[index - 1], y_list[index - 1],
- x_list[index], y_list[index],
- x_list[(index + 1) % n_data], y_list[(index + 1) % n_data],
- )
- cvx_list.append(offset_x)
- cvy_list.append(offset_y)
-
- return cvx_list, cvy_list
-
- def generate_road_map_info(self, nodes, obstacles):
-
- road_map_info_list = []
-
- for target_node in nodes:
- road_map_info = []
- for node_id, node in enumerate(nodes):
- if np.hypot(target_node.x - node.x,
- target_node.y - node.y) <= 0.1:
- continue
-
- is_valid = True
- for obstacle in obstacles:
- if not self.is_edge_valid(target_node, node, obstacle):
- is_valid = False
- break
- if is_valid:
- road_map_info.append(node_id)
-
- road_map_info_list.append(road_map_info)
-
- return road_map_info_list
-
- @staticmethod
- def is_edge_valid(target_node, node, obstacle):
-
- for i in range(len(obstacle.x_list) - 1):
- p1 = Geometry.Point(target_node.x, target_node.y)
- p2 = Geometry.Point(node.x, node.y)
- p3 = Geometry.Point(obstacle.x_list[i], obstacle.y_list[i])
- p4 = Geometry.Point(obstacle.x_list[i + 1], obstacle.y_list[i + 1])
-
- if Geometry.is_seg_intersect(p1, p2, p3, p4):
- return False
-
- return True
-
- def calc_offset_xy(self, px, py, x, y, nx, ny):
- p_vec = math.atan2(y - py, x - px)
- n_vec = math.atan2(ny - y, nx - x)
- offset_vec = math.atan2(math.sin(p_vec) + math.sin(n_vec),
- math.cos(p_vec) + math.cos(
- n_vec)) + math.pi / 2.0
- offset_x = x + self.expand_distance * math.cos(offset_vec)
- offset_y = y + self.expand_distance * math.sin(offset_vec)
- return offset_x, offset_y
-
- @staticmethod
- def plot_road_map(nodes, road_map_info_list):
- for i, node in enumerate(nodes):
- for index in road_map_info_list[i]:
- plt.plot([node.x, nodes[index].x],
- [node.y, nodes[index].y], "-b")
-
-
-class ObstaclePolygon:
-
- def __init__(self, x_list, y_list):
- self.x_list = x_list
- self.y_list = y_list
-
- self.close_polygon()
- self.make_clockwise()
-
- def make_clockwise(self):
- if not self.is_clockwise():
- self.x_list = list(reversed(self.x_list))
- self.y_list = list(reversed(self.y_list))
-
- def is_clockwise(self):
- n_data = len(self.x_list)
- eval_sum = sum([(self.x_list[i + 1] - self.x_list[i]) *
- (self.y_list[i + 1] + self.y_list[i])
- for i in range(n_data - 1)])
- eval_sum += (self.x_list[0] - self.x_list[n_data - 1]) * \
- (self.y_list[0] + self.y_list[n_data - 1])
- return eval_sum >= 0
-
- def close_polygon(self):
- is_x_same = self.x_list[0] == self.x_list[-1]
- is_y_same = self.y_list[0] == self.y_list[-1]
- if is_x_same and is_y_same:
- return # no need to close
-
- self.x_list.append(self.x_list[0])
- self.y_list.append(self.y_list[0])
-
- def plot(self):
- plt.plot(self.x_list, self.y_list, "-k")
-
-
-def main():
- print(__file__ + " start!!")
-
- # start and goal position
- sx, sy = 10.0, 10.0 # [m]
- gx, gy = 50.0, 50.0 # [m]
-
- expand_distance = 5.0 # [m]
-
- obstacles = [
- ObstaclePolygon(
- [20.0, 30.0, 15.0],
- [20.0, 20.0, 30.0],
- ),
- ObstaclePolygon(
- [40.0, 45.0, 50.0, 40.0],
- [50.0, 40.0, 20.0, 40.0],
- ),
- ObstaclePolygon(
- [20.0, 30.0, 30.0, 20.0],
- [40.0, 45.0, 60.0, 50.0],
- )
- ]
-
- if show_animation: # pragma: no cover
- plt.plot(sx, sy, "or")
- plt.plot(gx, gy, "ob")
- for ob in obstacles:
- ob.plot()
- plt.axis("equal")
- plt.pause(1.0)
-
- rx, ry = VisibilityRoadMap(expand_distance, do_plot=show_animation)\
- .planning(sx, sy, gx, gy, obstacles)
-
- if show_animation: # pragma: no cover
- plt.plot(rx, ry, "-r")
- plt.pause(0.1)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/VoronoiRoadMap/__init__.py b/PathPlanning/VoronoiRoadMap/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathPlanning/VoronoiRoadMap/dijkstra_search.py b/PathPlanning/VoronoiRoadMap/dijkstra_search.py
deleted file mode 100644
index 503ccc342eb..00000000000
--- a/PathPlanning/VoronoiRoadMap/dijkstra_search.py
+++ /dev/null
@@ -1,140 +0,0 @@
-"""
-
-Dijkstra Search library
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import matplotlib.pyplot as plt
-import math
-import numpy as np
-
-
-class DijkstraSearch:
- class Node:
- """
- Node class for dijkstra search
- """
-
- def __init__(self, x, y, cost=None, parent=None, edge_ids=None):
- self.x = x
- self.y = y
- self.cost = cost
- self.parent = parent
- self.edge_ids = edge_ids
-
- def __str__(self):
- return str(self.x) + "," + str(self.y) + "," + str(
- self.cost) + "," + str(self.parent)
-
- def __init__(self, show_animation):
- self.show_animation = show_animation
-
- def search(self, sx, sy, gx, gy, node_x, node_y, edge_ids_list):
- """
- Search shortest path
-
- s_x: start x positions [m]
- s_y: start y positions [m]
- gx: goal x position [m]
- gx: goal x position [m]
- node_x: node x position
- node_y: node y position
- edge_ids_list: edge_list each item includes a list of edge ids
- """
-
- start_node = self.Node(sx, sy, 0.0, -1)
- goal_node = self.Node(gx, gy, 0.0, -1)
- current_node = None
-
- open_set, close_set = dict(), dict()
- open_set[self.find_id(node_x, node_y, start_node)] = start_node
-
- while True:
- if self.has_node_in_set(close_set, goal_node):
- print("goal is found!")
- goal_node.parent = current_node.parent
- goal_node.cost = current_node.cost
- break
- elif not open_set:
- print("Cannot find path")
- break
-
- current_id = min(open_set, key=lambda o: open_set[o].cost)
- current_node = open_set[current_id]
-
- # show graph
- if self.show_animation and len(
- close_set.keys()) % 2 == 0: # pragma: no cover
- plt.plot(current_node.x, current_node.y, "xg")
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.pause(0.1)
-
- # Remove the item from the open set
- del open_set[current_id]
- # Add it to the closed set
- close_set[current_id] = current_node
-
- # expand search grid based on motion model
- for i in range(len(edge_ids_list[current_id])):
- n_id = edge_ids_list[current_id][i]
- dx = node_x[n_id] - current_node.x
- dy = node_y[n_id] - current_node.y
- d = math.hypot(dx, dy)
- node = self.Node(node_x[n_id], node_y[n_id],
- current_node.cost + d, current_id)
-
- if n_id in close_set:
- continue
- # Otherwise if it is already in the open set
- if n_id in open_set:
- if open_set[n_id].cost > node.cost:
- open_set[n_id] = node
- else:
- open_set[n_id] = node
-
- # generate final course
- rx, ry = self.generate_final_path(close_set, goal_node)
-
- return rx, ry
-
- @staticmethod
- def generate_final_path(close_set, goal_node):
- rx, ry = [goal_node.x], [goal_node.y]
- parent = goal_node.parent
- while parent != -1:
- n = close_set[parent]
- rx.append(n.x)
- ry.append(n.y)
- parent = n.parent
- rx, ry = rx[::-1], ry[::-1] # reverse it
- return rx, ry
-
- def has_node_in_set(self, target_set, node):
- for key in target_set:
- if self.is_same_node(target_set[key], node):
- return True
- return False
-
- def find_id(self, node_x_list, node_y_list, target_node):
- for i, _ in enumerate(node_x_list):
- if self.is_same_node_with_xy(node_x_list[i], node_y_list[i],
- target_node):
- return i
- return None
-
- @staticmethod
- def is_same_node_with_xy(node_x, node_y, node_b):
- dist = np.hypot(node_x - node_b.x,
- node_y - node_b.y)
- return dist <= 0.1
-
- @staticmethod
- def is_same_node(node_a, node_b):
- dist = np.hypot(node_a.x - node_b.x,
- node_a.y - node_b.y)
- return dist <= 0.1
diff --git a/PathPlanning/VoronoiRoadMap/voronoi_road_map.py b/PathPlanning/VoronoiRoadMap/voronoi_road_map.py
deleted file mode 100644
index a27e1b69285..00000000000
--- a/PathPlanning/VoronoiRoadMap/voronoi_road_map.py
+++ /dev/null
@@ -1,186 +0,0 @@
-"""
-
-Voronoi Road Map Planner
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import math
-import numpy as np
-import matplotlib.pyplot as plt
-from scipy.spatial import cKDTree, Voronoi
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent))
-
-from VoronoiRoadMap.dijkstra_search import DijkstraSearch
-
-show_animation = True
-
-
-class VoronoiRoadMapPlanner:
-
- def __init__(self):
- # parameter
- self.N_KNN = 10 # number of edge from one sampled point
- self.MAX_EDGE_LEN = 30.0 # [m] Maximum edge length
-
- def planning(self, sx, sy, gx, gy, ox, oy, robot_radius):
- obstacle_tree = cKDTree(np.vstack((ox, oy)).T)
-
- sample_x, sample_y = self.voronoi_sampling(sx, sy, gx, gy, ox, oy)
- if show_animation: # pragma: no cover
- plt.plot(sample_x, sample_y, ".b")
-
- road_map_info = self.generate_road_map_info(
- sample_x, sample_y, robot_radius, obstacle_tree)
-
- rx, ry = DijkstraSearch(show_animation).search(sx, sy, gx, gy,
- sample_x, sample_y,
- road_map_info)
- return rx, ry
-
- def is_collision(self, sx, sy, gx, gy, rr, obstacle_kd_tree):
- x = sx
- y = sy
- dx = gx - sx
- dy = gy - sy
- yaw = math.atan2(gy - sy, gx - sx)
- d = math.hypot(dx, dy)
-
- if d >= self.MAX_EDGE_LEN:
- return True
-
- D = rr
- n_step = round(d / D)
-
- for i in range(n_step):
- dist, _ = obstacle_kd_tree.query([x, y])
- if dist <= rr:
- return True # collision
- x += D * math.cos(yaw)
- y += D * math.sin(yaw)
-
- # goal point check
- dist, _ = obstacle_kd_tree.query([gx, gy])
- if dist <= rr:
- return True # collision
-
- return False # OK
-
- def generate_road_map_info(self, node_x, node_y, rr, obstacle_tree):
- """
- Road map generation
-
- node_x: [m] x positions of sampled points
- node_y: [m] y positions of sampled points
- rr: Robot Radius[m]
- obstacle_tree: KDTree object of obstacles
- """
-
- road_map = []
- n_sample = len(node_x)
- node_tree = cKDTree(np.vstack((node_x, node_y)).T)
-
- for (i, ix, iy) in zip(range(n_sample), node_x, node_y):
-
- dists, indexes = node_tree.query([ix, iy], k=n_sample)
-
- edge_id = []
-
- for ii in range(1, len(indexes)):
- nx = node_x[indexes[ii]]
- ny = node_y[indexes[ii]]
-
- if not self.is_collision(ix, iy, nx, ny, rr, obstacle_tree):
- edge_id.append(indexes[ii])
-
- if len(edge_id) >= self.N_KNN:
- break
-
- road_map.append(edge_id)
-
- # plot_road_map(road_map, sample_x, sample_y)
-
- return road_map
-
- @staticmethod
- def plot_road_map(road_map, sample_x, sample_y): # pragma: no cover
-
- for i, _ in enumerate(road_map):
- for ii in range(len(road_map[i])):
- ind = road_map[i][ii]
-
- plt.plot([sample_x[i], sample_x[ind]],
- [sample_y[i], sample_y[ind]], "-k")
-
- @staticmethod
- def voronoi_sampling(sx, sy, gx, gy, ox, oy):
- oxy = np.vstack((ox, oy)).T
-
- # generate voronoi point
- vor = Voronoi(oxy)
- sample_x = [ix for [ix, _] in vor.vertices]
- sample_y = [iy for [_, iy] in vor.vertices]
-
- sample_x.append(sx)
- sample_y.append(sy)
- sample_x.append(gx)
- sample_y.append(gy)
-
- return sample_x, sample_y
-
-
-def main():
- print(__file__ + " start!!")
-
- # start and goal position
- sx = 10.0 # [m]
- sy = 10.0 # [m]
- gx = 50.0 # [m]
- gy = 50.0 # [m]
- robot_size = 5.0 # [m]
-
- ox = []
- oy = []
-
- for i in range(60):
- ox.append(float(i))
- oy.append(0.0)
- for i in range(60):
- ox.append(60.0)
- oy.append(float(i))
- for i in range(61):
- ox.append(float(i))
- oy.append(60.0)
- for i in range(61):
- ox.append(0.0)
- oy.append(float(i))
- for i in range(40):
- ox.append(20.0)
- oy.append(float(i))
- for i in range(40):
- ox.append(40.0)
- oy.append(60.0 - i)
-
- if show_animation: # pragma: no cover
- plt.plot(ox, oy, ".k")
- plt.plot(sx, sy, "^r")
- plt.plot(gx, gy, "^c")
- plt.grid(True)
- plt.axis("equal")
-
- rx, ry = VoronoiRoadMapPlanner().planning(sx, sy, gx, gy, ox, oy,
- robot_size)
-
- assert rx, 'Cannot found path'
-
- if show_animation: # pragma: no cover
- plt.plot(rx, ry, "-r")
- plt.pause(0.1)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathPlanning/WavefrontCPP/map/test.png b/PathPlanning/WavefrontCPP/map/test.png
deleted file mode 100644
index 4abca0bf309..00000000000
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diff --git a/PathPlanning/WavefrontCPP/map/test_2.png b/PathPlanning/WavefrontCPP/map/test_2.png
deleted file mode 100644
index 0d27fa9f958..00000000000
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diff --git a/PathPlanning/WavefrontCPP/map/test_3.png b/PathPlanning/WavefrontCPP/map/test_3.png
deleted file mode 100644
index 1a50b87ccff..00000000000
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diff --git a/PathPlanning/WavefrontCPP/wavefront_coverage_path_planner.py b/PathPlanning/WavefrontCPP/wavefront_coverage_path_planner.py
deleted file mode 100644
index c5a139454bb..00000000000
--- a/PathPlanning/WavefrontCPP/wavefront_coverage_path_planner.py
+++ /dev/null
@@ -1,218 +0,0 @@
-"""
-Distance/Path Transform Wavefront Coverage Path Planner
-
-author: Todd Tang
-paper: Planning paths of complete coverage of an unstructured environment
- by a mobile robot - Zelinsky et.al.
-link: https://pinkwink.kr/attachment/cfile3.uf@1354654A4E8945BD13FE77.pdf
-"""
-
-import os
-import sys
-
-import matplotlib.pyplot as plt
-import numpy as np
-from scipy import ndimage
-
-do_animation = True
-
-
-def transform(
- grid_map, src, distance_type='chessboard',
- transform_type='path', alpha=0.01
-):
- """transform
-
- calculating transform of transform_type from src
- in given distance_type
-
- :param grid_map: 2d binary map
- :param src: distance transform source
- :param distance_type: type of distance used
- :param transform_type: type of transform used
- :param alpha: weight of Obstacle Transform used when using path_transform
- """
-
- n_rows, n_cols = grid_map.shape
-
- if n_rows == 0 or n_cols == 0:
- sys.exit('Empty grid_map.')
-
- inc_order = [[0, 1], [1, 1], [1, 0], [1, -1],
- [0, -1], [-1, -1], [-1, 0], [-1, 1]]
- if distance_type == 'chessboard':
- cost = [1, 1, 1, 1, 1, 1, 1, 1]
- elif distance_type == 'eculidean':
- cost = [1, np.sqrt(2), 1, np.sqrt(2), 1, np.sqrt(2), 1, np.sqrt(2)]
- else:
- sys.exit('Unsupported distance type.')
-
- transform_matrix = float('inf') * np.ones_like(grid_map, dtype=float)
- transform_matrix[src[0], src[1]] = 0
- if transform_type == 'distance':
- eT = np.zeros_like(grid_map)
- elif transform_type == 'path':
- eT = ndimage.distance_transform_cdt(1 - grid_map, distance_type)
- else:
- sys.exit('Unsupported transform type.')
-
- # set obstacle transform_matrix value to infinity
- for i in range(n_rows):
- for j in range(n_cols):
- if grid_map[i][j] == 1.0:
- transform_matrix[i][j] = float('inf')
- is_visited = np.zeros_like(transform_matrix, dtype=bool)
- is_visited[src[0], src[1]] = True
- traversal_queue = [src]
- calculated = set([(src[0] - 1) * n_cols + src[1]])
-
- def is_valid_neighbor(g_i, g_j):
- return 0 <= g_i < n_rows and 0 <= g_j < n_cols \
- and not grid_map[g_i][g_j]
-
- while traversal_queue:
- i, j = traversal_queue.pop(0)
- for k, inc in enumerate(inc_order):
- ni = i + inc[0]
- nj = j + inc[1]
- if is_valid_neighbor(ni, nj):
- is_visited[i][j] = True
-
- # update transform_matrix
- transform_matrix[i][j] = min(
- transform_matrix[i][j],
- transform_matrix[ni][nj] + cost[k] + alpha * eT[ni][nj])
-
- if not is_visited[ni][nj] \
- and ((ni - 1) * n_cols + nj) not in calculated:
- traversal_queue.append((ni, nj))
- calculated.add((ni - 1) * n_cols + nj)
-
- return transform_matrix
-
-
-def get_search_order_increment(start, goal):
- if start[0] >= goal[0] and start[1] >= goal[1]:
- order = [[1, 0], [0, 1], [-1, 0], [0, -1],
- [1, 1], [1, -1], [-1, 1], [-1, -1]]
- elif start[0] <= goal[0] and start[1] >= goal[1]:
- order = [[-1, 0], [0, 1], [1, 0], [0, -1],
- [-1, 1], [-1, -1], [1, 1], [1, -1]]
- elif start[0] >= goal[0] and start[1] <= goal[1]:
- order = [[1, 0], [0, -1], [-1, 0], [0, 1],
- [1, -1], [-1, -1], [1, 1], [-1, 1]]
- elif start[0] <= goal[0] and start[1] <= goal[1]:
- order = [[-1, 0], [0, -1], [0, 1], [1, 0],
- [-1, -1], [-1, 1], [1, -1], [1, 1]]
- else:
- sys.exit('get_search_order_increment: cannot determine \
- start=>goal increment order')
- return order
-
-
-def wavefront(transform_matrix, start, goal):
- """wavefront
-
- performing wavefront coverage path planning
-
- :param transform_matrix: the transform matrix
- :param start: start point of planning
- :param goal: goal point of planning
- """
-
- path = []
- n_rows, n_cols = transform_matrix.shape
-
- def is_valid_neighbor(g_i, g_j):
- is_i_valid_bounded = 0 <= g_i < n_rows
- is_j_valid_bounded = 0 <= g_j < n_cols
- if is_i_valid_bounded and is_j_valid_bounded:
- return not is_visited[g_i][g_j] and \
- transform_matrix[g_i][g_j] != float('inf')
- return False
-
- inc_order = get_search_order_increment(start, goal)
-
- current_node = start
- is_visited = np.zeros_like(transform_matrix, dtype=bool)
-
- while current_node != goal:
- i, j = current_node
- path.append((i, j))
- is_visited[i][j] = True
-
- max_T = float('-inf')
- i_max = (-1, -1)
- i_last = 0
- for i_last in range(len(path)):
- current_node = path[-1 - i_last] # get latest node in path
- for ci, cj in inc_order:
- ni, nj = current_node[0] + ci, current_node[1] + cj
- if is_valid_neighbor(ni, nj) and \
- transform_matrix[ni][nj] > max_T:
- i_max = (ni, nj)
- max_T = transform_matrix[ni][nj]
-
- if i_max != (-1, -1):
- break
-
- if i_max == (-1, -1):
- break
- else:
- current_node = i_max
- if i_last != 0:
- print('backtracing to', current_node)
- path.append(goal)
-
- return path
-
-
-def visualize_path(grid_map, start, goal, path): # pragma: no cover
- oy, ox = start
- gy, gx = goal
- px, py = np.transpose(np.flipud(np.fliplr(path)))
-
- if not do_animation:
- plt.imshow(grid_map, cmap='Greys')
- plt.plot(ox, oy, "-xy")
- plt.plot(px, py, "-r")
- plt.plot(gx, gy, "-pg")
- plt.show()
- else:
- for ipx, ipy in zip(px, py):
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.imshow(grid_map, cmap='Greys')
- plt.plot(ox, oy, "-xb")
- plt.plot(px, py, "-r")
- plt.plot(gx, gy, "-pg")
- plt.plot(ipx, ipy, "or")
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.1)
-
-
-def main():
- dir_path = os.path.dirname(os.path.realpath(__file__))
- img = plt.imread(os.path.join(dir_path, 'map', 'test.png'))
- img = 1 - img # revert pixel values
-
- start = (43, 0)
- goal = (0, 0)
-
- # distance transform wavefront
- DT = transform(img, goal, transform_type='distance')
- DT_path = wavefront(DT, start, goal)
- visualize_path(img, start, goal, DT_path)
-
- # path transform wavefront
- PT = transform(img, goal, transform_type='path', alpha=0.01)
- PT_path = wavefront(PT, start, goal)
- visualize_path(img, start, goal, PT_path)
-
-
-if __name__ == "__main__":
- main()
diff --git a/PathPlanning/__init__.py b/PathPlanning/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathTracking/__init__.py b/PathTracking/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathTracking/cgmres_nmpc/cgmres_nmpc.py b/PathTracking/cgmres_nmpc/cgmres_nmpc.py
deleted file mode 100644
index a582c9da810..00000000000
--- a/PathTracking/cgmres_nmpc/cgmres_nmpc.py
+++ /dev/null
@@ -1,616 +0,0 @@
-"""
-
-Nonlinear MPC simulation with CGMRES
-
-author Atsushi Sakai (@Atsushi_twi)
-
-Ref:
-Shunichi09/nonlinear_control: Implementing the nonlinear model predictive
-control, sliding mode control https://github.com/Shunichi09/PythonLinearNonlinearControl
-
-"""
-
-from math import cos, sin, radians, atan2
-
-import matplotlib.pyplot as plt
-import numpy as np
-
-U_A_MAX = 1.0
-U_OMEGA_MAX = radians(45.0)
-PHI_V = 0.01
-PHI_OMEGA = 0.01
-WB = 0.25 # [m] wheel base
-
-show_animation = True
-
-
-def differential_model(v, yaw, u_1, u_2):
- dx = cos(yaw) * v
- dy = sin(yaw) * v
- dv = u_1
- # tangent is not good for nonlinear optimization
- d_yaw = v / WB * sin(u_2)
-
- return dx, dy, d_yaw, dv
-
-
-class TwoWheeledSystem:
-
- def __init__(self, init_x, init_y, init_yaw, init_v):
- self.x = init_x
- self.y = init_y
- self.yaw = init_yaw
- self.v = init_v
- self.history_x = [init_x]
- self.history_y = [init_y]
- self.history_yaw = [init_yaw]
- self.history_v = [init_v]
-
- def update_state(self, u_1, u_2, dt=0.01):
- dx, dy, d_yaw, dv = differential_model(self.v, self.yaw, u_1, u_2)
-
- self.x += dt * dx
- self.y += dt * dy
- self.yaw += dt * d_yaw
- self.v += dt * dv
-
- # save
- self.history_x.append(self.x)
- self.history_y.append(self.y)
- self.history_yaw.append(self.yaw)
- self.history_v.append(self.v)
-
-
-class NMPCSimulatorSystem:
-
- def calc_predict_and_adjoint_state(self, x, y, yaw, v, u_1s, u_2s, N, dt):
- # by using state equation
- x_s, y_s, yaw_s, v_s = self._calc_predict_states(
- x, y, yaw, v, u_1s, u_2s, N, dt)
- # by using adjoint equation
- lam_1s, lam_2s, lam_3s, lam_4s = self._calc_adjoint_states(
- x_s, y_s, yaw_s, v_s, u_2s, N, dt)
-
- return x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s
-
- def _calc_predict_states(self, x, y, yaw, v, u_1s, u_2s, N, dt):
- x_s = [x]
- y_s = [y]
- yaw_s = [yaw]
- v_s = [v]
-
- for i in range(N):
- temp_x_1, temp_x_2, temp_x_3, temp_x_4 = self._predict_state_with_oylar(
- x_s[i], y_s[i], yaw_s[i], v_s[i], u_1s[i], u_2s[i], dt)
- x_s.append(temp_x_1)
- y_s.append(temp_x_2)
- yaw_s.append(temp_x_3)
- v_s.append(temp_x_4)
-
- return x_s, y_s, yaw_s, v_s
-
- def _calc_adjoint_states(self, x_s, y_s, yaw_s, v_s, u_2s, N, dt):
- lam_1s = [x_s[-1]]
- lam_2s = [y_s[-1]]
- lam_3s = [yaw_s[-1]]
- lam_4s = [v_s[-1]]
-
- # backward adjoint state calc
- for i in range(N - 1, 0, -1):
- temp_lam_1, temp_lam_2, temp_lam_3, temp_lam_4 = self._adjoint_state_with_oylar(
- yaw_s[i], v_s[i], lam_1s[0], lam_2s[0], lam_3s[0], lam_4s[0],
- u_2s[i], dt)
- lam_1s.insert(0, temp_lam_1)
- lam_2s.insert(0, temp_lam_2)
- lam_3s.insert(0, temp_lam_3)
- lam_4s.insert(0, temp_lam_4)
-
- return lam_1s, lam_2s, lam_3s, lam_4s
-
- @staticmethod
- def _predict_state_with_oylar(x, y, yaw, v, u_1, u_2, dt):
-
- dx, dy, dyaw, dv = differential_model(
- v, yaw, u_1, u_2)
-
- next_x_1 = x + dt * dx
- next_x_2 = y + dt * dy
- next_x_3 = yaw + dt * dyaw
- next_x_4 = v + dt * dv
-
- return next_x_1, next_x_2, next_x_3, next_x_4
-
- @staticmethod
- def _adjoint_state_with_oylar(yaw, v, lam_1, lam_2, lam_3, lam_4, u_2, dt):
-
- # ∂H/∂x
- pre_lam_1 = lam_1 + dt * 0.0
- pre_lam_2 = lam_2 + dt * 0.0
- tmp1 = - lam_1 * sin(yaw) * v + lam_2 * cos(yaw) * v
- pre_lam_3 = lam_3 + dt * tmp1
- tmp2 = lam_1 * cos(yaw) + lam_2 * sin(yaw) + lam_3 * sin(u_2) / WB
- pre_lam_4 = lam_4 + dt * tmp2
-
- return pre_lam_1, pre_lam_2, pre_lam_3, pre_lam_4
-
-
-class NMPCControllerCGMRES:
- """
- Attributes
- ------------
- zeta : float
- gain of optimal answer stability
- ht : float
- update value of NMPC this should be decided by zeta
- tf : float
- predict time
- alpha : float
- gain of predict time
- N : int
- predict step, discrete value
- threshold : float
- cgmres's threshold value
- input_num : int
- system input length, this should include dummy u and constraint variables
- max_iteration : int
- decide by the solved matrix size
- simulator : NMPCSimulatorSystem class
- u_1s : list of float
- estimated optimal system input
- u_2s : list of float
- estimated optimal system input
- dummy_u_1s : list of float
- estimated dummy input
- dummy_u_2s : list of float
- estimated dummy input
- raw_1s : list of float
- estimated constraint variable
- raw_2s : list of float
- estimated constraint variable
- history_u_1 : list of float
- time history of actual system input
- history_u_2 : list of float
- time history of actual system input
- history_dummy_u_1 : list of float
- time history of actual dummy u_1
- history_dummy_u_2 : list of float
- time history of actual dummy u_2
- history_raw_1 : list of float
- time history of actual raw_1
- history_raw_2 : list of float
- time history of actual raw_2
- history_f : list of float
- time history of error of optimal
- """
-
- def __init__(self):
- # parameters
- self.zeta = 100. # stability gain
- self.ht = 0.01 # difference approximation tick
- self.tf = 3.0 # final time
- self.alpha = 0.5 # time gain
- self.N = 10 # division number
- self.threshold = 0.001
- self.input_num = 6 # input number of dummy, constraints
- self.max_iteration = self.input_num * self.N
-
- # simulator
- self.simulator = NMPCSimulatorSystem()
-
- # initial input, initialize as 1.0
- self.u_1s = np.ones(self.N)
- self.u_2s = np.ones(self.N)
- self.dummy_u_1s = np.ones(self.N)
- self.dummy_u_2s = np.ones(self.N)
- self.raw_1s = np.zeros(self.N)
- self.raw_2s = np.zeros(self.N)
-
- self.history_u_1 = []
- self.history_u_2 = []
- self.history_dummy_u_1 = []
- self.history_dummy_u_2 = []
- self.history_raw_1 = []
- self.history_raw_2 = []
- self.history_f = []
-
- def calc_input(self, x, y, yaw, v, time):
-
- # calculating sampling time
- dt = self.tf * (1. - np.exp(-self.alpha * time)) / float(self.N)
-
- # x_dot
- x_1_dot, x_2_dot, x_3_dot, x_4_dot = differential_model(
- v, yaw, self.u_1s[0], self.u_2s[0])
-
- dx_1 = x_1_dot * self.ht
- dx_2 = x_2_dot * self.ht
- dx_3 = x_3_dot * self.ht
- dx_4 = x_4_dot * self.ht
-
- x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
- x + dx_1, y + dx_2, yaw + dx_3, v + dx_4, self.u_1s, self.u_2s,
- self.N, dt)
-
- # Fxt:F(U,x+hx˙,t+h)
- Fxt = self._calc_f(v_s, lam_3s, lam_4s,
- self.u_1s, self.u_2s, self.dummy_u_1s,
- self.dummy_u_2s,
- self.raw_1s, self.raw_2s, self.N)
-
- # F:F(U,x,t)
- x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
- x, y, yaw, v, self.u_1s, self.u_2s, self.N, dt)
-
- F = self._calc_f(v_s, lam_3s, lam_4s,
- self.u_1s, self.u_2s, self.dummy_u_1s, self.dummy_u_2s,
- self.raw_1s, self.raw_2s, self.N)
-
- right = -self.zeta * F - ((Fxt - F) / self.ht)
-
- du_1 = self.u_1s * self.ht
- du_2 = self.u_2s * self.ht
- ddummy_u_1 = self.dummy_u_1s * self.ht
- ddummy_u_2 = self.dummy_u_2s * self.ht
- draw_1 = self.raw_1s * self.ht
- draw_2 = self.raw_2s * self.ht
-
- x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
- x + dx_1, y + dx_2, yaw + dx_3, v + dx_4, self.u_1s + du_1,
- self.u_2s + du_2, self.N, dt)
-
- # Fuxt:F(U+hdU(0),x+hx˙,t+h)
- Fuxt = self._calc_f(v_s, lam_3s, lam_4s,
- self.u_1s + du_1, self.u_2s + du_2,
- self.dummy_u_1s + ddummy_u_1,
- self.dummy_u_2s + ddummy_u_2,
- self.raw_1s + draw_1, self.raw_2s + draw_2, self.N)
-
- left = ((Fuxt - Fxt) / self.ht)
-
- # calculating cgmres
- r0 = right - left
- r0_norm = np.linalg.norm(r0)
-
- vs = np.zeros((self.max_iteration, self.max_iteration + 1))
- vs[:, 0] = r0 / r0_norm
-
- hs = np.zeros((self.max_iteration + 1, self.max_iteration + 1))
-
- # in this case the state is 3(u and dummy_u)
- e = np.zeros((self.max_iteration + 1, 1))
- e[0] = 1.0
-
- ys_pre = None
-
- du_1_new, du_2_new, draw_1_new, draw_2_new = None, None, None, None
- ddummy_u_1_new, ddummy_u_2_new = None, None
-
- for i in range(self.max_iteration):
- du_1 = vs[::self.input_num, i] * self.ht
- du_2 = vs[1::self.input_num, i] * self.ht
- ddummy_u_1 = vs[2::self.input_num, i] * self.ht
- ddummy_u_2 = vs[3::self.input_num, i] * self.ht
- draw_1 = vs[4::self.input_num, i] * self.ht
- draw_2 = vs[5::self.input_num, i] * self.ht
-
- x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
- x + dx_1, y + dx_2, yaw + dx_3, v + dx_4, self.u_1s + du_1,
- self.u_2s + du_2, self.N, dt)
-
- Fuxt = self._calc_f(v_s, lam_3s, lam_4s,
- self.u_1s + du_1, self.u_2s + du_2,
- self.dummy_u_1s + ddummy_u_1,
- self.dummy_u_2s + ddummy_u_2,
- self.raw_1s + draw_1, self.raw_2s + draw_2,
- self.N)
-
- Av = ((Fuxt - Fxt) / self.ht)
-
- sum_Av = np.zeros(self.max_iteration)
-
- # Gram–Schmidt orthonormalization
- for j in range(i + 1):
- hs[j, i] = np.dot(Av, vs[:, j])
- sum_Av = sum_Av + hs[j, i] * vs[:, j]
-
- v_est = Av - sum_Av
-
- hs[i + 1, i] = np.linalg.norm(v_est)
-
- vs[:, i + 1] = v_est / hs[i + 1, i]
-
- inv_hs = np.linalg.pinv(hs[:i + 1, :i])
- ys = np.dot(inv_hs, r0_norm * e[:i + 1])
-
- judge_value = r0_norm * e[:i + 1] - np.dot(hs[:i + 1, :i], ys[:i])
-
- flag1 = np.linalg.norm(judge_value) < self.threshold
-
- flag2 = i == self.max_iteration - 1
- if flag1 or flag2:
- update_val = np.dot(vs[:, :i - 1], ys_pre[:i - 1]).flatten()
- du_1_new = du_1 + update_val[::self.input_num]
- du_2_new = du_2 + update_val[1::self.input_num]
- ddummy_u_1_new = ddummy_u_1 + update_val[2::self.input_num]
- ddummy_u_2_new = ddummy_u_2 + update_val[3::self.input_num]
- draw_1_new = draw_1 + update_val[4::self.input_num]
- draw_2_new = draw_2 + update_val[5::self.input_num]
- break
-
- ys_pre = ys
-
- # update input
- self.u_1s += du_1_new * self.ht
- self.u_2s += du_2_new * self.ht
- self.dummy_u_1s += ddummy_u_1_new * self.ht
- self.dummy_u_2s += ddummy_u_2_new * self.ht
- self.raw_1s += draw_1_new * self.ht
- self.raw_2s += draw_2_new * self.ht
-
- x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
- x, y, yaw, v, self.u_1s, self.u_2s, self.N, dt)
-
- F = self._calc_f(v_s, lam_3s, lam_4s,
- self.u_1s, self.u_2s, self.dummy_u_1s, self.dummy_u_2s,
- self.raw_1s, self.raw_2s, self.N)
-
- print("norm(F) = {0}".format(np.linalg.norm(F)))
-
- # for save
- self.history_f.append(np.linalg.norm(F))
- self.history_u_1.append(self.u_1s[0])
- self.history_u_2.append(self.u_2s[0])
- self.history_dummy_u_1.append(self.dummy_u_1s[0])
- self.history_dummy_u_2.append(self.dummy_u_2s[0])
- self.history_raw_1.append(self.raw_1s[0])
- self.history_raw_2.append(self.raw_2s[0])
-
- return self.u_1s, self.u_2s
-
- @staticmethod
- def _calc_f(v_s, lam_3s, lam_4s, u_1s, u_2s, dummy_u_1s, dummy_u_2s,
- raw_1s, raw_2s, N):
-
- F = []
- for i in range(N):
- # ∂H/∂u(xi, ui, λi)
- F.append(u_1s[i] + lam_4s[i] + 2.0 * raw_1s[i] * u_1s[i])
- F.append(u_2s[i] + lam_3s[i] * v_s[i] /
- WB * cos(u_2s[i]) ** 2 + 2.0 * raw_2s[i] * u_2s[i])
- F.append(-PHI_V + 2.0 * raw_1s[i] * dummy_u_1s[i])
- F.append(-PHI_OMEGA + 2.0 * raw_2s[i] * dummy_u_2s[i])
-
- # C(xi, ui, λi)
- F.append(u_1s[i] ** 2 + dummy_u_1s[i] ** 2 - U_A_MAX ** 2)
- F.append(u_2s[i] ** 2 + dummy_u_2s[i] ** 2 - U_OMEGA_MAX ** 2)
-
- return np.array(F)
-
-
-def plot_figures(plant_system, controller, iteration_num,
- dt): # pragma: no cover
- # figure
- # time history
- fig_p = plt.figure()
- fig_u = plt.figure()
- fig_f = plt.figure()
-
- # trajectory
- fig_t = plt.figure()
- fig_trajectory = fig_t.add_subplot(111)
- fig_trajectory.set_aspect('equal')
-
- x_1_fig = fig_p.add_subplot(411)
- x_2_fig = fig_p.add_subplot(412)
- x_3_fig = fig_p.add_subplot(413)
- x_4_fig = fig_p.add_subplot(414)
-
- u_1_fig = fig_u.add_subplot(411)
- u_2_fig = fig_u.add_subplot(412)
- dummy_1_fig = fig_u.add_subplot(413)
- dummy_2_fig = fig_u.add_subplot(414)
-
- raw_1_fig = fig_f.add_subplot(311)
- raw_2_fig = fig_f.add_subplot(312)
- f_fig = fig_f.add_subplot(313)
-
- x_1_fig.plot(np.arange(iteration_num) * dt, plant_system.history_x)
- x_1_fig.set_xlabel("time [s]")
- x_1_fig.set_ylabel("x")
-
- x_2_fig.plot(np.arange(iteration_num) * dt, plant_system.history_y)
- x_2_fig.set_xlabel("time [s]")
- x_2_fig.set_ylabel("y")
-
- x_3_fig.plot(np.arange(iteration_num) * dt, plant_system.history_yaw)
- x_3_fig.set_xlabel("time [s]")
- x_3_fig.set_ylabel("yaw")
-
- x_4_fig.plot(np.arange(iteration_num) * dt, plant_system.history_v)
- x_4_fig.set_xlabel("time [s]")
- x_4_fig.set_ylabel("v")
-
- u_1_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_u_1)
- u_1_fig.set_xlabel("time [s]")
- u_1_fig.set_ylabel("u_a")
-
- u_2_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_u_2)
- u_2_fig.set_xlabel("time [s]")
- u_2_fig.set_ylabel("u_omega")
-
- dummy_1_fig.plot(np.arange(iteration_num - 1) *
- dt, controller.history_dummy_u_1)
- dummy_1_fig.set_xlabel("time [s]")
- dummy_1_fig.set_ylabel("dummy u_1")
-
- dummy_2_fig.plot(np.arange(iteration_num - 1) *
- dt, controller.history_dummy_u_2)
- dummy_2_fig.set_xlabel("time [s]")
- dummy_2_fig.set_ylabel("dummy u_2")
-
- raw_1_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_raw_1)
- raw_1_fig.set_xlabel("time [s]")
- raw_1_fig.set_ylabel("raw_1")
-
- raw_2_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_raw_2)
- raw_2_fig.set_xlabel("time [s]")
- raw_2_fig.set_ylabel("raw_2")
-
- f_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_f)
- f_fig.set_xlabel("time [s]")
- f_fig.set_ylabel("optimal error")
-
- fig_trajectory.plot(plant_system.history_x,
- plant_system.history_y, "-r")
- fig_trajectory.set_xlabel("x [m]")
- fig_trajectory.set_ylabel("y [m]")
- fig_trajectory.axis("equal")
-
- # start state
- plot_car(plant_system.history_x[0],
- plant_system.history_y[0],
- plant_system.history_yaw[0],
- controller.history_u_2[0],
- )
-
- # goal state
- plot_car(0.0, 0.0, 0.0, 0.0)
-
- plt.show()
-
-
-def plot_car(x, y, yaw, steer=0.0, truck_color="-k"): # pragma: no cover
-
- # Vehicle parameters
- LENGTH = 0.4 # [m]
- WIDTH = 0.2 # [m]
- BACK_TO_WHEEL = 0.1 # [m]
- WHEEL_LEN = 0.03 # [m]
- WHEEL_WIDTH = 0.02 # [m]
- TREAD = 0.07 # [m]
-
- outline = np.array(
- [[-BACK_TO_WHEEL, (LENGTH - BACK_TO_WHEEL), (LENGTH - BACK_TO_WHEEL),
- -BACK_TO_WHEEL, -BACK_TO_WHEEL],
- [WIDTH / 2, WIDTH / 2, - WIDTH / 2, -WIDTH / 2, WIDTH / 2]])
-
- fr_wheel = np.array(
- [[WHEEL_LEN, -WHEEL_LEN, -WHEEL_LEN, WHEEL_LEN, WHEEL_LEN],
- [-WHEEL_WIDTH - TREAD, -WHEEL_WIDTH - TREAD, WHEEL_WIDTH -
- TREAD, WHEEL_WIDTH - TREAD, -WHEEL_WIDTH - TREAD]])
-
- rr_wheel = np.copy(fr_wheel)
-
- fl_wheel = np.copy(fr_wheel)
- fl_wheel[1, :] *= -1
- rl_wheel = np.copy(rr_wheel)
- rl_wheel[1, :] *= -1
-
- Rot1 = np.array([[cos(yaw), sin(yaw)],
- [-sin(yaw), cos(yaw)]])
- Rot2 = np.array([[cos(steer), sin(steer)],
- [-sin(steer), cos(steer)]])
-
- fr_wheel = (fr_wheel.T.dot(Rot2)).T
- fl_wheel = (fl_wheel.T.dot(Rot2)).T
- fr_wheel[0, :] += WB
- fl_wheel[0, :] += WB
-
- fr_wheel = (fr_wheel.T.dot(Rot1)).T
- fl_wheel = (fl_wheel.T.dot(Rot1)).T
-
- outline = (outline.T.dot(Rot1)).T
- rr_wheel = (rr_wheel.T.dot(Rot1)).T
- rl_wheel = (rl_wheel.T.dot(Rot1)).T
-
- outline[0, :] += x
- outline[1, :] += y
- fr_wheel[0, :] += x
- fr_wheel[1, :] += y
- rr_wheel[0, :] += x
- rr_wheel[1, :] += y
- fl_wheel[0, :] += x
- fl_wheel[1, :] += y
- rl_wheel[0, :] += x
- rl_wheel[1, :] += y
-
- plt.plot(np.array(outline[0, :]).flatten(),
- np.array(outline[1, :]).flatten(), truck_color)
- plt.plot(np.array(fr_wheel[0, :]).flatten(),
- np.array(fr_wheel[1, :]).flatten(), truck_color)
- plt.plot(np.array(rr_wheel[0, :]).flatten(),
- np.array(rr_wheel[1, :]).flatten(), truck_color)
- plt.plot(np.array(fl_wheel[0, :]).flatten(),
- np.array(fl_wheel[1, :]).flatten(), truck_color)
- plt.plot(np.array(rl_wheel[0, :]).flatten(),
- np.array(rl_wheel[1, :]).flatten(), truck_color)
- plt.plot(x, y, "*")
-
-
-def animation(plant, controller, dt):
- skip = 2 # skip index for animation
-
- for t in range(1, len(controller.history_u_1), skip):
- x = plant.history_x[t]
- y = plant.history_y[t]
- yaw = plant.history_yaw[t]
- v = plant.history_v[t]
- accel = controller.history_u_1[t]
- time = t * dt
-
- if abs(v) <= 0.01:
- steer = 0.0
- else:
- steer = atan2(controller.history_u_2[t] * WB / v, 1.0)
-
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(plant.history_x, plant.history_y, "-r", label="trajectory")
- plot_car(x, y, yaw, steer=steer)
- plt.axis("equal")
- plt.grid(True)
- plt.title("Time[s]:" + str(round(time, 2)) +
- ", accel[m/s]:" + str(round(accel, 2)) +
- ", speed[km/h]:" + str(round(v * 3.6, 2)))
- plt.pause(0.0001)
-
- plt.close("all")
-
-
-def main():
- # simulation time
- dt = 0.1
- iteration_time = 150.0 # [s]
-
- init_x = -4.5
- init_y = -2.5
- init_yaw = radians(45.0)
- init_v = -1.0
-
- # plant
- plant_system = TwoWheeledSystem(
- init_x, init_y, init_yaw, init_v)
-
- # controller
- controller = NMPCControllerCGMRES()
-
- iteration_num = int(iteration_time / dt)
- for i in range(1, iteration_num):
- time = float(i) * dt
- # make input
- u_1s, u_2s = controller.calc_input(
- plant_system.x, plant_system.y, plant_system.yaw, plant_system.v,
- time)
- # update state
- plant_system.update_state(u_1s[0], u_2s[0])
-
- if show_animation: # pragma: no cover
- animation(plant_system, controller, dt)
- plot_figures(plant_system, controller, iteration_num, dt)
-
-
-if __name__ == "__main__":
- main()
diff --git a/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py b/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
deleted file mode 100644
index 5831d02d300..00000000000
--- a/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
+++ /dev/null
@@ -1,321 +0,0 @@
-"""
-
-Path tracking simulation with LQR speed and steering control
-
-author Atsushi Sakai (@Atsushi_twi)
-
-"""
-import math
-import sys
-import matplotlib.pyplot as plt
-import numpy as np
-import scipy.linalg as la
-import pathlib
-
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-from utils.angle import angle_mod
-from PathPlanning.CubicSpline import cubic_spline_planner
-
-# === Parameters =====
-
-# LQR parameter
-lqr_Q = np.eye(5)
-lqr_R = np.eye(2)
-dt = 0.1 # time tick[s]
-L = 0.5 # Wheel base of the vehicle [m]
-max_steer = np.deg2rad(45.0) # maximum steering angle[rad]
-
-show_animation = True
-
-
-class State:
-
- def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
- self.x = x
- self.y = y
- self.yaw = yaw
- self.v = v
-
-
-def update(state, a, delta):
-
- if delta >= max_steer:
- delta = max_steer
- if delta <= - max_steer:
- delta = - max_steer
-
- state.x = state.x + state.v * math.cos(state.yaw) * dt
- state.y = state.y + state.v * math.sin(state.yaw) * dt
- state.yaw = state.yaw + state.v / L * math.tan(delta) * dt
- state.v = state.v + a * dt
-
- return state
-
-
-def pi_2_pi(angle):
- return angle_mod(angle)
-
-
-def solve_dare(A, B, Q, R):
- """
- solve a discrete time_Algebraic Riccati equation (DARE)
- """
- x = Q
- x_next = Q
- max_iter = 150
- eps = 0.01
-
- for i in range(max_iter):
- x_next = A.T @ x @ A - A.T @ x @ B @ \
- la.inv(R + B.T @ x @ B) @ B.T @ x @ A + Q
- if (abs(x_next - x)).max() < eps:
- break
- x = x_next
-
- return x_next
-
-
-def dlqr(A, B, Q, R):
- """Solve the discrete time lqr controller.
- x[k+1] = A x[k] + B u[k]
- cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
- # ref Bertsekas, p.151
- """
-
- # first, try to solve the ricatti equation
- X = solve_dare(A, B, Q, R)
-
- # compute the LQR gain
- K = la.inv(B.T @ X @ B + R) @ (B.T @ X @ A)
-
- eig_result = la.eig(A - B @ K)
-
- return K, X, eig_result[0]
-
-
-def lqr_speed_steering_control(state, cx, cy, cyaw, ck, pe, pth_e, sp, Q, R):
- ind, e = calc_nearest_index(state, cx, cy, cyaw)
-
- tv = sp[ind]
-
- k = ck[ind]
- v = state.v
- th_e = pi_2_pi(state.yaw - cyaw[ind])
-
- # A = [1.0, dt, 0.0, 0.0, 0.0
- # 0.0, 0.0, v, 0.0, 0.0]
- # 0.0, 0.0, 1.0, dt, 0.0]
- # 0.0, 0.0, 0.0, 0.0, 0.0]
- # 0.0, 0.0, 0.0, 0.0, 1.0]
- A = np.zeros((5, 5))
- A[0, 0] = 1.0
- A[0, 1] = dt
- A[1, 2] = v
- A[2, 2] = 1.0
- A[2, 3] = dt
- A[4, 4] = 1.0
-
- # B = [0.0, 0.0
- # 0.0, 0.0
- # 0.0, 0.0
- # v/L, 0.0
- # 0.0, dt]
- B = np.zeros((5, 2))
- B[3, 0] = v / L
- B[4, 1] = dt
-
- K, _, _ = dlqr(A, B, Q, R)
-
- # state vector
- # x = [e, dot_e, th_e, dot_th_e, delta_v]
- # e: lateral distance to the path
- # dot_e: derivative of e
- # th_e: angle difference to the path
- # dot_th_e: derivative of th_e
- # delta_v: difference between current speed and target speed
- x = np.zeros((5, 1))
- x[0, 0] = e
- x[1, 0] = (e - pe) / dt
- x[2, 0] = th_e
- x[3, 0] = (th_e - pth_e) / dt
- x[4, 0] = v - tv
-
- # input vector
- # u = [delta, accel]
- # delta: steering angle
- # accel: acceleration
- ustar = -K @ x
-
- # calc steering input
- ff = math.atan2(L * k, 1) # feedforward steering angle
- fb = pi_2_pi(ustar[0, 0]) # feedback steering angle
- delta = ff + fb
-
- # calc accel input
- accel = ustar[1, 0]
-
- return delta, ind, e, th_e, accel
-
-
-def calc_nearest_index(state, cx, cy, cyaw):
- dx = [state.x - icx for icx in cx]
- dy = [state.y - icy for icy in cy]
-
- d = [idx ** 2 + idy ** 2 for (idx, idy) in zip(dx, dy)]
-
- mind = min(d)
-
- ind = d.index(mind)
-
- mind = math.sqrt(mind)
-
- dxl = cx[ind] - state.x
- dyl = cy[ind] - state.y
-
- angle = pi_2_pi(cyaw[ind] - math.atan2(dyl, dxl))
- if angle < 0:
- mind *= -1
-
- return ind, mind
-
-
-def do_simulation(cx, cy, cyaw, ck, speed_profile, goal):
- T = 500.0 # max simulation time
- goal_dis = 0.3
- stop_speed = 0.05
-
- state = State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
-
- time = 0.0
- x = [state.x]
- y = [state.y]
- yaw = [state.yaw]
- v = [state.v]
- t = [0.0]
-
- e, e_th = 0.0, 0.0
-
- while T >= time:
- dl, target_ind, e, e_th, ai = lqr_speed_steering_control(
- state, cx, cy, cyaw, ck, e, e_th, speed_profile, lqr_Q, lqr_R)
-
- state = update(state, ai, dl)
-
- if abs(state.v) <= stop_speed:
- target_ind += 1
-
- time = time + dt
-
- # check goal
- dx = state.x - goal[0]
- dy = state.y - goal[1]
- if math.hypot(dx, dy) <= goal_dis:
- print("Goal")
- break
-
- x.append(state.x)
- y.append(state.y)
- yaw.append(state.yaw)
- v.append(state.v)
- t.append(time)
-
- if target_ind % 1 == 0 and show_animation:
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(cx, cy, "-r", label="course")
- plt.plot(x, y, "ob", label="trajectory")
- plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
- plt.axis("equal")
- plt.grid(True)
- plt.title("speed[km/h]:" + str(round(state.v * 3.6, 2))
- + ",target index:" + str(target_ind))
- plt.pause(0.0001)
-
- return t, x, y, yaw, v
-
-
-def calc_speed_profile(cyaw, target_speed):
- speed_profile = [target_speed] * len(cyaw)
-
- direction = 1.0
-
- # Set stop point
- for i in range(len(cyaw) - 1):
- dyaw = abs(cyaw[i + 1] - cyaw[i])
- switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
-
- if switch:
- direction *= -1
-
- if direction != 1.0:
- speed_profile[i] = - target_speed
- else:
- speed_profile[i] = target_speed
-
- if switch:
- speed_profile[i] = 0.0
-
- # speed down
- for i in range(40):
- speed_profile[-i] = target_speed / (50 - i)
- if speed_profile[-i] <= 1.0 / 3.6:
- speed_profile[-i] = 1.0 / 3.6
-
- return speed_profile
-
-
-def main():
- print("LQR steering control tracking start!!")
- ax = [0.0, 6.0, 12.5, 10.0, 17.5, 20.0, 25.0]
- ay = [0.0, -3.0, -5.0, 6.5, 3.0, 0.0, 0.0]
- goal = [ax[-1], ay[-1]]
-
- cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
- ax, ay, ds=0.1)
- target_speed = 10.0 / 3.6 # simulation parameter km/h -> m/s
-
- sp = calc_speed_profile(cyaw, target_speed)
-
- t, x, y, yaw, v = do_simulation(cx, cy, cyaw, ck, sp, goal)
-
- if show_animation: # pragma: no cover
- plt.close()
- plt.subplots(1)
- plt.plot(ax, ay, "xb", label="waypoints")
- plt.plot(cx, cy, "-r", label="target course")
- plt.plot(x, y, "-g", label="tracking")
- plt.grid(True)
- plt.axis("equal")
- plt.xlabel("x[m]")
- plt.ylabel("y[m]")
- plt.legend()
- plt.subplots(1)
-
- plt.plot(t, np.array(v)*3.6, label="speed")
- plt.grid(True)
- plt.xlabel("Time [sec]")
- plt.ylabel("Speed [m/s]")
- plt.legend()
-
- plt.subplots(1)
- plt.plot(s, [np.rad2deg(iyaw) for iyaw in cyaw], "-r", label="yaw")
- plt.grid(True)
- plt.legend()
- plt.xlabel("line length[m]")
- plt.ylabel("yaw angle[deg]")
-
- plt.subplots(1)
- plt.plot(s, ck, "-r", label="curvature")
- plt.grid(True)
- plt.legend()
- plt.xlabel("line length[m]")
- plt.ylabel("curvature [1/m]")
-
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathTracking/lqr_steer_control/__init__.py b/PathTracking/lqr_steer_control/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathTracking/lqr_steer_control/lqr_steer_control.py b/PathTracking/lqr_steer_control/lqr_steer_control.py
deleted file mode 100644
index 3c066917ff7..00000000000
--- a/PathTracking/lqr_steer_control/lqr_steer_control.py
+++ /dev/null
@@ -1,291 +0,0 @@
-"""
-
-Path tracking simulation with LQR steering control and PID speed control.
-
-author Atsushi Sakai (@Atsushi_twi)
-
-"""
-import scipy.linalg as la
-import matplotlib.pyplot as plt
-import math
-import numpy as np
-import sys
-import pathlib
-
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-from utils.angle import angle_mod
-from PathPlanning.CubicSpline import cubic_spline_planner
-
-Kp = 1.0 # speed proportional gain
-
-# LQR parameter
-Q = np.eye(4)
-R = np.eye(1)
-
-# parameters
-dt = 0.1 # time tick[s]
-L = 0.5 # Wheelbase of the vehicle [m]
-max_steer = np.deg2rad(45.0) # maximum steering angle[rad]
-
-show_animation = True
-# show_animation = False
-
-
-class State:
-
- def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
- self.x = x
- self.y = y
- self.yaw = yaw
- self.v = v
-
-
-def update(state, a, delta):
-
- if delta >= max_steer:
- delta = max_steer
- if delta <= - max_steer:
- delta = - max_steer
-
- state.x = state.x + state.v * math.cos(state.yaw) * dt
- state.y = state.y + state.v * math.sin(state.yaw) * dt
- state.yaw = state.yaw + state.v / L * math.tan(delta) * dt
- state.v = state.v + a * dt
-
- return state
-
-
-def pid_control(target, current):
- a = Kp * (target - current)
-
- return a
-
-
-def pi_2_pi(angle):
- return angle_mod(angle)
-
-
-def solve_DARE(A, B, Q, R):
- """
- solve a discrete time_Algebraic Riccati equation (DARE)
- """
- X = Q
- Xn = Q
- max_iter = 150
- eps = 0.01
-
- for i in range(max_iter):
- Xn = A.T @ X @ A - A.T @ X @ B @ \
- la.inv(R + B.T @ X @ B) @ B.T @ X @ A + Q
- if (abs(Xn - X)).max() < eps:
- break
- X = Xn
-
- return Xn
-
-
-def dlqr(A, B, Q, R):
- """Solve the discrete time lqr controller.
- x[k+1] = A x[k] + B u[k]
- cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
- # ref Bertsekas, p.151
- """
-
- # first, try to solve the ricatti equation
- X = solve_DARE(A, B, Q, R)
-
- # compute the LQR gain
- K = la.inv(B.T @ X @ B + R) @ (B.T @ X @ A)
-
- eigVals, eigVecs = la.eig(A - B @ K)
-
- return K, X, eigVals
-
-
-def lqr_steering_control(state, cx, cy, cyaw, ck, pe, pth_e):
- ind, e = calc_nearest_index(state, cx, cy, cyaw)
-
- k = ck[ind]
- v = state.v
- th_e = pi_2_pi(state.yaw - cyaw[ind])
-
- A = np.zeros((4, 4))
- A[0, 0] = 1.0
- A[0, 1] = dt
- A[1, 2] = v
- A[2, 2] = 1.0
- A[2, 3] = dt
- # print(A)
-
- B = np.zeros((4, 1))
- B[3, 0] = v / L
-
- K, _, _ = dlqr(A, B, Q, R)
-
- x = np.zeros((4, 1))
-
- x[0, 0] = e
- x[1, 0] = (e - pe) / dt
- x[2, 0] = th_e
- x[3, 0] = (th_e - pth_e) / dt
-
- ff = math.atan2(L * k, 1)
- fb = pi_2_pi((-K @ x)[0, 0])
-
- delta = ff + fb
-
- return delta, ind, e, th_e
-
-
-def calc_nearest_index(state, cx, cy, cyaw):
- dx = [state.x - icx for icx in cx]
- dy = [state.y - icy for icy in cy]
-
- d = [idx ** 2 + idy ** 2 for (idx, idy) in zip(dx, dy)]
-
- mind = min(d)
-
- ind = d.index(mind)
-
- mind = math.sqrt(mind)
-
- dxl = cx[ind] - state.x
- dyl = cy[ind] - state.y
-
- angle = pi_2_pi(cyaw[ind] - math.atan2(dyl, dxl))
- if angle < 0:
- mind *= -1
-
- return ind, mind
-
-
-def closed_loop_prediction(cx, cy, cyaw, ck, speed_profile, goal):
- T = 500.0 # max simulation time
- goal_dis = 0.3
- stop_speed = 0.05
-
- state = State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
-
- time = 0.0
- x = [state.x]
- y = [state.y]
- yaw = [state.yaw]
- v = [state.v]
- t = [0.0]
-
- e, e_th = 0.0, 0.0
-
- while T >= time:
- dl, target_ind, e, e_th = lqr_steering_control(
- state, cx, cy, cyaw, ck, e, e_th)
-
- ai = pid_control(speed_profile[target_ind], state.v)
- state = update(state, ai, dl)
-
- if abs(state.v) <= stop_speed:
- target_ind += 1
-
- time = time + dt
-
- # check goal
- dx = state.x - goal[0]
- dy = state.y - goal[1]
- if math.hypot(dx, dy) <= goal_dis:
- print("Goal")
- break
-
- x.append(state.x)
- y.append(state.y)
- yaw.append(state.yaw)
- v.append(state.v)
- t.append(time)
-
- if target_ind % 1 == 0 and show_animation:
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(cx, cy, "-r", label="course")
- plt.plot(x, y, "ob", label="trajectory")
- plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
- plt.axis("equal")
- plt.grid(True)
- plt.title("speed[km/h]:" + str(round(state.v * 3.6, 2))
- + ",target index:" + str(target_ind))
- plt.pause(0.0001)
-
- return t, x, y, yaw, v
-
-
-def calc_speed_profile(cx, cy, cyaw, target_speed):
- speed_profile = [target_speed] * len(cx)
-
- direction = 1.0
-
- # Set stop point
- for i in range(len(cx) - 1):
- dyaw = abs(cyaw[i + 1] - cyaw[i])
- switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
-
- if switch:
- direction *= -1
-
- if direction != 1.0:
- speed_profile[i] = - target_speed
- else:
- speed_profile[i] = target_speed
-
- if switch:
- speed_profile[i] = 0.0
-
- speed_profile[-1] = 0.0
-
- return speed_profile
-
-
-def main():
- print("LQR steering control tracking start!!")
- ax = [0.0, 6.0, 12.5, 10.0, 7.5, 3.0, -1.0]
- ay = [0.0, -3.0, -5.0, 6.5, 3.0, 5.0, -2.0]
- goal = [ax[-1], ay[-1]]
-
- cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
- ax, ay, ds=0.1)
- target_speed = 10.0 / 3.6 # simulation parameter km/h -> m/s
-
- sp = calc_speed_profile(cx, cy, cyaw, target_speed)
-
- t, x, y, yaw, v = closed_loop_prediction(cx, cy, cyaw, ck, sp, goal)
-
- if show_animation: # pragma: no cover
- plt.close()
- plt.subplots(1)
- plt.plot(ax, ay, "xb", label="input")
- plt.plot(cx, cy, "-r", label="spline")
- plt.plot(x, y, "-g", label="tracking")
- plt.grid(True)
- plt.axis("equal")
- plt.xlabel("x[m]")
- plt.ylabel("y[m]")
- plt.legend()
-
- plt.subplots(1)
- plt.plot(s, [np.rad2deg(iyaw) for iyaw in cyaw], "-r", label="yaw")
- plt.grid(True)
- plt.legend()
- plt.xlabel("line length[m]")
- plt.ylabel("yaw angle[deg]")
-
- plt.subplots(1)
- plt.plot(s, ck, "-r", label="curvature")
- plt.grid(True)
- plt.legend()
- plt.xlabel("line length[m]")
- plt.ylabel("curvature [1/m]")
-
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py b/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py
deleted file mode 100644
index eb2d7b6a738..00000000000
--- a/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py
+++ /dev/null
@@ -1,628 +0,0 @@
-"""
-
-Path tracking simulation with iterative linear model predictive control for speed and steer control
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-import matplotlib.pyplot as plt
-import time
-import cvxpy
-import math
-import numpy as np
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-from utils.angle import angle_mod
-
-from PathPlanning.CubicSpline import cubic_spline_planner
-
-NX = 4 # x = x, y, v, yaw
-NU = 2 # a = [accel, steer]
-T = 5 # horizon length
-
-# mpc parameters
-R = np.diag([0.01, 0.01]) # input cost matrix
-Rd = np.diag([0.01, 1.0]) # input difference cost matrix
-Q = np.diag([1.0, 1.0, 0.5, 0.5]) # state cost matrix
-Qf = Q # state final matrix
-GOAL_DIS = 1.5 # goal distance
-STOP_SPEED = 0.5 / 3.6 # stop speed
-MAX_TIME = 500.0 # max simulation time
-
-# iterative paramter
-MAX_ITER = 3 # Max iteration
-DU_TH = 0.1 # iteration finish param
-
-TARGET_SPEED = 10.0 / 3.6 # [m/s] target speed
-N_IND_SEARCH = 10 # Search index number
-
-DT = 0.2 # [s] time tick
-
-# Vehicle parameters
-LENGTH = 4.5 # [m]
-WIDTH = 2.0 # [m]
-BACKTOWHEEL = 1.0 # [m]
-WHEEL_LEN = 0.3 # [m]
-WHEEL_WIDTH = 0.2 # [m]
-TREAD = 0.7 # [m]
-WB = 2.5 # [m]
-
-MAX_STEER = np.deg2rad(45.0) # maximum steering angle [rad]
-MAX_DSTEER = np.deg2rad(30.0) # maximum steering speed [rad/s]
-MAX_SPEED = 55.0 / 3.6 # maximum speed [m/s]
-MIN_SPEED = -20.0 / 3.6 # minimum speed [m/s]
-MAX_ACCEL = 1.0 # maximum accel [m/ss]
-
-show_animation = True
-
-
-class State:
- """
- vehicle state class
- """
-
- def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
- self.x = x
- self.y = y
- self.yaw = yaw
- self.v = v
- self.predelta = None
-
-
-def pi_2_pi(angle):
- return angle_mod(angle)
-
-
-def get_linear_model_matrix(v, phi, delta):
-
- A = np.zeros((NX, NX))
- A[0, 0] = 1.0
- A[1, 1] = 1.0
- A[2, 2] = 1.0
- A[3, 3] = 1.0
- A[0, 2] = DT * math.cos(phi)
- A[0, 3] = - DT * v * math.sin(phi)
- A[1, 2] = DT * math.sin(phi)
- A[1, 3] = DT * v * math.cos(phi)
- A[3, 2] = DT * math.tan(delta) / WB
-
- B = np.zeros((NX, NU))
- B[2, 0] = DT
- B[3, 1] = DT * v / (WB * math.cos(delta) ** 2)
-
- C = np.zeros(NX)
- C[0] = DT * v * math.sin(phi) * phi
- C[1] = - DT * v * math.cos(phi) * phi
- C[3] = - DT * v * delta / (WB * math.cos(delta) ** 2)
-
- return A, B, C
-
-
-def plot_car(x, y, yaw, steer=0.0, cabcolor="-r", truckcolor="-k"): # pragma: no cover
-
- outline = np.array([[-BACKTOWHEEL, (LENGTH - BACKTOWHEEL), (LENGTH - BACKTOWHEEL), -BACKTOWHEEL, -BACKTOWHEEL],
- [WIDTH / 2, WIDTH / 2, - WIDTH / 2, -WIDTH / 2, WIDTH / 2]])
-
- fr_wheel = np.array([[WHEEL_LEN, -WHEEL_LEN, -WHEEL_LEN, WHEEL_LEN, WHEEL_LEN],
- [-WHEEL_WIDTH - TREAD, -WHEEL_WIDTH - TREAD, WHEEL_WIDTH - TREAD, WHEEL_WIDTH - TREAD, -WHEEL_WIDTH - TREAD]])
-
- rr_wheel = np.copy(fr_wheel)
-
- fl_wheel = np.copy(fr_wheel)
- fl_wheel[1, :] *= -1
- rl_wheel = np.copy(rr_wheel)
- rl_wheel[1, :] *= -1
-
- Rot1 = np.array([[math.cos(yaw), math.sin(yaw)],
- [-math.sin(yaw), math.cos(yaw)]])
- Rot2 = np.array([[math.cos(steer), math.sin(steer)],
- [-math.sin(steer), math.cos(steer)]])
-
- fr_wheel = (fr_wheel.T.dot(Rot2)).T
- fl_wheel = (fl_wheel.T.dot(Rot2)).T
- fr_wheel[0, :] += WB
- fl_wheel[0, :] += WB
-
- fr_wheel = (fr_wheel.T.dot(Rot1)).T
- fl_wheel = (fl_wheel.T.dot(Rot1)).T
-
- outline = (outline.T.dot(Rot1)).T
- rr_wheel = (rr_wheel.T.dot(Rot1)).T
- rl_wheel = (rl_wheel.T.dot(Rot1)).T
-
- outline[0, :] += x
- outline[1, :] += y
- fr_wheel[0, :] += x
- fr_wheel[1, :] += y
- rr_wheel[0, :] += x
- rr_wheel[1, :] += y
- fl_wheel[0, :] += x
- fl_wheel[1, :] += y
- rl_wheel[0, :] += x
- rl_wheel[1, :] += y
-
- plt.plot(np.array(outline[0, :]).flatten(),
- np.array(outline[1, :]).flatten(), truckcolor)
- plt.plot(np.array(fr_wheel[0, :]).flatten(),
- np.array(fr_wheel[1, :]).flatten(), truckcolor)
- plt.plot(np.array(rr_wheel[0, :]).flatten(),
- np.array(rr_wheel[1, :]).flatten(), truckcolor)
- plt.plot(np.array(fl_wheel[0, :]).flatten(),
- np.array(fl_wheel[1, :]).flatten(), truckcolor)
- plt.plot(np.array(rl_wheel[0, :]).flatten(),
- np.array(rl_wheel[1, :]).flatten(), truckcolor)
- plt.plot(x, y, "*")
-
-
-def update_state(state, a, delta):
-
- # input check
- if delta >= MAX_STEER:
- delta = MAX_STEER
- elif delta <= -MAX_STEER:
- delta = -MAX_STEER
-
- state.x = state.x + state.v * math.cos(state.yaw) * DT
- state.y = state.y + state.v * math.sin(state.yaw) * DT
- state.yaw = state.yaw + state.v / WB * math.tan(delta) * DT
- state.v = state.v + a * DT
-
- if state.v > MAX_SPEED:
- state.v = MAX_SPEED
- elif state.v < MIN_SPEED:
- state.v = MIN_SPEED
-
- return state
-
-
-def get_nparray_from_matrix(x):
- return np.array(x).flatten()
-
-
-def calc_nearest_index(state, cx, cy, cyaw, pind):
-
- dx = [state.x - icx for icx in cx[pind:(pind + N_IND_SEARCH)]]
- dy = [state.y - icy for icy in cy[pind:(pind + N_IND_SEARCH)]]
-
- d = [idx ** 2 + idy ** 2 for (idx, idy) in zip(dx, dy)]
-
- mind = min(d)
-
- ind = d.index(mind) + pind
-
- mind = math.sqrt(mind)
-
- dxl = cx[ind] - state.x
- dyl = cy[ind] - state.y
-
- angle = pi_2_pi(cyaw[ind] - math.atan2(dyl, dxl))
- if angle < 0:
- mind *= -1
-
- return ind, mind
-
-
-def predict_motion(x0, oa, od, xref):
- xbar = xref * 0.0
- for i, _ in enumerate(x0):
- xbar[i, 0] = x0[i]
-
- state = State(x=x0[0], y=x0[1], yaw=x0[3], v=x0[2])
- for (ai, di, i) in zip(oa, od, range(1, T + 1)):
- state = update_state(state, ai, di)
- xbar[0, i] = state.x
- xbar[1, i] = state.y
- xbar[2, i] = state.v
- xbar[3, i] = state.yaw
-
- return xbar
-
-
-def iterative_linear_mpc_control(xref, x0, dref, oa, od):
- """
- MPC control with updating operational point iteratively
- """
- ox, oy, oyaw, ov = None, None, None, None
-
- if oa is None or od is None:
- oa = [0.0] * T
- od = [0.0] * T
-
- for i in range(MAX_ITER):
- xbar = predict_motion(x0, oa, od, xref)
- poa, pod = oa[:], od[:]
- oa, od, ox, oy, oyaw, ov = linear_mpc_control(xref, xbar, x0, dref)
- du = sum(abs(oa - poa)) + sum(abs(od - pod)) # calc u change value
- if du <= DU_TH:
- break
- else:
- print("Iterative is max iter")
-
- return oa, od, ox, oy, oyaw, ov
-
-
-def linear_mpc_control(xref, xbar, x0, dref):
- """
- linear mpc control
-
- xref: reference point
- xbar: operational point
- x0: initial state
- dref: reference steer angle
- """
-
- x = cvxpy.Variable((NX, T + 1))
- u = cvxpy.Variable((NU, T))
-
- cost = 0.0
- constraints = []
-
- for t in range(T):
- cost += cvxpy.quad_form(u[:, t], R)
-
- if t != 0:
- cost += cvxpy.quad_form(xref[:, t] - x[:, t], Q)
-
- A, B, C = get_linear_model_matrix(
- xbar[2, t], xbar[3, t], dref[0, t])
- constraints += [x[:, t + 1] == A @ x[:, t] + B @ u[:, t] + C]
-
- if t < (T - 1):
- cost += cvxpy.quad_form(u[:, t + 1] - u[:, t], Rd)
- constraints += [cvxpy.abs(u[1, t + 1] - u[1, t]) <=
- MAX_DSTEER * DT]
-
- cost += cvxpy.quad_form(xref[:, T] - x[:, T], Qf)
-
- constraints += [x[:, 0] == x0]
- constraints += [x[2, :] <= MAX_SPEED]
- constraints += [x[2, :] >= MIN_SPEED]
- constraints += [cvxpy.abs(u[0, :]) <= MAX_ACCEL]
- constraints += [cvxpy.abs(u[1, :]) <= MAX_STEER]
-
- prob = cvxpy.Problem(cvxpy.Minimize(cost), constraints)
- prob.solve(solver=cvxpy.CLARABEL, verbose=False)
-
- if prob.status == cvxpy.OPTIMAL or prob.status == cvxpy.OPTIMAL_INACCURATE:
- ox = get_nparray_from_matrix(x.value[0, :])
- oy = get_nparray_from_matrix(x.value[1, :])
- ov = get_nparray_from_matrix(x.value[2, :])
- oyaw = get_nparray_from_matrix(x.value[3, :])
- oa = get_nparray_from_matrix(u.value[0, :])
- odelta = get_nparray_from_matrix(u.value[1, :])
-
- else:
- print("Error: Cannot solve mpc..")
- oa, odelta, ox, oy, oyaw, ov = None, None, None, None, None, None
-
- return oa, odelta, ox, oy, oyaw, ov
-
-
-def calc_ref_trajectory(state, cx, cy, cyaw, ck, sp, dl, pind):
- xref = np.zeros((NX, T + 1))
- dref = np.zeros((1, T + 1))
- ncourse = len(cx)
-
- ind, _ = calc_nearest_index(state, cx, cy, cyaw, pind)
-
- if pind >= ind:
- ind = pind
-
- xref[0, 0] = cx[ind]
- xref[1, 0] = cy[ind]
- xref[2, 0] = sp[ind]
- xref[3, 0] = cyaw[ind]
- dref[0, 0] = 0.0 # steer operational point should be 0
-
- travel = 0.0
-
- for i in range(T + 1):
- travel += abs(state.v) * DT
- dind = int(round(travel / dl))
-
- if (ind + dind) < ncourse:
- xref[0, i] = cx[ind + dind]
- xref[1, i] = cy[ind + dind]
- xref[2, i] = sp[ind + dind]
- xref[3, i] = cyaw[ind + dind]
- dref[0, i] = 0.0
- else:
- xref[0, i] = cx[ncourse - 1]
- xref[1, i] = cy[ncourse - 1]
- xref[2, i] = sp[ncourse - 1]
- xref[3, i] = cyaw[ncourse - 1]
- dref[0, i] = 0.0
-
- return xref, ind, dref
-
-
-def check_goal(state, goal, tind, nind):
-
- # check goal
- dx = state.x - goal[0]
- dy = state.y - goal[1]
- d = math.hypot(dx, dy)
-
- isgoal = (d <= GOAL_DIS)
-
- if abs(tind - nind) >= 5:
- isgoal = False
-
- isstop = (abs(state.v) <= STOP_SPEED)
-
- if isgoal and isstop:
- return True
-
- return False
-
-
-def do_simulation(cx, cy, cyaw, ck, sp, dl, initial_state):
- """
- Simulation
-
- cx: course x position list
- cy: course y position list
- cy: course yaw position list
- ck: course curvature list
- sp: speed profile
- dl: course tick [m]
-
- """
-
- goal = [cx[-1], cy[-1]]
-
- state = initial_state
-
- # initial yaw compensation
- if state.yaw - cyaw[0] >= math.pi:
- state.yaw -= math.pi * 2.0
- elif state.yaw - cyaw[0] <= -math.pi:
- state.yaw += math.pi * 2.0
-
- time = 0.0
- x = [state.x]
- y = [state.y]
- yaw = [state.yaw]
- v = [state.v]
- t = [0.0]
- d = [0.0]
- a = [0.0]
- target_ind, _ = calc_nearest_index(state, cx, cy, cyaw, 0)
-
- odelta, oa = None, None
-
- cyaw = smooth_yaw(cyaw)
-
- while MAX_TIME >= time:
- xref, target_ind, dref = calc_ref_trajectory(
- state, cx, cy, cyaw, ck, sp, dl, target_ind)
-
- x0 = [state.x, state.y, state.v, state.yaw] # current state
-
- oa, odelta, ox, oy, oyaw, ov = iterative_linear_mpc_control(
- xref, x0, dref, oa, odelta)
-
- di, ai = 0.0, 0.0
- if odelta is not None:
- di, ai = odelta[0], oa[0]
- state = update_state(state, ai, di)
-
- time = time + DT
-
- x.append(state.x)
- y.append(state.y)
- yaw.append(state.yaw)
- v.append(state.v)
- t.append(time)
- d.append(di)
- a.append(ai)
-
- if check_goal(state, goal, target_ind, len(cx)):
- print("Goal")
- break
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if ox is not None:
- plt.plot(ox, oy, "xr", label="MPC")
- plt.plot(cx, cy, "-r", label="course")
- plt.plot(x, y, "ob", label="trajectory")
- plt.plot(xref[0, :], xref[1, :], "xk", label="xref")
- plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
- plot_car(state.x, state.y, state.yaw, steer=di)
- plt.axis("equal")
- plt.grid(True)
- plt.title("Time[s]:" + str(round(time, 2))
- + ", speed[km/h]:" + str(round(state.v * 3.6, 2)))
- plt.pause(0.0001)
-
- return t, x, y, yaw, v, d, a
-
-
-def calc_speed_profile(cx, cy, cyaw, target_speed):
-
- speed_profile = [target_speed] * len(cx)
- direction = 1.0 # forward
-
- # Set stop point
- for i in range(len(cx) - 1):
- dx = cx[i + 1] - cx[i]
- dy = cy[i + 1] - cy[i]
-
- move_direction = math.atan2(dy, dx)
-
- if dx != 0.0 and dy != 0.0:
- dangle = abs(pi_2_pi(move_direction - cyaw[i]))
- if dangle >= math.pi / 4.0:
- direction = -1.0
- else:
- direction = 1.0
-
- if direction != 1.0:
- speed_profile[i] = - target_speed
- else:
- speed_profile[i] = target_speed
-
- speed_profile[-1] = 0.0
-
- return speed_profile
-
-
-def smooth_yaw(yaw):
-
- for i in range(len(yaw) - 1):
- dyaw = yaw[i + 1] - yaw[i]
-
- while dyaw >= math.pi / 2.0:
- yaw[i + 1] -= math.pi * 2.0
- dyaw = yaw[i + 1] - yaw[i]
-
- while dyaw <= -math.pi / 2.0:
- yaw[i + 1] += math.pi * 2.0
- dyaw = yaw[i + 1] - yaw[i]
-
- return yaw
-
-
-def get_straight_course(dl):
- ax = [0.0, 5.0, 10.0, 20.0, 30.0, 40.0, 50.0]
- ay = [0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
- cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
- ax, ay, ds=dl)
-
- return cx, cy, cyaw, ck
-
-
-def get_straight_course2(dl):
- ax = [0.0, -10.0, -20.0, -40.0, -50.0, -60.0, -70.0]
- ay = [0.0, -1.0, 1.0, 0.0, -1.0, 1.0, 0.0]
- cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
- ax, ay, ds=dl)
-
- return cx, cy, cyaw, ck
-
-
-def get_straight_course3(dl):
- ax = [0.0, -10.0, -20.0, -40.0, -50.0, -60.0, -70.0]
- ay = [0.0, -1.0, 1.0, 0.0, -1.0, 1.0, 0.0]
- cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
- ax, ay, ds=dl)
-
- cyaw = [i - math.pi for i in cyaw]
-
- return cx, cy, cyaw, ck
-
-
-def get_forward_course(dl):
- ax = [0.0, 60.0, 125.0, 50.0, 75.0, 30.0, -10.0]
- ay = [0.0, 0.0, 50.0, 65.0, 30.0, 50.0, -20.0]
- cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
- ax, ay, ds=dl)
-
- return cx, cy, cyaw, ck
-
-
-def get_switch_back_course(dl):
- ax = [0.0, 30.0, 6.0, 20.0, 35.0]
- ay = [0.0, 0.0, 20.0, 35.0, 20.0]
- cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
- ax, ay, ds=dl)
- ax = [35.0, 10.0, 0.0, 0.0]
- ay = [20.0, 30.0, 5.0, 0.0]
- cx2, cy2, cyaw2, ck2, s2 = cubic_spline_planner.calc_spline_course(
- ax, ay, ds=dl)
- cyaw2 = [i - math.pi for i in cyaw2]
- cx.extend(cx2)
- cy.extend(cy2)
- cyaw.extend(cyaw2)
- ck.extend(ck2)
-
- return cx, cy, cyaw, ck
-
-
-def main():
- print(__file__ + " start!!")
- start = time.time()
-
- dl = 1.0 # course tick
- # cx, cy, cyaw, ck = get_straight_course(dl)
- # cx, cy, cyaw, ck = get_straight_course2(dl)
- # cx, cy, cyaw, ck = get_straight_course3(dl)
- # cx, cy, cyaw, ck = get_forward_course(dl)
- cx, cy, cyaw, ck = get_switch_back_course(dl)
-
- sp = calc_speed_profile(cx, cy, cyaw, TARGET_SPEED)
-
- initial_state = State(x=cx[0], y=cy[0], yaw=cyaw[0], v=0.0)
-
- t, x, y, yaw, v, d, a = do_simulation(
- cx, cy, cyaw, ck, sp, dl, initial_state)
-
- elapsed_time = time.time() - start
- print(f"calc time:{elapsed_time:.6f} [sec]")
-
- if show_animation: # pragma: no cover
- plt.close("all")
- plt.subplots()
- plt.plot(cx, cy, "-r", label="spline")
- plt.plot(x, y, "-g", label="tracking")
- plt.grid(True)
- plt.axis("equal")
- plt.xlabel("x[m]")
- plt.ylabel("y[m]")
- plt.legend()
-
- plt.subplots()
- plt.plot(t, v, "-r", label="speed")
- plt.grid(True)
- plt.xlabel("Time [s]")
- plt.ylabel("Speed [kmh]")
-
- plt.show()
-
-
-def main2():
- print(__file__ + " start!!")
- start = time.time()
-
- dl = 1.0 # course tick
- cx, cy, cyaw, ck = get_straight_course3(dl)
-
- sp = calc_speed_profile(cx, cy, cyaw, TARGET_SPEED)
-
- initial_state = State(x=cx[0], y=cy[0], yaw=0.0, v=0.0)
-
- t, x, y, yaw, v, d, a = do_simulation(
- cx, cy, cyaw, ck, sp, dl, initial_state)
-
- elapsed_time = time.time() - start
- print(f"calc time:{elapsed_time:.6f} [sec]")
-
- if show_animation: # pragma: no cover
- plt.close("all")
- plt.subplots()
- plt.plot(cx, cy, "-r", label="spline")
- plt.plot(x, y, "-g", label="tracking")
- plt.grid(True)
- plt.axis("equal")
- plt.xlabel("x[m]")
- plt.ylabel("y[m]")
- plt.legend()
-
- plt.subplots()
- plt.plot(t, v, "-r", label="speed")
- plt.grid(True)
- plt.xlabel("Time [s]")
- plt.ylabel("Speed [kmh]")
-
- plt.show()
-
-
-if __name__ == '__main__':
- main()
- # main2()
diff --git a/PathTracking/move_to_pose/__init__.py b/PathTracking/move_to_pose/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/PathTracking/move_to_pose/move_to_pose.py b/PathTracking/move_to_pose/move_to_pose.py
deleted file mode 100644
index 34736a2e213..00000000000
--- a/PathTracking/move_to_pose/move_to_pose.py
+++ /dev/null
@@ -1,223 +0,0 @@
-"""
-
-Move to specified pose
-
-Author: Daniel Ingram (daniel-s-ingram)
- Atsushi Sakai (@Atsushi_twi)
- Seied Muhammad Yazdian (@Muhammad-Yazdian)
- Wang Zheng (@Aglargil)
-
-P. I. Corke, "Robotics, Vision & Control", Springer 2017, ISBN 978-3-319-54413-7
-
-"""
-
-import matplotlib.pyplot as plt
-import numpy as np
-import sys
-import pathlib
-
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-from utils.angle import angle_mod
-from random import random
-
-
-class PathFinderController:
- """
- Constructs an instantiate of the PathFinderController for navigating a
- 3-DOF wheeled robot on a 2D plane
-
- Parameters
- ----------
- Kp_rho : The linear velocity gain to translate the robot along a line
- towards the goal
- Kp_alpha : The angular velocity gain to rotate the robot towards the goal
- Kp_beta : The offset angular velocity gain accounting for smooth merging to
- the goal angle (i.e., it helps the robot heading to be parallel
- to the target angle.)
- """
-
- def __init__(self, Kp_rho, Kp_alpha, Kp_beta):
- self.Kp_rho = Kp_rho
- self.Kp_alpha = Kp_alpha
- self.Kp_beta = Kp_beta
-
- def calc_control_command(self, x_diff, y_diff, theta, theta_goal):
- """
- Returns the control command for the linear and angular velocities as
- well as the distance to goal
-
- Parameters
- ----------
- x_diff : The position of target with respect to current robot position
- in x direction
- y_diff : The position of target with respect to current robot position
- in y direction
- theta : The current heading angle of robot with respect to x axis
- theta_goal: The target angle of robot with respect to x axis
-
- Returns
- -------
- rho : The distance between the robot and the goal position
- v : Command linear velocity
- w : Command angular velocity
- """
-
- # Description of local variables:
- # - alpha is the angle to the goal relative to the heading of the robot
- # - beta is the angle between the robot's position and the goal
- # position plus the goal angle
- # - Kp_rho*rho and Kp_alpha*alpha drive the robot along a line towards
- # the goal
- # - Kp_beta*beta rotates the line so that it is parallel to the goal
- # angle
- #
- # Note:
- # we restrict alpha and beta (angle differences) to the range
- # [-pi, pi] to prevent unstable behavior e.g. difference going
- # from 0 rad to 2*pi rad with slight turn
-
- # Ref: The velocity v always has a constant sign which depends on the initial value of α.
- rho = np.hypot(x_diff, y_diff)
- v = self.Kp_rho * rho
-
- alpha = angle_mod(np.arctan2(y_diff, x_diff) - theta)
- beta = angle_mod(theta_goal - theta - alpha)
- if alpha > np.pi / 2 or alpha < -np.pi / 2:
- # recalculate alpha to make alpha in the range of [-pi/2, pi/2]
- alpha = angle_mod(np.arctan2(-y_diff, -x_diff) - theta)
- beta = angle_mod(theta_goal - theta - alpha)
- w = self.Kp_alpha * alpha - self.Kp_beta * beta
- v = -v
- else:
- w = self.Kp_alpha * alpha - self.Kp_beta * beta
-
- return rho, v, w
-
-
-# simulation parameters
-controller = PathFinderController(9, 15, 3)
-dt = 0.01
-MAX_SIM_TIME = 5 # seconds, robot will stop moving when time exceeds this value
-
-# Robot specifications
-MAX_LINEAR_SPEED = 15
-MAX_ANGULAR_SPEED = 7
-
-show_animation = True
-
-
-def move_to_pose(x_start, y_start, theta_start, x_goal, y_goal, theta_goal):
- x = x_start
- y = y_start
- theta = theta_start
-
- x_diff = x_goal - x
- y_diff = y_goal - y
-
- x_traj, y_traj, v_traj, w_traj = [x], [y], [0], [0]
-
- rho = np.hypot(x_diff, y_diff)
- t = 0
- while rho > 0.001 and t < MAX_SIM_TIME:
- t += dt
- x_traj.append(x)
- y_traj.append(y)
-
- x_diff = x_goal - x
- y_diff = y_goal - y
-
- rho, v, w = controller.calc_control_command(x_diff, y_diff, theta, theta_goal)
-
- if abs(v) > MAX_LINEAR_SPEED:
- v = np.sign(v) * MAX_LINEAR_SPEED
-
- if abs(w) > MAX_ANGULAR_SPEED:
- w = np.sign(w) * MAX_ANGULAR_SPEED
-
- v_traj.append(v)
- w_traj.append(w)
-
- theta = theta + w * dt
- x = x + v * np.cos(theta) * dt
- y = y + v * np.sin(theta) * dt
-
- if show_animation: # pragma: no cover
- plt.cla()
- plt.arrow(
- x_start,
- y_start,
- np.cos(theta_start),
- np.sin(theta_start),
- color="r",
- width=0.1,
- )
- plt.arrow(
- x_goal,
- y_goal,
- np.cos(theta_goal),
- np.sin(theta_goal),
- color="g",
- width=0.1,
- )
- plot_vehicle(x, y, theta, x_traj, y_traj)
-
- return x_traj, y_traj, v_traj, w_traj
-
-
-def plot_vehicle(x, y, theta, x_traj, y_traj): # pragma: no cover
- # Corners of triangular vehicle when pointing to the right (0 radians)
- p1_i = np.array([0.5, 0, 1]).T
- p2_i = np.array([-0.5, 0.25, 1]).T
- p3_i = np.array([-0.5, -0.25, 1]).T
-
- T = transformation_matrix(x, y, theta)
- p1 = np.matmul(T, p1_i)
- p2 = np.matmul(T, p2_i)
- p3 = np.matmul(T, p3_i)
-
- plt.plot([p1[0], p2[0]], [p1[1], p2[1]], "k-")
- plt.plot([p2[0], p3[0]], [p2[1], p3[1]], "k-")
- plt.plot([p3[0], p1[0]], [p3[1], p1[1]], "k-")
-
- plt.plot(x_traj, y_traj, "b--")
-
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- "key_release_event", lambda event: [exit(0) if event.key == "escape" else None]
- )
-
- plt.xlim(0, 20)
- plt.ylim(0, 20)
-
- plt.pause(dt)
-
-
-def transformation_matrix(x, y, theta):
- return np.array(
- [
- [np.cos(theta), -np.sin(theta), x],
- [np.sin(theta), np.cos(theta), y],
- [0, 0, 1],
- ]
- )
-
-
-def main():
- for i in range(5):
- x_start = 20.0 * random()
- y_start = 20.0 * random()
- theta_start: float = 2 * np.pi * random() - np.pi
- x_goal = 20 * random()
- y_goal = 20 * random()
- theta_goal = 2 * np.pi * random() - np.pi
- print(
- f"Initial x: {round(x_start, 2)} m\nInitial y: {round(y_start, 2)} m\nInitial theta: {round(theta_start, 2)} rad\n"
- )
- print(
- f"Goal x: {round(x_goal, 2)} m\nGoal y: {round(y_goal, 2)} m\nGoal theta: {round(theta_goal, 2)} rad\n"
- )
- move_to_pose(x_start, y_start, theta_start, x_goal, y_goal, theta_goal)
-
-
-if __name__ == "__main__":
- main()
diff --git a/PathTracking/move_to_pose/move_to_pose_robot.py b/PathTracking/move_to_pose/move_to_pose_robot.py
deleted file mode 100644
index fe9f0d06b35..00000000000
--- a/PathTracking/move_to_pose/move_to_pose_robot.py
+++ /dev/null
@@ -1,240 +0,0 @@
-"""
-
-Move to specified pose (with Robot class)
-
-Author: Daniel Ingram (daniel-s-ingram)
- Atsushi Sakai (@Atsushi_twi)
- Seied Muhammad Yazdian (@Muhammad-Yazdian)
-
-P.I. Corke, "Robotics, Vision & Control", Springer 2017, ISBN 978-3-319-54413-7
-
-"""
-
-import matplotlib.pyplot as plt
-import numpy as np
-import copy
-from move_to_pose import PathFinderController
-
-# Simulation parameters
-TIME_DURATION = 1000
-TIME_STEP = 0.01
-AT_TARGET_ACCEPTANCE_THRESHOLD = 0.01
-SHOW_ANIMATION = True
-PLOT_WINDOW_SIZE_X = 20
-PLOT_WINDOW_SIZE_Y = 20
-PLOT_FONT_SIZE = 8
-
-simulation_running = True
-all_robots_are_at_target = False
-
-
-class Pose:
- """2D pose"""
-
- def __init__(self, x, y, theta):
- self.x = x
- self.y = y
- self.theta = theta
-
-
-class Robot:
- """
- Constructs an instantiate of the 3-DOF wheeled Robot navigating on a
- 2D plane
-
- Parameters
- ----------
- name : (string)
- The name of the robot
- color : (string)
- The color of the robot
- max_linear_speed : (float)
- The maximum linear speed that the robot can go
- max_angular_speed : (float)
- The maximum angular speed that the robot can rotate about its vertical
- axis
- path_finder_controller : (PathFinderController)
- A configurable controller to finds the path and calculates command
- linear and angular velocities.
- """
-
- def __init__(self, name, color, max_linear_speed, max_angular_speed,
- path_finder_controller):
- self.name = name
- self.color = color
- self.MAX_LINEAR_SPEED = max_linear_speed
- self.MAX_ANGULAR_SPEED = max_angular_speed
- self.path_finder_controller = path_finder_controller
- self.x_traj = []
- self.y_traj = []
- self.pose = Pose(0, 0, 0)
- self.pose_start = Pose(0, 0, 0)
- self.pose_target = Pose(0, 0, 0)
- self.is_at_target = False
-
- def set_start_target_poses(self, pose_start, pose_target):
- """
- Sets the start and target positions of the robot
-
- Parameters
- ----------
- pose_start : (Pose)
- Start position of the robot (see the Pose class)
- pose_target : (Pose)
- Target position of the robot (see the Pose class)
- """
- self.pose_start = copy.copy(pose_start)
- self.pose_target = pose_target
- self.pose = pose_start
-
- def move(self, dt):
- """
- Moves the robot for one time step increment
-
- Parameters
- ----------
- dt : (float)
- time step
- """
- self.x_traj.append(self.pose.x)
- self.y_traj.append(self.pose.y)
-
- rho, linear_velocity, angular_velocity = \
- self.path_finder_controller.calc_control_command(
- self.pose_target.x - self.pose.x,
- self.pose_target.y - self.pose.y,
- self.pose.theta, self.pose_target.theta)
-
- if rho < AT_TARGET_ACCEPTANCE_THRESHOLD:
- self.is_at_target = True
-
- if abs(linear_velocity) > self.MAX_LINEAR_SPEED:
- linear_velocity = (np.sign(linear_velocity)
- * self.MAX_LINEAR_SPEED)
-
- if abs(angular_velocity) > self.MAX_ANGULAR_SPEED:
- angular_velocity = (np.sign(angular_velocity)
- * self.MAX_ANGULAR_SPEED)
-
- self.pose.theta = self.pose.theta + angular_velocity * dt
- self.pose.x = self.pose.x + linear_velocity * \
- np.cos(self.pose.theta) * dt
- self.pose.y = self.pose.y + linear_velocity * \
- np.sin(self.pose.theta) * dt
-
-
-def run_simulation(robots):
- """Simulates all robots simultaneously"""
- global all_robots_are_at_target
- global simulation_running
-
- robot_names = []
- for instance in robots:
- robot_names.append(instance.name)
-
- time = 0
- while simulation_running and time < TIME_DURATION:
- time += TIME_STEP
- robots_are_at_target = []
-
- for instance in robots:
- if not instance.is_at_target:
- instance.move(TIME_STEP)
- robots_are_at_target.append(instance.is_at_target)
-
- if all(robots_are_at_target):
- simulation_running = False
-
- if SHOW_ANIMATION:
- plt.cla()
- plt.xlim(0, PLOT_WINDOW_SIZE_X)
- plt.ylim(0, PLOT_WINDOW_SIZE_Y)
-
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
-
- plt.text(0.3, PLOT_WINDOW_SIZE_Y - 1,
- 'Time: {:.2f}'.format(time),
- fontsize=PLOT_FONT_SIZE)
-
- plt.text(0.3, PLOT_WINDOW_SIZE_Y - 2,
- 'Reached target: {} = '.format(robot_names)
- + str(robots_are_at_target),
- fontsize=PLOT_FONT_SIZE)
-
- for instance in robots:
- plt.arrow(instance.pose_start.x,
- instance.pose_start.y,
- np.cos(instance.pose_start.theta),
- np.sin(instance.pose_start.theta),
- color='r',
- width=0.1)
- plt.arrow(instance.pose_target.x,
- instance.pose_target.y,
- np.cos(instance.pose_target.theta),
- np.sin(instance.pose_target.theta),
- color='g',
- width=0.1)
- plot_vehicle(instance.pose.x,
- instance.pose.y,
- instance.pose.theta,
- instance.x_traj,
- instance.y_traj, instance.color)
-
- plt.pause(TIME_STEP)
-
-
-def plot_vehicle(x, y, theta, x_traj, y_traj, color):
- # Corners of triangular vehicle when pointing to the right (0 radians)
- p1_i = np.array([0.5, 0, 1]).T
- p2_i = np.array([-0.5, 0.25, 1]).T
- p3_i = np.array([-0.5, -0.25, 1]).T
-
- T = transformation_matrix(x, y, theta)
- p1 = T @ p1_i
- p2 = T @ p2_i
- p3 = T @ p3_i
-
- plt.plot([p1[0], p2[0]], [p1[1], p2[1]], color+'-')
- plt.plot([p2[0], p3[0]], [p2[1], p3[1]], color+'-')
- plt.plot([p3[0], p1[0]], [p3[1], p1[1]], color+'-')
-
- plt.plot(x_traj, y_traj, color+'--')
-
-
-def transformation_matrix(x, y, theta):
- return np.array([
- [np.cos(theta), -np.sin(theta), x],
- [np.sin(theta), np.cos(theta), y],
- [0, 0, 1]
- ])
-
-
-def main():
- pose_target = Pose(15, 15, -1)
-
- pose_start_1 = Pose(5, 2, 0)
- pose_start_2 = Pose(5, 2, 0)
- pose_start_3 = Pose(5, 2, 0)
-
- controller_1 = PathFinderController(5, 8, 2)
- controller_2 = PathFinderController(5, 16, 4)
- controller_3 = PathFinderController(10, 25, 6)
-
- robot_1 = Robot("Yellow Robot", "y", 12, 5, controller_1)
- robot_2 = Robot("Black Robot", "k", 16, 5, controller_2)
- robot_3 = Robot("Blue Robot", "b", 20, 5, controller_3)
-
- robot_1.set_start_target_poses(pose_start_1, pose_target)
- robot_2.set_start_target_poses(pose_start_2, pose_target)
- robot_3.set_start_target_poses(pose_start_3, pose_target)
-
- robots: list[Robot] = [robot_1, robot_2, robot_3]
-
- run_simulation(robots)
-
-
-if __name__ == '__main__':
- main()
diff --git a/PathTracking/pure_pursuit/pure_pursuit.py b/PathTracking/pure_pursuit/pure_pursuit.py
deleted file mode 100644
index ff995033a9e..00000000000
--- a/PathTracking/pure_pursuit/pure_pursuit.py
+++ /dev/null
@@ -1,215 +0,0 @@
-"""
-
-Path tracking simulation with pure pursuit steering and PID speed control.
-
-author: Atsushi Sakai (@Atsushi_twi)
- Guillaume Jacquenot (@Gjacquenot)
-
-"""
-import numpy as np
-import math
-import matplotlib.pyplot as plt
-
-# Parameters
-k = 0.1 # look forward gain
-Lfc = 2.0 # [m] look-ahead distance
-Kp = 1.0 # speed proportional gain
-dt = 0.1 # [s] time tick
-WB = 2.9 # [m] wheel base of vehicle
-
-show_animation = True
-
-
-class State:
-
- def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
- self.x = x
- self.y = y
- self.yaw = yaw
- self.v = v
- self.rear_x = self.x - ((WB / 2) * math.cos(self.yaw))
- self.rear_y = self.y - ((WB / 2) * math.sin(self.yaw))
-
- def update(self, a, delta):
- self.x += self.v * math.cos(self.yaw) * dt
- self.y += self.v * math.sin(self.yaw) * dt
- self.yaw += self.v / WB * math.tan(delta) * dt
- self.v += a * dt
- self.rear_x = self.x - ((WB / 2) * math.cos(self.yaw))
- self.rear_y = self.y - ((WB / 2) * math.sin(self.yaw))
-
- def calc_distance(self, point_x, point_y):
- dx = self.rear_x - point_x
- dy = self.rear_y - point_y
- return math.hypot(dx, dy)
-
-
-class States:
-
- def __init__(self):
- self.x = []
- self.y = []
- self.yaw = []
- self.v = []
- self.t = []
-
- def append(self, t, state):
- self.x.append(state.x)
- self.y.append(state.y)
- self.yaw.append(state.yaw)
- self.v.append(state.v)
- self.t.append(t)
-
-
-def proportional_control(target, current):
- a = Kp * (target - current)
-
- return a
-
-
-class TargetCourse:
-
- def __init__(self, cx, cy):
- self.cx = cx
- self.cy = cy
- self.old_nearest_point_index = None
-
- def search_target_index(self, state):
-
- # To speed up nearest point search, doing it at only first time.
- if self.old_nearest_point_index is None:
- # search nearest point index
- dx = [state.rear_x - icx for icx in self.cx]
- dy = [state.rear_y - icy for icy in self.cy]
- d = np.hypot(dx, dy)
- ind = np.argmin(d)
- self.old_nearest_point_index = ind
- else:
- ind = self.old_nearest_point_index
- distance_this_index = state.calc_distance(self.cx[ind],
- self.cy[ind])
- while True:
- distance_next_index = state.calc_distance(self.cx[ind + 1],
- self.cy[ind + 1])
- if distance_this_index < distance_next_index:
- break
- ind = ind + 1 if (ind + 1) < len(self.cx) else ind
- distance_this_index = distance_next_index
- self.old_nearest_point_index = ind
-
- Lf = k * state.v + Lfc # update look ahead distance
-
- # search look ahead target point index
- while Lf > state.calc_distance(self.cx[ind], self.cy[ind]):
- if (ind + 1) >= len(self.cx):
- break # not exceed goal
- ind += 1
-
- return ind, Lf
-
-
-def pure_pursuit_steer_control(state, trajectory, pind):
- ind, Lf = trajectory.search_target_index(state)
-
- if pind >= ind:
- ind = pind
-
- if ind < len(trajectory.cx):
- tx = trajectory.cx[ind]
- ty = trajectory.cy[ind]
- else: # toward goal
- tx = trajectory.cx[-1]
- ty = trajectory.cy[-1]
- ind = len(trajectory.cx) - 1
-
- alpha = math.atan2(ty - state.rear_y, tx - state.rear_x) - state.yaw
-
- delta = math.atan2(2.0 * WB * math.sin(alpha) / Lf, 1.0)
-
- return delta, ind
-
-
-def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"):
- """
- Plot arrow
- """
-
- if not isinstance(x, float):
- for ix, iy, iyaw in zip(x, y, yaw):
- plot_arrow(ix, iy, iyaw)
- else:
- plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),
- fc=fc, ec=ec, head_width=width, head_length=width)
- plt.plot(x, y)
-
-
-def main():
- # target course
- cx = np.arange(0, 50, 0.5)
- cy = [math.sin(ix / 5.0) * ix / 2.0 for ix in cx]
-
- target_speed = 10.0 / 3.6 # [m/s]
-
- T = 100.0 # max simulation time
-
- # initial state
- state = State(x=-0.0, y=-3.0, yaw=0.0, v=0.0)
-
- lastIndex = len(cx) - 1
- time = 0.0
- states = States()
- states.append(time, state)
- target_course = TargetCourse(cx, cy)
- target_ind, _ = target_course.search_target_index(state)
-
- while T >= time and lastIndex > target_ind:
-
- # Calc control input
- ai = proportional_control(target_speed, state.v)
- di, target_ind = pure_pursuit_steer_control(
- state, target_course, target_ind)
-
- state.update(ai, di) # Control vehicle
-
- time += dt
- states.append(time, state)
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plot_arrow(state.x, state.y, state.yaw)
- plt.plot(cx, cy, "-r", label="course")
- plt.plot(states.x, states.y, "-b", label="trajectory")
- plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
- plt.axis("equal")
- plt.grid(True)
- plt.title("Speed[km/h]:" + str(state.v * 3.6)[:4])
- plt.pause(0.001)
-
- # Test
- assert lastIndex >= target_ind, "Cannot goal"
-
- if show_animation: # pragma: no cover
- plt.cla()
- plt.plot(cx, cy, ".r", label="course")
- plt.plot(states.x, states.y, "-b", label="trajectory")
- plt.legend()
- plt.xlabel("x[m]")
- plt.ylabel("y[m]")
- plt.axis("equal")
- plt.grid(True)
-
- plt.subplots(1)
- plt.plot(states.t, [iv * 3.6 for iv in states.v], "-r")
- plt.xlabel("Time[s]")
- plt.ylabel("Speed[km/h]")
- plt.grid(True)
- plt.show()
-
-
-if __name__ == '__main__':
- print("Pure pursuit path tracking simulation start")
- main()
diff --git a/PathTracking/rear_wheel_feedback/rear_wheel_feedback.py b/PathTracking/rear_wheel_feedback/rear_wheel_feedback.py
deleted file mode 100644
index fd04fb6d171..00000000000
--- a/PathTracking/rear_wheel_feedback/rear_wheel_feedback.py
+++ /dev/null
@@ -1,234 +0,0 @@
-"""
-
-Path tracking simulation with rear wheel feedback steering control and PID speed control.
-
-author: Atsushi Sakai(@Atsushi_twi)
-
-"""
-import matplotlib.pyplot as plt
-import math
-import numpy as np
-import sys
-import pathlib
-from scipy import interpolate
-from scipy import optimize
-
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-from utils.angle import angle_mod
-
-Kp = 1.0 # speed proportional gain
-# steering control parameter
-KTH = 1.0
-KE = 0.5
-
-dt = 0.1 # [s]
-L = 2.9 # [m]
-
-show_animation = True
-
-class State:
- def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0, direction=1):
- self.x = x
- self.y = y
- self.yaw = yaw
- self.v = v
- self.direction = direction
-
- def update(self, a, delta, dt):
- self.x = self.x + self.v * math.cos(self.yaw) * dt
- self.y = self.y + self.v * math.sin(self.yaw) * dt
- self.yaw = self.yaw + self.v / L * math.tan(delta) * dt
- self.v = self.v + a * dt
-
-class CubicSplinePath:
- def __init__(self, x, y):
- x, y = map(np.asarray, (x, y))
- s = np.append([0],(np.cumsum(np.diff(x)**2) + np.cumsum(np.diff(y)**2))**0.5)
-
- self.X = interpolate.CubicSpline(s, x)
- self.Y = interpolate.CubicSpline(s, y)
-
- self.dX = self.X.derivative(1)
- self.ddX = self.X.derivative(2)
-
- self.dY = self.Y.derivative(1)
- self.ddY = self.Y.derivative(2)
-
- self.length = s[-1]
-
- def calc_yaw(self, s):
- dx, dy = self.dX(s), self.dY(s)
- return np.arctan2(dy, dx)
-
- def calc_curvature(self, s):
- dx, dy = self.dX(s), self.dY(s)
- ddx, ddy = self.ddX(s), self.ddY(s)
- return (ddy * dx - ddx * dy) / ((dx ** 2 + dy ** 2)**(3 / 2))
-
- def __find_nearest_point(self, s0, x, y):
- def calc_distance(_s, *args):
- _x, _y= self.X(_s), self.Y(_s)
- return (_x - args[0])**2 + (_y - args[1])**2
-
- def calc_distance_jacobian(_s, *args):
- _x, _y = self.X(_s), self.Y(_s)
- _dx, _dy = self.dX(_s), self.dY(_s)
- return 2*_dx*(_x - args[0])+2*_dy*(_y-args[1])
-
- minimum = optimize.fmin_cg(calc_distance, s0, calc_distance_jacobian, args=(x, y), full_output=True, disp=False)
- return minimum
-
- def calc_track_error(self, x, y, s0):
- ret = self.__find_nearest_point(s0, x, y)
-
- s = ret[0][0]
- e = ret[1]
-
- k = self.calc_curvature(s)
- yaw = self.calc_yaw(s)
-
- dxl = self.X(s) - x
- dyl = self.Y(s) - y
- angle = pi_2_pi(yaw - math.atan2(dyl, dxl))
- if angle < 0:
- e*= -1
-
- return e, k, yaw, s
-
-def pid_control(target, current):
- a = Kp * (target - current)
- return a
-
-def pi_2_pi(angle):
- return angle_mod(angle)
-
-def rear_wheel_feedback_control(state, e, k, yaw_ref):
- v = state.v
- th_e = pi_2_pi(state.yaw - yaw_ref)
-
- omega = v * k * math.cos(th_e) / (1.0 - k * e) - \
- KTH * abs(v) * th_e - KE * v * math.sin(th_e) * e / th_e
-
- if th_e == 0.0 or omega == 0.0:
- return 0.0
-
- delta = math.atan2(L * omega / v, 1.0)
-
- return delta
-
-
-def simulate(path_ref, goal):
- T = 500.0 # max simulation time
- goal_dis = 0.3
-
- state = State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
-
- time = 0.0
- x = [state.x]
- y = [state.y]
- yaw = [state.yaw]
- v = [state.v]
- t = [0.0]
- goal_flag = False
-
- s = np.arange(0, path_ref.length, 0.1)
- e, k, yaw_ref, s0 = path_ref.calc_track_error(state.x, state.y, 0.0)
-
- while T >= time:
- e, k, yaw_ref, s0 = path_ref.calc_track_error(state.x, state.y, s0)
- di = rear_wheel_feedback_control(state, e, k, yaw_ref)
-
- speed_ref = calc_target_speed(state, yaw_ref)
- ai = pid_control(speed_ref, state.v)
- state.update(ai, di, dt)
-
- time = time + dt
-
- # check goal
- dx = state.x - goal[0]
- dy = state.y - goal[1]
- if math.hypot(dx, dy) <= goal_dis:
- print("Goal")
- goal_flag = True
- break
-
- x.append(state.x)
- y.append(state.y)
- yaw.append(state.yaw)
- v.append(state.v)
- t.append(time)
-
- if show_animation:
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(path_ref.X(s), path_ref.Y(s), "-r", label="course")
- plt.plot(x, y, "ob", label="trajectory")
- plt.plot(path_ref.X(s0), path_ref.Y(s0), "xg", label="target")
- plt.axis("equal")
- plt.grid(True)
- plt.title(f"speed[km/h]:{round(state.v * 3.6, 2):.2f}, target s-param:{s0:.2f}")
- plt.pause(0.0001)
-
- return t, x, y, yaw, v, goal_flag
-
-def calc_target_speed(state, yaw_ref):
- target_speed = 10.0 / 3.6
-
- dyaw = yaw_ref - state.yaw
- switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
-
- if switch:
- state.direction *= -1
- return 0.0
-
- if state.direction != 1:
- return -target_speed
-
- return target_speed
-
-def main():
- print("rear wheel feedback tracking start!!")
- ax = [0.0, 6.0, 12.5, 5.0, 7.5, 3.0, -1.0]
- ay = [0.0, 0.0, 5.0, 6.5, 3.0, 5.0, -2.0]
- goal = [ax[-1], ay[-1]]
-
- reference_path = CubicSplinePath(ax, ay)
- s = np.arange(0, reference_path.length, 0.1)
-
- t, x, y, yaw, v, goal_flag = simulate(reference_path, goal)
-
- # Test
- assert goal_flag, "Cannot goal"
-
- if show_animation: # pragma: no cover
- plt.close()
- plt.subplots(1)
- plt.plot(ax, ay, "xb", label="input")
- plt.plot(reference_path.X(s), reference_path.Y(s), "-r", label="spline")
- plt.plot(x, y, "-g", label="tracking")
- plt.grid(True)
- plt.axis("equal")
- plt.xlabel("x[m]")
- plt.ylabel("y[m]")
- plt.legend()
-
- plt.subplots(1)
- plt.plot(s, np.rad2deg(reference_path.calc_yaw(s)), "-r", label="yaw")
- plt.grid(True)
- plt.legend()
- plt.xlabel("line length[m]")
- plt.ylabel("yaw angle[deg]")
-
- plt.subplots(1)
- plt.plot(s, reference_path.calc_curvature(s), "-r", label="curvature")
- plt.grid(True)
- plt.legend()
- plt.xlabel("line length[m]")
- plt.ylabel("curvature [1/m]")
-
- plt.show()
-
-if __name__ == '__main__':
- main()
diff --git a/PathTracking/stanley_controller/stanley_controller.py b/PathTracking/stanley_controller/stanley_controller.py
deleted file mode 100644
index bc98175f178..00000000000
--- a/PathTracking/stanley_controller/stanley_controller.py
+++ /dev/null
@@ -1,212 +0,0 @@
-"""
-
-Path tracking simulation with Stanley steering control and PID speed control.
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-Ref:
- - [Stanley: The robot that won the DARPA grand challenge](http://isl.ecst.csuchico.edu/DOCS/darpa2005/DARPA%202005%20Stanley.pdf)
- - [Autonomous Automobile Path Tracking](https://www.ri.cmu.edu/pub_files/2009/2/Automatic_Steering_Methods_for_Autonomous_Automobile_Path_Tracking.pdf)
-
-"""
-import numpy as np
-import matplotlib.pyplot as plt
-import sys
-import pathlib
-
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-from utils.angle import angle_mod
-from PathPlanning.CubicSpline import cubic_spline_planner
-
-k = 0.5 # control gain
-Kp = 1.0 # speed proportional gain
-dt = 0.1 # [s] time difference
-L = 2.9 # [m] Wheel base of vehicle
-max_steer = np.radians(30.0) # [rad] max steering angle
-
-show_animation = True
-
-
-class State:
- """
- Class representing the state of a vehicle.
-
- :param x: (float) x-coordinate
- :param y: (float) y-coordinate
- :param yaw: (float) yaw angle
- :param v: (float) speed
- """
-
- def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
- """Instantiate the object."""
- super().__init__()
- self.x = x
- self.y = y
- self.yaw = yaw
- self.v = v
-
- def update(self, acceleration, delta):
- """
- Update the state of the vehicle.
-
- Stanley Control uses bicycle model.
-
- :param acceleration: (float) Acceleration
- :param delta: (float) Steering
- """
- delta = np.clip(delta, -max_steer, max_steer)
-
- self.x += self.v * np.cos(self.yaw) * dt
- self.y += self.v * np.sin(self.yaw) * dt
- self.yaw += self.v / L * np.tan(delta) * dt
- self.yaw = normalize_angle(self.yaw)
- self.v += acceleration * dt
-
-
-def pid_control(target, current):
- """
- Proportional control for the speed.
-
- :param target: (float)
- :param current: (float)
- :return: (float)
- """
- return Kp * (target - current)
-
-
-def stanley_control(state, cx, cy, cyaw, last_target_idx):
- """
- Stanley steering control.
-
- :param state: (State object)
- :param cx: ([float])
- :param cy: ([float])
- :param cyaw: ([float])
- :param last_target_idx: (int)
- :return: (float, int)
- """
- current_target_idx, error_front_axle = calc_target_index(state, cx, cy)
-
- if last_target_idx >= current_target_idx:
- current_target_idx = last_target_idx
-
- # theta_e corrects the heading error
- theta_e = normalize_angle(cyaw[current_target_idx] - state.yaw)
- # theta_d corrects the cross track error
- theta_d = np.arctan2(k * error_front_axle, state.v)
- # Steering control
- delta = theta_e + theta_d
-
- return delta, current_target_idx
-
-
-def normalize_angle(angle):
- """
- Normalize an angle to [-pi, pi].
-
- :param angle: (float)
- :return: (float) Angle in radian in [-pi, pi]
- """
- return angle_mod(angle)
-
-
-def calc_target_index(state, cx, cy):
- """
- Compute index in the trajectory list of the target.
-
- :param state: (State object)
- :param cx: [float]
- :param cy: [float]
- :return: (int, float)
- """
- # Calc front axle position
- fx = state.x + L * np.cos(state.yaw)
- fy = state.y + L * np.sin(state.yaw)
-
- # Search nearest point index
- dx = [fx - icx for icx in cx]
- dy = [fy - icy for icy in cy]
- d = np.hypot(dx, dy)
- target_idx = np.argmin(d)
-
- # Project RMS error onto front axle vector
- front_axle_vec = [-np.cos(state.yaw + np.pi / 2),
- -np.sin(state.yaw + np.pi / 2)]
- error_front_axle = np.dot([dx[target_idx], dy[target_idx]], front_axle_vec)
-
- return target_idx, error_front_axle
-
-
-def main():
- """Plot an example of Stanley steering control on a cubic spline."""
- # target course
- ax = [0.0, 100.0, 100.0, 50.0, 60.0]
- ay = [0.0, 0.0, -30.0, -20.0, 0.0]
-
- cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
- ax, ay, ds=0.1)
-
- target_speed = 30.0 / 3.6 # [m/s]
-
- max_simulation_time = 100.0
-
- # Initial state
- state = State(x=-0.0, y=5.0, yaw=np.radians(20.0), v=0.0)
-
- last_idx = len(cx) - 1
- time = 0.0
- x = [state.x]
- y = [state.y]
- yaw = [state.yaw]
- v = [state.v]
- t = [0.0]
- target_idx, _ = calc_target_index(state, cx, cy)
-
- while max_simulation_time >= time and last_idx > target_idx:
- ai = pid_control(target_speed, state.v)
- di, target_idx = stanley_control(state, cx, cy, cyaw, target_idx)
- state.update(ai, di)
-
- time += dt
-
- x.append(state.x)
- y.append(state.y)
- yaw.append(state.yaw)
- v.append(state.v)
- t.append(time)
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect('key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(cx, cy, ".r", label="course")
- plt.plot(x, y, "-b", label="trajectory")
- plt.plot(cx[target_idx], cy[target_idx], "xg", label="target")
- plt.axis("equal")
- plt.grid(True)
- plt.title("Speed[km/h]:" + str(state.v * 3.6)[:4])
- plt.pause(0.001)
-
- # Test
- assert last_idx >= target_idx, "Cannot reach goal"
-
- if show_animation: # pragma: no cover
- plt.plot(cx, cy, ".r", label="course")
- plt.plot(x, y, "-b", label="trajectory")
- plt.legend()
- plt.xlabel("x[m]")
- plt.ylabel("y[m]")
- plt.axis("equal")
- plt.grid(True)
-
- plt.subplots(1)
- plt.plot(t, [iv * 3.6 for iv in v], "-r")
- plt.xlabel("Time[s]")
- plt.ylabel("Speed[km/h]")
- plt.grid(True)
- plt.show()
-
-
-if __name__ == '__main__':
- main()
diff --git a/README.md b/README.md
deleted file mode 100644
index 9e605435cee..00000000000
--- a/README.md
+++ /dev/null
@@ -1,658 +0,0 @@
-<img src="https://github.com/AtsushiSakai/PythonRobotics/raw/master/icon.png?raw=true" align="right" width="300" alt="header pic"/>
-
-# PythonRobotics
-
-
-
-[](https://ci.appveyor.com/project/AtsushiSakai/pythonrobotics)
-
-Python codes and [textbook](https://atsushisakai.github.io/PythonRobotics/index.html) for robotics algorithm.
-
-
-# Table of Contents
- * [What is this?](#what-is-this)
- * [Requirements](#requirements)
- * [Documentation](#documentation)
- * [How to use](#how-to-use)
- * [Localization](#localization)
- * [Extended Kalman Filter localization](#extended-kalman-filter-localization)
- * [Particle filter localization](#particle-filter-localization)
- * [Histogram filter localization](#histogram-filter-localization)
- * [Mapping](#mapping)
- * [Gaussian grid map](#gaussian-grid-map)
- * [Ray casting grid map](#ray-casting-grid-map)
- * [Lidar to grid map](#lidar-to-grid-map)
- * [k-means object clustering](#k-means-object-clustering)
- * [Rectangle fitting](#rectangle-fitting)
- * [SLAM](#slam)
- * [Iterative Closest Point (ICP) Matching](#iterative-closest-point-icp-matching)
- * [FastSLAM 1.0](#fastslam-10)
- * [Path Planning](#path-planning)
- * [Dynamic Window Approach](#dynamic-window-approach)
- * [Grid based search](#grid-based-search)
- * [Dijkstra algorithm](#dijkstra-algorithm)
- * [A* algorithm](#a-algorithm)
- * [D* algorithm](#d-algorithm)
- * [D* Lite algorithm](#d-lite-algorithm)
- * [Potential Field algorithm](#potential-field-algorithm)
- * [Grid based coverage path planning](#grid-based-coverage-path-planning)
- * [State Lattice Planning](#state-lattice-planning)
- * [Biased polar sampling](#biased-polar-sampling)
- * [Lane sampling](#lane-sampling)
- * [Probabilistic Road-Map (PRM) planning](#probabilistic-road-map-prm-planning)
- * [Rapidly-Exploring Random Trees (RRT)](#rapidly-exploring-random-trees-rrt)
- * [RRT*](#rrt)
- * [RRT* with reeds-shepp path](#rrt-with-reeds-shepp-path)
- * [LQR-RRT*](#lqr-rrt)
- * [Quintic polynomials planning](#quintic-polynomials-planning)
- * [Reeds Shepp planning](#reeds-shepp-planning)
- * [LQR based path planning](#lqr-based-path-planning)
- * [Optimal Trajectory in a Frenet Frame](#optimal-trajectory-in-a-frenet-frame)
- * [Path Tracking](#path-tracking)
- * [move to a pose control](#move-to-a-pose-control)
- * [Stanley control](#stanley-control)
- * [Rear wheel feedback control](#rear-wheel-feedback-control)
- * [Linear–quadratic regulator (LQR) speed and steering control](#linearquadratic-regulator-lqr-speed-and-steering-control)
- * [Model predictive speed and steering control](#model-predictive-speed-and-steering-control)
- * [Nonlinear Model predictive control with C-GMRES](#nonlinear-model-predictive-control-with-c-gmres)
- * [Arm Navigation](#arm-navigation)
- * [N joint arm to point control](#n-joint-arm-to-point-control)
- * [Arm navigation with obstacle avoidance](#arm-navigation-with-obstacle-avoidance)
- * [Aerial Navigation](#aerial-navigation)
- * [drone 3d trajectory following](#drone-3d-trajectory-following)
- * [rocket powered landing](#rocket-powered-landing)
- * [Bipedal](#bipedal)
- * [bipedal planner with inverted pendulum](#bipedal-planner-with-inverted-pendulum)
- * [License](#license)
- * [Use-case](#use-case)
- * [Contribution](#contribution)
- * [Citing](#citing)
- * [Support](#support)
- * [Sponsors](#sponsors)
- * [JetBrains](#JetBrains)
- * [1Password](#1password)
- * [Authors](#authors)
-
-# What is PythonRobotics?
-
-PythonRobotics is a Python code collection and a [textbook](https://atsushisakai.github.io/PythonRobotics/index.html) of robotics algorithms.
-
-Features:
-
-1. Easy to read for understanding each algorithm's basic idea.
-
-2. Widely used and practical algorithms are selected.
-
-3. Minimum dependency.
-
-See this documentation
-
-- [Getting Started — PythonRobotics documentation](https://atsushisakai.github.io/PythonRobotics/getting_started.html#what-is-pythonrobotics)
-
-or this Youtube video:
-
-- [PythonRobotics project audio overview](https://www.youtube.com/watch?v=uMeRnNoJAfU)
-
-or this paper for more details:
-
-- [\[1808\.10703\] PythonRobotics: a Python code collection of robotics algorithms](https://arxiv.org/abs/1808.10703) ([BibTeX](https://github.com/AtsushiSakai/PythonRoboticsPaper/blob/master/python_robotics.bib))
-
-
-# Requirements to run the code
-
-For running each sample code:
-
-- [Python 3.12.x](https://www.python.org/)
-
-- [NumPy](https://numpy.org/)
-
-- [SciPy](https://scipy.org/)
-
-- [Matplotlib](https://matplotlib.org/)
-
-- [cvxpy](https://www.cvxpy.org/)
-
-For development:
-
-- [pytest](https://pytest.org/) (for unit tests)
-
-- [pytest-xdist](https://pypi.org/project/pytest-xdist/) (for parallel unit tests)
-
-- [mypy](https://mypy-lang.org/) (for type check)
-
-- [sphinx](https://www.sphinx-doc.org/) (for document generation)
-
-- [pycodestyle](https://pypi.org/project/pycodestyle/) (for code style check)
-
-# Documentation (Textbook)
-
-This README only shows some examples of this project.
-
-If you are interested in other examples or mathematical backgrounds of each algorithm,
-
-You can check the full documentation (textbook) online: [Welcome to PythonRobotics’s documentation\! — PythonRobotics documentation](https://atsushisakai.github.io/PythonRobotics/index.html)
-
-All animation gifs are stored here: [AtsushiSakai/PythonRoboticsGifs: Animation gifs of PythonRobotics](https://github.com/AtsushiSakai/PythonRoboticsGifs)
-
-# How to use
-
-1. Clone this repo.
-
- ```terminal
- git clone https://github.com/AtsushiSakai/PythonRobotics.git
- ```
-
-
-2. Install the required libraries.
-
-- using conda :
-
- ```terminal
- conda env create -f requirements/environment.yml
- ```
-
-- using pip :
-
- ```terminal
- pip install -r requirements/requirements.txt
- ```
-
-
-3. Execute python script in each directory.
-
-4. Add star to this repo if you like it :smiley:.
-
-# Localization
-
-## Extended Kalman Filter localization
-
-<img src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/extended_kalman_filter/animation.gif" width="640" alt="EKF pic">
-
-Ref:
-
-- [documentation](https://atsushisakai.github.io/PythonRobotics/modules/localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization.html)
-
-## Particle filter localization
-
-
-
-This is a sensor fusion localization with Particle Filter(PF).
-
-The blue line is true trajectory, the black line is dead reckoning trajectory,
-
-and the red line is an estimated trajectory with PF.
-
-It is assumed that the robot can measure a distance from landmarks (RFID).
-
-These measurements are used for PF localization.
-
-Ref:
-
-- [PROBABILISTIC ROBOTICS](http://www.probabilistic-robotics.org/)
-
-
-## Histogram filter localization
-
-
-
-This is a 2D localization example with Histogram filter.
-
-The red cross is true position, black points are RFID positions.
-
-The blue grid shows a position probability of histogram filter.
-
-In this simulation, x,y are unknown, yaw is known.
-
-The filter integrates speed input and range observations from RFID for localization.
-
-Initial position is not needed.
-
-Ref:
-
-- [PROBABILISTIC ROBOTICS](http://www.probabilistic-robotics.org/)
-
-# Mapping
-
-## Gaussian grid map
-
-This is a 2D Gaussian grid mapping example.
-
-
-
-## Ray casting grid map
-
-This is a 2D ray casting grid mapping example.
-
-
-
-## Lidar to grid map
-
-This example shows how to convert a 2D range measurement to a grid map.
-
-
-
-## k-means object clustering
-
-This is a 2D object clustering with k-means algorithm.
-
-
-
-## Rectangle fitting
-
-This is a 2D rectangle fitting for vehicle detection.
-
-
-
-
-# SLAM
-
-Simultaneous Localization and Mapping(SLAM) examples
-
-## Iterative Closest Point (ICP) Matching
-
-This is a 2D ICP matching example with singular value decomposition.
-
-It can calculate a rotation matrix, and a translation vector between points and points.
-
-
-
-Ref:
-
-- [Introduction to Mobile Robotics: Iterative Closest Point Algorithm](https://cs.gmu.edu/~kosecka/cs685/cs685-icp.pdf)
-
-
-## FastSLAM 1.0
-
-This is a feature based SLAM example using FastSLAM 1.0.
-
-The blue line is ground truth, the black line is dead reckoning, the red line is the estimated trajectory with FastSLAM.
-
-The red points are particles of FastSLAM.
-
-Black points are landmarks, blue crosses are estimated landmark positions by FastSLAM.
-
-
-
-
-
-Ref:
-
-- [PROBABILISTIC ROBOTICS](http://www.probabilistic-robotics.org/)
-
-- [SLAM simulations by Tim Bailey](http://www-personal.acfr.usyd.edu.au/tbailey/software/slam_simulations.htm)
-
-
-# Path Planning
-
-## Dynamic Window Approach
-
-This is a 2D navigation sample code with Dynamic Window Approach.
-
-- [The Dynamic Window Approach to Collision Avoidance](https://www.ri.cmu.edu/pub_files/pub1/fox_dieter_1997_1/fox_dieter_1997_1.pdf)
-
-
-
-
-## Grid based search
-
-### Dijkstra algorithm
-
-This is a 2D grid based the shortest path planning with Dijkstra's algorithm.
-
-
-
-In the animation, cyan points are searched nodes.
-
-### A\* algorithm
-
-This is a 2D grid based the shortest path planning with A star algorithm.
-
-
-
-In the animation, cyan points are searched nodes.
-
-Its heuristic is 2D Euclid distance.
-
-### D\* algorithm
-
-This is a 2D grid based the shortest path planning with D star algorithm.
-
-
-
-The animation shows a robot finding its path avoiding an obstacle using the D* search algorithm.
-
-Ref:
-
-- [D* Algorithm Wikipedia](https://en.wikipedia.org/wiki/D*)
-
-### D\* Lite algorithm
-
-This algorithm finds the shortest path between two points while rerouting when obstacles are discovered. It has been implemented here for a 2D grid.
-
-
-
-The animation shows a robot finding its path and rerouting to avoid obstacles as they are discovered using the D* Lite search algorithm.
-
-Refs:
-
-- [D* Lite](http://idm-lab.org/bib/abstracts/papers/aaai02b.pdf)
-- [Improved Fast Replanning for Robot Navigation in Unknown Terrain](http://www.cs.cmu.edu/~maxim/files/dlite_icra02.pdf)
-
-### Potential Field algorithm
-
-This is a 2D grid based path planning with Potential Field algorithm.
-
-
-
-In the animation, the blue heat map shows potential value on each grid.
-
-Ref:
-
-- [Robotic Motion Planning:Potential Functions](https://www.cs.cmu.edu/~motionplanning/lecture/Chap4-Potential-Field_howie.pdf)
-
-### Grid based coverage path planning
-
-This is a 2D grid based coverage path planning simulation.
-
-
-
-## State Lattice Planning
-
-This script is a path planning code with state lattice planning.
-
-This code uses the model predictive trajectory generator to solve boundary problem.
-
-Ref:
-
-- [Optimal rough terrain trajectory generation for wheeled mobile robots](https://journals.sagepub.com/doi/pdf/10.1177/0278364906075328)
-
-- [State Space Sampling of Feasible Motions for High-Performance Mobile Robot Navigation in Complex Environments](https://www.frc.ri.cmu.edu/~alonzo/pubs/papers/JFR_08_SS_Sampling.pdf)
-
-
-### Biased polar sampling
-
-
-
-
-### Lane sampling
-
-
-
-## Probabilistic Road-Map (PRM) planning
-
-
-
-This PRM planner uses Dijkstra method for graph search.
-
-In the animation, blue points are sampled points,
-
-Cyan crosses means searched points with Dijkstra method,
-
-The red line is the final path of PRM.
-
-Ref:
-
-- [Probabilistic roadmap \- Wikipedia](https://en.wikipedia.org/wiki/Probabilistic_roadmap)
-
-
-
-## Rapidly-Exploring Random Trees (RRT)
-
-### RRT\*
-
-
-
-This is a path planning code with RRT\*
-
-Black circles are obstacles, green line is a searched tree, red crosses are start and goal positions.
-
-Ref:
-
-- [Incremental Sampling-based Algorithms for Optimal Motion Planning](https://arxiv.org/abs/1005.0416)
-
-- [Sampling-based Algorithms for Optimal Motion Planning](https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=bddbc99f97173430aa49a0ada53ab5bade5902fa)
-
-### RRT\* with reeds-shepp path
-
-
-
-Path planning for a car robot with RRT\* and reeds shepp path planner.
-
-### LQR-RRT\*
-
-This is a path planning simulation with LQR-RRT\*.
-
-A double integrator motion model is used for LQR local planner.
-
-
-
-Ref:
-
-- [LQR\-RRT\*: Optimal Sampling\-Based Motion Planning with Automatically Derived Extension Heuristics](https://lis.csail.mit.edu/pubs/perez-icra12.pdf)
-
-- [MahanFathi/LQR\-RRTstar: LQR\-RRT\* method is used for random motion planning of a simple pendulum in its phase plot](https://github.com/MahanFathi/LQR-RRTstar)
-
-
-## Quintic polynomials planning
-
-Motion planning with quintic polynomials.
-
-
-
-It can calculate a 2D path, velocity, and acceleration profile based on quintic polynomials.
-
-Ref:
-
-- [Local Path Planning And Motion Control For Agv In Positioning](https://ieeexplore.ieee.org/document/637936/)
-
-## Reeds Shepp planning
-
-A sample code with Reeds Shepp path planning.
-
-
-
-Ref:
-
-- [15.3.2 Reeds\-Shepp Curves](http://planning.cs.uiuc.edu/node822.html)
-
-- [optimal paths for a car that goes both forwards and backwards](https://pdfs.semanticscholar.org/932e/c495b1d0018fd59dee12a0bf74434fac7af4.pdf)
-
-- [ghliu/pyReedsShepp: Implementation of Reeds Shepp curve\.](https://github.com/ghliu/pyReedsShepp)
-
-
-## LQR based path planning
-
-A sample code using LQR based path planning for double integrator model.
-
-
-
-
-## Optimal Trajectory in a Frenet Frame
-
-
-
-This is optimal trajectory generation in a Frenet Frame.
-
-The cyan line is the target course and black crosses are obstacles.
-
-The red line is the predicted path.
-
-Ref:
-
-- [Optimal Trajectory Generation for Dynamic Street Scenarios in a Frenet Frame](https://www.researchgate.net/profile/Moritz_Werling/publication/224156269_Optimal_Trajectory_Generation_for_Dynamic_Street_Scenarios_in_a_Frenet_Frame/links/54f749df0cf210398e9277af.pdf)
-
-- [Optimal trajectory generation for dynamic street scenarios in a Frenet Frame](https://www.youtube.com/watch?v=Cj6tAQe7UCY)
-
-
-# Path Tracking
-
-## move to a pose control
-
-This is a simulation of moving to a pose control
-
-
-
-Ref:
-
-- [P. I. Corke, "Robotics, Vision and Control" \| SpringerLink p102](https://link.springer.com/book/10.1007/978-3-642-20144-8)
-
-
-## Stanley control
-
-Path tracking simulation with Stanley steering control and PID speed control.
-
-
-
-Ref:
-
-- [Stanley: The robot that won the DARPA grand challenge](http://robots.stanford.edu/papers/thrun.stanley05.pdf)
-
-- [Automatic Steering Methods for Autonomous Automobile Path Tracking](https://www.ri.cmu.edu/pub_files/2009/2/Automatic_Steering_Methods_for_Autonomous_Automobile_Path_Tracking.pdf)
-
-
-
-## Rear wheel feedback control
-
-Path tracking simulation with rear wheel feedback steering control and PID speed control.
-
-
-
-Ref:
-
-- [A Survey of Motion Planning and Control Techniques for Self-driving Urban Vehicles](https://arxiv.org/abs/1604.07446)
-
-
-## Linear–quadratic regulator (LQR) speed and steering control
-
-Path tracking simulation with LQR speed and steering control.
-
-
-
-Ref:
-
-- [Towards fully autonomous driving: Systems and algorithms \- IEEE Conference Publication](https://ieeexplore.ieee.org/document/5940562/)
-
-
-## Model predictive speed and steering control
-
-Path tracking simulation with iterative linear model predictive speed and steering control.
-
-<img src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/model_predictive_speed_and_steer_control/animation.gif" width="640" alt="MPC pic">
-
-Ref:
-
-- [documentation](https://atsushisakai.github.io/PythonRobotics/modules/path_tracking/model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control.html)
-
-- [Real\-time Model Predictive Control \(MPC\), ACADO, Python \| Work\-is\-Playing](http://grauonline.de/wordpress/?page_id=3244)
-
-## Nonlinear Model predictive control with C-GMRES
-
-A motion planning and path tracking simulation with NMPC of C-GMRES
-
-
-
-Ref:
-
-- [documentation](https://atsushisakai.github.io/PythonRobotics/modules/path_tracking/cgmres_nmpc/cgmres_nmpc.html)
-
-
-# Arm Navigation
-
-## N joint arm to point control
-
-N joint arm to a point control simulation.
-
-This is an interactive simulation.
-
-You can set the goal position of the end effector with left-click on the plotting area.
-
-
-
-In this simulation N = 10, however, you can change it.
-
-## Arm navigation with obstacle avoidance
-
-Arm navigation with obstacle avoidance simulation.
-
-
-
-
-# Aerial Navigation
-
-## drone 3d trajectory following
-
-This is a 3d trajectory following simulation for a quadrotor.
-
-
-
-## rocket powered landing
-
-This is a 3d trajectory generation simulation for a rocket powered landing.
-
-
-
-Ref:
-
-- [documentation](https://atsushisakai.github.io/PythonRobotics/modules/aerial_navigation/rocket_powered_landing/rocket_powered_landing.html)
-
-# Bipedal
-
-## bipedal planner with inverted pendulum
-
-This is a bipedal planner for modifying footsteps for an inverted pendulum.
-
-You can set the footsteps, and the planner will modify those automatically.
-
-
-
-# License
-
-MIT
-
-# Use-case
-
-If this project helps your robotics project, please let me know with creating an issue.
-
-Your robot's video, which is using PythonRobotics, is very welcome!!
-
-This is a list of user's comment and references:[users\_comments](https://github.com/AtsushiSakai/PythonRobotics/blob/master/users_comments.md)
-
-# Contribution
-
-Any contribution is welcome!!
-
-Please check this document:[How To Contribute — PythonRobotics documentation](https://atsushisakai.github.io/PythonRobotics/modules/0_getting_started/3_how_to_contribute.html)
-
-# Citing
-
-If you use this project's code for your academic work, we encourage you to cite [our papers](https://arxiv.org/abs/1808.10703)
-
-If you use this project's code in industry, we'd love to hear from you as well; feel free to reach out to the developers directly.
-
-# <a id="support"></a>Supporting this project
-
-If you or your company would like to support this project, please consider:
-
-- [Sponsor @AtsushiSakai on GitHub Sponsors](https://github.com/sponsors/AtsushiSakai)
-
-- [Become a backer or sponsor on Patreon](https://www.patreon.com/myenigma)
-
-- [One-time donation via PayPal](https://www.paypal.com/paypalme/myenigmapay/)
-
-If you would like to support us in some other way, please contact with creating an issue.
-
-## <a id="sponsors"></a>Sponsors
-
-### <a id="JetBrains"></a>[JetBrains](https://www.jetbrains.com/)
-
-They are providing a free license of their IDEs for this OSS development.
-
-### [1Password](https://github.com/1Password/for-open-source)
-
-They are providing a free license of their 1Password team license for this OSS project.
-
-
-# Authors
-
-- [Contributors to AtsushiSakai/PythonRobotics](https://github.com/AtsushiSakai/PythonRobotics/graphs/contributors)
-
diff --git a/SECURITY.md b/SECURITY.md
deleted file mode 100644
index 53dcafa450c..00000000000
--- a/SECURITY.md
+++ /dev/null
@@ -1,13 +0,0 @@
-# Security Policy
-
-## Supported Versions
-
-In this project, we are only support latest code.
-
-| Version | Supported |
-| ------- | ------------------ |
-| latest | :white_check_mark: |
-
-## Reporting a Vulnerability
-
-If you find any security related problem, let us know by creating an issue about it.
diff --git a/SLAM/EKFSLAM/ekf_slam.py b/SLAM/EKFSLAM/ekf_slam.py
deleted file mode 100644
index 5c4417d7c34..00000000000
--- a/SLAM/EKFSLAM/ekf_slam.py
+++ /dev/null
@@ -1,263 +0,0 @@
-"""
-Extended Kalman Filter SLAM example
-
-author: Atsushi Sakai (@Atsushi_twi)
-"""
-
-import math
-
-import matplotlib.pyplot as plt
-import numpy as np
-from utils.angle import angle_mod
-
-# EKF state covariance
-Cx = np.diag([0.5, 0.5, np.deg2rad(30.0)]) ** 2
-
-# Simulation parameter
-Q_sim = np.diag([0.2, np.deg2rad(1.0)]) ** 2
-R_sim = np.diag([1.0, np.deg2rad(10.0)]) ** 2
-
-DT = 0.1 # time tick [s]
-SIM_TIME = 50.0 # simulation time [s]
-MAX_RANGE = 20.0 # maximum observation range
-M_DIST_TH = 2.0 # Threshold of Mahalanobis distance for data association.
-STATE_SIZE = 3 # State size [x,y,yaw]
-LM_SIZE = 2 # LM state size [x,y]
-
-show_animation = True
-
-
-def ekf_slam(xEst, PEst, u, z):
- # Predict
- G, Fx = jacob_motion(xEst, u)
- xEst[0:STATE_SIZE] = motion_model(xEst[0:STATE_SIZE], u)
- PEst = G.T @ PEst @ G + Fx.T @ Cx @ Fx
- initP = np.eye(2)
-
- # Update
- for iz in range(len(z[:, 0])): # for each observation
- min_id = search_correspond_landmark_id(xEst, PEst, z[iz, 0:2])
-
- nLM = calc_n_lm(xEst)
- if min_id == nLM:
- print("New LM")
- # Extend state and covariance matrix
- xAug = np.vstack((xEst, calc_landmark_position(xEst, z[iz, :])))
- PAug = np.vstack((np.hstack((PEst, np.zeros((len(xEst), LM_SIZE)))),
- np.hstack((np.zeros((LM_SIZE, len(xEst))), initP))))
- xEst = xAug
- PEst = PAug
- lm = get_landmark_position_from_state(xEst, min_id)
- y, S, H = calc_innovation(lm, xEst, PEst, z[iz, 0:2], min_id)
-
- K = (PEst @ H.T) @ np.linalg.inv(S)
- xEst = xEst + (K @ y)
- PEst = (np.eye(len(xEst)) - (K @ H)) @ PEst
-
- xEst[2] = pi_2_pi(xEst[2])
-
- return xEst, PEst
-
-
-def calc_input():
- v = 1.0 # [m/s]
- yaw_rate = 0.1 # [rad/s]
- u = np.array([[v, yaw_rate]]).T
- return u
-
-
-def observation(xTrue, xd, u, RFID):
- xTrue = motion_model(xTrue, u)
-
- # add noise to gps x-y
- z = np.zeros((0, 3))
-
- for i in range(len(RFID[:, 0])):
-
- dx = RFID[i, 0] - xTrue[0, 0]
- dy = RFID[i, 1] - xTrue[1, 0]
- d = math.hypot(dx, dy)
- angle = pi_2_pi(math.atan2(dy, dx) - xTrue[2, 0])
- if d <= MAX_RANGE:
- dn = d + np.random.randn() * Q_sim[0, 0] ** 0.5 # add noise
- angle_n = angle + np.random.randn() * Q_sim[1, 1] ** 0.5 # add noise
- zi = np.array([dn, angle_n, i])
- z = np.vstack((z, zi))
-
- # add noise to input
- ud = np.array([[
- u[0, 0] + np.random.randn() * R_sim[0, 0] ** 0.5,
- u[1, 0] + np.random.randn() * R_sim[1, 1] ** 0.5]]).T
-
- xd = motion_model(xd, ud)
- return xTrue, z, xd, ud
-
-
-def motion_model(x, u):
- F = np.array([[1.0, 0, 0],
- [0, 1.0, 0],
- [0, 0, 1.0]])
-
- B = np.array([[DT * math.cos(x[2, 0]), 0],
- [DT * math.sin(x[2, 0]), 0],
- [0.0, DT]])
-
- x = (F @ x) + (B @ u)
- return x
-
-
-def calc_n_lm(x):
- n = int((len(x) - STATE_SIZE) / LM_SIZE)
- return n
-
-
-def jacob_motion(x, u):
- Fx = np.hstack((np.eye(STATE_SIZE), np.zeros(
- (STATE_SIZE, LM_SIZE * calc_n_lm(x)))))
-
- jF = np.array([[0.0, 0.0, -DT * u[0, 0] * math.sin(x[2, 0])],
- [0.0, 0.0, DT * u[0, 0] * math.cos(x[2, 0])],
- [0.0, 0.0, 0.0]], dtype=float)
-
- G = np.eye(len(x)) + Fx.T @ jF @ Fx
-
- return G, Fx,
-
-
-def calc_landmark_position(x, z):
- zp = np.zeros((2, 1))
-
- zp[0, 0] = x[0, 0] + z[0] * math.cos(x[2, 0] + z[1])
- zp[1, 0] = x[1, 0] + z[0] * math.sin(x[2, 0] + z[1])
-
- return zp
-
-
-def get_landmark_position_from_state(x, ind):
- lm = x[STATE_SIZE + LM_SIZE * ind: STATE_SIZE + LM_SIZE * (ind + 1), :]
-
- return lm
-
-
-def search_correspond_landmark_id(xAug, PAug, zi):
- """
- Landmark association with Mahalanobis distance
- """
-
- nLM = calc_n_lm(xAug)
-
- min_dist = []
-
- for i in range(nLM):
- lm = get_landmark_position_from_state(xAug, i)
- y, S, H = calc_innovation(lm, xAug, PAug, zi, i)
- min_dist.append(y.T @ np.linalg.inv(S) @ y)
-
- min_dist.append(M_DIST_TH) # new landmark
-
- min_id = min_dist.index(min(min_dist))
-
- return min_id
-
-
-def calc_innovation(lm, xEst, PEst, z, LMid):
- delta = lm - xEst[0:2]
- q = (delta.T @ delta)[0, 0]
- z_angle = math.atan2(delta[1, 0], delta[0, 0]) - xEst[2, 0]
- zp = np.array([[math.sqrt(q), pi_2_pi(z_angle)]])
- y = (z - zp).T
- y[1] = pi_2_pi(y[1])
- H = jacob_h(q, delta, xEst, LMid + 1)
- S = H @ PEst @ H.T + Cx[0:2, 0:2]
-
- return y, S, H
-
-
-def jacob_h(q, delta, x, i):
- sq = math.sqrt(q)
- G = np.array([[-sq * delta[0, 0], - sq * delta[1, 0], 0, sq * delta[0, 0], sq * delta[1, 0]],
- [delta[1, 0], - delta[0, 0], - q, - delta[1, 0], delta[0, 0]]])
-
- G = G / q
- nLM = calc_n_lm(x)
- F1 = np.hstack((np.eye(3), np.zeros((3, 2 * nLM))))
- F2 = np.hstack((np.zeros((2, 3)), np.zeros((2, 2 * (i - 1))),
- np.eye(2), np.zeros((2, 2 * nLM - 2 * i))))
-
- F = np.vstack((F1, F2))
-
- H = G @ F
-
- return H
-
-
-def pi_2_pi(angle):
- return angle_mod(angle)
-
-
-def main():
- print(__file__ + " start!!")
-
- time = 0.0
-
- # RFID positions [x, y]
- RFID = np.array([[10.0, -2.0],
- [15.0, 10.0],
- [3.0, 15.0],
- [-5.0, 20.0]])
-
- # State Vector [x y yaw v]'
- xEst = np.zeros((STATE_SIZE, 1))
- xTrue = np.zeros((STATE_SIZE, 1))
- PEst = np.eye(STATE_SIZE)
-
- xDR = np.zeros((STATE_SIZE, 1)) # Dead reckoning
-
- # history
- hxEst = xEst
- hxTrue = xTrue
- hxDR = xTrue
-
- while SIM_TIME >= time:
- time += DT
- u = calc_input()
-
- xTrue, z, xDR, ud = observation(xTrue, xDR, u, RFID)
-
- xEst, PEst = ekf_slam(xEst, PEst, ud, z)
-
- x_state = xEst[0:STATE_SIZE]
-
- # store data history
- hxEst = np.hstack((hxEst, x_state))
- hxDR = np.hstack((hxDR, xDR))
- hxTrue = np.hstack((hxTrue, xTrue))
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
-
- plt.plot(RFID[:, 0], RFID[:, 1], "*k")
- plt.plot(xEst[0], xEst[1], ".r")
-
- # plot landmark
- for i in range(calc_n_lm(xEst)):
- plt.plot(xEst[STATE_SIZE + i * 2],
- xEst[STATE_SIZE + i * 2 + 1], "xg")
-
- plt.plot(hxTrue[0, :],
- hxTrue[1, :], "-b")
- plt.plot(hxDR[0, :],
- hxDR[1, :], "-k")
- plt.plot(hxEst[0, :],
- hxEst[1, :], "-r")
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.001)
-
-
-if __name__ == '__main__':
- main()
diff --git a/SLAM/FastSLAM1/fast_slam1.py b/SLAM/FastSLAM1/fast_slam1.py
deleted file mode 100644
index 98f8a664177..00000000000
--- a/SLAM/FastSLAM1/fast_slam1.py
+++ /dev/null
@@ -1,394 +0,0 @@
-"""
-
-FastSLAM 1.0 example
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import math
-
-import matplotlib.pyplot as plt
-import numpy as np
-from utils.angle import angle_mod
-
-# Fast SLAM covariance
-Q = np.diag([3.0, np.deg2rad(10.0)]) ** 2
-R = np.diag([1.0, np.deg2rad(20.0)]) ** 2
-
-# Simulation parameter
-Q_SIM = np.diag([0.3, np.deg2rad(2.0)]) ** 2
-R_SIM = np.diag([0.5, np.deg2rad(10.0)]) ** 2
-OFFSET_YAW_RATE_NOISE = 0.01
-
-DT = 0.1 # time tick [s]
-SIM_TIME = 50.0 # simulation time [s]
-MAX_RANGE = 20.0 # maximum observation range
-M_DIST_TH = 2.0 # Threshold of Mahalanobis distance for data association.
-STATE_SIZE = 3 # State size [x,y,yaw]
-LM_SIZE = 2 # LM state size [x,y]
-N_PARTICLE = 100 # number of particle
-NTH = N_PARTICLE / 1.5 # Number of particle for re-sampling
-
-show_animation = True
-
-
-class Particle:
-
- def __init__(self, n_landmark):
- self.w = 1.0 / N_PARTICLE
- self.x = 0.0
- self.y = 0.0
- self.yaw = 0.0
- # landmark x-y positions
- self.lm = np.zeros((n_landmark, LM_SIZE))
- # landmark position covariance
- self.lmP = np.zeros((n_landmark * LM_SIZE, LM_SIZE))
-
-
-def fast_slam1(particles, u, z):
- particles = predict_particles(particles, u)
-
- particles = update_with_observation(particles, z)
-
- particles = resampling(particles)
-
- return particles
-
-
-def normalize_weight(particles):
- sum_w = sum([p.w for p in particles])
-
- try:
- for i in range(N_PARTICLE):
- particles[i].w /= sum_w
- except ZeroDivisionError:
- for i in range(N_PARTICLE):
- particles[i].w = 1.0 / N_PARTICLE
-
- return particles
-
- return particles
-
-
-def calc_final_state(particles):
- x_est = np.zeros((STATE_SIZE, 1))
-
- particles = normalize_weight(particles)
-
- for i in range(N_PARTICLE):
- x_est[0, 0] += particles[i].w * particles[i].x
- x_est[1, 0] += particles[i].w * particles[i].y
- x_est[2, 0] += particles[i].w * particles[i].yaw
-
- x_est[2, 0] = pi_2_pi(x_est[2, 0])
-
- return x_est
-
-
-def predict_particles(particles, u):
- for i in range(N_PARTICLE):
- px = np.zeros((STATE_SIZE, 1))
- px[0, 0] = particles[i].x
- px[1, 0] = particles[i].y
- px[2, 0] = particles[i].yaw
- ud = u + (np.random.randn(1, 2) @ R ** 0.5).T # add noise
- px = motion_model(px, ud)
- particles[i].x = px[0, 0]
- particles[i].y = px[1, 0]
- particles[i].yaw = px[2, 0]
-
- return particles
-
-
-def add_new_landmark(particle, z, Q_cov):
- r = z[0]
- b = z[1]
- lm_id = int(z[2])
-
- s = math.sin(pi_2_pi(particle.yaw + b))
- c = math.cos(pi_2_pi(particle.yaw + b))
-
- particle.lm[lm_id, 0] = particle.x + r * c
- particle.lm[lm_id, 1] = particle.y + r * s
-
- # covariance
- dx = r * c
- dy = r * s
- d2 = dx**2 + dy**2
- d = math.sqrt(d2)
- Gz = np.array([[dx / d, dy / d],
- [-dy / d2, dx / d2]])
- particle.lmP[2 * lm_id:2 * lm_id + 2] = np.linalg.inv(
- Gz) @ Q_cov @ np.linalg.inv(Gz.T)
-
- return particle
-
-
-def compute_jacobians(particle, xf, Pf, Q_cov):
- dx = xf[0, 0] - particle.x
- dy = xf[1, 0] - particle.y
- d2 = dx ** 2 + dy ** 2
- d = math.sqrt(d2)
-
- zp = np.array(
- [d, pi_2_pi(math.atan2(dy, dx) - particle.yaw)]).reshape(2, 1)
-
- Hv = np.array([[-dx / d, -dy / d, 0.0],
- [dy / d2, -dx / d2, -1.0]])
-
- Hf = np.array([[dx / d, dy / d],
- [-dy / d2, dx / d2]])
-
- Sf = Hf @ Pf @ Hf.T + Q_cov
-
- return zp, Hv, Hf, Sf
-
-
-def update_kf_with_cholesky(xf, Pf, v, Q_cov, Hf):
- PHt = Pf @ Hf.T
- S = Hf @ PHt + Q_cov
-
- S = (S + S.T) * 0.5
- s_chol = np.linalg.cholesky(S).T
- s_chol_inv = np.linalg.inv(s_chol)
- W1 = PHt @ s_chol_inv
- W = W1 @ s_chol_inv.T
-
- x = xf + W @ v
- P = Pf - W1 @ W1.T
-
- return x, P
-
-
-def update_landmark(particle, z, Q_cov):
- lm_id = int(z[2])
- xf = np.array(particle.lm[lm_id, :]).reshape(2, 1)
- Pf = np.array(particle.lmP[2 * lm_id:2 * lm_id + 2, :])
-
- zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q)
-
- dz = z[0:2].reshape(2, 1) - zp
- dz[1, 0] = pi_2_pi(dz[1, 0])
-
- xf, Pf = update_kf_with_cholesky(xf, Pf, dz, Q_cov, Hf)
-
- particle.lm[lm_id, :] = xf.T
- particle.lmP[2 * lm_id:2 * lm_id + 2, :] = Pf
-
- return particle
-
-
-def compute_weight(particle, z, Q_cov):
- lm_id = int(z[2])
- xf = np.array(particle.lm[lm_id, :]).reshape(2, 1)
- Pf = np.array(particle.lmP[2 * lm_id:2 * lm_id + 2])
- zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q_cov)
-
- dx = z[0:2].reshape(2, 1) - zp
- dx[1, 0] = pi_2_pi(dx[1, 0])
-
- try:
- invS = np.linalg.inv(Sf)
- except np.linalg.linalg.LinAlgError:
- print("singular")
- return 1.0
-
- num = np.exp(-0.5 * (dx.T @ invS @ dx))[0, 0]
- den = 2.0 * math.pi * math.sqrt(np.linalg.det(Sf))
-
- w = num / den
-
- return w
-
-
-def update_with_observation(particles, z):
- for iz in range(len(z[0, :])):
-
- landmark_id = int(z[2, iz])
-
- for ip in range(N_PARTICLE):
- # new landmark
- if abs(particles[ip].lm[landmark_id, 0]) <= 0.01:
- particles[ip] = add_new_landmark(particles[ip], z[:, iz], Q)
- # known landmark
- else:
- w = compute_weight(particles[ip], z[:, iz], Q)
- particles[ip].w *= w
- particles[ip] = update_landmark(particles[ip], z[:, iz], Q)
-
- return particles
-
-
-def resampling(particles):
- """
- low variance re-sampling
- """
-
- particles = normalize_weight(particles)
-
- pw = []
- for i in range(N_PARTICLE):
- pw.append(particles[i].w)
-
- pw = np.array(pw)
-
- n_eff = 1.0 / (pw @ pw.T) # Effective particle number
-
- if n_eff < NTH: # resampling
- w_cum = np.cumsum(pw)
- base = np.cumsum(pw * 0.0 + 1 / N_PARTICLE) - 1 / N_PARTICLE
- resample_id = base + np.random.rand(base.shape[0]) / N_PARTICLE
-
- indexes = []
- index = 0
- for ip in range(N_PARTICLE):
- while (index < w_cum.shape[0] - 1) \
- and (resample_id[ip] > w_cum[index]):
- index += 1
- indexes.append(index)
-
- tmp_particles = particles[:]
- for i in range(len(indexes)):
- particles[i].x = tmp_particles[indexes[i]].x
- particles[i].y = tmp_particles[indexes[i]].y
- particles[i].yaw = tmp_particles[indexes[i]].yaw
- particles[i].lm = tmp_particles[indexes[i]].lm[:, :]
- particles[i].lmP = tmp_particles[indexes[i]].lmP[:, :]
- particles[i].w = 1.0 / N_PARTICLE
-
- return particles
-
-
-def calc_input(time):
- if time <= 3.0: # wait at first
- v = 0.0
- yaw_rate = 0.0
- else:
- v = 1.0 # [m/s]
- yaw_rate = 0.1 # [rad/s]
-
- u = np.array([v, yaw_rate]).reshape(2, 1)
-
- return u
-
-
-def observation(x_true, xd, u, rfid):
- # calc true state
- x_true = motion_model(x_true, u)
-
- # add noise to range observation
- z = np.zeros((3, 0))
- for i in range(len(rfid[:, 0])):
-
- dx = rfid[i, 0] - x_true[0, 0]
- dy = rfid[i, 1] - x_true[1, 0]
- d = math.hypot(dx, dy)
- angle = pi_2_pi(math.atan2(dy, dx) - x_true[2, 0])
- if d <= MAX_RANGE:
- dn = d + np.random.randn() * Q_SIM[0, 0] ** 0.5 # add noise
- angle_with_noize = angle + np.random.randn() * Q_SIM[
- 1, 1] ** 0.5 # add noise
- zi = np.array([dn, pi_2_pi(angle_with_noize), i]).reshape(3, 1)
- z = np.hstack((z, zi))
-
- # add noise to input
- ud1 = u[0, 0] + np.random.randn() * R_SIM[0, 0] ** 0.5
- ud2 = u[1, 0] + np.random.randn() * R_SIM[
- 1, 1] ** 0.5 + OFFSET_YAW_RATE_NOISE
- ud = np.array([ud1, ud2]).reshape(2, 1)
-
- xd = motion_model(xd, ud)
-
- return x_true, z, xd, ud
-
-
-def motion_model(x, u):
- F = np.array([[1.0, 0, 0],
- [0, 1.0, 0],
- [0, 0, 1.0]])
-
- B = np.array([[DT * math.cos(x[2, 0]), 0],
- [DT * math.sin(x[2, 0]), 0],
- [0.0, DT]])
-
- x = F @ x + B @ u
-
- x[2, 0] = pi_2_pi(x[2, 0])
-
- return x
-
-
-def pi_2_pi(angle):
- return angle_mod(angle)
-
-
-def main():
- print(__file__ + " start!!")
-
- time = 0.0
-
- # RFID positions [x, y]
- rfid = np.array([[10.0, -2.0],
- [15.0, 10.0],
- [15.0, 15.0],
- [10.0, 20.0],
- [3.0, 15.0],
- [-5.0, 20.0],
- [-5.0, 5.0],
- [-10.0, 15.0]
- ])
- n_landmark = rfid.shape[0]
-
- # State Vector [x y yaw v]'
- x_est = np.zeros((STATE_SIZE, 1)) # SLAM estimation
- x_true = np.zeros((STATE_SIZE, 1)) # True state
- x_dr = np.zeros((STATE_SIZE, 1)) # Dead reckoning
-
- # history
- hist_x_est = x_est
- hist_x_true = x_true
- hist_x_dr = x_dr
-
- particles = [Particle(n_landmark) for _ in range(N_PARTICLE)]
-
- while SIM_TIME >= time:
- time += DT
- u = calc_input(time)
-
- x_true, z, x_dr, ud = observation(x_true, x_dr, u, rfid)
-
- particles = fast_slam1(particles, ud, z)
-
- x_est = calc_final_state(particles)
-
- x_state = x_est[0: STATE_SIZE]
-
- # store data history
- hist_x_est = np.hstack((hist_x_est, x_state))
- hist_x_dr = np.hstack((hist_x_dr, x_dr))
- hist_x_true = np.hstack((hist_x_true, x_true))
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event', lambda event:
- [exit(0) if event.key == 'escape' else None])
- plt.plot(rfid[:, 0], rfid[:, 1], "*k")
-
- for i in range(N_PARTICLE):
- plt.plot(particles[i].x, particles[i].y, ".r")
- plt.plot(particles[i].lm[:, 0], particles[i].lm[:, 1], "xb")
-
- plt.plot(hist_x_true[0, :], hist_x_true[1, :], "-b")
- plt.plot(hist_x_dr[0, :], hist_x_dr[1, :], "-k")
- plt.plot(hist_x_est[0, :], hist_x_est[1, :], "-r")
- plt.plot(x_est[0], x_est[1], "xk")
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.001)
-
-
-if __name__ == '__main__':
- main()
diff --git a/SLAM/FastSLAM2/fast_slam2.py b/SLAM/FastSLAM2/fast_slam2.py
deleted file mode 100644
index d4cf0d84ddd..00000000000
--- a/SLAM/FastSLAM2/fast_slam2.py
+++ /dev/null
@@ -1,426 +0,0 @@
-"""
-
-FastSLAM 2.0 example
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-"""
-
-import math
-
-import matplotlib.pyplot as plt
-import numpy as np
-from utils.angle import angle_mod
-
-# Fast SLAM covariance
-Q = np.diag([3.0, np.deg2rad(10.0)]) ** 2
-R = np.diag([1.0, np.deg2rad(20.0)]) ** 2
-
-# Simulation parameter
-Q_SIM = np.diag([0.3, np.deg2rad(2.0)]) ** 2
-R_SIM = np.diag([0.5, np.deg2rad(10.0)]) ** 2
-OFFSET_YAW_RATE_NOISE = 0.01
-
-DT = 0.1 # time tick [s]
-SIM_TIME = 50.0 # simulation time [s]
-MAX_RANGE = 20.0 # maximum observation range
-M_DIST_TH = 2.0 # Threshold of Mahalanobis distance for data association.
-STATE_SIZE = 3 # State size [x,y,yaw]
-LM_SIZE = 2 # LM state size [x,y]
-N_PARTICLE = 100 # number of particle
-NTH = N_PARTICLE / 1.5 # Number of particle for re-sampling
-
-show_animation = True
-
-
-class Particle:
-
- def __init__(self, n_landmark):
- self.w = 1.0 / N_PARTICLE
- self.x = 0.0
- self.y = 0.0
- self.yaw = 0.0
- self.P = np.eye(3)
- # landmark x-y positions
- self.lm = np.zeros((n_landmark, LM_SIZE))
- # landmark position covariance
- self.lmP = np.zeros((n_landmark * LM_SIZE, LM_SIZE))
-
-
-def fast_slam2(particles, u, z):
- particles = predict_particles(particles, u)
-
- particles = update_with_observation(particles, z)
-
- particles = resampling(particles)
-
- return particles
-
-
-def normalize_weight(particles):
- sum_w = sum([p.w for p in particles])
-
- try:
- for i in range(N_PARTICLE):
- particles[i].w /= sum_w
- except ZeroDivisionError:
- for i in range(N_PARTICLE):
- particles[i].w = 1.0 / N_PARTICLE
-
- return particles
-
- return particles
-
-
-def calc_final_state(particles):
- x_est = np.zeros((STATE_SIZE, 1))
-
- particles = normalize_weight(particles)
-
- for i in range(N_PARTICLE):
- x_est[0, 0] += particles[i].w * particles[i].x
- x_est[1, 0] += particles[i].w * particles[i].y
- x_est[2, 0] += particles[i].w * particles[i].yaw
-
- x_est[2, 0] = pi_2_pi(x_est[2, 0])
-
- return x_est
-
-
-def predict_particles(particles, u):
- for i in range(N_PARTICLE):
- px = np.zeros((STATE_SIZE, 1))
- px[0, 0] = particles[i].x
- px[1, 0] = particles[i].y
- px[2, 0] = particles[i].yaw
- ud = u + (np.random.randn(1, 2) @ R ** 0.5).T # add noise
- px = motion_model(px, ud)
- particles[i].x = px[0, 0]
- particles[i].y = px[1, 0]
- particles[i].yaw = px[2, 0]
-
- return particles
-
-
-def add_new_lm(particle, z, Q_cov):
- r = z[0]
- b = z[1]
- lm_id = int(z[2])
-
- s = math.sin(pi_2_pi(particle.yaw + b))
- c = math.cos(pi_2_pi(particle.yaw + b))
-
- particle.lm[lm_id, 0] = particle.x + r * c
- particle.lm[lm_id, 1] = particle.y + r * s
-
- # covariance
- dx = r * c
- dy = r * s
- d2 = dx ** 2 + dy ** 2
- d = math.sqrt(d2)
- Gz = np.array([[dx / d, dy / d],
- [-dy / d2, dx / d2]])
- particle.lmP[2 * lm_id:2 * lm_id + 2] = np.linalg.inv(
- Gz) @ Q_cov @ np.linalg.inv(Gz.T)
-
- return particle
-
-
-def compute_jacobians(particle, xf, Pf, Q_cov):
- dx = xf[0, 0] - particle.x
- dy = xf[1, 0] - particle.y
- d2 = dx ** 2 + dy ** 2
- d = math.sqrt(d2)
-
- zp = np.array(
- [d, pi_2_pi(math.atan2(dy, dx) - particle.yaw)]).reshape(2, 1)
-
- Hv = np.array([[-dx / d, -dy / d, 0.0],
- [dy / d2, -dx / d2, -1.0]])
-
- Hf = np.array([[dx / d, dy / d],
- [-dy / d2, dx / d2]])
-
- Sf = Hf @ Pf @ Hf.T + Q_cov
-
- return zp, Hv, Hf, Sf
-
-
-def update_kf_with_cholesky(xf, Pf, v, Q_cov, Hf):
- PHt = Pf @ Hf.T
- S = Hf @ PHt + Q_cov
-
- S = (S + S.T) * 0.5
- SChol = np.linalg.cholesky(S).T
- SCholInv = np.linalg.inv(SChol)
- W1 = PHt @ SCholInv
- W = W1 @ SCholInv.T
-
- x = xf + W @ v
- P = Pf - W1 @ W1.T
-
- return x, P
-
-
-def update_landmark(particle, z, Q_cov):
- lm_id = int(z[2])
- xf = np.array(particle.lm[lm_id, :]).reshape(2, 1)
- Pf = np.array(particle.lmP[2 * lm_id:2 * lm_id + 2])
-
- zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q_cov)
-
- dz = z[0:2].reshape(2, 1) - zp
- dz[1, 0] = pi_2_pi(dz[1, 0])
-
- xf, Pf = update_kf_with_cholesky(xf, Pf, dz, Q, Hf)
-
- particle.lm[lm_id, :] = xf.T
- particle.lmP[2 * lm_id:2 * lm_id + 2, :] = Pf
-
- return particle
-
-
-def compute_weight(particle, z, Q_cov):
- lm_id = int(z[2])
- xf = np.array(particle.lm[lm_id, :]).reshape(2, 1)
- Pf = np.array(particle.lmP[2 * lm_id:2 * lm_id + 2])
- zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q_cov)
-
- dz = z[0:2].reshape(2, 1) - zp
- dz[1, 0] = pi_2_pi(dz[1, 0])
-
- try:
- invS = np.linalg.inv(Sf)
- except np.linalg.linalg.LinAlgError:
- return 1.0
-
- num = np.exp(-0.5 * dz.T @ invS @ dz)[0, 0]
- den = 2.0 * math.pi * math.sqrt(np.linalg.det(Sf))
-
- w = num / den
-
- return w
-
-
-def proposal_sampling(particle, z, Q_cov):
- lm_id = int(z[2])
- xf = particle.lm[lm_id, :].reshape(2, 1)
- Pf = particle.lmP[2 * lm_id:2 * lm_id + 2]
- # State
- x = np.array([particle.x, particle.y, particle.yaw]).reshape(3, 1)
- P = particle.P
- zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q_cov)
-
- Sfi = np.linalg.inv(Sf)
- dz = z[0:2].reshape(2, 1) - zp
- dz[1] = pi_2_pi(dz[1])
-
- Pi = np.linalg.inv(P)
-
- particle.P = np.linalg.inv(Hv.T @ Sfi @ Hv + Pi) # proposal covariance
- x += particle.P @ Hv.T @ Sfi @ dz # proposal mean
-
- particle.x = x[0, 0]
- particle.y = x[1, 0]
- particle.yaw = x[2, 0]
-
- return particle
-
-
-def update_with_observation(particles, z):
- for iz in range(len(z[0, :])):
- landmark_id = int(z[2, iz])
-
- for ip in range(N_PARTICLE):
- # new landmark
- if abs(particles[ip].lm[landmark_id, 0]) <= 0.01:
- particles[ip] = add_new_lm(particles[ip], z[:, iz], Q)
- # known landmark
- else:
- w = compute_weight(particles[ip], z[:, iz], Q)
- particles[ip].w *= w
-
- particles[ip] = update_landmark(particles[ip], z[:, iz], Q)
- particles[ip] = proposal_sampling(particles[ip], z[:, iz], Q)
-
- return particles
-
-
-def resampling(particles):
- """
- low variance re-sampling
- """
-
- particles = normalize_weight(particles)
-
- pw = []
- for i in range(N_PARTICLE):
- pw.append(particles[i].w)
-
- pw = np.array(pw)
-
- n_eff = 1.0 / (pw @ pw.T) # Effective particle number
-
- if n_eff < NTH: # resampling
- w_cum = np.cumsum(pw)
- base = np.cumsum(pw * 0.0 + 1 / N_PARTICLE) - 1 / N_PARTICLE
- resample_id = base + np.random.rand(base.shape[0]) / N_PARTICLE
-
- indexes = []
- index = 0
- for ip in range(N_PARTICLE):
- while (index < w_cum.shape[0] - 1) \
- and (resample_id[ip] > w_cum[index]):
- index += 1
- indexes.append(index)
-
- tmp_particles = particles[:]
- for i in range(len(indexes)):
- particles[i].x = tmp_particles[indexes[i]].x
- particles[i].y = tmp_particles[indexes[i]].y
- particles[i].yaw = tmp_particles[indexes[i]].yaw
- particles[i].lm = tmp_particles[indexes[i]].lm[:, :]
- particles[i].lmP = tmp_particles[indexes[i]].lmP[:, :]
- particles[i].w = 1.0 / N_PARTICLE
-
- return particles
-
-
-def calc_input(time):
- if time <= 3.0: # wait at first
- v = 0.0
- yaw_rate = 0.0
- else:
- v = 1.0 # [m/s]
- yaw_rate = 0.1 # [rad/s]
-
- u = np.array([v, yaw_rate]).reshape(2, 1)
-
- return u
-
-
-def observation(x_true, xd, u, rfid):
- # calc true state
- x_true = motion_model(x_true, u)
-
- # add noise to range observation
- z = np.zeros((3, 0))
-
- for i in range(len(rfid[:, 0])):
-
- dx = rfid[i, 0] - x_true[0, 0]
- dy = rfid[i, 1] - x_true[1, 0]
- d = math.hypot(dx, dy)
- angle = pi_2_pi(math.atan2(dy, dx) - x_true[2, 0])
- if d <= MAX_RANGE:
- dn = d + np.random.randn() * Q_SIM[0, 0] ** 0.5 # add noise
- angle_noise = np.random.randn() * Q_SIM[1, 1] ** 0.5
- angle_with_noise = angle + angle_noise # add noise
- zi = np.array([dn, pi_2_pi(angle_with_noise), i]).reshape(3, 1)
- z = np.hstack((z, zi))
-
- # add noise to input
- ud1 = u[0, 0] + np.random.randn() * R_SIM[0, 0] ** 0.5
- ud2 = u[1, 0] + np.random.randn() * R_SIM[
- 1, 1] ** 0.5 + OFFSET_YAW_RATE_NOISE
- ud = np.array([ud1, ud2]).reshape(2, 1)
-
- xd = motion_model(xd, ud)
-
- return x_true, z, xd, ud
-
-
-def motion_model(x, u):
- F = np.array([[1.0, 0, 0],
- [0, 1.0, 0],
- [0, 0, 1.0]])
-
- B = np.array([[DT * math.cos(x[2, 0]), 0],
- [DT * math.sin(x[2, 0]), 0],
- [0.0, DT]])
-
- x = F @ x + B @ u
-
- x[2, 0] = pi_2_pi(x[2, 0])
-
- return x
-
-
-def pi_2_pi(angle):
- return angle_mod(angle)
-
-
-def main():
- print(__file__ + " start!!")
-
- time = 0.0
-
- # RFID positions [x, y]
- rfid = np.array([[10.0, -2.0],
- [15.0, 10.0],
- [15.0, 15.0],
- [10.0, 20.0],
- [3.0, 15.0],
- [-5.0, 20.0],
- [-5.0, 5.0],
- [-10.0, 15.0]
- ])
- n_landmark = rfid.shape[0]
-
- # State Vector [x y yaw v]'
- x_est = np.zeros((STATE_SIZE, 1)) # SLAM estimation
- x_true = np.zeros((STATE_SIZE, 1)) # True state
- x_dr = np.zeros((STATE_SIZE, 1)) # Dead reckoning
-
- # history
- hist_x_est = x_est
- hist_x_true = x_true
- hist_x_dr = x_dr
-
- particles = [Particle(n_landmark) for _ in range(N_PARTICLE)]
-
- while SIM_TIME >= time:
- time += DT
- u = calc_input(time)
-
- x_true, z, x_dr, ud = observation(x_true, x_dr, u, rfid)
-
- particles = fast_slam2(particles, ud, z)
-
- x_est = calc_final_state(particles)
-
- x_state = x_est[0: STATE_SIZE]
-
- # store data history
- hist_x_est = np.hstack((hist_x_est, x_state))
- hist_x_dr = np.hstack((hist_x_dr, x_dr))
- hist_x_true = np.hstack((hist_x_true, x_true))
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(rfid[:, 0], rfid[:, 1], "*k")
-
- for iz in range(len(z[:, 0])):
- landmark_id = int(z[2, iz])
- plt.plot([x_est[0][0], rfid[landmark_id, 0]], [
- x_est[1][0], rfid[landmark_id, 1]], "-k")
-
- for i in range(N_PARTICLE):
- plt.plot(particles[i].x, particles[i].y, ".r")
- plt.plot(particles[i].lm[:, 0], particles[i].lm[:, 1], "xb")
-
- plt.plot(hist_x_true[0, :], hist_x_true[1, :], "-b")
- plt.plot(hist_x_dr[0, :], hist_x_dr[1, :], "-k")
- plt.plot(hist_x_est[0, :], hist_x_est[1, :], "-r")
- plt.plot(x_est[0], x_est[1], "xk")
- plt.axis("equal")
- plt.grid(True)
- plt.pause(0.001)
-
-
-if __name__ == '__main__':
- main()
diff --git a/SLAM/GraphBasedSLAM/data/README.rst b/SLAM/GraphBasedSLAM/data/README.rst
deleted file mode 100644
index 15bc5b6c03f..00000000000
--- a/SLAM/GraphBasedSLAM/data/README.rst
+++ /dev/null
@@ -1,6 +0,0 @@
-Acknowledgments and References
-==============================
-
-Thanks to Luca Larlone for allowing inclusion of the `Intel dataset <https://lucacarlone.mit.edu/datasets/>`_ in this repo.
-
-1. Carlone, L. and Censi, A., 2014. `From angular manifolds to the integer lattice: Guaranteed orientation estimation with application to pose graph optimization <https://arxiv.org/pdf/1211.3063>`_. IEEE Transactions on Robotics, 30(2), pp.475-492.
diff --git a/SLAM/GraphBasedSLAM/data/input_INTEL.g2o b/SLAM/GraphBasedSLAM/data/input_INTEL.g2o
deleted file mode 100644
index 16f3a2600cb..00000000000
--- a/SLAM/GraphBasedSLAM/data/input_INTEL.g2o
+++ /dev/null
@@ -1,2711 +0,0 @@
-VERTEX_SE2 0 0.000000 0.000000 0.000000
-VERTEX_SE2 1 0.000000 0.000000 -0.000642
-VERTEX_SE2 2 0.000000 0.000000 -0.001180
-VERTEX_SE2 3 0.011002 -0.000975 -0.003562
-VERTEX_SE2 4 0.641008 -0.011200 -0.007444
-VERTEX_SE2 5 0.696016 -0.011716 -0.098726
-VERTEX_SE2 6 0.700269 -0.015435 -0.895998
-VERTEX_SE2 7 0.693956 0.004213 -1.511535
-VERTEX_SE2 8 0.699263 0.026693 -2.125069
-VERTEX_SE2 9 0.716114 0.041122 -2.763139
-VERTEX_SE2 10 0.728981 0.043219 2.905515
-VERTEX_SE2 11 0.733203 0.040537 2.231236
-VERTEX_SE2 12 0.733186 0.041545 1.581762
-VERTEX_SE2 13 0.738753 0.059070 0.922264
-VERTEX_SE2 14 0.759658 0.073750 0.314025
-VERTEX_SE2 15 0.768572 0.074357 -0.210903
-VERTEX_SE2 16 1.062493 0.014152 -0.229595
-VERTEX_SE2 17 1.663647 -0.133115 -0.260823
-VERTEX_SE2 18 2.287001 -0.296480 -0.271000
-VERTEX_SE2 19 2.914298 -0.494254 -0.319576
-VERTEX_SE2 20 3.527220 -0.693985 -0.308933
-VERTEX_SE2 21 4.152895 -0.850915 -0.191238
-VERTEX_SE2 22 4.779015 -0.992339 -0.168556
-VERTEX_SE2 23 5.423978 -1.030005 -0.054484
-VERTEX_SE2 24 6.064382 -1.090997 -0.105423
-VERTEX_SE2 25 6.707928 -1.144401 -0.096821
-VERTEX_SE2 26 7.315680 -1.224079 -0.137153
-VERTEX_SE2 27 7.929761 -1.294250 -0.121079
-VERTEX_SE2 28 8.510243 -1.372635 -0.125240
-VERTEX_SE2 29 8.886549 -1.416447 -0.094136
-VERTEX_SE2 30 8.893462 -1.418023 -0.625522
-VERTEX_SE2 31 9.005697 -1.557779 -0.893355
-VERTEX_SE2 32 9.398300 -2.067296 -0.911506
-VERTEX_SE2 33 9.800909 -2.566880 -0.858368
-VERTEX_SE2 34 10.230894 -3.045076 -0.834898
-VERTEX_SE2 35 10.670845 -3.512974 -0.797906
-VERTEX_SE2 36 11.118351 -3.980273 -0.803680
-VERTEX_SE2 37 11.413882 -4.282108 -0.793023
-VERTEX_SE2 38 11.416535 -4.285316 -1.109584
-VERTEX_SE2 39 11.425445 -4.316267 -1.276487
-VERTEX_SE2 40 11.612551 -4.916547 -1.255922
-VERTEX_SE2 41 11.808527 -5.541274 -1.284316
-VERTEX_SE2 42 11.976726 -6.133098 -1.303279
-VERTEX_SE2 43 12.132495 -6.760248 -1.339357
-VERTEX_SE2 44 12.273339 -7.389611 -1.372003
-VERTEX_SE2 45 12.381155 -8.023418 -1.427426
-VERTEX_SE2 46 12.464524 -8.661631 -1.446702
-VERTEX_SE2 47 12.536773 -9.300726 -1.488240
-VERTEX_SE2 48 12.585187 -9.946461 -1.494639
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-EDGE_SE2 195 467 -0.091210 1.365140 1.118420 21.523802 -18.224556 0.000000 43.008191 0.000000 557.077827
-EDGE_SE2 195 484 0.655807 2.573505 -2.009240 11.219291 -0.565783 0.000000 14.070164 0.000000 276.074540
-EDGE_SE2 195 494 0.855236 -0.512254 -0.301250 16.102937 20.540136 0.000000 95.628725 0.000000 1476.449250
-EDGE_SE2 195 988 1.415155 -0.856188 3.052380 16.022409 10.041613 0.000000 31.642140 0.000000 152.236812
-EDGE_SE2 195 994 -2.192048 -0.521524 3.098765 11.750475 -2.253964 0.000000 19.057069 0.000000 148.810613
-EDGE_SE2 201 494 -2.683977 -0.793909 -0.034430 11.276756 -0.496479 0.000000 12.599187 0.000000 2336.349413
-EDGE_SE2 201 500 1.004735 -0.526385 0.314340 45.186413 33.298498 0.000000 43.650514 0.000000 1447.186686
-EDGE_SE2 201 982 1.557172 -0.467671 -3.046225 14.919173 9.340266 0.000000 34.020554 0.000000 152.700298
-EDGE_SE2 201 988 -2.053188 -0.978041 -2.963985 11.683303 -2.092334 0.000000 18.762142 0.000000 159.102109
-EDGE_SE2 203 500 -0.236863 -0.548090 0.348290 153.663942 -134.464803 0.000000 137.946777 0.000000 1375.223806
-EDGE_SE2 203 508 1.553867 1.875066 1.399800 12.536000 2.482853 0.000000 15.437455 0.000000 434.100125
-EDGE_SE2 203 522 1.780329 -0.307182 0.021130 11.822071 3.657498 0.000000 29.926926 0.000000 2397.606666
-EDGE_SE2 203 982 0.313263 -0.470658 -3.012275 253.866414 119.649456 0.000000 70.084044 0.000000 155.295388
-EDGE_SE2 209 508 -2.161765 2.058644 1.468780 11.180293 -0.053576 0.000000 11.152602 0.000000 410.180706
-EDGE_SE2 209 522 -1.785428 -0.102806 0.090110 11.132515 0.656456 0.000000 31.244975 0.000000 2103.775347
-EDGE_SE2 209 528 1.736233 0.012599 -0.097130 11.350617 -2.286079 0.000000 32.931671 0.000000 2076.939411
-EDGE_SE2 209 976 0.433683 -0.153481 -3.063330 87.280240 171.295909 0.000000 396.336584 0.000000 151.417412
-EDGE_SE2 220 528 -1.597199 -1.638814 1.311310 13.034804 3.414597 0.000000 17.172093 0.000000 467.976033
-EDGE_SE2 220 532 -0.939792 0.407621 1.225630 94.950637 -5.379789 0.000000 11.456320 0.000000 504.700895
-EDGE_SE2 220 564 -0.623480 0.251998 -0.012190 38.845567 71.101745 0.000000 193.391889 0.000000 2440.146629
-EDGE_SE2 220 567 -0.002013 0.298972 1.481540 21.284937 -105.664807 0.000000 1108.540123 0.000000 405.973278
-EDGE_SE2 220 570 -0.062402 1.946160 1.542860 11.165977 -0.913492 0.000000 26.320380 0.000000 386.629607
-EDGE_SE2 220 575 -0.123656 2.505837 -2.951275 15.792523 -0.664538 0.000000 11.205444 0.000000 160.127317
-EDGE_SE2 220 959 2.587973 -0.016000 2.926965 11.274656 -0.773198 0.000000 14.766597 0.000000 162.116000
-EDGE_SE2 220 965 -1.062787 0.305497 3.105010 15.212918 16.523642 0.000000 77.674651 0.000000 148.358205
-EDGE_SE2 226 231 1.660221 0.126920 -0.049820 11.505996 -3.114430 0.000000 35.674411 0.000000 2268.351350
-EDGE_SE2 226 588 -0.273207 -0.444423 -0.016160 274.806053 -156.291042 0.000000 103.744249 0.000000 2421.117227
-EDGE_SE2 226 597 2.185242 1.674700 1.403760 12.078039 1.038206 0.000000 12.225850 0.000000 432.671013
-EDGE_SE2 226 953 2.006857 -0.437847 3.116305 11.557944 2.329386 0.000000 23.254435 0.000000 147.545120
-EDGE_SE2 226 959 -1.129223 -0.150509 2.830935 23.235807 -25.544568 0.000000 64.928953 0.000000 170.345385
-EDGE_SE2 923 1175 0.749610 0.273000 0.106670 19.536607 -34.047517 0.000000 148.697481 0.000000 2041.285424
-EDGE_SE2 929 1175 -2.005899 0.102421 -0.392910 12.648561 -4.320259 0.000000 23.251108 0.000000 1288.528106
-EDGE_SE2 939 1188 0.696432 1.755817 -0.065270 26.430265 -4.946684 0.000000 12.708437 0.000000 2203.031036
-EDGE_SE2 1029 1217 1.008685 -0.037889 -3.114265 11.476877 5.630362 0.000000 97.781127 0.000000 147.691473
-EDGE_SE2 1044 1217 2.098504 -0.838430 0.479890 15.976239 4.188481 0.000000 14.717054 0.000000 1141.513725
-EDGE_SE2 1050 1210 -0.300235 -2.565672 1.536560 11.137270 0.317303 0.000000 14.960021 0.000000 388.552520
-EDGE_SE2 1050 1217 0.231465 1.668290 1.559140 11.493589 3.014437 0.000000 34.868922 0.000000 381.726156
-EDGE_SE2 1056 1217 2.128743 -0.472375 -0.931160 15.353750 -4.908186 0.000000 16.789250 0.000000 670.352902
-EDGE_SE2 1061 1210 1.269232 -1.441319 -2.909610 23.568115 6.644624 0.000000 14.655385 0.000000 163.558506
-EDGE_SE2 1075 1210 -1.662329 0.436026 -1.599840 32.701727 -4.997844 0.000000 12.268023 0.000000 369.868006
-EDGE_SE2 1084 1210 2.070374 1.896269 1.836205 12.355692 0.641825 0.000000 11.442098 0.000000 310.788312
-EDGE_SE2 1088 1210 0.609503 -1.485166 0.536770 38.204841 -4.021013 0.000000 11.707874 0.000000 1058.576530
-EDGE_SE2 1093 1210 -0.233452 -0.529583 1.494360 42.853783 90.090527 0.000000 266.801722 0.000000 401.810926
-EDGE_SE2 1098 1210 -0.378280 -0.172442 -2.937025 38.903093 -122.470929 0.000000 550.803768 0.000000 161.288572
-EDGE_SE2 1138 1188 0.583736 -1.006358 1.671805 21.764394 -23.563240 0.000000 63.228969 0.000000 350.211491
-EDGE_SE2 1147 1188 -2.232188 0.113982 2.992915 11.195782 -0.864255 0.000000 19.932721 0.000000 156.804966
-EDGE_SE2 1150 1188 -0.789302 2.834301 1.697150 11.120354 -0.063189 0.000000 11.543094 0.000000 343.660651
-EDGE_SE2 1158 1175 0.586855 -0.249767 2.829060 13.000858 20.975969 0.000000 243.941877 0.000000 170.512281
diff --git a/SLAM/GraphBasedSLAM/graph_based_slam.py b/SLAM/GraphBasedSLAM/graph_based_slam.py
deleted file mode 100644
index edd20a959c2..00000000000
--- a/SLAM/GraphBasedSLAM/graph_based_slam.py
+++ /dev/null
@@ -1,322 +0,0 @@
-"""
-
-Graph based SLAM example
-
-author: Atsushi Sakai (@Atsushi_twi)
-
-Ref
-
-[A Tutorial on Graph-Based SLAM]
-(http://www2.informatik.uni-freiburg.de/~stachnis/pdf/grisetti10titsmag.pdf)
-
-"""
-import sys
-import pathlib
-sys.path.append(str(pathlib.Path(__file__).parent.parent.parent))
-
-import copy
-import itertools
-import math
-
-import matplotlib.pyplot as plt
-import numpy as np
-from scipy.spatial.transform import Rotation as Rot
-from utils.angle import angle_mod
-
-# Simulation parameter
-Q_sim = np.diag([0.2, np.deg2rad(1.0)]) ** 2
-R_sim = np.diag([0.1, np.deg2rad(10.0)]) ** 2
-
-DT = 2.0 # time tick [s]
-SIM_TIME = 100.0 # simulation time [s]
-MAX_RANGE = 30.0 # maximum observation range
-STATE_SIZE = 3 # State size [x,y,yaw]
-
-# Covariance parameter of Graph Based SLAM
-C_SIGMA1 = 0.1
-C_SIGMA2 = 0.1
-C_SIGMA3 = np.deg2rad(1.0)
-
-MAX_ITR = 20 # Maximum iteration
-
-show_graph_d_time = 20.0 # [s]
-show_animation = True
-
-
-class Edge:
-
- def __init__(self):
- self.e = np.zeros((3, 1))
- self.omega = np.zeros((3, 3)) # information matrix
- self.d1 = 0.0
- self.d2 = 0.0
- self.yaw1 = 0.0
- self.yaw2 = 0.0
- self.angle1 = 0.0
- self.angle2 = 0.0
- self.id1 = 0
- self.id2 = 0
-
-
-def cal_observation_sigma():
- sigma = np.zeros((3, 3))
- sigma[0, 0] = C_SIGMA1 ** 2
- sigma[1, 1] = C_SIGMA2 ** 2
- sigma[2, 2] = C_SIGMA3 ** 2
-
- return sigma
-
-
-def calc_3d_rotational_matrix(angle):
- return Rot.from_euler('z', angle).as_matrix()
-
-
-def calc_edge(x1, y1, yaw1, x2, y2, yaw2, d1,
- angle1, d2, angle2, t1, t2):
- edge = Edge()
-
- tangle1 = pi_2_pi(yaw1 + angle1)
- tangle2 = pi_2_pi(yaw2 + angle2)
- tmp1 = d1 * math.cos(tangle1)
- tmp2 = d2 * math.cos(tangle2)
- tmp3 = d1 * math.sin(tangle1)
- tmp4 = d2 * math.sin(tangle2)
-
- edge.e[0, 0] = x2 - x1 - tmp1 + tmp2
- edge.e[1, 0] = y2 - y1 - tmp3 + tmp4
- edge.e[2, 0] = 0
-
- Rt1 = calc_3d_rotational_matrix(tangle1)
- Rt2 = calc_3d_rotational_matrix(tangle2)
-
- sig1 = cal_observation_sigma()
- sig2 = cal_observation_sigma()
-
- edge.omega = np.linalg.inv(Rt1 @ sig1 @ Rt1.T + Rt2 @ sig2 @ Rt2.T)
-
- edge.d1, edge.d2 = d1, d2
- edge.yaw1, edge.yaw2 = yaw1, yaw2
- edge.angle1, edge.angle2 = angle1, angle2
- edge.id1, edge.id2 = t1, t2
-
- return edge
-
-
-def calc_edges(x_list, z_list):
- edges = []
- cost = 0.0
- z_ids = list(itertools.combinations(range(len(z_list)), 2))
-
- for (t1, t2) in z_ids:
- x1, y1, yaw1 = x_list[0, t1], x_list[1, t1], x_list[2, t1]
- x2, y2, yaw2 = x_list[0, t2], x_list[1, t2], x_list[2, t2]
-
- if z_list[t1] is None or z_list[t2] is None:
- continue # No observation
-
- for iz1 in range(len(z_list[t1][:, 0])):
- for iz2 in range(len(z_list[t2][:, 0])):
- if z_list[t1][iz1, 3] == z_list[t2][iz2, 3]:
- d1 = z_list[t1][iz1, 0]
- angle1, _ = z_list[t1][iz1, 1], z_list[t1][iz1, 2]
- d2 = z_list[t2][iz2, 0]
- angle2, _ = z_list[t2][iz2, 1], z_list[t2][iz2, 2]
-
- edge = calc_edge(x1, y1, yaw1, x2, y2, yaw2, d1,
- angle1, d2, angle2, t1, t2)
-
- edges.append(edge)
- cost += (edge.e.T @ edge.omega @ edge.e)[0, 0]
-
- print("cost:", cost, ",n_edge:", len(edges))
- return edges
-
-
-def calc_jacobian(edge):
- t1 = edge.yaw1 + edge.angle1
- A = np.array([[-1.0, 0, edge.d1 * math.sin(t1)],
- [0, -1.0, -edge.d1 * math.cos(t1)],
- [0, 0, 0]])
-
- t2 = edge.yaw2 + edge.angle2
- B = np.array([[1.0, 0, -edge.d2 * math.sin(t2)],
- [0, 1.0, edge.d2 * math.cos(t2)],
- [0, 0, 0]])
-
- return A, B
-
-
-def fill_H_and_b(H, b, edge):
- A, B = calc_jacobian(edge)
-
- id1 = edge.id1 * STATE_SIZE
- id2 = edge.id2 * STATE_SIZE
-
- H[id1:id1 + STATE_SIZE, id1:id1 + STATE_SIZE] += A.T @ edge.omega @ A
- H[id1:id1 + STATE_SIZE, id2:id2 + STATE_SIZE] += A.T @ edge.omega @ B
- H[id2:id2 + STATE_SIZE, id1:id1 + STATE_SIZE] += B.T @ edge.omega @ A
- H[id2:id2 + STATE_SIZE, id2:id2 + STATE_SIZE] += B.T @ edge.omega @ B
-
- b[id1:id1 + STATE_SIZE] += (A.T @ edge.omega @ edge.e)
- b[id2:id2 + STATE_SIZE] += (B.T @ edge.omega @ edge.e)
-
- return H, b
-
-
-def graph_based_slam(x_init, hz):
- print("start graph based slam")
-
- z_list = copy.deepcopy(hz)
-
- x_opt = copy.deepcopy(x_init)
- nt = x_opt.shape[1]
- n = nt * STATE_SIZE
-
- for itr in range(MAX_ITR):
- edges = calc_edges(x_opt, z_list)
-
- H = np.zeros((n, n))
- b = np.zeros((n, 1))
-
- for edge in edges:
- H, b = fill_H_and_b(H, b, edge)
-
- # to fix origin
- H[0:STATE_SIZE, 0:STATE_SIZE] += np.identity(STATE_SIZE)
-
- dx = - np.linalg.inv(H) @ b
-
- for i in range(nt):
- x_opt[0:3, i] += dx[i * 3:i * 3 + 3, 0]
-
- diff = (dx.T @ dx)[0, 0]
- print("iteration: %d, diff: %f" % (itr + 1, diff))
- if diff < 1.0e-5:
- break
-
- return x_opt
-
-
-def calc_input():
- v = 1.0 # [m/s]
- yaw_rate = 0.1 # [rad/s]
- u = np.array([[v, yaw_rate]]).T
- return u
-
-
-def observation(xTrue, xd, u, RFID):
- xTrue = motion_model(xTrue, u)
-
- # add noise to gps x-y
- z = np.zeros((0, 4))
-
- for i in range(len(RFID[:, 0])):
-
- dx = RFID[i, 0] - xTrue[0, 0]
- dy = RFID[i, 1] - xTrue[1, 0]
- d = math.hypot(dx, dy)
- angle = pi_2_pi(math.atan2(dy, dx)) - xTrue[2, 0]
- phi = pi_2_pi(math.atan2(dy, dx))
- if d <= MAX_RANGE:
- dn = d + np.random.randn() * Q_sim[0, 0] # add noise
- angle_noise = np.random.randn() * Q_sim[1, 1]
- angle += angle_noise
- phi += angle_noise
- zi = np.array([dn, angle, phi, i])
- z = np.vstack((z, zi))
-
- # add noise to input
- ud1 = u[0, 0] + np.random.randn() * R_sim[0, 0]
- ud2 = u[1, 0] + np.random.randn() * R_sim[1, 1]
- ud = np.array([[ud1, ud2]]).T
-
- xd = motion_model(xd, ud)
-
- return xTrue, z, xd, ud
-
-
-def motion_model(x, u):
- F = np.array([[1.0, 0, 0],
- [0, 1.0, 0],
- [0, 0, 1.0]])
-
- B = np.array([[DT * math.cos(x[2, 0]), 0],
- [DT * math.sin(x[2, 0]), 0],
- [0.0, DT]])
-
- x = F @ x + B @ u
-
- return x
-
-
-def pi_2_pi(angle):
- return angle_mod(angle)
-
-
-def main():
- print(__file__ + " start!!")
-
- time = 0.0
-
- # RFID positions [x, y, yaw]
- RFID = np.array([[10.0, -2.0, 0.0],
- [15.0, 10.0, 0.0],
- [3.0, 15.0, 0.0],
- [-5.0, 20.0, 0.0],
- [-5.0, 5.0, 0.0]
- ])
-
- # State Vector [x y yaw v]'
- xTrue = np.zeros((STATE_SIZE, 1))
- xDR = np.zeros((STATE_SIZE, 1)) # Dead reckoning
-
- # history
- hxTrue = []
- hxDR = []
- hz = []
- d_time = 0.0
- init = False
- while SIM_TIME >= time:
-
- if not init:
- hxTrue = xTrue
- hxDR = xTrue
- init = True
- else:
- hxDR = np.hstack((hxDR, xDR))
- hxTrue = np.hstack((hxTrue, xTrue))
-
- time += DT
- d_time += DT
- u = calc_input()
-
- xTrue, z, xDR, ud = observation(xTrue, xDR, u, RFID)
-
- hz.append(z)
-
- if d_time >= show_graph_d_time:
- x_opt = graph_based_slam(hxDR, hz)
- d_time = 0.0
-
- if show_animation: # pragma: no cover
- plt.cla()
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- plt.plot(RFID[:, 0], RFID[:, 1], "*k")
-
- plt.plot(hxTrue[0, :].flatten(),
- hxTrue[1, :].flatten(), "-b")
- plt.plot(hxDR[0, :].flatten(),
- hxDR[1, :].flatten(), "-k")
- plt.plot(x_opt[0, :].flatten(),
- x_opt[1, :].flatten(), "-r")
- plt.axis("equal")
- plt.grid(True)
- plt.title("Time" + str(time)[0:5])
- plt.pause(1.0)
-
-
-if __name__ == '__main__':
- main()
diff --git a/SLAM/GraphBasedSLAM/graphslam/__init__.py b/SLAM/GraphBasedSLAM/graphslam/__init__.py
deleted file mode 100644
index 6aa2872e77f..00000000000
--- a/SLAM/GraphBasedSLAM/graphslam/__init__.py
+++ /dev/null
@@ -1,9 +0,0 @@
-# Copyright (c) 2020 Jeff Irion and contributors
-#
-# This file originated from the `graphslam` package:
-#
-# https://github.com/JeffLIrion/python-graphslam
-
-"""Graph SLAM solver in Python.
-
-"""
diff --git a/SLAM/GraphBasedSLAM/graphslam/edge/__init__.py b/SLAM/GraphBasedSLAM/graphslam/edge/__init__.py
deleted file mode 100644
index afb85490871..00000000000
--- a/SLAM/GraphBasedSLAM/graphslam/edge/__init__.py
+++ /dev/null
@@ -1,5 +0,0 @@
-# Copyright (c) 2020 Jeff Irion and contributors
-#
-# This file originated from the `graphslam` package:
-#
-# https://github.com/JeffLIrion/python-graphslam
diff --git a/SLAM/GraphBasedSLAM/graphslam/edge/edge_odometry.py b/SLAM/GraphBasedSLAM/graphslam/edge/edge_odometry.py
deleted file mode 100644
index b247b97b437..00000000000
--- a/SLAM/GraphBasedSLAM/graphslam/edge/edge_odometry.py
+++ /dev/null
@@ -1,180 +0,0 @@
-# Copyright (c) 2020 Jeff Irion and contributors
-#
-# This file originated from the `graphslam` package:
-#
-# https://github.com/JeffLIrion/python-graphslam
-
-r"""A class for odometry edges.
-
-"""
-
-
-import numpy as np
-import matplotlib.pyplot as plt
-
-
-#: The difference that will be used for numerical differentiation
-EPSILON = 1e-6
-
-
-class EdgeOdometry:
- r"""A class for representing odometry edges in Graph SLAM.
-
- Parameters
- ----------
- vertices : list[graphslam.vertex.Vertex]
- A list of the vertices constrained by the edge
- information : np.ndarray
- The information matrix :math:`\Omega_j` associated with the edge
- estimate : graphslam.pose.se2.PoseSE2
- The expected measurement :math:`\mathbf{z}_j`
-
- Attributes
- ----------
- vertices : list[graphslam.vertex.Vertex]
- A list of the vertices constrained by the edge
- information : np.ndarray
- The information matrix :math:`\Omega_j` associated with the edge
- estimate : PoseSE2
- The expected measurement :math:`\mathbf{z}_j`
-
- """
- def __init__(self, vertex_ids, information, estimate, vertices=None):
- self.vertex_ids = vertex_ids
- self.information = information
- self.estimate = estimate
- self.vertices = vertices
-
- def calc_error(self):
- r"""Calculate the error for the edge: :math:`\mathbf{e}_j \in \mathbb{R}^\bullet`.
-
- .. math::
-
- \mathbf{e}_j = \mathbf{z}_j - (p_2 \ominus p_1)
-
-
- Returns
- -------
- np.ndarray
- The error for the edge
-
- """
- return (self.estimate - (self.vertices[1].pose - self.vertices[0].pose)).to_compact()
-
- def calc_chi2(self):
- r"""Calculate the :math:`\chi^2` error for the edge.
-
- .. math::
-
- \mathbf{e}_j^T \Omega_j \mathbf{e}_j
-
-
- Returns
- -------
- float
- The :math:`\chi^2` error for the edge
-
- """
- err = self.calc_error()
-
- return np.dot(np.dot(np.transpose(err), self.information), err)
-
- def calc_chi2_gradient_hessian(self):
- r"""Calculate the edge's contributions to the graph's :math:`\chi^2` error, gradient (:math:`\mathbf{b}`), and Hessian (:math:`H`).
-
- Returns
- -------
- float
- The :math:`\chi^2` error for the edge
- dict
- The edge's contribution(s) to the gradient
- dict
- The edge's contribution(s) to the Hessian
-
- """
- chi2 = self.calc_chi2()
-
- err = self.calc_error()
-
- jacobians = self.calc_jacobians()
-
- return chi2, {v.index: np.dot(np.dot(np.transpose(err), self.information), jacobian) for v, jacobian in zip(self.vertices, jacobians)}, {(self.vertices[i].index, self.vertices[j].index): np.dot(np.dot(np.transpose(jacobians[i]), self.information), jacobians[j]) for i in range(len(jacobians)) for j in range(i, len(jacobians))}
-
- def calc_jacobians(self):
- r"""Calculate the Jacobian of the edge's error with respect to each constrained pose.
-
- .. math::
-
- \frac{\partial}{\partial \Delta \mathbf{x}^k} \left[ \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k) \right]
-
-
- Returns
- -------
- list[np.ndarray]
- The Jacobian matrices for the edge with respect to each constrained pose
-
- """
- err = self.calc_error()
-
- # The dimensionality of the compact pose representation
- dim = len(self.vertices[0].pose.to_compact())
-
- return [self._calc_jacobian(err, dim, i) for i in range(len(self.vertices))]
-
- def _calc_jacobian(self, err, dim, vertex_index):
- r"""Calculate the Jacobian of the edge with respect to the specified vertex's pose.
-
- Parameters
- ----------
- err : np.ndarray
- The current error for the edge (see :meth:`EdgeOdometry.calc_error`)
- dim : int
- The dimensionality of the compact pose representation
- vertex_index : int
- The index of the vertex (pose) for which we are computing the Jacobian
-
- Returns
- -------
- np.ndarray
- The Jacobian of the edge with respect to the specified vertex's pose
-
- """
- jacobian = np.zeros(err.shape + (dim,))
- p0 = self.vertices[vertex_index].pose.copy()
-
- for d in range(dim):
- # update the pose
- delta_pose = np.zeros(dim)
- delta_pose[d] = EPSILON
- self.vertices[vertex_index].pose += delta_pose
-
- # compute the numerical derivative
- jacobian[:, d] = (self.calc_error() - err) / EPSILON
-
- # restore the pose
- self.vertices[vertex_index].pose = p0.copy()
-
- return jacobian
-
- def to_g2o(self):
- """Export the edge to the .g2o format.
-
- Returns
- -------
- str
- The edge in .g2o format
-
- """
- return "EDGE_SE2 {} {} {} {} {} ".format(self.vertex_ids[0], self.vertex_ids[1], self.estimate[0], self.estimate[1], self.estimate[2]) + " ".join([str(x) for x in self.information[np.triu_indices(3, 0)]]) + "\n"
-
- def plot(self, color='b'):
- """Plot the edge.
-
- Parameters
- ----------
- color : str
- The color that will be used to plot the edge
-
- """
- xy = np.array([v.pose.position for v in self.vertices])
- plt.plot(xy[:, 0], xy[:, 1], color=color)
diff --git a/SLAM/GraphBasedSLAM/graphslam/graph.py b/SLAM/GraphBasedSLAM/graphslam/graph.py
deleted file mode 100644
index 672f63d60e2..00000000000
--- a/SLAM/GraphBasedSLAM/graphslam/graph.py
+++ /dev/null
@@ -1,282 +0,0 @@
-# Copyright (c) 2020 Jeff Irion and contributors
-#
-# This file originated from the `graphslam` package:
-#
-# https://github.com/JeffLIrion/python-graphslam
-
-r"""A ``Graph`` class that stores the edges and vertices required for Graph SLAM.
-
-"""
-
-import warnings
-from collections import defaultdict
-from functools import reduce
-
-import matplotlib.pyplot as plt
-import numpy as np
-from scipy.sparse import SparseEfficiencyWarning, lil_matrix
-from scipy.sparse.linalg import spsolve
-
-warnings.simplefilter("ignore", SparseEfficiencyWarning)
-warnings.filterwarnings("ignore", category=SparseEfficiencyWarning)
-
-
-# pylint: disable=too-few-public-methods
-class _Chi2GradientHessian:
- r"""A class that is used to aggregate the :math:`\chi^2` error, gradient, and Hessian.
-
- Parameters
- ----------
- dim : int
- The compact dimensionality of the poses
-
- Attributes
- ----------
- chi2 : float
- The :math:`\chi^2` error
- dim : int
- The compact dimensionality of the poses
- gradient : defaultdict
- The contributions to the gradient vector
- hessian : defaultdict
- The contributions to the Hessian matrix
-
- """
-
- def __init__(self, dim):
- self.chi2 = 0.
- self.dim = dim
- self.gradient = defaultdict(lambda: np.zeros(dim))
- self.hessian = defaultdict(lambda: np.zeros((dim, dim)))
-
- @staticmethod
- def update(chi2_grad_hess, incoming):
- r"""Update the :math:`\chi^2` error and the gradient and Hessian dictionaries.
-
- Parameters
- ----------
- chi2_grad_hess : _Chi2GradientHessian
- The ``_Chi2GradientHessian`` that will be updated
- incoming : tuple
-
- """
- chi2_grad_hess.chi2 += incoming[0]
-
- for idx, contrib in incoming[1].items():
- chi2_grad_hess.gradient[idx] += contrib
-
- for (idx1, idx2), contrib in incoming[2].items():
- if idx1 <= idx2:
- chi2_grad_hess.hessian[idx1, idx2] += contrib
- else:
- chi2_grad_hess.hessian[idx2, idx1] += np.transpose(contrib)
-
- return chi2_grad_hess
-
-
-class Graph(object):
- r"""A graph that will be optimized via Graph SLAM.
-
- Parameters
- ----------
- edges : list[graphslam.edge.edge_odometry.EdgeOdometry]
- A list of the vertices in the graph
- vertices : list[graphslam.vertex.Vertex]
- A list of the vertices in the graph
-
- Attributes
- ----------
- _chi2 : float, None
- The current :math:`\chi^2` error, or ``None`` if it has not yet been computed
- _edges : list[graphslam.edge.edge_odometry.EdgeOdometry]
- A list of the edges (i.e., constraints) in the graph
- _gradient : numpy.ndarray, None
- The gradient :math:`\mathbf{b}` of the :math:`\chi^2` error, or ``None`` if it has not yet been computed
- _hessian : scipy.sparse.lil_matrix, None
- The Hessian matrix :math:`H`, or ``None`` if it has not yet been computed
- _vertices : list[graphslam.vertex.Vertex]
- A list of the vertices in the graph
-
- """
-
- def __init__(self, edges, vertices):
- # The vertices and edges lists
- self._edges = edges
- self._vertices = vertices
-
- # The chi^2 error, gradient, and Hessian
- self._chi2 = None
- self._gradient = None
- self._hessian = None
-
- self._link_edges()
-
- def _link_edges(self):
- """Fill in the ``vertices`` attributes for the graph's edges.
-
- """
- index_id_dict = {i: v.id for i, v in enumerate(self._vertices)}
- id_index_dict = {v_id: v_index for v_index, v_id in
- index_id_dict.items()}
-
- # Fill in the vertices' `index` attribute
- for v in self._vertices:
- v.index = id_index_dict[v.id]
-
- for e in self._edges:
- e.vertices = [self._vertices[id_index_dict[v_id]] for v_id in
- e.vertex_ids]
-
- def calc_chi2(self):
- r"""Calculate the :math:`\chi^2` error for the ``Graph``.
-
- Returns
- -------
- float
- The :math:`\chi^2` error
-
- """
- self._chi2 = sum((e.calc_chi2() for e in self._edges))
- return self._chi2
-
- def _calc_chi2_gradient_hessian(self):
- r"""Calculate the :math:`\chi^2` error, the gradient :math:`\mathbf{b}`, and the Hessian :math:`H`.
-
- """
- n = len(self._vertices)
- dim = len(self._vertices[0].pose.to_compact())
- chi2_gradient_hessian = reduce(_Chi2GradientHessian.update,
- (e.calc_chi2_gradient_hessian()
- for e in self._edges),
- _Chi2GradientHessian(dim))
-
- self._chi2 = chi2_gradient_hessian.chi2
-
- # Fill in the gradient vector
- self._gradient = np.zeros(n * dim, dtype=float)
- for idx, cont in chi2_gradient_hessian.gradient.items():
- self._gradient[idx * dim: (idx + 1) * dim] += cont
-
- # Fill in the Hessian matrix
- self._hessian = lil_matrix((n * dim, n * dim), dtype=float)
- for (row_idx, col_idx), cont in chi2_gradient_hessian.hessian.items():
- x_start = row_idx * dim
- x_end = (row_idx + 1) * dim
- y_start = col_idx * dim
- y_end = (col_idx + 1) * dim
- self._hessian[x_start:x_end, y_start:y_end] = cont
-
- if row_idx != col_idx:
- x_start = col_idx * dim
- x_end = (col_idx + 1) * dim
- y_start = row_idx * dim
- y_end = (row_idx + 1) * dim
- self._hessian[x_start:x_end, y_start:y_end] = \
- np.transpose(cont)
-
- def optimize(self, tol=1e-4, max_iter=20, fix_first_pose=True):
- r"""Optimize the :math:`\chi^2` error for the ``Graph``.
-
- Parameters
- ----------
- tol : float
- If the relative decrease in the :math:`\chi^2` error between iterations is less than ``tol``, we will stop
- max_iter : int
- The maximum number of iterations
- fix_first_pose : bool
- If ``True``, we will fix the first pose
-
- """
- n = len(self._vertices)
- dim = len(self._vertices[0].pose.to_compact())
-
- # Previous iteration's chi^2 error
- chi2_prev = -1.
-
- # For displaying the optimization progress
- print("\nIteration chi^2 rel. change")
- print("--------- ----- -----------")
-
- for i in range(max_iter):
- self._calc_chi2_gradient_hessian()
-
- # Check for convergence (from the previous iteration); this avoids having to calculate chi^2 twice
- if i > 0:
- rel_diff = (chi2_prev - self._chi2) / (
- chi2_prev + np.finfo(float).eps)
- print(
- "{:9d} {:20.4f} {:18.6f}".format(i, self._chi2, -rel_diff))
- if self._chi2 < chi2_prev and rel_diff < tol:
- return
- else:
- print("{:9d} {:20.4f}".format(i, self._chi2))
-
- # Update the previous iteration's chi^2 error
- chi2_prev = self._chi2
-
- # Hold the first pose fixed
- if fix_first_pose:
- self._hessian[:dim, :] = 0.
- self._hessian[:, :dim] = 0.
- self._hessian[:dim, :dim] += np.eye(dim)
- self._gradient[:dim] = 0.
-
- # Solve for the updates
- dx = spsolve(self._hessian, -self._gradient)
-
- # Apply the updates
- for v, dx_i in zip(self._vertices, np.split(dx, n)):
- v.pose += dx_i
-
- # If we reached the maximum number of iterations, print out the final iteration's results
- self.calc_chi2()
- rel_diff = (chi2_prev - self._chi2) / (chi2_prev + np.finfo(float).eps)
- print("{:9d} {:20.4f} {:18.6f}".format(
- max_iter, self._chi2, -rel_diff))
-
- def to_g2o(self, outfile):
- """Save the graph in .g2o format.
-
- Parameters
- ----------
- outfile : str
- The path where the graph will be saved
-
- """
- with open(outfile, 'w') as f:
- for v in self._vertices:
- f.write(v.to_g2o())
-
- for e in self._edges:
- f.write(e.to_g2o())
-
- def plot(self, vertex_color='r', vertex_marker='o', vertex_markersize=3,
- edge_color='b', title=None):
- """Plot the graph.
-
- Parameters
- ----------
- vertex_color : str
- The color that will be used to plot the vertices
- vertex_marker : str
- The marker that will be used to plot the vertices
- vertex_markersize : int
- The size of the plotted vertices
- edge_color : str
- The color that will be used to plot the edges
- title : str, None
- The title that will be used for the plot
-
- """
- plt.figure()
-
- for e in self._edges:
- e.plot(edge_color)
-
- for v in self._vertices:
- v.plot(vertex_color, vertex_marker, vertex_markersize)
-
- if title:
- plt.title(title)
-
- plt.show()
diff --git a/SLAM/GraphBasedSLAM/graphslam/load.py b/SLAM/GraphBasedSLAM/graphslam/load.py
deleted file mode 100644
index ebf42914566..00000000000
--- a/SLAM/GraphBasedSLAM/graphslam/load.py
+++ /dev/null
@@ -1,66 +0,0 @@
-# Copyright (c) 2020 Jeff Irion and contributors
-#
-# This file originated from the `graphslam` package:
-#
-# https://github.com/JeffLIrion/python-graphslam
-
-"""Functions for loading graphs.
-
-"""
-
-import logging
-
-import numpy as np
-
-from .edge.edge_odometry import EdgeOdometry
-from .graph import Graph
-from .pose.se2 import PoseSE2
-from .util import upper_triangular_matrix_to_full_matrix
-from .vertex import Vertex
-
-_LOGGER = logging.getLogger(__name__)
-
-
-def load_g2o_se2(infile):
- """Load an :math:`SE(2)` graph from a .g2o file.
-
- Parameters
- ----------
- infile : str
- The path to the .g2o file
-
- Returns
- -------
- Graph
- The loaded graph
-
- """
- edges = []
- vertices = []
-
- with open(infile) as f:
- for line in f.readlines():
- if line.startswith("VERTEX_SE2"):
- numbers = line[10:].split()
- arr = np.array([float(number) for number in numbers[1:]],
- dtype=float)
- p = PoseSE2(arr[:2], arr[2])
- v = Vertex(int(numbers[0]), p)
- vertices.append(v)
- continue
-
- if line.startswith("EDGE_SE2"):
- numbers = line[9:].split()
- arr = np.array([float(number) for number in numbers[2:]],
- dtype=float)
- vertex_ids = [int(numbers[0]), int(numbers[1])]
- estimate = PoseSE2(arr[:2], arr[2])
- information = upper_triangular_matrix_to_full_matrix(arr[3:], 3)
- e = EdgeOdometry(vertex_ids, information, estimate)
- edges.append(e)
- continue
-
- if line.strip():
- _LOGGER.warning("Line not supported -- '%s'", line.rstrip())
-
- return Graph(edges, vertices)
diff --git a/SLAM/GraphBasedSLAM/graphslam/pose/__init__.py b/SLAM/GraphBasedSLAM/graphslam/pose/__init__.py
deleted file mode 100644
index afb85490871..00000000000
--- a/SLAM/GraphBasedSLAM/graphslam/pose/__init__.py
+++ /dev/null
@@ -1,5 +0,0 @@
-# Copyright (c) 2020 Jeff Irion and contributors
-#
-# This file originated from the `graphslam` package:
-#
-# https://github.com/JeffLIrion/python-graphslam
diff --git a/SLAM/GraphBasedSLAM/graphslam/pose/se2.py b/SLAM/GraphBasedSLAM/graphslam/pose/se2.py
deleted file mode 100644
index 2a32e765f7d..00000000000
--- a/SLAM/GraphBasedSLAM/graphslam/pose/se2.py
+++ /dev/null
@@ -1,184 +0,0 @@
-# Copyright (c) 2020 Jeff Irion and contributors
-#
-# This file originated from the `graphslam` package:
-#
-# https://github.com/JeffLIrion/python-graphslam
-
-r"""Representation of a pose in :math:`SE(2)`.
-
-"""
-
-import math
-import numpy as np
-
-from ..util import neg_pi_to_pi
-
-
-class PoseSE2(np.ndarray):
- r"""A representation of a pose in :math:`SE(2)`.
-
- Parameters
- ----------
- position : np.ndarray, list
- The position in :math:`\mathbb{R}^2`
- orientation : float
- The angle of the pose (in radians)
-
- """
-
- def __new__(cls, position, orientation):
- obj = np.array([position[0], position[1], neg_pi_to_pi(orientation)],
- dtype=float).view(cls)
- return obj
-
- # pylint: disable=arguments-differ
- def copy(self):
- """Return a copy of the pose.
-
- Returns
- -------
- PoseSE2
- A copy of the pose
-
- """
- return PoseSE2(self[:2], self[2])
-
- def to_array(self):
- """Return the pose as a numpy array.
-
- Returns
- -------
- np.ndarray
- The pose as a numpy array
-
- """
- return np.array(self)
-
- def to_compact(self):
- """Return the pose as a compact numpy array.
-
- Returns
- -------
- np.ndarray
- The pose as a compact numpy array
-
- """
- return np.array(self)
-
- def to_matrix(self):
- """Return the pose as an :math:`SE(2)` matrix.
-
- Returns
- -------
- np.ndarray
- The pose as an :math:`SE(2)` matrix
-
- """
- return np.array([[np.cos(self[2]), -np.sin(self[2]), self[0]],
- [np.sin(self[2]), np.cos(self[2]), self[1]],
- [0., 0., 1.]], dtype=float)
-
- @classmethod
- def from_matrix(cls, matrix):
- """Return the pose as an :math:`SE(2)` matrix.
-
- Parameters
- ----------
- matrix : np.ndarray
- The :math:`SE(2)` matrix that will be converted to a `PoseSE2` instance
-
- Returns
- -------
- PoseSE2
- The matrix as a `PoseSE2` object
-
- """
- return cls([matrix[0, 2], matrix[1, 2]],
- math.atan2(matrix[1, 0], matrix[0, 0]))
-
- # ======================================================================= #
- # #
- # Properties #
- # #
- # ======================================================================= #
- @property
- def position(self):
- """Return the pose's position.
-
- Returns
- -------
- np.ndarray
- The position portion of the pose
-
- """
- return np.array(self[:2])
-
- @property
- def orientation(self):
- """Return the pose's orientation.
-
- Returns
- -------
- float
- The angle of the pose
-
- """
- return self[2]
-
- @property
- def inverse(self):
- """Return the pose's inverse.
-
- Returns
- -------
- PoseSE2
- The pose's inverse
-
- """
- return PoseSE2([-self[0] * np.cos(self[2]) - self[1] * np.sin(self[2]),
- self[0] * np.sin(self[2]) - self[1] * np.cos(self[2])],
- -self[2])
-
- # ======================================================================= #
- # #
- # Magic Methods #
- # #
- # ======================================================================= #
- def __add__(self, other):
- r"""Add poses (i.e., pose composition): :math:`p_1 \oplus p_2`.
-
- Parameters
- ----------
- other : PoseSE2
- The other pose
-
- Returns
- -------
- PoseSE2
- The result of pose composition
-
- """
- return PoseSE2(
- [self[0] + other[0] * np.cos(self[2]) - other[1] * np.sin(self[2]),
- self[1] + other[0] * np.sin(self[2]) + other[1] * np.cos(self[2])
- ], neg_pi_to_pi(self[2] + other[2]))
-
- def __sub__(self, other):
- r"""Subtract poses (i.e., inverse pose composition): :math:`p_1 \ominus p_2`.
-
- Parameters
- ----------
- other : PoseSE2
- The other pose
-
- Returns
- -------
- PoseSE2
- The result of inverse pose composition
-
- """
- return PoseSE2([(self[0] - other[0]) * np.cos(other[2]) + (
- self[1] - other[1]) * np.sin(other[2]),
- (other[0] - self[0]) * np.sin(other[2]) + (
- self[1] - other[1]) * np.cos(other[2])],
- neg_pi_to_pi(self[2] - other[2]))
diff --git a/SLAM/GraphBasedSLAM/graphslam/util.py b/SLAM/GraphBasedSLAM/graphslam/util.py
deleted file mode 100644
index 619aff20afd..00000000000
--- a/SLAM/GraphBasedSLAM/graphslam/util.py
+++ /dev/null
@@ -1,77 +0,0 @@
-# Copyright (c) 2020 Jeff Irion and contributors
-#
-# This file originated from the `graphslam` package:
-#
-# https://github.com/JeffLIrion/python-graphslam
-
-"""Utility functions used throughout the package.
-
-"""
-
-import numpy as np
-
-
-TWO_PI = 2 * np.pi
-
-
-def neg_pi_to_pi(angle):
- r"""Normalize ``angle`` to be in :math:`[-\pi, \pi)`.
-
- Parameters
- ----------
- angle : float
- An angle (in radians)
-
- Returns
- -------
- float
- The angle normalized to :math:`[-\pi, \pi)`
-
- """
- return (angle + np.pi) % (TWO_PI) - np.pi
-
-
-def solve_for_edge_dimensionality(n):
- r"""Solve for the dimensionality of an edge.
-
- In a .g2o file, an edge is specified as ``<estimate> <information matrix>``, where only the upper triangular portion of the matrix is provided.
-
- This solves the problem:
-
- .. math::
-
- d + \frac{d (d + 1)}{2} = n
-
- Returns
- -------
- int
- The dimensionality of the edge
-
- """
- return int(round(np.sqrt(2 * n + 2.25) - 1.5))
-
-
-def upper_triangular_matrix_to_full_matrix(arr, n):
- """Given an upper triangular matrix, return the full matrix.
-
- Parameters
- ----------
- arr : np.ndarray
- The upper triangular portion of the matrix
- n : int
- The size of the matrix
-
- Returns
- -------
- mat : np.ndarray
- The full matrix
-
- """
- triu0 = np.triu_indices(n, 0)
- tril1 = np.tril_indices(n, -1)
-
- mat = np.zeros((n, n), dtype=float)
- mat[triu0] = arr
- mat[tril1] = mat.T[tril1]
-
- return mat
diff --git a/SLAM/GraphBasedSLAM/graphslam/vertex.py b/SLAM/GraphBasedSLAM/graphslam/vertex.py
deleted file mode 100644
index 6fb1f0d0985..00000000000
--- a/SLAM/GraphBasedSLAM/graphslam/vertex.py
+++ /dev/null
@@ -1,67 +0,0 @@
-# Copyright (c) 2020 Jeff Irion and contributors
-#
-# This file originated from the `graphslam` package:
-#
-# https://github.com/JeffLIrion/python-graphslam
-
-"""A ``Vertex`` class.
-
-"""
-
-import matplotlib.pyplot as plt
-
-
-# pylint: disable=too-few-public-methods
-class Vertex:
- """A class for representing a vertex in Graph SLAM.
-
- Parameters
- ----------
- vertex_id : int
- The vertex's unique ID
- pose : graphslam.pose.se2.PoseSE2
- The pose associated with the vertex
- vertex_index : int, None
- The vertex's index in the graph's ``vertices`` list
-
- Attributes
- ----------
- id : int
- The vertex's unique ID
- index : int, None
- The vertex's index in the graph's ``vertices`` list
- pose : graphslam.pose.se2.PoseSE2
- The pose associated with the vertex
-
- """
- def __init__(self, vertex_id, pose, vertex_index=None):
- self.id = vertex_id
- self.pose = pose
- self.index = vertex_index
-
- def to_g2o(self):
- """Export the vertex to the .g2o format.
-
- Returns
- -------
- str
- The vertex in .g2o format
-
- """
- return "VERTEX_SE2 {} {} {} {}\n".format(self.id, self.pose[0], self.pose[1], self.pose[2])
-
- def plot(self, color='r', marker='o', markersize=3):
- """Plot the vertex.
-
- Parameters
- ----------
- color : str
- The color that will be used to plot the vertex
- marker : str
- The marker that will be used to plot the vertex
- markersize : int
- The size of the plotted vertex
-
- """
- x, y = self.pose.position
- plt.plot(x, y, color=color, marker=marker, markersize=markersize)
diff --git a/SLAM/__init__.py b/SLAM/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/SLAM/iterative_closest_point/iterative_closest_point.py b/SLAM/iterative_closest_point/iterative_closest_point.py
deleted file mode 100644
index 2b44de2c071..00000000000
--- a/SLAM/iterative_closest_point/iterative_closest_point.py
+++ /dev/null
@@ -1,205 +0,0 @@
-"""
-Iterative Closest Point (ICP) SLAM example
-author: Atsushi Sakai (@Atsushi_twi), Göktuğ Karakaşlı, Shamil Gemuev
-"""
-
-import math
-
-from mpl_toolkits.mplot3d import Axes3D # noqa: F401 unused import
-import matplotlib.pyplot as plt
-import numpy as np
-
-# ICP parameters
-EPS = 0.0001
-MAX_ITER = 100
-
-show_animation = True
-
-
-def icp_matching(previous_points, current_points):
- """
- Iterative Closest Point matching
- - input
- previous_points: 2D or 3D points in the previous frame
- current_points: 2D or 3D points in the current frame
- - output
- R: Rotation matrix
- T: Translation vector
- """
- H = None # homogeneous transformation matrix
-
- dError = np.inf
- preError = np.inf
- count = 0
-
- if show_animation:
- fig = plt.figure()
- if previous_points.shape[0] == 3:
- fig.add_subplot(111, projection='3d')
-
- while dError >= EPS:
- count += 1
-
- if show_animation: # pragma: no cover
- plot_points(previous_points, current_points, fig)
- plt.pause(0.1)
-
- indexes, error = nearest_neighbor_association(previous_points, current_points)
- Rt, Tt = svd_motion_estimation(previous_points[:, indexes], current_points)
- # update current points
- current_points = (Rt @ current_points) + Tt[:, np.newaxis]
-
- dError = preError - error
- print("Residual:", error)
-
- if dError < 0: # prevent matrix H changing, exit loop
- print("Not Converge...", preError, dError, count)
- break
-
- preError = error
- H = update_homogeneous_matrix(H, Rt, Tt)
-
- if dError <= EPS:
- print("Converge", error, dError, count)
- break
- elif MAX_ITER <= count:
- print("Not Converge...", error, dError, count)
- break
-
- R = np.array(H[0:-1, 0:-1])
- T = np.array(H[0:-1, -1])
-
- return R, T
-
-
-def update_homogeneous_matrix(Hin, R, T):
-
- r_size = R.shape[0]
- H = np.zeros((r_size + 1, r_size + 1))
-
- H[0:r_size, 0:r_size] = R
- H[0:r_size, r_size] = T
- H[r_size, r_size] = 1.0
-
- if Hin is None:
- return H
- else:
- return Hin @ H
-
-
-def nearest_neighbor_association(previous_points, current_points):
-
- # calc the sum of residual errors
- delta_points = previous_points - current_points
- d = np.linalg.norm(delta_points, axis=0)
- error = sum(d)
-
- # calc index with nearest neighbor assosiation
- d = np.linalg.norm(np.repeat(current_points, previous_points.shape[1], axis=1)
- - np.tile(previous_points, (1, current_points.shape[1])), axis=0)
- indexes = np.argmin(d.reshape(current_points.shape[1], previous_points.shape[1]), axis=1)
-
- return indexes, error
-
-
-def svd_motion_estimation(previous_points, current_points):
- pm = np.mean(previous_points, axis=1)
- cm = np.mean(current_points, axis=1)
-
- p_shift = previous_points - pm[:, np.newaxis]
- c_shift = current_points - cm[:, np.newaxis]
-
- W = c_shift @ p_shift.T
- u, s, vh = np.linalg.svd(W)
-
- R = (u @ vh).T
- t = pm - (R @ cm)
-
- return R, t
-
-
-def plot_points(previous_points, current_points, figure):
- # for stopping simulation with the esc key.
- plt.gcf().canvas.mpl_connect(
- 'key_release_event',
- lambda event: [exit(0) if event.key == 'escape' else None])
- if previous_points.shape[0] == 3:
- plt.clf()
- axes = figure.add_subplot(111, projection='3d')
- axes.scatter(previous_points[0, :], previous_points[1, :],
- previous_points[2, :], c="r", marker=".")
- axes.scatter(current_points[0, :], current_points[1, :],
- current_points[2, :], c="b", marker=".")
- axes.scatter(0.0, 0.0, 0.0, c="r", marker="x")
- figure.canvas.draw()
- else:
- plt.cla()
- plt.plot(previous_points[0, :], previous_points[1, :], ".r")
- plt.plot(current_points[0, :], current_points[1, :], ".b")
- plt.plot(0.0, 0.0, "xr")
- plt.axis("equal")
-
-
-def main():
- print(__file__ + " start!!")
-
- # simulation parameters
- nPoint = 1000
- fieldLength = 50.0
- motion = [0.5, 2.0, np.deg2rad(-10.0)] # movement [x[m],y[m],yaw[deg]]
-
- nsim = 3 # number of simulation
-
- for _ in range(nsim):
-
- # previous points
- px = (np.random.rand(nPoint) - 0.5) * fieldLength
- py = (np.random.rand(nPoint) - 0.5) * fieldLength
- previous_points = np.vstack((px, py))
-
- # current points
- cx = [math.cos(motion[2]) * x - math.sin(motion[2]) * y + motion[0]
- for (x, y) in zip(px, py)]
- cy = [math.sin(motion[2]) * x + math.cos(motion[2]) * y + motion[1]
- for (x, y) in zip(px, py)]
- current_points = np.vstack((cx, cy))
-
- R, T = icp_matching(previous_points, current_points)
- print("R:", R)
- print("T:", T)
-
-
-def main_3d_points():
- print(__file__ + " start!!")
-
- # simulation parameters for 3d point set
- nPoint = 1000
- fieldLength = 50.0
- motion = [0.5, 2.0, -5, np.deg2rad(-10.0)] # [x[m],y[m],z[m],roll[deg]]
-
- nsim = 3 # number of simulation
-
- for _ in range(nsim):
-
- # previous points
- px = (np.random.rand(nPoint) - 0.5) * fieldLength
- py = (np.random.rand(nPoint) - 0.5) * fieldLength
- pz = (np.random.rand(nPoint) - 0.5) * fieldLength
- previous_points = np.vstack((px, py, pz))
-
- # current points
- cx = [math.cos(motion[3]) * x - math.sin(motion[3]) * z + motion[0]
- for (x, z) in zip(px, pz)]
- cy = [y + motion[1] for y in py]
- cz = [math.sin(motion[3]) * x + math.cos(motion[3]) * z + motion[2]
- for (x, z) in zip(px, pz)]
- current_points = np.vstack((cx, cy, cz))
-
- R, T = icp_matching(previous_points, current_points)
- print("R:", R)
- print("T:", T)
-
-
-if __name__ == '__main__':
- main()
- main_3d_points()
diff --git a/__init__.py b/__init__.py
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+ <h1>Source code for Mapping.ndt_map.ndt_map</h1><div class="highlight"><pre>
+<span></span><span class="sd">"""</span>
+<span class="sd">Normal Distribution Transform (NDTGrid) mapping sample</span>
+<span class="sd">"""</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
+
+<span class="kn">from</span> <span class="nn">Mapping.grid_map_lib.grid_map_lib</span> <span class="kn">import</span> <span class="n">GridMap</span>
+<span class="kn">from</span> <span class="nn">utils.plot</span> <span class="kn">import</span> <span class="n">plot_covariance_ellipse</span>
+
+
+<div class="viewcode-block" id="NDTMap"><a class="viewcode-back" href="../../../modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap">[docs]</a><span class="k">class</span> <span class="nc">NDTMap</span><span class="p">:</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Normal Distribution Transform (NDT) map class</span>
+
+<span class="sd"> :param ox: obstacle x position list</span>
+<span class="sd"> :param oy: obstacle y position list</span>
+<span class="sd"> :param resolution: grid resolution [m]</span>
+<span class="sd"> """</span>
+
+<div class="viewcode-block" id="NDTMap.NDTGrid"><a class="viewcode-back" href="../../../modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid">[docs]</a> <span class="k">class</span> <span class="nc">NDTGrid</span><span class="p">:</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> NDT grid</span>
+<span class="sd"> """</span>
+
+ <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+ <span class="c1">#: Number of points in the NDTGrid grid</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">n_points</span> <span class="o">=</span> <span class="mi">0</span>
+ <span class="c1">#: Mean x position of points in the NDTGrid cell</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">mean_x</span> <span class="o">=</span> <span class="kc">None</span>
+ <span class="c1">#: Mean y position of points in the NDTGrid cell</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">mean_y</span> <span class="o">=</span> <span class="kc">None</span>
+ <span class="c1">#: Center x position of the NDT grid</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">center_grid_x</span> <span class="o">=</span> <span class="kc">None</span>
+ <span class="c1">#: Center y position of the NDT grid</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">center_grid_y</span> <span class="o">=</span> <span class="kc">None</span>
+ <span class="c1">#: Covariance matrix of the NDT grid</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">covariance</span> <span class="o">=</span> <span class="kc">None</span>
+ <span class="c1">#: Eigen vectors of the NDT grid</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">eig_vec</span> <span class="o">=</span> <span class="kc">None</span>
+ <span class="c1">#: Eigen values of the NDT grid</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">eig_values</span> <span class="o">=</span> <span class="kc">None</span></div>
+
+ <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">,</span> <span class="n">resolution</span><span class="p">):</span>
+ <span class="c1">#: Minimum number of points in the NDT grid</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">min_n_points</span> <span class="o">=</span> <span class="mi">3</span>
+ <span class="c1">#: Resolution of the NDT grid [m]</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">resolution</span> <span class="o">=</span> <span class="n">resolution</span>
+ <span class="n">width</span> <span class="o">=</span> <span class="nb">int</span><span class="p">((</span><span class="nb">max</span><span class="p">(</span><span class="n">ox</span><span class="p">)</span> <span class="o">-</span> <span class="nb">min</span><span class="p">(</span><span class="n">ox</span><span class="p">))</span><span class="o">/</span><span class="n">resolution</span><span class="p">)</span> <span class="o">+</span> <span class="mi">3</span> <span class="c1"># rounding up + right and left margin</span>
+ <span class="n">height</span> <span class="o">=</span> <span class="nb">int</span><span class="p">((</span><span class="nb">max</span><span class="p">(</span><span class="n">oy</span><span class="p">)</span> <span class="o">-</span> <span class="nb">min</span><span class="p">(</span><span class="n">oy</span><span class="p">))</span><span class="o">/</span><span class="n">resolution</span><span class="p">)</span> <span class="o">+</span> <span class="mi">3</span>
+ <span class="n">center_x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">ox</span><span class="p">)</span>
+ <span class="n">center_y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">oy</span><span class="p">)</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">ox</span> <span class="o">=</span> <span class="n">ox</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">oy</span> <span class="o">=</span> <span class="n">oy</span>
+ <span class="c1">#: NDT grid index map</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">grid_index_map</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_create_grid_index_map</span><span class="p">(</span><span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">)</span>
+
+ <span class="c1">#: NDT grid map. Each grid contains NDTGrid object</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">_construct_grid_map</span><span class="p">(</span><span class="n">center_x</span><span class="p">,</span> <span class="n">center_y</span><span class="p">,</span> <span class="n">height</span><span class="p">,</span> <span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">,</span> <span class="n">resolution</span><span class="p">,</span> <span class="n">width</span><span class="p">)</span>
+
+ <span class="k">def</span> <span class="nf">_construct_grid_map</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">center_x</span><span class="p">,</span> <span class="n">center_y</span><span class="p">,</span> <span class="n">height</span><span class="p">,</span> <span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">,</span> <span class="n">resolution</span><span class="p">,</span> <span class="n">width</span><span class="p">):</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">grid_map</span> <span class="o">=</span> <span class="n">GridMap</span><span class="p">(</span><span class="n">width</span><span class="p">,</span> <span class="n">height</span><span class="p">,</span> <span class="n">resolution</span><span class="p">,</span> <span class="n">center_x</span><span class="p">,</span> <span class="n">center_y</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">NDTGrid</span><span class="p">())</span>
+ <span class="k">for</span> <span class="n">grid_index</span><span class="p">,</span> <span class="n">inds</span> <span class="ow">in</span> <span class="bp">self</span><span class="o">.</span><span class="n">grid_index_map</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+ <span class="n">ndt</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">NDTGrid</span><span class="p">()</span>
+ <span class="n">ndt</span><span class="o">.</span><span class="n">n_points</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">inds</span><span class="p">)</span>
+ <span class="k">if</span> <span class="n">ndt</span><span class="o">.</span><span class="n">n_points</span> <span class="o">>=</span> <span class="bp">self</span><span class="o">.</span><span class="n">min_n_points</span><span class="p">:</span>
+ <span class="n">ndt</span><span class="o">.</span><span class="n">mean_x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">ox</span><span class="p">[</span><span class="n">inds</span><span class="p">])</span>
+ <span class="n">ndt</span><span class="o">.</span><span class="n">mean_y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">oy</span><span class="p">[</span><span class="n">inds</span><span class="p">])</span>
+ <span class="n">ndt</span><span class="o">.</span><span class="n">center_grid_x</span><span class="p">,</span> <span class="n">ndt</span><span class="o">.</span><span class="n">center_grid_y</span> <span class="o">=</span> \
+ <span class="bp">self</span><span class="o">.</span><span class="n">grid_map</span><span class="o">.</span><span class="n">calc_grid_central_xy_position_from_grid_index</span><span class="p">(</span><span class="n">grid_index</span><span class="p">)</span>
+ <span class="n">ndt</span><span class="o">.</span><span class="n">covariance</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cov</span><span class="p">(</span><span class="n">ox</span><span class="p">[</span><span class="n">inds</span><span class="p">],</span> <span class="n">oy</span><span class="p">[</span><span class="n">inds</span><span class="p">])</span>
+ <span class="n">ndt</span><span class="o">.</span><span class="n">eig_values</span><span class="p">,</span> <span class="n">ndt</span><span class="o">.</span><span class="n">eig_vec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">ndt</span><span class="o">.</span><span class="n">covariance</span><span class="p">)</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">grid_map</span><span class="o">.</span><span class="n">data</span><span class="p">[</span><span class="n">grid_index</span><span class="p">]</span> <span class="o">=</span> <span class="n">ndt</span>
+
+ <span class="k">def</span> <span class="nf">_create_grid_index_map</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">):</span>
+ <span class="n">grid_index_map</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">ox</span><span class="p">)):</span>
+ <span class="n">grid_index</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">grid_map</span><span class="o">.</span><span class="n">calc_grid_index_from_xy_pos</span><span class="p">(</span><span class="n">ox</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">oy</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+ <span class="n">grid_index_map</span><span class="p">[</span><span class="n">grid_index</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">grid_index_map</span></div>
+
+
+<span class="k">def</span> <span class="nf">create_dummy_observation_data</span><span class="p">():</span>
+ <span class="n">ox</span> <span class="o">=</span> <span class="p">[]</span>
+ <span class="n">oy</span> <span class="o">=</span> <span class="p">[]</span>
+ <span class="c1"># left corridor</span>
+ <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="o">-</span><span class="mi">50</span><span class="p">,</span> <span class="mi">50</span><span class="p">):</span>
+ <span class="n">ox</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="o">-</span><span class="mf">20.0</span><span class="p">)</span>
+ <span class="n">oy</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
+ <span class="c1"># right corridor 1</span>
+ <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="o">-</span><span class="mi">50</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span>
+ <span class="n">ox</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mf">20.0</span><span class="p">)</span>
+ <span class="n">oy</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
+ <span class="c1"># right corridor 2</span>
+ <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">50</span><span class="p">):</span>
+ <span class="n">ox</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+ <span class="n">oy</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+ <span class="c1"># right corridor 3</span>
+ <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">50</span><span class="p">):</span>
+ <span class="n">ox</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+ <span class="n">oy</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">x</span><span class="o">/</span><span class="mf">2.0</span><span class="o">+</span><span class="mi">10</span><span class="p">)</span>
+ <span class="c1"># right corridor 4</span>
+ <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span> <span class="mi">50</span><span class="p">):</span>
+ <span class="n">ox</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="mi">20</span><span class="p">)</span>
+ <span class="n">oy</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
+ <span class="n">ox</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">ox</span><span class="p">)</span>
+ <span class="n">oy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">oy</span><span class="p">)</span>
+ <span class="c1"># Adding random noize</span>
+ <span class="n">ox</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">ox</span><span class="p">))</span> <span class="o">*</span> <span class="mf">1.0</span>
+ <span class="n">oy</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">ox</span><span class="p">))</span> <span class="o">*</span> <span class="mf">1.0</span>
+ <span class="k">return</span> <span class="n">ox</span><span class="p">,</span> <span class="n">oy</span>
+
+
+<span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
+ <span class="nb">print</span><span class="p">(</span><span class="vm">__file__</span> <span class="o">+</span> <span class="s2">" start!!"</span><span class="p">)</span>
+
+ <span class="n">ox</span><span class="p">,</span> <span class="n">oy</span> <span class="o">=</span> <span class="n">create_dummy_observation_data</span><span class="p">()</span>
+ <span class="n">grid_resolution</span> <span class="o">=</span> <span class="mf">10.0</span>
+ <span class="n">ndt_map</span> <span class="o">=</span> <span class="n">NDTMap</span><span class="p">(</span><span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">,</span> <span class="n">grid_resolution</span><span class="p">)</span>
+
+ <span class="c1"># plot raw observation</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">,</span> <span class="s2">".r"</span><span class="p">)</span>
+
+ <span class="c1"># plot grid clustering</span>
+ <span class="p">[</span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">ox</span><span class="p">[</span><span class="n">inds</span><span class="p">],</span> <span class="n">oy</span><span class="p">[</span><span class="n">inds</span><span class="p">],</span> <span class="s2">"x"</span><span class="p">)</span> <span class="k">for</span> <span class="n">inds</span> <span class="ow">in</span> <span class="n">ndt_map</span><span class="o">.</span><span class="n">grid_index_map</span><span class="o">.</span><span class="n">values</span><span class="p">()]</span>
+
+ <span class="c1"># plot ndt grid map</span>
+ <span class="p">[</span><span class="n">plot_covariance_ellipse</span><span class="p">(</span><span class="n">ndt</span><span class="o">.</span><span class="n">mean_x</span><span class="p">,</span> <span class="n">ndt</span><span class="o">.</span><span class="n">mean_y</span><span class="p">,</span> <span class="n">ndt</span><span class="o">.</span><span class="n">covariance</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"-k"</span><span class="p">)</span> <span class="k">for</span> <span class="n">ndt</span> <span class="ow">in</span> <span class="n">ndt_map</span><span class="o">.</span><span class="n">grid_map</span><span class="o">.</span><span class="n">data</span> <span class="k">if</span> <span class="n">ndt</span><span class="o">.</span><span class="n">n_points</span> <span class="o">></span> <span class="mi">0</span><span class="p">]</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+
+<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
+ <span class="n">main</span><span class="p">()</span>
+</pre></div>
+
+ </div>
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+
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+
+ <h1>Source code for Mapping.normal_vector_estimation.normal_vector_estimation</h1><div class="highlight"><pre>
+<span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">pyplot</span> <span class="k">as</span> <span class="n">plt</span>
+
+<span class="kn">from</span> <span class="nn">utils.plot</span> <span class="kn">import</span> <span class="n">plot_3d_vector_arrow</span><span class="p">,</span> <span class="n">plot_triangle</span><span class="p">,</span> <span class="n">set_equal_3d_axis</span>
+
+<span class="n">show_animation</span> <span class="o">=</span> <span class="kc">True</span>
+
+
+<div class="viewcode-block" id="calc_normal_vector"><a class="viewcode-back" href="../../../modules/mapping/normal_vector_estimation/normal_vector_estimation.html#Mapping.normal_vector_estimation.normal_vector_estimation.calc_normal_vector">[docs]</a><span class="k">def</span> <span class="nf">calc_normal_vector</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""Calculate normal vector of triangle</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> p1 : np.array</span>
+<span class="sd"> 3D point</span>
+<span class="sd"> p2 : np.array</span>
+<span class="sd"> 3D point</span>
+<span class="sd"> p3 : np.array</span>
+<span class="sd"> 3D point</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> normal_vector : np.array</span>
+<span class="sd"> normal vector (3,)</span>
+
+<span class="sd"> """</span>
+ <span class="c1"># calculate two vectors of triangle</span>
+ <span class="n">v1</span> <span class="o">=</span> <span class="n">p2</span> <span class="o">-</span> <span class="n">p1</span>
+ <span class="n">v2</span> <span class="o">=</span> <span class="n">p3</span> <span class="o">-</span> <span class="n">p1</span>
+
+ <span class="c1"># calculate normal vector</span>
+ <span class="n">normal_vector</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cross</span><span class="p">(</span><span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">)</span>
+
+ <span class="c1"># normalize vector</span>
+ <span class="n">normal_vector</span> <span class="o">=</span> <span class="n">normal_vector</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">normal_vector</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">normal_vector</span></div>
+
+
+<span class="k">def</span> <span class="nf">sample_3d_points_from_a_plane</span><span class="p">(</span><span class="n">num_samples</span><span class="p">,</span> <span class="n">normal</span><span class="p">):</span>
+ <span class="n">points_2d</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="p">(</span><span class="n">num_samples</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span> <span class="c1"># 2D points on a plane</span>
+ <span class="n">d</span> <span class="o">=</span> <span class="mi">0</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">points_2d</span><span class="p">)):</span>
+ <span class="n">point_3d</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">points_2d</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="mi">0</span><span class="p">)</span>
+ <span class="n">d</span> <span class="o">+=</span> <span class="n">normal</span> <span class="o">@</span> <span class="n">point_3d</span>
+ <span class="n">d</span> <span class="o">/=</span> <span class="nb">len</span><span class="p">(</span><span class="n">points_2d</span><span class="p">)</span>
+
+ <span class="n">points_3d</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">points_2d</span><span class="p">),</span> <span class="mi">3</span><span class="p">))</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">points_2d</span><span class="p">)):</span>
+ <span class="n">point_2d</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">points_2d</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="mi">0</span><span class="p">)</span>
+ <span class="n">projection_length</span> <span class="o">=</span> <span class="p">(</span><span class="n">d</span> <span class="o">-</span> <span class="n">normal</span> <span class="o">@</span> <span class="n">point_2d</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">normal</span><span class="p">)</span>
+ <span class="n">points_3d</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">point_2d</span> <span class="o">+</span> <span class="n">projection_length</span> <span class="o">*</span> <span class="n">normal</span>
+
+ <span class="k">return</span> <span class="n">points_3d</span>
+
+
+<span class="k">def</span> <span class="nf">distance_to_plane</span><span class="p">(</span><span class="n">point</span><span class="p">,</span> <span class="n">normal</span><span class="p">,</span> <span class="n">origin</span><span class="p">):</span>
+ <span class="n">dot_product</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">normal</span><span class="p">,</span> <span class="n">point</span><span class="p">)</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">normal</span><span class="p">,</span> <span class="n">origin</span><span class="p">)</span>
+ <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">isclose</span><span class="p">(</span><span class="n">dot_product</span><span class="p">,</span> <span class="mi">0</span><span class="p">):</span>
+ <span class="k">return</span> <span class="mf">0.0</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">distance</span> <span class="o">=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">dot_product</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">normal</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">distance</span>
+
+
+<div class="viewcode-block" id="ransac_normal_vector_estimation"><a class="viewcode-back" href="../../../modules/mapping/normal_vector_estimation/normal_vector_estimation.html#Mapping.normal_vector_estimation.normal_vector_estimation.ransac_normal_vector_estimation">[docs]</a><span class="k">def</span> <span class="nf">ransac_normal_vector_estimation</span><span class="p">(</span><span class="n">points_3d</span><span class="p">,</span> <span class="n">inlier_radio_th</span><span class="o">=</span><span class="mf">0.7</span><span class="p">,</span>
+ <span class="n">inlier_dist</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">p</span><span class="o">=</span><span class="mf">0.99</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> RANSAC based normal vector estimation</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> points_3d : np.array</span>
+<span class="sd"> 3D points (N, 3)</span>
+<span class="sd"> inlier_radio_th : float</span>
+<span class="sd"> Inlier ratio threshold. If inlier ratio is larger than this value,</span>
+<span class="sd"> the iteration is stopped. Default is 0.7.</span>
+<span class="sd"> inlier_dist : float</span>
+<span class="sd"> Inlier distance threshold. If distance between points and estimated</span>
+<span class="sd"> plane is smaller than this value, the point is inlier. Default is 0.1.</span>
+<span class="sd"> p : float</span>
+<span class="sd"> Probability that at least one of the sets of random samples does not</span>
+<span class="sd"> include an outlier. If this probability is near 1, the iteration</span>
+<span class="sd"> number is large. Default is 0.99.</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> center_vector : np.array</span>
+<span class="sd"> Center of estimated plane. (3,)</span>
+<span class="sd"> normal_vector : np.array</span>
+<span class="sd"> Normal vector of estimated plane. (3,)</span>
+
+<span class="sd"> """</span>
+ <span class="n">center</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">points_3d</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+
+ <span class="n">max_iter</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">floor</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="mf">1.0</span><span class="o">-</span><span class="n">p</span><span class="p">)</span><span class="o">/</span><span class="n">np</span><span class="o">.</span><span class="n">log</span><span class="p">(</span><span class="mf">1.0</span><span class="o">-</span><span class="p">(</span><span class="mf">1.0</span><span class="o">-</span><span class="n">inlier_radio_th</span><span class="p">)</span><span class="o">**</span><span class="mi">3</span><span class="p">)))</span>
+
+ <span class="k">for</span> <span class="n">ite</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">max_iter</span><span class="p">):</span>
+ <span class="c1"># Random sampling</span>
+ <span class="n">sampled_ids</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="n">points_3d</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">size</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span>
+ <span class="n">replace</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
+ <span class="n">sampled_points</span> <span class="o">=</span> <span class="n">points_3d</span><span class="p">[</span><span class="n">sampled_ids</span><span class="p">,</span> <span class="p">:]</span>
+ <span class="n">p1</span> <span class="o">=</span> <span class="n">sampled_points</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]</span>
+ <span class="n">p2</span> <span class="o">=</span> <span class="n">sampled_points</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]</span>
+ <span class="n">p3</span> <span class="o">=</span> <span class="n">sampled_points</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="p">:]</span>
+ <span class="n">normal_vector</span> <span class="o">=</span> <span class="n">calc_normal_vector</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">)</span>
+
+ <span class="c1"># calc inlier ratio</span>
+ <span class="n">n_inliner</span> <span class="o">=</span> <span class="mi">0</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">points_3d</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
+ <span class="n">p</span> <span class="o">=</span> <span class="n">points_3d</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:]</span>
+ <span class="k">if</span> <span class="n">distance_to_plane</span><span class="p">(</span><span class="n">p</span><span class="p">,</span> <span class="n">normal_vector</span><span class="p">,</span> <span class="n">center</span><span class="p">)</span> <span class="o"><=</span> <span class="n">inlier_dist</span><span class="p">:</span>
+ <span class="n">n_inliner</span> <span class="o">+=</span> <span class="mi">1</span>
+ <span class="n">inlier_ratio</span> <span class="o">=</span> <span class="n">n_inliner</span> <span class="o">/</span> <span class="n">points_3d</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+ <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Iter:</span><span class="si">{</span><span class="n">ite</span><span class="si">}</span><span class="s2">, </span><span class="si">{</span><span class="n">inlier_ratio</span><span class="si">=}</span><span class="s2">"</span><span class="p">)</span>
+ <span class="k">if</span> <span class="n">inlier_ratio</span> <span class="o">></span> <span class="n">inlier_radio_th</span><span class="p">:</span>
+ <span class="k">return</span> <span class="n">center</span><span class="p">,</span> <span class="n">normal_vector</span>
+
+ <span class="k">return</span> <span class="n">center</span><span class="p">,</span> <span class="kc">None</span></div>
+
+
+<span class="k">def</span> <span class="nf">main1</span><span class="p">():</span>
+ <span class="n">p1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">])</span>
+ <span class="n">p2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">])</span>
+ <span class="n">p3</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">])</span>
+
+ <span class="n">center</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">([</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">],</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
+ <span class="n">normal_vector</span> <span class="o">=</span> <span class="n">calc_normal_vector</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">)</span>
+ <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">center</span><span class="si">=}</span><span class="s2">"</span><span class="p">)</span>
+ <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">normal_vector</span><span class="si">=}</span><span class="s2">"</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">show_animation</span><span class="p">:</span>
+ <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+ <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
+ <span class="n">set_equal_3d_axis</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">])</span>
+ <span class="n">plot_triangle</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">,</span> <span class="n">ax</span><span class="p">)</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">center</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">center</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">center</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="s2">"ro"</span><span class="p">)</span>
+ <span class="n">plot_3d_vector_arrow</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">center</span><span class="p">,</span> <span class="n">center</span> <span class="o">+</span> <span class="n">normal_vector</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+
+<span class="k">def</span> <span class="nf">main2</span><span class="p">(</span><span class="n">rng</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+ <span class="n">true_normal</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">])</span>
+ <span class="n">true_normal</span> <span class="o">=</span> <span class="n">true_normal</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">true_normal</span><span class="p">)</span>
+ <span class="n">num_samples</span> <span class="o">=</span> <span class="mi">100</span>
+ <span class="n">noise_scale</span> <span class="o">=</span> <span class="mf">0.1</span>
+
+ <span class="n">points_3d</span> <span class="o">=</span> <span class="n">sample_3d_points_from_a_plane</span><span class="p">(</span><span class="n">num_samples</span><span class="p">,</span> <span class="n">true_normal</span><span class="p">)</span>
+ <span class="c1"># add random noise</span>
+ <span class="n">points_3d</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="n">size</span><span class="o">=</span><span class="n">points_3d</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">scale</span><span class="o">=</span><span class="n">noise_scale</span><span class="p">)</span>
+
+ <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">points_3d</span><span class="o">.</span><span class="n">shape</span><span class="si">=}</span><span class="s2">"</span><span class="p">)</span>
+
+ <span class="n">center</span><span class="p">,</span> <span class="n">estimated_normal</span> <span class="o">=</span> <span class="n">ransac_normal_vector_estimation</span><span class="p">(</span>
+ <span class="n">points_3d</span><span class="p">,</span> <span class="n">inlier_dist</span><span class="o">=</span><span class="n">noise_scale</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">estimated_normal</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"Failed to estimate normal vector"</span><span class="p">)</span>
+ <span class="k">return</span>
+
+ <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">true_normal</span><span class="si">=}</span><span class="s2">"</span><span class="p">)</span>
+ <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">estimated_normal</span><span class="si">=}</span><span class="s2">"</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">show_animation</span><span class="p">:</span>
+ <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+ <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">points_3d</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">points_3d</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">points_3d</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">],</span> <span class="s2">".r"</span><span class="p">)</span>
+ <span class="n">plot_3d_vector_arrow</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">center</span><span class="p">,</span> <span class="n">center</span> <span class="o">+</span> <span class="n">true_normal</span><span class="p">)</span>
+ <span class="n">plot_3d_vector_arrow</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">center</span><span class="p">,</span> <span class="n">center</span> <span class="o">+</span> <span class="n">estimated_normal</span><span class="p">)</span>
+ <span class="n">set_equal_3d_axis</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="p">[</span><span class="o">-</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">])</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"RANSAC based Normal vector estimation"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+
+<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
+ <span class="c1"># main1()</span>
+ <span class="n">main2</span><span class="p">()</span>
+</pre></div>
+
+ </div>
+ </div>
+ <footer>
+
+ <hr/>
+
+ <div role="contentinfo">
+ <p>© Copyright 2018-2021, Atsushi Sakai.</p>
+ </div>
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+ <h1>Source code for Mapping.point_cloud_sampling.point_cloud_sampling</h1><div class="highlight"><pre>
+<span></span><span class="sd">"""</span>
+<span class="sd">Point cloud sampling example codes. This code supports</span>
+<span class="sd">- Voxel point sampling</span>
+<span class="sd">- Farthest point sampling</span>
+<span class="sd">- Poisson disk sampling</span>
+
+<span class="sd">"""</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">numpy.typing</span> <span class="k">as</span> <span class="nn">npt</span>
+<span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">defaultdict</span>
+
+<span class="n">do_plot</span> <span class="o">=</span> <span class="kc">True</span>
+
+
+<div class="viewcode-block" id="voxel_point_sampling"><a class="viewcode-back" href="../../../modules/mapping/point_cloud_sampling/point_cloud_sampling.html#Mapping.point_cloud_sampling.point_cloud_sampling.voxel_point_sampling">[docs]</a><span class="k">def</span> <span class="nf">voxel_point_sampling</span><span class="p">(</span><span class="n">original_points</span><span class="p">:</span> <span class="n">npt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">voxel_size</span><span class="p">:</span> <span class="nb">float</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Voxel Point Sampling function.</span>
+<span class="sd"> This function sample N-dimensional points with voxel grid.</span>
+<span class="sd"> Points in a same voxel grid will be merged by mean operation for sampling.</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> original_points : (M, N) N-dimensional points for sampling.</span>
+<span class="sd"> The number of points is M.</span>
+<span class="sd"> voxel_size : voxel grid size</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> sampled points (M', N)</span>
+<span class="sd"> """</span>
+ <span class="n">voxel_dict</span> <span class="o">=</span> <span class="n">defaultdict</span><span class="p">(</span><span class="nb">list</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">original_points</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]):</span>
+ <span class="n">xyz</span> <span class="o">=</span> <span class="n">original_points</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="p">:]</span>
+ <span class="n">xyz_index</span> <span class="o">=</span> <span class="nb">tuple</span><span class="p">(</span><span class="n">xyz</span> <span class="o">//</span> <span class="n">voxel_size</span><span class="p">)</span>
+ <span class="n">voxel_dict</span><span class="p">[</span><span class="n">xyz_index</span><span class="p">]</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">xyz</span><span class="p">)</span>
+ <span class="n">points</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">mean</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span> <span class="k">for</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">voxel_dict</span><span class="o">.</span><span class="n">values</span><span class="p">()])</span>
+ <span class="k">return</span> <span class="n">points</span></div>
+
+
+<div class="viewcode-block" id="farthest_point_sampling"><a class="viewcode-back" href="../../../modules/mapping/point_cloud_sampling/point_cloud_sampling.html#Mapping.point_cloud_sampling.point_cloud_sampling.farthest_point_sampling">[docs]</a><span class="k">def</span> <span class="nf">farthest_point_sampling</span><span class="p">(</span><span class="n">orig_points</span><span class="p">:</span> <span class="n">npt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span>
+ <span class="n">n_points</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">seed</span><span class="p">:</span> <span class="nb">int</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Farthest point sampling function</span>
+<span class="sd"> This function sample N-dimensional points with the farthest point policy.</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> orig_points : (M, N) N-dimensional points for sampling.</span>
+<span class="sd"> The number of points is M.</span>
+<span class="sd"> n_points : number of points for sampling</span>
+<span class="sd"> seed : random seed number</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> sampled points (n_points, N)</span>
+
+<span class="sd"> """</span>
+ <span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="n">seed</span><span class="p">)</span>
+ <span class="n">n_orig_points</span> <span class="o">=</span> <span class="n">orig_points</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+ <span class="n">first_point_id</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">n_orig_points</span><span class="p">))</span>
+ <span class="n">min_distances</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">n_orig_points</span><span class="p">)</span> <span class="o">*</span> <span class="nb">float</span><span class="p">(</span><span class="s2">"inf"</span><span class="p">)</span>
+ <span class="n">selected_ids</span> <span class="o">=</span> <span class="p">[</span><span class="n">first_point_id</span><span class="p">]</span>
+ <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">selected_ids</span><span class="p">)</span> <span class="o"><</span> <span class="n">n_points</span><span class="p">:</span>
+ <span class="n">base_point</span> <span class="o">=</span> <span class="n">orig_points</span><span class="p">[</span><span class="n">selected_ids</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="p">:]</span>
+ <span class="n">distances</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span><span class="n">orig_points</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="p">:]</span> <span class="o">-</span> <span class="n">base_point</span><span class="p">,</span>
+ <span class="n">axis</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
+ <span class="n">min_distances</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">minimum</span><span class="p">(</span><span class="n">min_distances</span><span class="p">,</span> <span class="n">distances</span><span class="p">)</span>
+ <span class="n">distances_rank</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">argsort</span><span class="p">(</span><span class="o">-</span><span class="n">min_distances</span><span class="p">)</span> <span class="c1"># Farthest order</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">distances_rank</span><span class="p">:</span> <span class="c1"># From the farthest point</span>
+ <span class="k">if</span> <span class="n">i</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">selected_ids</span><span class="p">:</span> <span class="c1"># if not selected yes, select it</span>
+ <span class="n">selected_ids</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">i</span><span class="p">)</span>
+ <span class="k">break</span>
+ <span class="k">return</span> <span class="n">orig_points</span><span class="p">[</span><span class="n">selected_ids</span><span class="p">,</span> <span class="p">:]</span></div>
+
+
+<div class="viewcode-block" id="poisson_disk_sampling"><a class="viewcode-back" href="../../../modules/mapping/point_cloud_sampling/point_cloud_sampling.html#Mapping.point_cloud_sampling.point_cloud_sampling.poisson_disk_sampling">[docs]</a><span class="k">def</span> <span class="nf">poisson_disk_sampling</span><span class="p">(</span><span class="n">orig_points</span><span class="p">:</span> <span class="n">npt</span><span class="o">.</span><span class="n">NDArray</span><span class="p">,</span> <span class="n">n_points</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+ <span class="n">min_distance</span><span class="p">:</span> <span class="nb">float</span><span class="p">,</span> <span class="n">seed</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span> <span class="n">MAX_ITER</span><span class="o">=</span><span class="mi">1000</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Poisson disk sampling function</span>
+<span class="sd"> This function sample N-dimensional points randomly until the number of</span>
+<span class="sd"> points keeping minimum distance between selected points.</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> orig_points : (M, N) N-dimensional points for sampling.</span>
+<span class="sd"> The number of points is M.</span>
+<span class="sd"> n_points : number of points for sampling</span>
+<span class="sd"> min_distance : minimum distance between selected points.</span>
+<span class="sd"> seed : random seed number</span>
+<span class="sd"> MAX_ITER : Maximum number of iteration. Default is 1000.</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> sampled points (n_points or less, N)</span>
+<span class="sd"> """</span>
+ <span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="n">seed</span><span class="p">)</span>
+ <span class="n">selected_id</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">orig_points</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
+ <span class="n">selected_ids</span> <span class="o">=</span> <span class="p">[</span><span class="n">selected_id</span><span class="p">]</span>
+ <span class="n">loop</span> <span class="o">=</span> <span class="mi">0</span>
+ <span class="k">while</span> <span class="nb">len</span><span class="p">(</span><span class="n">selected_ids</span><span class="p">)</span> <span class="o"><</span> <span class="n">n_points</span> <span class="ow">and</span> <span class="n">loop</span> <span class="o"><=</span> <span class="n">MAX_ITER</span><span class="p">:</span>
+ <span class="n">selected_id</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">choice</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">orig_points</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
+ <span class="n">base_point</span> <span class="o">=</span> <span class="n">orig_points</span><span class="p">[</span><span class="n">selected_id</span><span class="p">,</span> <span class="p">:]</span>
+ <span class="n">distances</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">(</span>
+ <span class="n">orig_points</span><span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">newaxis</span><span class="p">,</span> <span class="n">selected_ids</span><span class="p">]</span> <span class="o">-</span> <span class="n">base_point</span><span class="p">,</span>
+ <span class="n">axis</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
+ <span class="k">if</span> <span class="nb">min</span><span class="p">(</span><span class="n">distances</span><span class="p">)</span> <span class="o">>=</span> <span class="n">min_distance</span><span class="p">:</span>
+ <span class="n">selected_ids</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">selected_id</span><span class="p">)</span>
+ <span class="n">loop</span> <span class="o">+=</span> <span class="mi">1</span>
+ <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">selected_ids</span><span class="p">)</span> <span class="o">!=</span> <span class="n">n_points</span><span class="p">:</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"Could not find the specified number of points..."</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">orig_points</span><span class="p">[</span><span class="n">selected_ids</span><span class="p">,</span> <span class="p">:]</span></div>
+
+
+<span class="k">def</span> <span class="nf">plot_sampled_points</span><span class="p">(</span><span class="n">original_points</span><span class="p">,</span> <span class="n">sampled_points</span><span class="p">,</span> <span class="n">method_name</span><span class="p">):</span>
+ <span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+ <span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">original_points</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">original_points</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span>
+ <span class="n">original_points</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">],</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"."</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Original points"</span><span class="p">)</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">scatter</span><span class="p">(</span><span class="n">sampled_points</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">sampled_points</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span>
+ <span class="n">sampled_points</span><span class="p">[:,</span> <span class="mi">2</span><span class="p">],</span> <span class="n">marker</span><span class="o">=</span><span class="s2">"o"</span><span class="p">,</span>
+ <span class="n">label</span><span class="o">=</span><span class="s2">"Filtered points"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="n">method_name</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+
+
+<span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
+ <span class="n">n_points</span> <span class="o">=</span> <span class="mi">1000</span>
+ <span class="n">seed</span> <span class="o">=</span> <span class="mi">1234</span>
+ <span class="n">rng</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">default_rng</span><span class="p">(</span><span class="n">seed</span><span class="p">)</span>
+
+ <span class="n">x</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">,</span> <span class="n">n_points</span><span class="p">)</span>
+ <span class="n">y</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">n_points</span><span class="p">)</span>
+ <span class="n">z</span> <span class="o">=</span> <span class="n">rng</span><span class="o">.</span><span class="n">normal</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">,</span> <span class="n">n_points</span><span class="p">)</span>
+ <span class="n">original_points</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">))</span><span class="o">.</span><span class="n">T</span>
+ <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">original_points</span><span class="o">.</span><span class="n">shape</span><span class="si">=}</span><span class="s2">"</span><span class="p">)</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"Voxel point sampling"</span><span class="p">)</span>
+ <span class="n">voxel_size</span> <span class="o">=</span> <span class="mf">20.0</span>
+ <span class="n">voxel_sampling_points</span> <span class="o">=</span> <span class="n">voxel_point_sampling</span><span class="p">(</span><span class="n">original_points</span><span class="p">,</span> <span class="n">voxel_size</span><span class="p">)</span>
+ <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">voxel_sampling_points</span><span class="o">.</span><span class="n">shape</span><span class="si">=}</span><span class="s2">"</span><span class="p">)</span>
+
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"Farthest point sampling"</span><span class="p">)</span>
+ <span class="n">n_points</span> <span class="o">=</span> <span class="mi">20</span>
+ <span class="n">farthest_sampling_points</span> <span class="o">=</span> <span class="n">farthest_point_sampling</span><span class="p">(</span><span class="n">original_points</span><span class="p">,</span>
+ <span class="n">n_points</span><span class="p">,</span> <span class="n">seed</span><span class="p">)</span>
+ <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">farthest_sampling_points</span><span class="o">.</span><span class="n">shape</span><span class="si">=}</span><span class="s2">"</span><span class="p">)</span>
+
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"Poisson disk sampling"</span><span class="p">)</span>
+ <span class="n">n_points</span> <span class="o">=</span> <span class="mi">20</span>
+ <span class="n">min_distance</span> <span class="o">=</span> <span class="mf">10.0</span>
+ <span class="n">poisson_disk_points</span> <span class="o">=</span> <span class="n">poisson_disk_sampling</span><span class="p">(</span><span class="n">original_points</span><span class="p">,</span> <span class="n">n_points</span><span class="p">,</span>
+ <span class="n">min_distance</span><span class="p">,</span> <span class="n">seed</span><span class="p">)</span>
+ <span class="nb">print</span><span class="p">(</span><span class="sa">f</span><span class="s2">"</span><span class="si">{</span><span class="n">poisson_disk_points</span><span class="o">.</span><span class="n">shape</span><span class="si">=}</span><span class="s2">"</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">do_plot</span><span class="p">:</span>
+ <span class="n">plot_sampled_points</span><span class="p">(</span><span class="n">original_points</span><span class="p">,</span> <span class="n">voxel_sampling_points</span><span class="p">,</span>
+ <span class="s2">"Voxel point sampling"</span><span class="p">)</span>
+ <span class="n">plot_sampled_points</span><span class="p">(</span><span class="n">original_points</span><span class="p">,</span> <span class="n">farthest_sampling_points</span><span class="p">,</span>
+ <span class="s2">"Farthest point sampling"</span><span class="p">)</span>
+ <span class="n">plot_sampled_points</span><span class="p">(</span><span class="n">original_points</span><span class="p">,</span> <span class="n">poisson_disk_points</span><span class="p">,</span>
+ <span class="s2">"poisson disk sampling"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+
+<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
+ <span class="n">main</span><span class="p">()</span>
+</pre></div>
+
+ </div>
+ </div>
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+
+ <hr/>
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+ <div role="contentinfo">
+ <p>© Copyright 2018-2021, Atsushi Sakai.</p>
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diff --git a/_modules/Mapping/rectangle_fitting/rectangle_fitting.html b/_modules/Mapping/rectangle_fitting/rectangle_fitting.html
new file mode 100644
index 00000000000..d2aa0724a7a
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+
+ <h1>Source code for Mapping.rectangle_fitting.rectangle_fitting</h1><div class="highlight"><pre>
+<span></span><span class="sd">"""</span>
+
+<span class="sd">Object shape recognition with L-shape fitting</span>
+
+<span class="sd">author: Atsushi Sakai (@Atsushi_twi)</span>
+
+<span class="sd">Ref:</span>
+<span class="sd">- Efficient L-Shape Fitting for Vehicle Detection Using Laser Scanners -</span>
+<span class="sd">The Robotics Institute Carnegie Mellon University</span>
+<span class="sd">https://www.ri.cmu.edu/publications/</span>
+<span class="sd">efficient-l-shape-fitting-for-vehicle-detection-using-laser-scanners/</span>
+
+<span class="sd">"""</span>
+
+<span class="kn">import</span> <span class="nn">sys</span>
+<span class="kn">import</span> <span class="nn">pathlib</span>
+<span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">pathlib</span><span class="o">.</span><span class="n">Path</span><span class="p">(</span><span class="vm">__file__</span><span class="p">)</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">parent</span><span class="p">))</span>
+
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">itertools</span>
+<span class="kn">from</span> <span class="nn">enum</span> <span class="kn">import</span> <span class="n">Enum</span>
+
+<span class="kn">from</span> <span class="nn">utils.angle</span> <span class="kn">import</span> <span class="n">rot_mat_2d</span>
+
+<span class="kn">from</span> <span class="nn">Mapping.rectangle_fitting.simulator</span> \
+ <span class="kn">import</span> <span class="nn">VehicleSimulator</span><span class="o">,</span> <span class="nn">LidarSimulator</span>
+
+<span class="n">show_animation</span> <span class="o">=</span> <span class="kc">True</span>
+
+
+<div class="viewcode-block" id="LShapeFitting"><a class="viewcode-back" href="../../../modules/mapping/rectangle_fitting/rectangle_fitting.html#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting">[docs]</a><span class="k">class</span> <span class="nc">LShapeFitting</span><span class="p">:</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> LShapeFitting class. You can use this class by initializing the class and</span>
+<span class="sd"> changing the parameters, and then calling the fitting method.</span>
+
+<span class="sd"> """</span>
+
+<div class="viewcode-block" id="LShapeFitting.Criteria"><a class="viewcode-back" href="../../../modules/mapping/rectangle_fitting/rectangle_fitting.html#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.Criteria">[docs]</a> <span class="k">class</span> <span class="nc">Criteria</span><span class="p">(</span><span class="n">Enum</span><span class="p">):</span>
+ <span class="n">AREA</span> <span class="o">=</span> <span class="mi">1</span>
+ <span class="n">CLOSENESS</span> <span class="o">=</span> <span class="mi">2</span>
+ <span class="n">VARIANCE</span> <span class="o">=</span> <span class="mi">3</span></div>
+
+ <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Default parameter settings</span>
+<span class="sd"> """</span>
+ <span class="c1">#: Fitting criteria parameter</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">criteria</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">Criteria</span><span class="o">.</span><span class="n">VARIANCE</span>
+ <span class="c1">#: Minimum distance for closeness criteria parameter [m]</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">min_dist_of_closeness_criteria</span> <span class="o">=</span> <span class="mf">0.01</span>
+ <span class="c1">#: Angle difference parameter [deg]</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">d_theta_deg_for_search</span> <span class="o">=</span> <span class="mf">1.0</span>
+ <span class="c1">#: Range segmentation parameter [m]</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">R0</span> <span class="o">=</span> <span class="mf">3.0</span>
+ <span class="c1">#: Range segmentation parameter [m]</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">Rd</span> <span class="o">=</span> <span class="mf">0.001</span>
+
+<div class="viewcode-block" id="LShapeFitting.fitting"><a class="viewcode-back" href="../../../modules/mapping/rectangle_fitting/rectangle_fitting.html#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.fitting">[docs]</a> <span class="k">def</span> <span class="nf">fitting</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Fitting L-shape model to object points</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> ox : x positions of range points from an object</span>
+<span class="sd"> oy : y positions of range points from an object</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> rects: Fitting rectangles</span>
+<span class="sd"> id_sets: id sets of each cluster</span>
+
+<span class="sd"> """</span>
+ <span class="c1"># step1: Adaptive Range Segmentation</span>
+ <span class="n">id_sets</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_adoptive_range_segmentation</span><span class="p">(</span><span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">)</span>
+
+ <span class="c1"># step2 Rectangle search</span>
+ <span class="n">rects</span> <span class="o">=</span> <span class="p">[]</span>
+ <span class="k">for</span> <span class="n">ids</span> <span class="ow">in</span> <span class="n">id_sets</span><span class="p">:</span> <span class="c1"># for each cluster</span>
+ <span class="n">cx</span> <span class="o">=</span> <span class="p">[</span><span class="n">ox</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">ox</span><span class="p">))</span> <span class="k">if</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">ids</span><span class="p">]</span>
+ <span class="n">cy</span> <span class="o">=</span> <span class="p">[</span><span class="n">oy</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">oy</span><span class="p">))</span> <span class="k">if</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">ids</span><span class="p">]</span>
+ <span class="n">rects</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">_rectangle_search</span><span class="p">(</span><span class="n">cx</span><span class="p">,</span> <span class="n">cy</span><span class="p">))</span>
+
+ <span class="k">return</span> <span class="n">rects</span><span class="p">,</span> <span class="n">id_sets</span></div>
+
+ <span class="nd">@staticmethod</span>
+ <span class="k">def</span> <span class="nf">_calc_area_criterion</span><span class="p">(</span><span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">):</span>
+ <span class="n">c1_max</span><span class="p">,</span> <span class="n">c1_min</span><span class="p">,</span> <span class="n">c2_max</span><span class="p">,</span> <span class="n">c2_min</span> <span class="o">=</span> <span class="n">LShapeFitting</span><span class="o">.</span><span class="n">_find_min_max</span><span class="p">(</span><span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">)</span>
+ <span class="n">alpha</span> <span class="o">=</span> <span class="o">-</span><span class="p">(</span><span class="n">c1_max</span> <span class="o">-</span> <span class="n">c1_min</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">c2_max</span> <span class="o">-</span> <span class="n">c2_min</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">alpha</span>
+
+ <span class="k">def</span> <span class="nf">_calc_closeness_criterion</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">):</span>
+ <span class="n">c1_max</span><span class="p">,</span> <span class="n">c1_min</span><span class="p">,</span> <span class="n">c2_max</span><span class="p">,</span> <span class="n">c2_min</span> <span class="o">=</span> <span class="n">LShapeFitting</span><span class="o">.</span><span class="n">_find_min_max</span><span class="p">(</span><span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">)</span>
+
+ <span class="c1"># Vectorization</span>
+ <span class="n">d1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">minimum</span><span class="p">(</span><span class="n">c1_max</span> <span class="o">-</span> <span class="n">c1</span><span class="p">,</span> <span class="n">c1</span> <span class="o">-</span> <span class="n">c1_min</span><span class="p">)</span>
+ <span class="n">d2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">minimum</span><span class="p">(</span><span class="n">c2_max</span> <span class="o">-</span> <span class="n">c2</span><span class="p">,</span> <span class="n">c2</span> <span class="o">-</span> <span class="n">c2_min</span><span class="p">)</span>
+ <span class="n">d</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">maximum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">minimum</span><span class="p">(</span><span class="n">d1</span><span class="p">,</span> <span class="n">d2</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">min_dist_of_closeness_criteria</span><span class="p">)</span>
+ <span class="n">beta</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">/</span> <span class="n">d</span><span class="p">)</span><span class="o">.</span><span class="n">sum</span><span class="p">()</span>
+
+ <span class="k">return</span> <span class="n">beta</span>
+
+ <span class="nd">@staticmethod</span>
+ <span class="k">def</span> <span class="nf">_calc_variance_criterion</span><span class="p">(</span><span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">):</span>
+ <span class="n">c1_max</span><span class="p">,</span> <span class="n">c1_min</span><span class="p">,</span> <span class="n">c2_max</span><span class="p">,</span> <span class="n">c2_min</span> <span class="o">=</span> <span class="n">LShapeFitting</span><span class="o">.</span><span class="n">_find_min_max</span><span class="p">(</span><span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">)</span>
+
+ <span class="c1"># Vectorization</span>
+ <span class="n">d1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">minimum</span><span class="p">(</span><span class="n">c1_max</span> <span class="o">-</span> <span class="n">c1</span><span class="p">,</span> <span class="n">c1</span> <span class="o">-</span> <span class="n">c1_min</span><span class="p">)</span>
+ <span class="n">d2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">minimum</span><span class="p">(</span><span class="n">c2_max</span> <span class="o">-</span> <span class="n">c2</span><span class="p">,</span> <span class="n">c2</span> <span class="o">-</span> <span class="n">c2_min</span><span class="p">)</span>
+ <span class="n">e1</span> <span class="o">=</span> <span class="n">d1</span><span class="p">[</span><span class="n">d1</span> <span class="o"><</span> <span class="n">d2</span><span class="p">]</span>
+ <span class="n">e2</span> <span class="o">=</span> <span class="n">d2</span><span class="p">[</span><span class="n">d1</span> <span class="o">>=</span> <span class="n">d2</span><span class="p">]</span>
+ <span class="n">v1</span> <span class="o">=</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">var</span><span class="p">(</span><span class="n">e1</span><span class="p">)</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">e1</span><span class="p">)</span> <span class="o">></span> <span class="mi">0</span> <span class="k">else</span> <span class="mf">0.</span>
+ <span class="n">v2</span> <span class="o">=</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">var</span><span class="p">(</span><span class="n">e2</span><span class="p">)</span> <span class="k">if</span> <span class="nb">len</span><span class="p">(</span><span class="n">e2</span><span class="p">)</span> <span class="o">></span> <span class="mi">0</span> <span class="k">else</span> <span class="mf">0.</span>
+ <span class="n">gamma</span> <span class="o">=</span> <span class="n">v1</span> <span class="o">+</span> <span class="n">v2</span>
+
+ <span class="k">return</span> <span class="n">gamma</span>
+
+ <span class="nd">@staticmethod</span>
+ <span class="k">def</span> <span class="nf">_find_min_max</span><span class="p">(</span><span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">):</span>
+ <span class="n">c1_max</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span>
+ <span class="n">c2_max</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">c2</span><span class="p">)</span>
+ <span class="n">c1_min</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">c1</span><span class="p">)</span>
+ <span class="n">c2_min</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">c2</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">c1_max</span><span class="p">,</span> <span class="n">c1_min</span><span class="p">,</span> <span class="n">c2_max</span><span class="p">,</span> <span class="n">c2_min</span>
+
+ <span class="k">def</span> <span class="nf">_rectangle_search</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
+
+ <span class="n">xy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">])</span><span class="o">.</span><span class="n">T</span>
+
+ <span class="n">d_theta</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">d_theta_deg_for_search</span><span class="p">)</span>
+ <span class="n">min_cost</span> <span class="o">=</span> <span class="p">(</span><span class="o">-</span><span class="nb">float</span><span class="p">(</span><span class="s1">'inf'</span><span class="p">),</span> <span class="kc">None</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">theta</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mf">2.0</span> <span class="o">-</span> <span class="n">d_theta</span><span class="p">,</span> <span class="n">d_theta</span><span class="p">):</span>
+
+ <span class="n">c</span> <span class="o">=</span> <span class="n">xy</span> <span class="o">@</span> <span class="n">rot_mat_2d</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
+ <span class="n">c1</span> <span class="o">=</span> <span class="n">c</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">c2</span> <span class="o">=</span> <span class="n">c</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span>
+
+ <span class="c1"># Select criteria</span>
+ <span class="n">cost</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="k">if</span> <span class="bp">self</span><span class="o">.</span><span class="n">criteria</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">Criteria</span><span class="o">.</span><span class="n">AREA</span><span class="p">:</span>
+ <span class="n">cost</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_calc_area_criterion</span><span class="p">(</span><span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">)</span>
+ <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">criteria</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">Criteria</span><span class="o">.</span><span class="n">CLOSENESS</span><span class="p">:</span>
+ <span class="n">cost</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_calc_closeness_criterion</span><span class="p">(</span><span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">)</span>
+ <span class="k">elif</span> <span class="bp">self</span><span class="o">.</span><span class="n">criteria</span> <span class="o">==</span> <span class="bp">self</span><span class="o">.</span><span class="n">Criteria</span><span class="o">.</span><span class="n">VARIANCE</span><span class="p">:</span>
+ <span class="n">cost</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_calc_variance_criterion</span><span class="p">(</span><span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">min_cost</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o"><</span> <span class="n">cost</span><span class="p">:</span>
+ <span class="n">min_cost</span> <span class="o">=</span> <span class="p">(</span><span class="n">cost</span><span class="p">,</span> <span class="n">theta</span><span class="p">)</span>
+
+ <span class="c1"># calc best rectangle</span>
+ <span class="n">sin_s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">min_cost</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+ <span class="n">cos_s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">min_cost</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+
+ <span class="n">c1_s</span> <span class="o">=</span> <span class="n">xy</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">cos_s</span><span class="p">,</span> <span class="n">sin_s</span><span class="p">])</span><span class="o">.</span><span class="n">T</span>
+ <span class="n">c2_s</span> <span class="o">=</span> <span class="n">xy</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="n">sin_s</span><span class="p">,</span> <span class="n">cos_s</span><span class="p">])</span><span class="o">.</span><span class="n">T</span>
+
+ <span class="n">rect</span> <span class="o">=</span> <span class="n">RectangleData</span><span class="p">()</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">cos_s</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">sin_s</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">c1_s</span><span class="p">)</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="n">sin_s</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">cos_s</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">c2_s</span><span class="p">)</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">cos_s</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">b</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">sin_s</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">c1_s</span><span class="p">)</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span><span class="n">sin_s</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">b</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="n">cos_s</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">c2_s</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">rect</span>
+
+ <span class="k">def</span> <span class="nf">_adoptive_range_segmentation</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">):</span>
+
+ <span class="c1"># Setup initial cluster</span>
+ <span class="n">segment_list</span> <span class="o">=</span> <span class="p">[]</span>
+ <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">ox</span><span class="p">):</span>
+ <span class="n">c</span> <span class="o">=</span> <span class="nb">set</span><span class="p">()</span>
+ <span class="n">r</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">R0</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">Rd</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">norm</span><span class="p">([</span><span class="n">ox</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">oy</span><span class="p">[</span><span class="n">i</span><span class="p">]])</span>
+ <span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">ox</span><span class="p">):</span>
+ <span class="n">d</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hypot</span><span class="p">(</span><span class="n">ox</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="n">ox</span><span class="p">[</span><span class="n">j</span><span class="p">],</span> <span class="n">oy</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="n">oy</span><span class="p">[</span><span class="n">j</span><span class="p">])</span>
+ <span class="k">if</span> <span class="n">d</span> <span class="o"><=</span> <span class="n">r</span><span class="p">:</span>
+ <span class="n">c</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">j</span><span class="p">)</span>
+ <span class="n">segment_list</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
+
+ <span class="c1"># Merge cluster</span>
+ <span class="k">while</span> <span class="kc">True</span><span class="p">:</span>
+ <span class="n">no_change</span> <span class="o">=</span> <span class="kc">True</span>
+ <span class="k">for</span> <span class="p">(</span><span class="n">c1</span><span class="p">,</span> <span class="n">c2</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">list</span><span class="p">(</span><span class="n">itertools</span><span class="o">.</span><span class="n">permutations</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">segment_list</span><span class="p">)),</span> <span class="mi">2</span><span class="p">)):</span>
+ <span class="k">if</span> <span class="n">segment_list</span><span class="p">[</span><span class="n">c1</span><span class="p">]</span> <span class="o">&</span> <span class="n">segment_list</span><span class="p">[</span><span class="n">c2</span><span class="p">]:</span>
+ <span class="n">segment_list</span><span class="p">[</span><span class="n">c1</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="n">segment_list</span><span class="p">[</span><span class="n">c1</span><span class="p">]</span> <span class="o">|</span> <span class="n">segment_list</span><span class="o">.</span><span class="n">pop</span><span class="p">(</span><span class="n">c2</span><span class="p">))</span>
+ <span class="n">no_change</span> <span class="o">=</span> <span class="kc">False</span>
+ <span class="k">break</span>
+ <span class="k">if</span> <span class="n">no_change</span><span class="p">:</span>
+ <span class="k">break</span>
+
+ <span class="k">return</span> <span class="n">segment_list</span></div>
+
+
+<span class="k">class</span> <span class="nc">RectangleData</span><span class="p">:</span>
+
+ <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="mi">4</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">b</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="mi">4</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">c</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="mi">4</span>
+
+ <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_x</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_y</span> <span class="o">=</span> <span class="p">[</span><span class="kc">None</span><span class="p">]</span> <span class="o">*</span> <span class="mi">5</span>
+
+ <span class="k">def</span> <span class="nf">plot</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">calc_rect_contour</span><span class="p">()</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">rect_c_x</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_y</span><span class="p">,</span> <span class="s2">"-r"</span><span class="p">)</span>
+
+ <span class="k">def</span> <span class="nf">calc_rect_contour</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+
+ <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_x</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">calc_cross_point</span><span class="p">(</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">])</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_x</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">calc_cross_point</span><span class="p">(</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">3</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">3</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">3</span><span class="p">])</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_x</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_y</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">calc_cross_point</span><span class="p">(</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="mi">2</span><span class="p">:</span><span class="mi">4</span><span class="p">])</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_x</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_y</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">calc_cross_point</span><span class="p">(</span>
+ <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span> <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="mi">3</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">]])</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_x</span><span class="p">[</span><span class="mi">4</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_y</span><span class="p">[</span><span class="mi">4</span><span class="p">]</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_x</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">rect_c_y</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+
+ <span class="nd">@staticmethod</span>
+ <span class="k">def</span> <span class="nf">calc_cross_point</span><span class="p">(</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">c</span><span class="p">):</span>
+ <span class="n">x</span> <span class="o">=</span> <span class="p">(</span><span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="o">-</span><span class="n">c</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="o">-</span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">/</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+ <span class="n">y</span> <span class="o">=</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="o">-</span><span class="n">c</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="o">-</span><span class="n">c</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">b</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">b</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+ <span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span>
+
+
+<span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
+
+ <span class="c1"># simulation parameters</span>
+ <span class="n">sim_time</span> <span class="o">=</span> <span class="mf">30.0</span> <span class="c1"># simulation time</span>
+ <span class="n">dt</span> <span class="o">=</span> <span class="mf">0.2</span> <span class="c1"># time tick</span>
+
+ <span class="n">angle_resolution</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">3.0</span><span class="p">)</span> <span class="c1"># sensor angle resolution</span>
+
+ <span class="n">v1</span> <span class="o">=</span> <span class="n">VehicleSimulator</span><span class="p">(</span><span class="o">-</span><span class="mf">10.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">90.0</span><span class="p">),</span>
+ <span class="mf">0.0</span><span class="p">,</span> <span class="mf">50.0</span> <span class="o">/</span> <span class="mf">3.6</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">)</span>
+ <span class="n">v2</span> <span class="o">=</span> <span class="n">VehicleSimulator</span><span class="p">(</span><span class="mf">20.0</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">180.0</span><span class="p">),</span>
+ <span class="mf">0.0</span><span class="p">,</span> <span class="mf">50.0</span> <span class="o">/</span> <span class="mf">3.6</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">)</span>
+
+ <span class="n">l_shape_fitting</span> <span class="o">=</span> <span class="n">LShapeFitting</span><span class="p">()</span>
+ <span class="n">lidar_sim</span> <span class="o">=</span> <span class="n">LidarSimulator</span><span class="p">()</span>
+
+ <span class="n">time</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="k">while</span> <span class="n">time</span> <span class="o"><=</span> <span class="n">sim_time</span><span class="p">:</span>
+ <span class="n">time</span> <span class="o">+=</span> <span class="n">dt</span>
+
+ <span class="n">v1</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">dt</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">)</span>
+ <span class="n">v2</span><span class="o">.</span><span class="n">update</span><span class="p">(</span><span class="n">dt</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.05</span><span class="p">)</span>
+
+ <span class="n">ox</span><span class="p">,</span> <span class="n">oy</span> <span class="o">=</span> <span class="n">lidar_sim</span><span class="o">.</span><span class="n">get_observation_points</span><span class="p">([</span><span class="n">v1</span><span class="p">,</span> <span class="n">v2</span><span class="p">],</span> <span class="n">angle_resolution</span><span class="p">)</span>
+
+ <span class="n">rects</span><span class="p">,</span> <span class="n">id_sets</span> <span class="o">=</span> <span class="n">l_shape_fitting</span><span class="o">.</span><span class="n">fitting</span><span class="p">(</span><span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">show_animation</span><span class="p">:</span> <span class="c1"># pragma: no cover</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">cla</span><span class="p">()</span>
+ <span class="c1"># for stopping simulation with the esc key.</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">gcf</span><span class="p">()</span><span class="o">.</span><span class="n">canvas</span><span class="o">.</span><span class="n">mpl_connect</span><span class="p">(</span>
+ <span class="s1">'key_release_event'</span><span class="p">,</span>
+ <span class="k">lambda</span> <span class="n">event</span><span class="p">:</span> <span class="p">[</span><span class="n">exit</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span> <span class="k">if</span> <span class="n">event</span><span class="o">.</span><span class="n">key</span> <span class="o">==</span> <span class="s1">'escape'</span> <span class="k">else</span> <span class="kc">None</span><span class="p">])</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="s2">"*r"</span><span class="p">)</span>
+ <span class="n">v1</span><span class="o">.</span><span class="n">plot</span><span class="p">()</span>
+ <span class="n">v2</span><span class="o">.</span><span class="n">plot</span><span class="p">()</span>
+
+ <span class="c1"># Plot range observation</span>
+ <span class="k">for</span> <span class="n">ids</span> <span class="ow">in</span> <span class="n">id_sets</span><span class="p">:</span>
+ <span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="n">ox</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">ox</span><span class="p">))</span> <span class="k">if</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">ids</span><span class="p">]</span>
+ <span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="n">oy</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">ox</span><span class="p">))</span> <span class="k">if</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">ids</span><span class="p">]</span>
+
+ <span class="k">for</span> <span class="p">(</span><span class="n">ix</span><span class="p">,</span> <span class="n">iy</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">ix</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">iy</span><span class="p">],</span> <span class="s2">"-og"</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">ox</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">ox</span><span class="p">))</span> <span class="k">if</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">ids</span><span class="p">],</span>
+ <span class="p">[</span><span class="n">oy</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">ox</span><span class="p">))</span> <span class="k">if</span> <span class="n">i</span> <span class="ow">in</span> <span class="n">ids</span><span class="p">],</span>
+ <span class="s2">"o"</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">rect</span> <span class="ow">in</span> <span class="n">rects</span><span class="p">:</span>
+ <span class="n">rect</span><span class="o">.</span><span class="n">plot</span><span class="p">()</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">pause</span><span class="p">(</span><span class="mf">0.1</span><span class="p">)</span>
+
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"Done"</span><span class="p">)</span>
+
+
+<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
+ <span class="n">main</span><span class="p">()</span>
+</pre></div>
+
+ </div>
+ </div>
+ <footer>
+
+ <hr/>
+
+ <div role="contentinfo">
+ <p>© Copyright 2018-2021, Atsushi Sakai.</p>
+ </div>
+
+ Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
+ <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
+ provided by <a href="https://readthedocs.org">Read the Docs</a>.
+
+
+</footer>
+ </div>
+ </div>
+ </section>
+ </div>
+ <script>
+ jQuery(function () {
+ SphinxRtdTheme.Navigation.enable(true);
+ });
+ </script>
+
+</body>
+</html>
\ No newline at end of file
diff --git a/_modules/PathPlanning/BSplinePath/bspline_path.html b/_modules/PathPlanning/BSplinePath/bspline_path.html
new file mode 100644
index 00000000000..3725c430746
--- /dev/null
+++ b/_modules/PathPlanning/BSplinePath/bspline_path.html
@@ -0,0 +1,285 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
+<head>
+ <meta charset="utf-8" />
+ <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+ <title>PathPlanning.BSplinePath.bspline_path — PythonRobotics documentation</title>
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+ <link rel="stylesheet" href="../../../_static/custom.css" type="text/css" />
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+ <!--[if lt IE 9]>
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+ <li>PathPlanning.BSplinePath.bspline_path</li>
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+ <h1>Source code for PathPlanning.BSplinePath.bspline_path</h1><div class="highlight"><pre>
+<span></span><span class="sd">"""</span>
+
+<span class="sd">Path Planner with B-Spline</span>
+
+<span class="sd">author: Atsushi Sakai (@Atsushi_twi)</span>
+
+<span class="sd">"""</span>
+<span class="kn">import</span> <span class="nn">sys</span>
+<span class="kn">import</span> <span class="nn">pathlib</span>
+<span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">pathlib</span><span class="o">.</span><span class="n">Path</span><span class="p">(</span><span class="vm">__file__</span><span class="p">)</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">parent</span><span class="p">))</span>
+
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">scipy.interpolate</span> <span class="k">as</span> <span class="nn">interpolate</span>
+
+<span class="kn">from</span> <span class="nn">utils.plot</span> <span class="kn">import</span> <span class="n">plot_curvature</span>
+
+
+<div class="viewcode-block" id="approximate_b_spline_path"><a class="viewcode-back" href="../../../modules/path_planning/bspline_path/bspline_path.html#PathPlanning.BSplinePath.bspline_path.approximate_b_spline_path">[docs]</a><span class="k">def</span> <span class="nf">approximate_b_spline_path</span><span class="p">(</span><span class="n">x</span><span class="p">:</span> <span class="nb">list</span><span class="p">,</span>
+ <span class="n">y</span><span class="p">:</span> <span class="nb">list</span><span class="p">,</span>
+ <span class="n">n_path_points</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+ <span class="n">degree</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">3</span><span class="p">,</span>
+ <span class="n">s</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span>
+ <span class="p">)</span> <span class="o">-></span> <span class="nb">tuple</span><span class="p">:</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Approximate points with a B-Spline path</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> x : array_like</span>
+<span class="sd"> x position list of approximated points</span>
+<span class="sd"> y : array_like</span>
+<span class="sd"> y position list of approximated points</span>
+<span class="sd"> n_path_points : int</span>
+<span class="sd"> number of path points</span>
+<span class="sd"> degree : int, optional</span>
+<span class="sd"> B Spline curve degree. Must be 2<= k <= 5. Default: 3.</span>
+<span class="sd"> s : int, optional</span>
+<span class="sd"> smoothing parameter. If this value is bigger, the path will be</span>
+<span class="sd"> smoother, but it will be less accurate. If this value is smaller,</span>
+<span class="sd"> the path will be more accurate, but it will be less smooth.</span>
+<span class="sd"> When `s` is 0, it is equivalent to the interpolation. Default is None,</span>
+<span class="sd"> in this case `s` will be `len(x)`.</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> x : array</span>
+<span class="sd"> x positions of the result path</span>
+<span class="sd"> y : array</span>
+<span class="sd"> y positions of the result path</span>
+<span class="sd"> heading : array</span>
+<span class="sd"> heading of the result path</span>
+<span class="sd"> curvature : array</span>
+<span class="sd"> curvature of the result path</span>
+
+<span class="sd"> """</span>
+ <span class="n">distances</span> <span class="o">=</span> <span class="n">_calc_distance_vector</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+
+ <span class="n">spl_i_x</span> <span class="o">=</span> <span class="n">interpolate</span><span class="o">.</span><span class="n">UnivariateSpline</span><span class="p">(</span><span class="n">distances</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="n">degree</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="n">s</span><span class="p">)</span>
+ <span class="n">spl_i_y</span> <span class="o">=</span> <span class="n">interpolate</span><span class="o">.</span><span class="n">UnivariateSpline</span><span class="p">(</span><span class="n">distances</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">k</span><span class="o">=</span><span class="n">degree</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="n">s</span><span class="p">)</span>
+
+ <span class="n">sampled</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">distances</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">n_path_points</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">_evaluate_spline</span><span class="p">(</span><span class="n">sampled</span><span class="p">,</span> <span class="n">spl_i_x</span><span class="p">,</span> <span class="n">spl_i_y</span><span class="p">)</span></div>
+
+
+<div class="viewcode-block" id="interpolate_b_spline_path"><a class="viewcode-back" href="../../../modules/path_planning/bspline_path/bspline_path.html#PathPlanning.BSplinePath.bspline_path.interpolate_b_spline_path">[docs]</a><span class="k">def</span> <span class="nf">interpolate_b_spline_path</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span>
+ <span class="n">n_path_points</span><span class="p">:</span> <span class="nb">int</span><span class="p">,</span>
+ <span class="n">degree</span><span class="p">:</span> <span class="nb">int</span> <span class="o">=</span> <span class="mi">3</span><span class="p">)</span> <span class="o">-></span> <span class="nb">tuple</span><span class="p">:</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Interpolate x-y points with a B-Spline path</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> x : array_like</span>
+<span class="sd"> x positions of interpolated points</span>
+<span class="sd"> y : array_like</span>
+<span class="sd"> y positions of interpolated points</span>
+<span class="sd"> n_path_points : int</span>
+<span class="sd"> number of path points</span>
+<span class="sd"> degree : int, optional</span>
+<span class="sd"> B-Spline degree. Must be 2<= k <= 5. Default: 3</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> x : array</span>
+<span class="sd"> x positions of the result path</span>
+<span class="sd"> y : array</span>
+<span class="sd"> y positions of the result path</span>
+<span class="sd"> heading : array</span>
+<span class="sd"> heading of the result path</span>
+<span class="sd"> curvature : array</span>
+<span class="sd"> curvature of the result path</span>
+
+<span class="sd"> """</span>
+ <span class="k">return</span> <span class="n">approximate_b_spline_path</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">n_path_points</span><span class="p">,</span> <span class="n">degree</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mf">0.0</span><span class="p">)</span></div>
+
+
+<span class="k">def</span> <span class="nf">_calc_distance_vector</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
+ <span class="n">dx</span><span class="p">,</span> <span class="n">dy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
+ <span class="n">distances</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">([</span><span class="n">np</span><span class="o">.</span><span class="n">hypot</span><span class="p">(</span><span class="n">idx</span><span class="p">,</span> <span class="n">idy</span><span class="p">)</span> <span class="k">for</span> <span class="n">idx</span><span class="p">,</span> <span class="n">idy</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">)])</span>
+ <span class="n">distances</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(([</span><span class="mf">0.0</span><span class="p">],</span> <span class="n">distances</span><span class="p">))</span>
+ <span class="n">distances</span> <span class="o">/=</span> <span class="n">distances</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+ <span class="k">return</span> <span class="n">distances</span>
+
+
+<span class="k">def</span> <span class="nf">_evaluate_spline</span><span class="p">(</span><span class="n">sampled</span><span class="p">,</span> <span class="n">spl_i_x</span><span class="p">,</span> <span class="n">spl_i_y</span><span class="p">):</span>
+ <span class="n">x</span> <span class="o">=</span> <span class="n">spl_i_x</span><span class="p">(</span><span class="n">sampled</span><span class="p">)</span>
+ <span class="n">y</span> <span class="o">=</span> <span class="n">spl_i_y</span><span class="p">(</span><span class="n">sampled</span><span class="p">)</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="n">spl_i_x</span><span class="o">.</span><span class="n">derivative</span><span class="p">(</span><span class="mi">1</span><span class="p">)(</span><span class="n">sampled</span><span class="p">)</span>
+ <span class="n">dy</span> <span class="o">=</span> <span class="n">spl_i_y</span><span class="o">.</span><span class="n">derivative</span><span class="p">(</span><span class="mi">1</span><span class="p">)(</span><span class="n">sampled</span><span class="p">)</span>
+ <span class="n">heading</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arctan2</span><span class="p">(</span><span class="n">dy</span><span class="p">,</span> <span class="n">dx</span><span class="p">)</span>
+ <span class="n">ddx</span> <span class="o">=</span> <span class="n">spl_i_x</span><span class="o">.</span><span class="n">derivative</span><span class="p">(</span><span class="mi">2</span><span class="p">)(</span><span class="n">sampled</span><span class="p">)</span>
+ <span class="n">ddy</span> <span class="o">=</span> <span class="n">spl_i_y</span><span class="o">.</span><span class="n">derivative</span><span class="p">(</span><span class="mi">2</span><span class="p">)(</span><span class="n">sampled</span><span class="p">)</span>
+ <span class="n">curvature</span> <span class="o">=</span> <span class="p">(</span><span class="n">ddy</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">-</span> <span class="n">ddx</span> <span class="o">*</span> <span class="n">dy</span><span class="p">)</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">power</span><span class="p">(</span><span class="n">dx</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">+</span> <span class="n">dy</span> <span class="o">*</span> <span class="n">dy</span><span class="p">,</span> <span class="mf">2.0</span> <span class="o">/</span> <span class="mf">3.0</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="n">y</span><span class="p">,</span> <span class="n">heading</span><span class="p">,</span> <span class="n">curvature</span><span class="p">,</span>
+
+
+<span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
+ <span class="nb">print</span><span class="p">(</span><span class="vm">__file__</span> <span class="o">+</span> <span class="s2">" start!!"</span><span class="p">)</span>
+ <span class="c1"># way points</span>
+ <span class="n">way_point_x</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="mf">4.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]</span>
+ <span class="n">way_point_y</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">]</span>
+ <span class="n">n_course_point</span> <span class="o">=</span> <span class="mi">50</span> <span class="c1"># sampling number</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+ <span class="n">rax</span><span class="p">,</span> <span class="n">ray</span><span class="p">,</span> <span class="n">heading</span><span class="p">,</span> <span class="n">curvature</span> <span class="o">=</span> <span class="n">approximate_b_spline_path</span><span class="p">(</span>
+ <span class="n">way_point_x</span><span class="p">,</span> <span class="n">way_point_y</span><span class="p">,</span> <span class="n">n_course_point</span><span class="p">,</span> <span class="n">s</span><span class="o">=</span><span class="mf">0.5</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rax</span><span class="p">,</span> <span class="n">ray</span><span class="p">,</span> <span class="s1">'-r'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Approximated B-Spline path"</span><span class="p">)</span>
+ <span class="n">plot_curvature</span><span class="p">(</span><span class="n">rax</span><span class="p">,</span> <span class="n">ray</span><span class="p">,</span> <span class="n">heading</span><span class="p">,</span> <span class="n">curvature</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"B-Spline approximation"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">way_point_x</span><span class="p">,</span> <span class="n">way_point_y</span><span class="p">,</span> <span class="s1">'-og'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"way points"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">()</span>
+ <span class="n">rix</span><span class="p">,</span> <span class="n">riy</span><span class="p">,</span> <span class="n">heading</span><span class="p">,</span> <span class="n">curvature</span> <span class="o">=</span> <span class="n">interpolate_b_spline_path</span><span class="p">(</span>
+ <span class="n">way_point_x</span><span class="p">,</span> <span class="n">way_point_y</span><span class="p">,</span> <span class="n">n_course_point</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rix</span><span class="p">,</span> <span class="n">riy</span><span class="p">,</span> <span class="s1">'-b'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Interpolated B-Spline path"</span><span class="p">)</span>
+ <span class="n">plot_curvature</span><span class="p">(</span><span class="n">rix</span><span class="p">,</span> <span class="n">riy</span><span class="p">,</span> <span class="n">heading</span><span class="p">,</span> <span class="n">curvature</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="s2">"B-Spline interpolation"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">way_point_x</span><span class="p">,</span> <span class="n">way_point_y</span><span class="p">,</span> <span class="s1">'-og'</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"way points"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+
+<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
+ <span class="n">main</span><span class="p">()</span>
+</pre></div>
+
+ </div>
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+
+ <h1>Source code for PathPlanning.CubicSpline.cubic_spline_planner</h1><div class="highlight"><pre>
+<span></span><span class="sd">"""</span>
+<span class="sd">Cubic spline planner</span>
+
+<span class="sd">Author: Atsushi Sakai(@Atsushi_twi)</span>
+
+<span class="sd">"""</span>
+<span class="kn">import</span> <span class="nn">math</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">bisect</span>
+
+
+<div class="viewcode-block" id="CubicSpline1D"><a class="viewcode-back" href="../../../modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D">[docs]</a><span class="k">class</span> <span class="nc">CubicSpline1D</span><span class="p">:</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> 1D Cubic Spline class</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> x : list</span>
+<span class="sd"> x coordinates for data points. This x coordinates must be</span>
+<span class="sd"> sorted</span>
+<span class="sd"> in ascending order.</span>
+<span class="sd"> y : list</span>
+<span class="sd"> y coordinates for data points</span>
+
+<span class="sd"> Examples</span>
+<span class="sd"> --------</span>
+<span class="sd"> You can interpolate 1D data points.</span>
+
+<span class="sd"> >>> import numpy as np</span>
+<span class="sd"> >>> import matplotlib.pyplot as plt</span>
+<span class="sd"> >>> x = np.arange(5)</span>
+<span class="sd"> >>> y = [1.7, -6, 5, 6.5, 0.0]</span>
+<span class="sd"> >>> sp = CubicSpline1D(x, y)</span>
+<span class="sd"> >>> xi = np.linspace(0.0, 5.0)</span>
+<span class="sd"> >>> yi = [sp.calc_position(x) for x in xi]</span>
+<span class="sd"> >>> plt.plot(x, y, "xb", label="Data points")</span>
+<span class="sd"> >>> plt.plot(xi, yi , "r", label="Cubic spline interpolation")</span>
+<span class="sd"> >>> plt.grid(True)</span>
+<span class="sd"> >>> plt.legend()</span>
+<span class="sd"> >>> plt.show()</span>
+
+<span class="sd"> .. image:: cubic_spline_1d.png</span>
+
+<span class="sd"> """</span>
+
+ <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
+
+ <span class="n">h</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+ <span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">h</span> <span class="o"><</span> <span class="mi">0</span><span class="p">):</span>
+ <span class="k">raise</span> <span class="ne">ValueError</span><span class="p">(</span><span class="s2">"x coordinates must be sorted in ascending order"</span><span class="p">)</span>
+
+ <span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">d</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="n">x</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">=</span> <span class="n">y</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">nx</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="c1"># dimension of x</span>
+
+ <span class="c1"># calc coefficient a</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">a</span> <span class="o">=</span> <span class="p">[</span><span class="n">iy</span> <span class="k">for</span> <span class="n">iy</span> <span class="ow">in</span> <span class="n">y</span><span class="p">]</span>
+
+ <span class="c1"># calc coefficient c</span>
+ <span class="n">A</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__calc_A</span><span class="p">(</span><span class="n">h</span><span class="p">)</span>
+ <span class="n">B</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__calc_B</span><span class="p">(</span><span class="n">h</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">)</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">solve</span><span class="p">(</span><span class="n">A</span><span class="p">,</span> <span class="n">B</span><span class="p">)</span>
+
+ <span class="c1"># calc spline coefficient b and d</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nx</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+ <span class="n">d</span> <span class="o">=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">/</span> <span class="p">(</span><span class="mf">3.0</span> <span class="o">*</span> <span class="n">h</span><span class="p">[</span><span class="n">i</span><span class="p">])</span>
+ <span class="n">b</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="n">h</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> \
+ <span class="o">-</span> <span class="n">h</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">/</span> <span class="mf">3.0</span> <span class="o">*</span> <span class="p">(</span><span class="mf">2.0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">d</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">d</span><span class="p">)</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
+
+<div class="viewcode-block" id="CubicSpline1D.calc_position"><a class="viewcode-back" href="../../../modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_position">[docs]</a> <span class="k">def</span> <span class="nf">calc_position</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Calc `y` position for given `x`.</span>
+
+<span class="sd"> if `x` is outside the data point's `x` range, return None.</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> y : float</span>
+<span class="sd"> y position for given x.</span>
+<span class="sd"> """</span>
+ <span class="k">if</span> <span class="n">x</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
+ <span class="k">return</span> <span class="kc">None</span>
+ <span class="k">elif</span> <span class="n">x</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
+ <span class="k">return</span> <span class="kc">None</span>
+
+ <span class="n">i</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__search_index</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+ <span class="n">position</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">+</span> \
+ <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">**</span> <span class="mf">2.0</span> <span class="o">+</span> <span class="bp">self</span><span class="o">.</span><span class="n">d</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">**</span> <span class="mf">3.0</span>
+
+ <span class="k">return</span> <span class="n">position</span></div>
+
+<div class="viewcode-block" id="CubicSpline1D.calc_first_derivative"><a class="viewcode-back" href="../../../modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_first_derivative">[docs]</a> <span class="k">def</span> <span class="nf">calc_first_derivative</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Calc first derivative at given x.</span>
+
+<span class="sd"> if x is outside the input x, return None</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> dy : float</span>
+<span class="sd"> first derivative for given x.</span>
+<span class="sd"> """</span>
+
+ <span class="k">if</span> <span class="n">x</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
+ <span class="k">return</span> <span class="kc">None</span>
+ <span class="k">elif</span> <span class="n">x</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
+ <span class="k">return</span> <span class="kc">None</span>
+
+ <span class="n">i</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__search_index</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+ <span class="n">dy</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">b</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">+</span> <span class="mf">3.0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">d</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">**</span> <span class="mf">2.0</span>
+ <span class="k">return</span> <span class="n">dy</span></div>
+
+<div class="viewcode-block" id="CubicSpline1D.calc_second_derivative"><a class="viewcode-back" href="../../../modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_second_derivative">[docs]</a> <span class="k">def</span> <span class="nf">calc_second_derivative</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Calc second derivative at given x.</span>
+
+<span class="sd"> if x is outside the input x, return None</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> ddy : float</span>
+<span class="sd"> second derivative for given x.</span>
+<span class="sd"> """</span>
+
+ <span class="k">if</span> <span class="n">x</span> <span class="o"><</span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">]:</span>
+ <span class="k">return</span> <span class="kc">None</span>
+ <span class="k">elif</span> <span class="n">x</span> <span class="o">></span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]:</span>
+ <span class="k">return</span> <span class="kc">None</span>
+
+ <span class="n">i</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__search_index</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="n">x</span> <span class="o">-</span> <span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+ <span class="n">ddy</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="mf">6.0</span> <span class="o">*</span> <span class="bp">self</span><span class="o">.</span><span class="n">d</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">*</span> <span class="n">dx</span>
+ <span class="k">return</span> <span class="n">ddy</span></div>
+
+ <span class="k">def</span> <span class="nf">__search_index</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> search data segment index</span>
+<span class="sd"> """</span>
+ <span class="k">return</span> <span class="n">bisect</span><span class="o">.</span><span class="n">bisect</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span>
+
+ <span class="k">def</span> <span class="nf">__calc_A</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">h</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> calc matrix A for spline coefficient c</span>
+<span class="sd"> """</span>
+ <span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="bp">self</span><span class="o">.</span><span class="n">nx</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nx</span><span class="p">))</span>
+ <span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nx</span> <span class="o">-</span> <span class="mi">1</span><span class="p">):</span>
+ <span class="k">if</span> <span class="n">i</span> <span class="o">!=</span> <span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nx</span> <span class="o">-</span> <span class="mi">2</span><span class="p">):</span>
+ <span class="n">A</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="p">(</span><span class="n">h</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="n">h</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span>
+ <span class="n">A</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">h</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+ <span class="n">A</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">h</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+
+ <span class="n">A</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="n">A</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">nx</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nx</span> <span class="o">-</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="n">A</span><span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">nx</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="bp">self</span><span class="o">.</span><span class="n">nx</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span>
+ <span class="k">return</span> <span class="n">A</span>
+
+ <span class="k">def</span> <span class="nf">__calc_B</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">h</span><span class="p">,</span> <span class="n">a</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> calc matrix B for spline coefficient c</span>
+<span class="sd"> """</span>
+ <span class="n">B</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nx</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">nx</span> <span class="o">-</span> <span class="mi">2</span><span class="p">):</span>
+ <span class="n">B</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mf">3.0</span> <span class="o">*</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span> <span class="o">/</span> <span class="n">h</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span>\
+ <span class="o">-</span> <span class="mf">3.0</span> <span class="o">*</span> <span class="p">(</span><span class="n">a</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">/</span> <span class="n">h</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
+ <span class="k">return</span> <span class="n">B</span></div>
+
+
+<div class="viewcode-block" id="CubicSpline2D"><a class="viewcode-back" href="../../../modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D">[docs]</a><span class="k">class</span> <span class="nc">CubicSpline2D</span><span class="p">:</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Cubic CubicSpline2D class</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> x : list</span>
+<span class="sd"> x coordinates for data points.</span>
+<span class="sd"> y : list</span>
+<span class="sd"> y coordinates for data points.</span>
+
+<span class="sd"> Examples</span>
+<span class="sd"> --------</span>
+<span class="sd"> You can interpolate a 2D data points.</span>
+
+<span class="sd"> >>> import matplotlib.pyplot as plt</span>
+<span class="sd"> >>> x = [-2.5, 0.0, 2.5, 5.0, 7.5, 3.0, -1.0]</span>
+<span class="sd"> >>> y = [0.7, -6, 5, 6.5, 0.0, 5.0, -2.0]</span>
+<span class="sd"> >>> ds = 0.1 # [m] distance of each interpolated points</span>
+<span class="sd"> >>> sp = CubicSpline2D(x, y)</span>
+<span class="sd"> >>> s = np.arange(0, sp.s[-1], ds)</span>
+<span class="sd"> >>> rx, ry, ryaw, rk = [], [], [], []</span>
+<span class="sd"> >>> for i_s in s:</span>
+<span class="sd"> ... ix, iy = sp.calc_position(i_s)</span>
+<span class="sd"> ... rx.append(ix)</span>
+<span class="sd"> ... ry.append(iy)</span>
+<span class="sd"> ... ryaw.append(sp.calc_yaw(i_s))</span>
+<span class="sd"> ... rk.append(sp.calc_curvature(i_s))</span>
+<span class="sd"> >>> plt.subplots(1)</span>
+<span class="sd"> >>> plt.plot(x, y, "xb", label="Data points")</span>
+<span class="sd"> >>> plt.plot(rx, ry, "-r", label="Cubic spline path")</span>
+<span class="sd"> >>> plt.grid(True)</span>
+<span class="sd"> >>> plt.axis("equal")</span>
+<span class="sd"> >>> plt.xlabel("x[m]")</span>
+<span class="sd"> >>> plt.ylabel("y[m]")</span>
+<span class="sd"> >>> plt.legend()</span>
+<span class="sd"> >>> plt.show()</span>
+
+<span class="sd"> .. image:: cubic_spline_2d_path.png</span>
+
+<span class="sd"> >>> plt.subplots(1)</span>
+<span class="sd"> >>> plt.plot(s, [np.rad2deg(iyaw) for iyaw in ryaw], "-r", label="yaw")</span>
+<span class="sd"> >>> plt.grid(True)</span>
+<span class="sd"> >>> plt.legend()</span>
+<span class="sd"> >>> plt.xlabel("line length[m]")</span>
+<span class="sd"> >>> plt.ylabel("yaw angle[deg]")</span>
+
+<span class="sd"> .. image:: cubic_spline_2d_yaw.png</span>
+
+<span class="sd"> >>> plt.subplots(1)</span>
+<span class="sd"> >>> plt.plot(s, rk, "-r", label="curvature")</span>
+<span class="sd"> >>> plt.grid(True)</span>
+<span class="sd"> >>> plt.legend()</span>
+<span class="sd"> >>> plt.xlabel("line length[m]")</span>
+<span class="sd"> >>> plt.ylabel("curvature [1/m]")</span>
+
+<span class="sd"> .. image:: cubic_spline_2d_curvature.png</span>
+<span class="sd"> """</span>
+
+ <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">s</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">__calc_s</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">sx</span> <span class="o">=</span> <span class="n">CubicSpline1D</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">s</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">sy</span> <span class="o">=</span> <span class="n">CubicSpline1D</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">s</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+
+ <span class="k">def</span> <span class="nf">__calc_s</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">):</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+ <span class="n">dy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diff</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">ds</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hypot</span><span class="p">(</span><span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">)</span>
+ <span class="n">s</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+ <span class="n">s</span><span class="o">.</span><span class="n">extend</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">ds</span><span class="p">))</span>
+ <span class="k">return</span> <span class="n">s</span>
+
+<div class="viewcode-block" id="CubicSpline2D.calc_position"><a class="viewcode-back" href="../../../modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_position">[docs]</a> <span class="k">def</span> <span class="nf">calc_position</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">s</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> calc position</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> s : float</span>
+<span class="sd"> distance from the start point. if `s` is outside the data point's</span>
+<span class="sd"> range, return None.</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> x : float</span>
+<span class="sd"> x position for given s.</span>
+<span class="sd"> y : float</span>
+<span class="sd"> y position for given s.</span>
+<span class="sd"> """</span>
+ <span class="n">x</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sx</span><span class="o">.</span><span class="n">calc_position</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
+ <span class="n">y</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sy</span><span class="o">.</span><span class="n">calc_position</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span></div>
+
+<div class="viewcode-block" id="CubicSpline2D.calc_curvature"><a class="viewcode-back" href="../../../modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_curvature">[docs]</a> <span class="k">def</span> <span class="nf">calc_curvature</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">s</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> calc curvature</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> s : float</span>
+<span class="sd"> distance from the start point. if `s` is outside the data point's</span>
+<span class="sd"> range, return None.</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> k : float</span>
+<span class="sd"> curvature for given s.</span>
+<span class="sd"> """</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sx</span><span class="o">.</span><span class="n">calc_first_derivative</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
+ <span class="n">ddx</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sx</span><span class="o">.</span><span class="n">calc_second_derivative</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
+ <span class="n">dy</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sy</span><span class="o">.</span><span class="n">calc_first_derivative</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
+ <span class="n">ddy</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sy</span><span class="o">.</span><span class="n">calc_second_derivative</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
+ <span class="n">k</span> <span class="o">=</span> <span class="p">(</span><span class="n">ddy</span> <span class="o">*</span> <span class="n">dx</span> <span class="o">-</span> <span class="n">ddx</span> <span class="o">*</span> <span class="n">dy</span><span class="p">)</span> <span class="o">/</span> <span class="p">((</span><span class="n">dx</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">dy</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span><span class="o">**</span><span class="p">(</span><span class="mi">3</span> <span class="o">/</span> <span class="mi">2</span><span class="p">))</span>
+ <span class="k">return</span> <span class="n">k</span></div>
+
+<div class="viewcode-block" id="CubicSpline2D.calc_yaw"><a class="viewcode-back" href="../../../modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_yaw">[docs]</a> <span class="k">def</span> <span class="nf">calc_yaw</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">s</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> calc yaw</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> s : float</span>
+<span class="sd"> distance from the start point. if `s` is outside the data point's</span>
+<span class="sd"> range, return None.</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> yaw : float</span>
+<span class="sd"> yaw angle (tangent vector) for given s.</span>
+<span class="sd"> """</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sx</span><span class="o">.</span><span class="n">calc_first_derivative</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
+ <span class="n">dy</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">sy</span><span class="o">.</span><span class="n">calc_first_derivative</span><span class="p">(</span><span class="n">s</span><span class="p">)</span>
+ <span class="n">yaw</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">dy</span><span class="p">,</span> <span class="n">dx</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">yaw</span></div></div>
+
+
+<span class="k">def</span> <span class="nf">calc_spline_course</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">ds</span><span class="o">=</span><span class="mf">0.1</span><span class="p">):</span>
+ <span class="n">sp</span> <span class="o">=</span> <span class="n">CubicSpline2D</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+ <span class="n">s</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">sp</span><span class="o">.</span><span class="n">s</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">ds</span><span class="p">))</span>
+
+ <span class="n">rx</span><span class="p">,</span> <span class="n">ry</span><span class="p">,</span> <span class="n">ryaw</span><span class="p">,</span> <span class="n">rk</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
+ <span class="k">for</span> <span class="n">i_s</span> <span class="ow">in</span> <span class="n">s</span><span class="p">:</span>
+ <span class="n">ix</span><span class="p">,</span> <span class="n">iy</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">calc_position</span><span class="p">(</span><span class="n">i_s</span><span class="p">)</span>
+ <span class="n">rx</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">ix</span><span class="p">)</span>
+ <span class="n">ry</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">iy</span><span class="p">)</span>
+ <span class="n">ryaw</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">calc_yaw</span><span class="p">(</span><span class="n">i_s</span><span class="p">))</span>
+ <span class="n">rk</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">calc_curvature</span><span class="p">(</span><span class="n">i_s</span><span class="p">))</span>
+
+ <span class="k">return</span> <span class="n">rx</span><span class="p">,</span> <span class="n">ry</span><span class="p">,</span> <span class="n">ryaw</span><span class="p">,</span> <span class="n">rk</span><span class="p">,</span> <span class="n">s</span>
+
+
+<span class="k">def</span> <span class="nf">main_1d</span><span class="p">():</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"CubicSpline1D test"</span><span class="p">)</span>
+ <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+ <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+ <span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.7</span><span class="p">,</span> <span class="o">-</span><span class="mi">6</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mf">6.5</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]</span>
+ <span class="n">sp</span> <span class="o">=</span> <span class="n">CubicSpline1D</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+ <span class="n">xi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s2">"xb"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Data points"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xi</span><span class="p">,</span> <span class="p">[</span><span class="n">sp</span><span class="o">.</span><span class="n">calc_position</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">xi</span><span class="p">],</span> <span class="s2">"r"</span><span class="p">,</span>
+ <span class="n">label</span><span class="o">=</span><span class="s2">"Cubic spline interpolation"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+
+<span class="k">def</span> <span class="nf">main_2d</span><span class="p">():</span> <span class="c1"># pragma: no cover</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"CubicSpline1D 2D test"</span><span class="p">)</span>
+ <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+ <span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">,</span> <span class="mf">7.5</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="p">]</span>
+ <span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.7</span><span class="p">,</span> <span class="o">-</span><span class="mi">6</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mf">6.5</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.0</span><span class="p">]</span>
+ <span class="n">ds</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="c1"># [m] distance of each interpolated points</span>
+
+ <span class="n">sp</span> <span class="o">=</span> <span class="n">CubicSpline2D</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+ <span class="n">s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">sp</span><span class="o">.</span><span class="n">s</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">ds</span><span class="p">)</span>
+
+ <span class="n">rx</span><span class="p">,</span> <span class="n">ry</span><span class="p">,</span> <span class="n">ryaw</span><span class="p">,</span> <span class="n">rk</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
+ <span class="k">for</span> <span class="n">i_s</span> <span class="ow">in</span> <span class="n">s</span><span class="p">:</span>
+ <span class="n">ix</span><span class="p">,</span> <span class="n">iy</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">calc_position</span><span class="p">(</span><span class="n">i_s</span><span class="p">)</span>
+ <span class="n">rx</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">ix</span><span class="p">)</span>
+ <span class="n">ry</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">iy</span><span class="p">)</span>
+ <span class="n">ryaw</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">calc_yaw</span><span class="p">(</span><span class="n">i_s</span><span class="p">))</span>
+ <span class="n">rk</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">calc_curvature</span><span class="p">(</span><span class="n">i_s</span><span class="p">))</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s2">"xb"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Data points"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rx</span><span class="p">,</span> <span class="n">ry</span><span class="p">,</span> <span class="s2">"-r"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Cubic spline path"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"x[m]"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"y[m]"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">rad2deg</span><span class="p">(</span><span class="n">iyaw</span><span class="p">)</span> <span class="k">for</span> <span class="n">iyaw</span> <span class="ow">in</span> <span class="n">ryaw</span><span class="p">],</span> <span class="s2">"-r"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"yaw"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"line length[m]"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"yaw angle[deg]"</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">rk</span><span class="p">,</span> <span class="s2">"-r"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"curvature"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"line length[m]"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"curvature [1/m]"</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+
+<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
+ <span class="c1"># main_1d()</span>
+ <span class="n">main_2d</span><span class="p">()</span>
+</pre></div>
+
+ </div>
+ </div>
+ <footer>
+
+ <hr/>
+
+ <div role="contentinfo">
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+
+ <h1>Source code for PathPlanning.DubinsPath.dubins_path_planner</h1><div class="highlight"><pre>
+<span></span><span class="sd">"""</span>
+
+<span class="sd">Dubins path planner sample code</span>
+
+<span class="sd">author Atsushi Sakai(@Atsushi_twi)</span>
+
+<span class="sd">"""</span>
+<span class="kn">import</span> <span class="nn">sys</span>
+<span class="kn">import</span> <span class="nn">pathlib</span>
+<span class="n">sys</span><span class="o">.</span><span class="n">path</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">str</span><span class="p">(</span><span class="n">pathlib</span><span class="o">.</span><span class="n">Path</span><span class="p">(</span><span class="vm">__file__</span><span class="p">)</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">parent</span><span class="o">.</span><span class="n">parent</span><span class="p">))</span>
+
+<span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sin</span><span class="p">,</span> <span class="n">cos</span><span class="p">,</span> <span class="n">atan2</span><span class="p">,</span> <span class="n">sqrt</span><span class="p">,</span> <span class="n">acos</span><span class="p">,</span> <span class="n">pi</span><span class="p">,</span> <span class="n">hypot</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">utils.angle</span> <span class="kn">import</span> <span class="n">angle_mod</span><span class="p">,</span> <span class="n">rot_mat_2d</span>
+
+<span class="n">show_animation</span> <span class="o">=</span> <span class="kc">True</span>
+
+
+<div class="viewcode-block" id="plan_dubins_path"><a class="viewcode-back" href="../../../modules/path_planning/dubins_path/dubins_path.html#PathPlanning.DubinsPath.dubins_path_planner.plan_dubins_path">[docs]</a><span class="k">def</span> <span class="nf">plan_dubins_path</span><span class="p">(</span><span class="n">s_x</span><span class="p">,</span> <span class="n">s_y</span><span class="p">,</span> <span class="n">s_yaw</span><span class="p">,</span> <span class="n">g_x</span><span class="p">,</span> <span class="n">g_y</span><span class="p">,</span> <span class="n">g_yaw</span><span class="p">,</span> <span class="n">curvature</span><span class="p">,</span>
+ <span class="n">step_size</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">selected_types</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Plan dubins path</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> s_x : float</span>
+<span class="sd"> x position of the start point [m]</span>
+<span class="sd"> s_y : float</span>
+<span class="sd"> y position of the start point [m]</span>
+<span class="sd"> s_yaw : float</span>
+<span class="sd"> yaw angle of the start point [rad]</span>
+<span class="sd"> g_x : float</span>
+<span class="sd"> x position of the goal point [m]</span>
+<span class="sd"> g_y : float</span>
+<span class="sd"> y position of the end point [m]</span>
+<span class="sd"> g_yaw : float</span>
+<span class="sd"> yaw angle of the end point [rad]</span>
+<span class="sd"> curvature : float</span>
+<span class="sd"> curvature for curve [1/m]</span>
+<span class="sd"> step_size : float (optional)</span>
+<span class="sd"> step size between two path points [m]. Default is 0.1</span>
+<span class="sd"> selected_types : a list of string or None</span>
+<span class="sd"> selected path planning types. If None, all types are used for</span>
+<span class="sd"> path planning, and minimum path length result is returned.</span>
+<span class="sd"> You can select used path plannings types by a string list.</span>
+<span class="sd"> e.g.: ["RSL", "RSR"]</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> x_list: array</span>
+<span class="sd"> x positions of the path</span>
+<span class="sd"> y_list: array</span>
+<span class="sd"> y positions of the path</span>
+<span class="sd"> yaw_list: array</span>
+<span class="sd"> yaw angles of the path</span>
+<span class="sd"> modes: array</span>
+<span class="sd"> mode list of the path</span>
+<span class="sd"> lengths: array</span>
+<span class="sd"> arrow_length list of the path segments.</span>
+
+<span class="sd"> Examples</span>
+<span class="sd"> --------</span>
+<span class="sd"> You can generate a dubins path.</span>
+
+<span class="sd"> >>> start_x = 1.0 # [m]</span>
+<span class="sd"> >>> start_y = 1.0 # [m]</span>
+<span class="sd"> >>> start_yaw = np.deg2rad(45.0) # [rad]</span>
+<span class="sd"> >>> end_x = -3.0 # [m]</span>
+<span class="sd"> >>> end_y = -3.0 # [m]</span>
+<span class="sd"> >>> end_yaw = np.deg2rad(-45.0) # [rad]</span>
+<span class="sd"> >>> curvature = 1.0</span>
+<span class="sd"> >>> path_x, path_y, path_yaw, mode, _ = plan_dubins_path(</span>
+<span class="sd"> start_x, start_y, start_yaw, end_x, end_y, end_yaw, curvature)</span>
+<span class="sd"> >>> plt.plot(path_x, path_y, label="final course " + "".join(mode))</span>
+<span class="sd"> >>> plot_arrow(start_x, start_y, start_yaw)</span>
+<span class="sd"> >>> plot_arrow(end_x, end_y, end_yaw)</span>
+<span class="sd"> >>> plt.legend()</span>
+<span class="sd"> >>> plt.grid(True)</span>
+<span class="sd"> >>> plt.axis("equal")</span>
+<span class="sd"> >>> plt.show()</span>
+
+<span class="sd"> .. image:: dubins_path.jpg</span>
+<span class="sd"> """</span>
+ <span class="k">if</span> <span class="n">selected_types</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+ <span class="n">planning_funcs</span> <span class="o">=</span> <span class="n">_PATH_TYPE_MAP</span><span class="o">.</span><span class="n">values</span><span class="p">()</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">planning_funcs</span> <span class="o">=</span> <span class="p">[</span><span class="n">_PATH_TYPE_MAP</span><span class="p">[</span><span class="n">ptype</span><span class="p">]</span> <span class="k">for</span> <span class="n">ptype</span> <span class="ow">in</span> <span class="n">selected_types</span><span class="p">]</span>
+
+ <span class="c1"># calculate local goal x, y, yaw</span>
+ <span class="n">l_rot</span> <span class="o">=</span> <span class="n">rot_mat_2d</span><span class="p">(</span><span class="n">s_yaw</span><span class="p">)</span>
+ <span class="n">le_xy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">stack</span><span class="p">([</span><span class="n">g_x</span> <span class="o">-</span> <span class="n">s_x</span><span class="p">,</span> <span class="n">g_y</span> <span class="o">-</span> <span class="n">s_y</span><span class="p">])</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">l_rot</span>
+ <span class="n">local_goal_x</span> <span class="o">=</span> <span class="n">le_xy</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+ <span class="n">local_goal_y</span> <span class="o">=</span> <span class="n">le_xy</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+ <span class="n">local_goal_yaw</span> <span class="o">=</span> <span class="n">g_yaw</span> <span class="o">-</span> <span class="n">s_yaw</span>
+
+ <span class="n">lp_x</span><span class="p">,</span> <span class="n">lp_y</span><span class="p">,</span> <span class="n">lp_yaw</span><span class="p">,</span> <span class="n">modes</span><span class="p">,</span> <span class="n">lengths</span> <span class="o">=</span> <span class="n">_dubins_path_planning_from_origin</span><span class="p">(</span>
+ <span class="n">local_goal_x</span><span class="p">,</span> <span class="n">local_goal_y</span><span class="p">,</span> <span class="n">local_goal_yaw</span><span class="p">,</span> <span class="n">curvature</span><span class="p">,</span> <span class="n">step_size</span><span class="p">,</span>
+ <span class="n">planning_funcs</span><span class="p">)</span>
+
+ <span class="c1"># Convert a local coordinate path to the global coordinate</span>
+ <span class="n">rot</span> <span class="o">=</span> <span class="n">rot_mat_2d</span><span class="p">(</span><span class="o">-</span><span class="n">s_yaw</span><span class="p">)</span>
+ <span class="n">converted_xy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">stack</span><span class="p">([</span><span class="n">lp_x</span><span class="p">,</span> <span class="n">lp_y</span><span class="p">])</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">rot</span>
+ <span class="n">x_list</span> <span class="o">=</span> <span class="n">converted_xy</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">s_x</span>
+ <span class="n">y_list</span> <span class="o">=</span> <span class="n">converted_xy</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">s_y</span>
+ <span class="n">yaw_list</span> <span class="o">=</span> <span class="n">angle_mod</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">lp_yaw</span><span class="p">)</span> <span class="o">+</span> <span class="n">s_yaw</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">x_list</span><span class="p">,</span> <span class="n">y_list</span><span class="p">,</span> <span class="n">yaw_list</span><span class="p">,</span> <span class="n">modes</span><span class="p">,</span> <span class="n">lengths</span></div>
+
+
+<span class="k">def</span> <span class="nf">_mod2pi</span><span class="p">(</span><span class="n">theta</span><span class="p">):</span>
+ <span class="k">return</span> <span class="n">angle_mod</span><span class="p">(</span><span class="n">theta</span><span class="p">,</span> <span class="n">zero_2_2pi</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+
+
+<span class="k">def</span> <span class="nf">_calc_trig_funcs</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">):</span>
+ <span class="n">sin_a</span> <span class="o">=</span> <span class="n">sin</span><span class="p">(</span><span class="n">alpha</span><span class="p">)</span>
+ <span class="n">sin_b</span> <span class="o">=</span> <span class="n">sin</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
+ <span class="n">cos_a</span> <span class="o">=</span> <span class="n">cos</span><span class="p">(</span><span class="n">alpha</span><span class="p">)</span>
+ <span class="n">cos_b</span> <span class="o">=</span> <span class="n">cos</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
+ <span class="n">cos_ab</span> <span class="o">=</span> <span class="n">cos</span><span class="p">(</span><span class="n">alpha</span> <span class="o">-</span> <span class="n">beta</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">sin_a</span><span class="p">,</span> <span class="n">sin_b</span><span class="p">,</span> <span class="n">cos_a</span><span class="p">,</span> <span class="n">cos_b</span><span class="p">,</span> <span class="n">cos_ab</span>
+
+
+<span class="k">def</span> <span class="nf">_LSL</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
+ <span class="n">sin_a</span><span class="p">,</span> <span class="n">sin_b</span><span class="p">,</span> <span class="n">cos_a</span><span class="p">,</span> <span class="n">cos_b</span><span class="p">,</span> <span class="n">cos_ab</span> <span class="o">=</span> <span class="n">_calc_trig_funcs</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">)</span>
+ <span class="n">mode</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"L"</span><span class="p">,</span> <span class="s2">"S"</span><span class="p">,</span> <span class="s2">"L"</span><span class="p">]</span>
+ <span class="n">p_squared</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">d</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">-</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">cos_ab</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="p">(</span><span class="n">sin_a</span> <span class="o">-</span> <span class="n">sin_b</span><span class="p">))</span>
+ <span class="k">if</span> <span class="n">p_squared</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span> <span class="c1"># invalid configuration</span>
+ <span class="k">return</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">mode</span>
+ <span class="n">tmp</span> <span class="o">=</span> <span class="n">atan2</span><span class="p">((</span><span class="n">cos_b</span> <span class="o">-</span> <span class="n">cos_a</span><span class="p">),</span> <span class="n">d</span> <span class="o">+</span> <span class="n">sin_a</span> <span class="o">-</span> <span class="n">sin_b</span><span class="p">)</span>
+ <span class="n">d1</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="o">-</span><span class="n">alpha</span> <span class="o">+</span> <span class="n">tmp</span><span class="p">)</span>
+ <span class="n">d2</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">p_squared</span><span class="p">)</span>
+ <span class="n">d3</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="n">beta</span> <span class="o">-</span> <span class="n">tmp</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">d1</span><span class="p">,</span> <span class="n">d2</span><span class="p">,</span> <span class="n">d3</span><span class="p">,</span> <span class="n">mode</span>
+
+
+<span class="k">def</span> <span class="nf">_RSR</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
+ <span class="n">sin_a</span><span class="p">,</span> <span class="n">sin_b</span><span class="p">,</span> <span class="n">cos_a</span><span class="p">,</span> <span class="n">cos_b</span><span class="p">,</span> <span class="n">cos_ab</span> <span class="o">=</span> <span class="n">_calc_trig_funcs</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">)</span>
+ <span class="n">mode</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"R"</span><span class="p">,</span> <span class="s2">"S"</span><span class="p">,</span> <span class="s2">"R"</span><span class="p">]</span>
+ <span class="n">p_squared</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">d</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">-</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">cos_ab</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="p">(</span><span class="n">sin_b</span> <span class="o">-</span> <span class="n">sin_a</span><span class="p">))</span>
+ <span class="k">if</span> <span class="n">p_squared</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
+ <span class="k">return</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">mode</span>
+ <span class="n">tmp</span> <span class="o">=</span> <span class="n">atan2</span><span class="p">((</span><span class="n">cos_a</span> <span class="o">-</span> <span class="n">cos_b</span><span class="p">),</span> <span class="n">d</span> <span class="o">-</span> <span class="n">sin_a</span> <span class="o">+</span> <span class="n">sin_b</span><span class="p">)</span>
+ <span class="n">d1</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="n">alpha</span> <span class="o">-</span> <span class="n">tmp</span><span class="p">)</span>
+ <span class="n">d2</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">p_squared</span><span class="p">)</span>
+ <span class="n">d3</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="o">-</span><span class="n">beta</span> <span class="o">+</span> <span class="n">tmp</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">d1</span><span class="p">,</span> <span class="n">d2</span><span class="p">,</span> <span class="n">d3</span><span class="p">,</span> <span class="n">mode</span>
+
+
+<span class="k">def</span> <span class="nf">_LSR</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
+ <span class="n">sin_a</span><span class="p">,</span> <span class="n">sin_b</span><span class="p">,</span> <span class="n">cos_a</span><span class="p">,</span> <span class="n">cos_b</span><span class="p">,</span> <span class="n">cos_ab</span> <span class="o">=</span> <span class="n">_calc_trig_funcs</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">)</span>
+ <span class="n">p_squared</span> <span class="o">=</span> <span class="o">-</span><span class="mi">2</span> <span class="o">+</span> <span class="n">d</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">cos_ab</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="p">(</span><span class="n">sin_a</span> <span class="o">+</span> <span class="n">sin_b</span><span class="p">))</span>
+ <span class="n">mode</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"L"</span><span class="p">,</span> <span class="s2">"S"</span><span class="p">,</span> <span class="s2">"R"</span><span class="p">]</span>
+ <span class="k">if</span> <span class="n">p_squared</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
+ <span class="k">return</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">mode</span>
+ <span class="n">d1</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">p_squared</span><span class="p">)</span>
+ <span class="n">tmp</span> <span class="o">=</span> <span class="n">atan2</span><span class="p">((</span><span class="o">-</span><span class="n">cos_a</span> <span class="o">-</span> <span class="n">cos_b</span><span class="p">),</span> <span class="p">(</span><span class="n">d</span> <span class="o">+</span> <span class="n">sin_a</span> <span class="o">+</span> <span class="n">sin_b</span><span class="p">))</span> <span class="o">-</span> <span class="n">atan2</span><span class="p">(</span><span class="o">-</span><span class="mf">2.0</span><span class="p">,</span> <span class="n">d1</span><span class="p">)</span>
+ <span class="n">d2</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="o">-</span><span class="n">alpha</span> <span class="o">+</span> <span class="n">tmp</span><span class="p">)</span>
+ <span class="n">d3</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="o">-</span><span class="n">_mod2pi</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span> <span class="o">+</span> <span class="n">tmp</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">d2</span><span class="p">,</span> <span class="n">d1</span><span class="p">,</span> <span class="n">d3</span><span class="p">,</span> <span class="n">mode</span>
+
+
+<span class="k">def</span> <span class="nf">_RSL</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
+ <span class="n">sin_a</span><span class="p">,</span> <span class="n">sin_b</span><span class="p">,</span> <span class="n">cos_a</span><span class="p">,</span> <span class="n">cos_b</span><span class="p">,</span> <span class="n">cos_ab</span> <span class="o">=</span> <span class="n">_calc_trig_funcs</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">)</span>
+ <span class="n">p_squared</span> <span class="o">=</span> <span class="n">d</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">+</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">cos_ab</span><span class="p">)</span> <span class="o">-</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="p">(</span><span class="n">sin_a</span> <span class="o">+</span> <span class="n">sin_b</span><span class="p">))</span>
+ <span class="n">mode</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"R"</span><span class="p">,</span> <span class="s2">"S"</span><span class="p">,</span> <span class="s2">"L"</span><span class="p">]</span>
+ <span class="k">if</span> <span class="n">p_squared</span> <span class="o"><</span> <span class="mi">0</span><span class="p">:</span>
+ <span class="k">return</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">mode</span>
+ <span class="n">d1</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">p_squared</span><span class="p">)</span>
+ <span class="n">tmp</span> <span class="o">=</span> <span class="n">atan2</span><span class="p">((</span><span class="n">cos_a</span> <span class="o">+</span> <span class="n">cos_b</span><span class="p">),</span> <span class="p">(</span><span class="n">d</span> <span class="o">-</span> <span class="n">sin_a</span> <span class="o">-</span> <span class="n">sin_b</span><span class="p">))</span> <span class="o">-</span> <span class="n">atan2</span><span class="p">(</span><span class="mf">2.0</span><span class="p">,</span> <span class="n">d1</span><span class="p">)</span>
+ <span class="n">d2</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="n">alpha</span> <span class="o">-</span> <span class="n">tmp</span><span class="p">)</span>
+ <span class="n">d3</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="n">beta</span> <span class="o">-</span> <span class="n">tmp</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">d2</span><span class="p">,</span> <span class="n">d1</span><span class="p">,</span> <span class="n">d3</span><span class="p">,</span> <span class="n">mode</span>
+
+
+<span class="k">def</span> <span class="nf">_RLR</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
+ <span class="n">sin_a</span><span class="p">,</span> <span class="n">sin_b</span><span class="p">,</span> <span class="n">cos_a</span><span class="p">,</span> <span class="n">cos_b</span><span class="p">,</span> <span class="n">cos_ab</span> <span class="o">=</span> <span class="n">_calc_trig_funcs</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">)</span>
+ <span class="n">mode</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"R"</span><span class="p">,</span> <span class="s2">"L"</span><span class="p">,</span> <span class="s2">"R"</span><span class="p">]</span>
+ <span class="n">tmp</span> <span class="o">=</span> <span class="p">(</span><span class="mf">6.0</span> <span class="o">-</span> <span class="n">d</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">cos_ab</span> <span class="o">+</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="p">(</span><span class="n">sin_a</span> <span class="o">-</span> <span class="n">sin_b</span><span class="p">))</span> <span class="o">/</span> <span class="mf">8.0</span>
+ <span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span> <span class="o">></span> <span class="mf">1.0</span><span class="p">:</span>
+ <span class="k">return</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">mode</span>
+ <span class="n">d2</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">pi</span> <span class="o">-</span> <span class="n">acos</span><span class="p">(</span><span class="n">tmp</span><span class="p">))</span>
+ <span class="n">d1</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="n">alpha</span> <span class="o">-</span> <span class="n">atan2</span><span class="p">(</span><span class="n">cos_a</span> <span class="o">-</span> <span class="n">cos_b</span><span class="p">,</span> <span class="n">d</span> <span class="o">-</span> <span class="n">sin_a</span> <span class="o">+</span> <span class="n">sin_b</span><span class="p">)</span> <span class="o">+</span> <span class="n">d2</span> <span class="o">/</span> <span class="mf">2.0</span><span class="p">)</span>
+ <span class="n">d3</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="n">alpha</span> <span class="o">-</span> <span class="n">beta</span> <span class="o">-</span> <span class="n">d1</span> <span class="o">+</span> <span class="n">d2</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">d1</span><span class="p">,</span> <span class="n">d2</span><span class="p">,</span> <span class="n">d3</span><span class="p">,</span> <span class="n">mode</span>
+
+
+<span class="k">def</span> <span class="nf">_LRL</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">d</span><span class="p">):</span>
+ <span class="n">sin_a</span><span class="p">,</span> <span class="n">sin_b</span><span class="p">,</span> <span class="n">cos_a</span><span class="p">,</span> <span class="n">cos_b</span><span class="p">,</span> <span class="n">cos_ab</span> <span class="o">=</span> <span class="n">_calc_trig_funcs</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">)</span>
+ <span class="n">mode</span> <span class="o">=</span> <span class="p">[</span><span class="s2">"L"</span><span class="p">,</span> <span class="s2">"R"</span><span class="p">,</span> <span class="s2">"L"</span><span class="p">]</span>
+ <span class="n">tmp</span> <span class="o">=</span> <span class="p">(</span><span class="mf">6.0</span> <span class="o">-</span> <span class="n">d</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">cos_ab</span> <span class="o">+</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">d</span> <span class="o">*</span> <span class="p">(</span><span class="o">-</span> <span class="n">sin_a</span> <span class="o">+</span> <span class="n">sin_b</span><span class="p">))</span> <span class="o">/</span> <span class="mf">8.0</span>
+ <span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span> <span class="o">></span> <span class="mf">1.0</span><span class="p">:</span>
+ <span class="k">return</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="n">mode</span>
+ <span class="n">d2</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">pi</span> <span class="o">-</span> <span class="n">acos</span><span class="p">(</span><span class="n">tmp</span><span class="p">))</span>
+ <span class="n">d1</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="o">-</span><span class="n">alpha</span> <span class="o">-</span> <span class="n">atan2</span><span class="p">(</span><span class="n">cos_a</span> <span class="o">-</span> <span class="n">cos_b</span><span class="p">,</span> <span class="n">d</span> <span class="o">+</span> <span class="n">sin_a</span> <span class="o">-</span> <span class="n">sin_b</span><span class="p">)</span> <span class="o">+</span> <span class="n">d2</span> <span class="o">/</span> <span class="mf">2.0</span><span class="p">)</span>
+ <span class="n">d3</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="n">_mod2pi</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span> <span class="o">-</span> <span class="n">alpha</span> <span class="o">-</span> <span class="n">d1</span> <span class="o">+</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="n">d2</span><span class="p">))</span>
+ <span class="k">return</span> <span class="n">d1</span><span class="p">,</span> <span class="n">d2</span><span class="p">,</span> <span class="n">d3</span><span class="p">,</span> <span class="n">mode</span>
+
+
+<span class="n">_PATH_TYPE_MAP</span> <span class="o">=</span> <span class="p">{</span><span class="s2">"LSL"</span><span class="p">:</span> <span class="n">_LSL</span><span class="p">,</span> <span class="s2">"RSR"</span><span class="p">:</span> <span class="n">_RSR</span><span class="p">,</span> <span class="s2">"LSR"</span><span class="p">:</span> <span class="n">_LSR</span><span class="p">,</span> <span class="s2">"RSL"</span><span class="p">:</span> <span class="n">_RSL</span><span class="p">,</span>
+ <span class="s2">"RLR"</span><span class="p">:</span> <span class="n">_RLR</span><span class="p">,</span> <span class="s2">"LRL"</span><span class="p">:</span> <span class="n">_LRL</span><span class="p">,</span> <span class="p">}</span>
+
+
+<span class="k">def</span> <span class="nf">_dubins_path_planning_from_origin</span><span class="p">(</span><span class="n">end_x</span><span class="p">,</span> <span class="n">end_y</span><span class="p">,</span> <span class="n">end_yaw</span><span class="p">,</span> <span class="n">curvature</span><span class="p">,</span>
+ <span class="n">step_size</span><span class="p">,</span> <span class="n">planning_funcs</span><span class="p">):</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="n">end_x</span>
+ <span class="n">dy</span> <span class="o">=</span> <span class="n">end_y</span>
+ <span class="n">d</span> <span class="o">=</span> <span class="n">hypot</span><span class="p">(</span><span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">)</span> <span class="o">*</span> <span class="n">curvature</span>
+
+ <span class="n">theta</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="n">atan2</span><span class="p">(</span><span class="n">dy</span><span class="p">,</span> <span class="n">dx</span><span class="p">))</span>
+ <span class="n">alpha</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="o">-</span><span class="n">theta</span><span class="p">)</span>
+ <span class="n">beta</span> <span class="o">=</span> <span class="n">_mod2pi</span><span class="p">(</span><span class="n">end_yaw</span> <span class="o">-</span> <span class="n">theta</span><span class="p">)</span>
+
+ <span class="n">best_cost</span> <span class="o">=</span> <span class="nb">float</span><span class="p">(</span><span class="s2">"inf"</span><span class="p">)</span>
+ <span class="n">b_d1</span><span class="p">,</span> <span class="n">b_d2</span><span class="p">,</span> <span class="n">b_d3</span><span class="p">,</span> <span class="n">b_mode</span> <span class="o">=</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span><span class="p">,</span> <span class="kc">None</span>
+
+ <span class="k">for</span> <span class="n">planner</span> <span class="ow">in</span> <span class="n">planning_funcs</span><span class="p">:</span>
+ <span class="n">d1</span><span class="p">,</span> <span class="n">d2</span><span class="p">,</span> <span class="n">d3</span><span class="p">,</span> <span class="n">mode</span> <span class="o">=</span> <span class="n">planner</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">beta</span><span class="p">,</span> <span class="n">d</span><span class="p">)</span>
+ <span class="k">if</span> <span class="n">d1</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+ <span class="k">continue</span>
+
+ <span class="n">cost</span> <span class="o">=</span> <span class="p">(</span><span class="nb">abs</span><span class="p">(</span><span class="n">d1</span><span class="p">)</span> <span class="o">+</span> <span class="nb">abs</span><span class="p">(</span><span class="n">d2</span><span class="p">)</span> <span class="o">+</span> <span class="nb">abs</span><span class="p">(</span><span class="n">d3</span><span class="p">))</span>
+ <span class="k">if</span> <span class="n">best_cost</span> <span class="o">></span> <span class="n">cost</span><span class="p">:</span> <span class="c1"># Select minimum length one.</span>
+ <span class="n">b_d1</span><span class="p">,</span> <span class="n">b_d2</span><span class="p">,</span> <span class="n">b_d3</span><span class="p">,</span> <span class="n">b_mode</span><span class="p">,</span> <span class="n">best_cost</span> <span class="o">=</span> <span class="n">d1</span><span class="p">,</span> <span class="n">d2</span><span class="p">,</span> <span class="n">d3</span><span class="p">,</span> <span class="n">mode</span><span class="p">,</span> <span class="n">cost</span>
+
+ <span class="n">lengths</span> <span class="o">=</span> <span class="p">[</span><span class="n">b_d1</span><span class="p">,</span> <span class="n">b_d2</span><span class="p">,</span> <span class="n">b_d3</span><span class="p">]</span>
+ <span class="n">x_list</span><span class="p">,</span> <span class="n">y_list</span><span class="p">,</span> <span class="n">yaw_list</span> <span class="o">=</span> <span class="n">_generate_local_course</span><span class="p">(</span><span class="n">lengths</span><span class="p">,</span> <span class="n">b_mode</span><span class="p">,</span>
+ <span class="n">curvature</span><span class="p">,</span> <span class="n">step_size</span><span class="p">)</span>
+
+ <span class="n">lengths</span> <span class="o">=</span> <span class="p">[</span><span class="n">length</span> <span class="o">/</span> <span class="n">curvature</span> <span class="k">for</span> <span class="n">length</span> <span class="ow">in</span> <span class="n">lengths</span><span class="p">]</span>
+
+ <span class="k">return</span> <span class="n">x_list</span><span class="p">,</span> <span class="n">y_list</span><span class="p">,</span> <span class="n">yaw_list</span><span class="p">,</span> <span class="n">b_mode</span><span class="p">,</span> <span class="n">lengths</span>
+
+
+<span class="k">def</span> <span class="nf">_interpolate</span><span class="p">(</span><span class="n">length</span><span class="p">,</span> <span class="n">mode</span><span class="p">,</span> <span class="n">max_curvature</span><span class="p">,</span> <span class="n">origin_x</span><span class="p">,</span> <span class="n">origin_y</span><span class="p">,</span>
+ <span class="n">origin_yaw</span><span class="p">,</span> <span class="n">path_x</span><span class="p">,</span> <span class="n">path_y</span><span class="p">,</span> <span class="n">path_yaw</span><span class="p">):</span>
+ <span class="k">if</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">"S"</span><span class="p">:</span>
+ <span class="n">path_x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">origin_x</span> <span class="o">+</span> <span class="n">length</span> <span class="o">/</span> <span class="n">max_curvature</span> <span class="o">*</span> <span class="n">cos</span><span class="p">(</span><span class="n">origin_yaw</span><span class="p">))</span>
+ <span class="n">path_y</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">origin_y</span> <span class="o">+</span> <span class="n">length</span> <span class="o">/</span> <span class="n">max_curvature</span> <span class="o">*</span> <span class="n">sin</span><span class="p">(</span><span class="n">origin_yaw</span><span class="p">))</span>
+ <span class="n">path_yaw</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">origin_yaw</span><span class="p">)</span>
+ <span class="k">else</span><span class="p">:</span> <span class="c1"># curve</span>
+ <span class="n">ldx</span> <span class="o">=</span> <span class="n">sin</span><span class="p">(</span><span class="n">length</span><span class="p">)</span> <span class="o">/</span> <span class="n">max_curvature</span>
+ <span class="n">ldy</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="k">if</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">"L"</span><span class="p">:</span> <span class="c1"># left turn</span>
+ <span class="n">ldy</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">cos</span><span class="p">(</span><span class="n">length</span><span class="p">))</span> <span class="o">/</span> <span class="n">max_curvature</span>
+ <span class="k">elif</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">"R"</span><span class="p">:</span> <span class="c1"># right turn</span>
+ <span class="n">ldy</span> <span class="o">=</span> <span class="p">(</span><span class="mf">1.0</span> <span class="o">-</span> <span class="n">cos</span><span class="p">(</span><span class="n">length</span><span class="p">))</span> <span class="o">/</span> <span class="o">-</span><span class="n">max_curvature</span>
+ <span class="n">gdx</span> <span class="o">=</span> <span class="n">cos</span><span class="p">(</span><span class="o">-</span><span class="n">origin_yaw</span><span class="p">)</span> <span class="o">*</span> <span class="n">ldx</span> <span class="o">+</span> <span class="n">sin</span><span class="p">(</span><span class="o">-</span><span class="n">origin_yaw</span><span class="p">)</span> <span class="o">*</span> <span class="n">ldy</span>
+ <span class="n">gdy</span> <span class="o">=</span> <span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="o">-</span><span class="n">origin_yaw</span><span class="p">)</span> <span class="o">*</span> <span class="n">ldx</span> <span class="o">+</span> <span class="n">cos</span><span class="p">(</span><span class="o">-</span><span class="n">origin_yaw</span><span class="p">)</span> <span class="o">*</span> <span class="n">ldy</span>
+ <span class="n">path_x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">origin_x</span> <span class="o">+</span> <span class="n">gdx</span><span class="p">)</span>
+ <span class="n">path_y</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">origin_y</span> <span class="o">+</span> <span class="n">gdy</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">"L"</span><span class="p">:</span> <span class="c1"># left turn</span>
+ <span class="n">path_yaw</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">origin_yaw</span> <span class="o">+</span> <span class="n">length</span><span class="p">)</span>
+ <span class="k">elif</span> <span class="n">mode</span> <span class="o">==</span> <span class="s2">"R"</span><span class="p">:</span> <span class="c1"># right turn</span>
+ <span class="n">path_yaw</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">origin_yaw</span> <span class="o">-</span> <span class="n">length</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">path_x</span><span class="p">,</span> <span class="n">path_y</span><span class="p">,</span> <span class="n">path_yaw</span>
+
+
+<span class="k">def</span> <span class="nf">_generate_local_course</span><span class="p">(</span><span class="n">lengths</span><span class="p">,</span> <span class="n">modes</span><span class="p">,</span> <span class="n">max_curvature</span><span class="p">,</span> <span class="n">step_size</span><span class="p">):</span>
+ <span class="n">p_x</span><span class="p">,</span> <span class="n">p_y</span><span class="p">,</span> <span class="n">p_yaw</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.0</span><span class="p">]</span>
+
+ <span class="k">for</span> <span class="p">(</span><span class="n">mode</span><span class="p">,</span> <span class="n">length</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">modes</span><span class="p">,</span> <span class="n">lengths</span><span class="p">):</span>
+ <span class="k">if</span> <span class="n">length</span> <span class="o">==</span> <span class="mf">0.0</span><span class="p">:</span>
+ <span class="k">continue</span>
+
+ <span class="c1"># set origin state</span>
+ <span class="n">origin_x</span><span class="p">,</span> <span class="n">origin_y</span><span class="p">,</span> <span class="n">origin_yaw</span> <span class="o">=</span> <span class="n">p_x</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">p_y</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">p_yaw</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+
+ <span class="n">current_length</span> <span class="o">=</span> <span class="n">step_size</span>
+ <span class="k">while</span> <span class="nb">abs</span><span class="p">(</span><span class="n">current_length</span> <span class="o">+</span> <span class="n">step_size</span><span class="p">)</span> <span class="o"><=</span> <span class="nb">abs</span><span class="p">(</span><span class="n">length</span><span class="p">):</span>
+ <span class="n">p_x</span><span class="p">,</span> <span class="n">p_y</span><span class="p">,</span> <span class="n">p_yaw</span> <span class="o">=</span> <span class="n">_interpolate</span><span class="p">(</span><span class="n">current_length</span><span class="p">,</span> <span class="n">mode</span><span class="p">,</span> <span class="n">max_curvature</span><span class="p">,</span>
+ <span class="n">origin_x</span><span class="p">,</span> <span class="n">origin_y</span><span class="p">,</span> <span class="n">origin_yaw</span><span class="p">,</span>
+ <span class="n">p_x</span><span class="p">,</span> <span class="n">p_y</span><span class="p">,</span> <span class="n">p_yaw</span><span class="p">)</span>
+ <span class="n">current_length</span> <span class="o">+=</span> <span class="n">step_size</span>
+
+ <span class="n">p_x</span><span class="p">,</span> <span class="n">p_y</span><span class="p">,</span> <span class="n">p_yaw</span> <span class="o">=</span> <span class="n">_interpolate</span><span class="p">(</span><span class="n">length</span><span class="p">,</span> <span class="n">mode</span><span class="p">,</span> <span class="n">max_curvature</span><span class="p">,</span> <span class="n">origin_x</span><span class="p">,</span>
+ <span class="n">origin_y</span><span class="p">,</span> <span class="n">origin_yaw</span><span class="p">,</span> <span class="n">p_x</span><span class="p">,</span> <span class="n">p_y</span><span class="p">,</span> <span class="n">p_yaw</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">p_x</span><span class="p">,</span> <span class="n">p_y</span><span class="p">,</span> <span class="n">p_yaw</span>
+
+
+<span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"Dubins path planner sample start!!"</span><span class="p">)</span>
+ <span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+ <span class="kn">from</span> <span class="nn">utils.plot</span> <span class="kn">import</span> <span class="n">plot_arrow</span>
+
+ <span class="n">start_x</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="c1"># [m]</span>
+ <span class="n">start_y</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="c1"># [m]</span>
+ <span class="n">start_yaw</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">45.0</span><span class="p">)</span> <span class="c1"># [rad]</span>
+
+ <span class="n">end_x</span> <span class="o">=</span> <span class="o">-</span><span class="mf">3.0</span> <span class="c1"># [m]</span>
+ <span class="n">end_y</span> <span class="o">=</span> <span class="o">-</span><span class="mf">3.0</span> <span class="c1"># [m]</span>
+ <span class="n">end_yaw</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="o">-</span><span class="mf">45.0</span><span class="p">)</span> <span class="c1"># [rad]</span>
+
+ <span class="n">curvature</span> <span class="o">=</span> <span class="mf">1.0</span>
+
+ <span class="n">path_x</span><span class="p">,</span> <span class="n">path_y</span><span class="p">,</span> <span class="n">path_yaw</span><span class="p">,</span> <span class="n">mode</span><span class="p">,</span> <span class="n">lengths</span> <span class="o">=</span> <span class="n">plan_dubins_path</span><span class="p">(</span><span class="n">start_x</span><span class="p">,</span>
+ <span class="n">start_y</span><span class="p">,</span>
+ <span class="n">start_yaw</span><span class="p">,</span>
+ <span class="n">end_x</span><span class="p">,</span>
+ <span class="n">end_y</span><span class="p">,</span>
+ <span class="n">end_yaw</span><span class="p">,</span>
+ <span class="n">curvature</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">show_animation</span><span class="p">:</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">path_x</span><span class="p">,</span> <span class="n">path_y</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">""</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">mode</span><span class="p">))</span>
+ <span class="n">plot_arrow</span><span class="p">(</span><span class="n">start_x</span><span class="p">,</span> <span class="n">start_y</span><span class="p">,</span> <span class="n">start_yaw</span><span class="p">)</span>
+ <span class="n">plot_arrow</span><span class="p">(</span><span class="n">end_x</span><span class="p">,</span> <span class="n">end_y</span><span class="p">,</span> <span class="n">end_yaw</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+
+<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
+ <span class="n">main</span><span class="p">()</span>
+</pre></div>
+
+ </div>
+ </div>
+ <footer>
+
+ <hr/>
+
+ <div role="contentinfo">
+ <p>© Copyright 2018-2021, Atsushi Sakai.</p>
+ </div>
+
+ Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
+ <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
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+
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+</footer>
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+ </section>
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+ jQuery(function () {
+ SphinxRtdTheme.Navigation.enable(true);
+ });
+ </script>
+
+</body>
+</html>
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new file mode 100644
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+++ b/_modules/index.html
@@ -0,0 +1,140 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
+<head>
+ <meta charset="utf-8" />
+ <meta name="viewport" content="width=device-width, initial-scale=1.0" />
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+ <link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
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+ <p class="caption" role="heading"><span class="caption-text">Contents</span></p>
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+<li class="toctree-l1"><a class="reference internal" href="../getting_started.html">Getting Started</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/introduction.html">Introduction</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/localization/localization.html">Localization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/slam/slam.html">SLAM</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/path_planning/path_planning.html">Path Planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/bipedal/bipedal.html">Bipedal</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/control/control.html">Control</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/utils/utils.html">Utilities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../modules/appendix/appendix.html">Appendix</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../how_to_contribute.html">How To Contribute</a></li>
+</ul>
+
+ </div>
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+ </nav>
+
+ <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" >
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+ <a href="../index.html">PythonRobotics</a>
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+ <div role="navigation" aria-label="Page navigation">
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+ <hr/>
+</div>
+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+ <div itemprop="articleBody">
+
+ <h1>All modules for which code is available</h1>
+<ul><li><a href="Mapping/ndt_map/ndt_map.html">Mapping.ndt_map.ndt_map</a></li>
+<li><a href="Mapping/normal_vector_estimation/normal_vector_estimation.html">Mapping.normal_vector_estimation.normal_vector_estimation</a></li>
+<li><a href="Mapping/point_cloud_sampling/point_cloud_sampling.html">Mapping.point_cloud_sampling.point_cloud_sampling</a></li>
+<li><a href="Mapping/rectangle_fitting/rectangle_fitting.html">Mapping.rectangle_fitting.rectangle_fitting</a></li>
+<li><a href="PathPlanning/BSplinePath/bspline_path.html">PathPlanning.BSplinePath.bspline_path</a></li>
+<li><a href="PathPlanning/CubicSpline/cubic_spline_planner.html">PathPlanning.CubicSpline.cubic_spline_planner</a></li>
+<li><a href="PathPlanning/DubinsPath/dubins_path_planner.html">PathPlanning.DubinsPath.dubins_path_planner</a></li>
+<li><a href="utils/plot.html">utils.plot</a></li>
+</ul>
+
+ </div>
+ </div>
+ <footer>
+
+ <hr/>
+
+ <div role="contentinfo">
+ <p>© Copyright 2018-2021, Atsushi Sakai.</p>
+ </div>
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+ <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
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+ jQuery(function () {
+ SphinxRtdTheme.Navigation.enable(true);
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+++ b/_modules/utils/plot.html
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+<html class="writer-html5" lang="en" >
+<head>
+ <meta charset="utf-8" />
+ <meta name="viewport" content="width=device-width, initial-scale=1.0" />
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+ <h1>Source code for utils.plot</h1><div class="highlight"><pre>
+<span></span><span class="sd">"""</span>
+<span class="sd">Matplotlib based plotting utilities</span>
+<span class="sd">"""</span>
+<span class="kn">import</span> <span class="nn">math</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">art3d</span>
+<span class="kn">from</span> <span class="nn">matplotlib.patches</span> <span class="kn">import</span> <span class="n">FancyArrowPatch</span>
+<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d.proj3d</span> <span class="kn">import</span> <span class="n">proj_transform</span>
+<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">Axes3D</span>
+
+<span class="kn">from</span> <span class="nn">utils.angle</span> <span class="kn">import</span> <span class="n">rot_mat_2d</span>
+
+
+<span class="k">def</span> <span class="nf">plot_covariance_ellipse</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">cov</span><span class="p">,</span> <span class="n">chi2</span><span class="o">=</span><span class="mf">3.0</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"-r"</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> This function plots an ellipse that represents a covariance matrix. The ellipse is centered at (x, y) and its shape, size and rotation are determined by the covariance matrix.</span>
+
+<span class="sd"> Parameters:</span>
+<span class="sd"> x : (float) The x-coordinate of the center of the ellipse.</span>
+<span class="sd"> y : (float) The y-coordinate of the center of the ellipse.</span>
+<span class="sd"> cov : (numpy.ndarray) A 2x2 covariance matrix that determines the shape, size, and rotation of the ellipse.</span>
+<span class="sd"> chi2 : (float, optional) A scalar value that scales the ellipse size. This value is typically set based on chi-squared distribution quantiles to achieve certain confidence levels (e.g., 3.0 corresponds to ~95% confidence for a 2D Gaussian). Defaults to 3.0.</span>
+<span class="sd"> color : (str, optional) The color and line style of the ellipse plot, following matplotlib conventions. Defaults to "-r" (a red solid line).</span>
+<span class="sd"> ax : (matplotlib.axes.Axes, optional) The Axes object to draw the ellipse on. If None (default), a new figure and axes are created.</span>
+
+<span class="sd"> Returns:</span>
+<span class="sd"> None. This function plots the covariance ellipse on the specified axes.</span>
+<span class="sd"> """</span>
+ <span class="n">eig_val</span><span class="p">,</span> <span class="n">eig_vec</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">eig</span><span class="p">(</span><span class="n">cov</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">eig_val</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">>=</span> <span class="n">eig_val</span><span class="p">[</span><span class="mi">1</span><span class="p">]:</span>
+ <span class="n">big_ind</span> <span class="o">=</span> <span class="mi">0</span>
+ <span class="n">small_ind</span> <span class="o">=</span> <span class="mi">1</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">big_ind</span> <span class="o">=</span> <span class="mi">1</span>
+ <span class="n">small_ind</span> <span class="o">=</span> <span class="mi">0</span>
+ <span class="n">a</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">chi2</span> <span class="o">*</span> <span class="n">eig_val</span><span class="p">[</span><span class="n">big_ind</span><span class="p">])</span>
+ <span class="n">b</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">chi2</span> <span class="o">*</span> <span class="n">eig_val</span><span class="p">[</span><span class="n">small_ind</span><span class="p">])</span>
+ <span class="n">angle</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">eig_vec</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">big_ind</span><span class="p">],</span> <span class="n">eig_vec</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">big_ind</span><span class="p">])</span>
+ <span class="n">plot_ellipse</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="n">color</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="n">ax</span><span class="p">)</span>
+
+
+<span class="k">def</span> <span class="nf">plot_ellipse</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">,</span> <span class="n">angle</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"-r"</span><span class="p">,</span> <span class="n">ax</span><span class="o">=</span><span class="kc">None</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> This function plots an ellipse based on the given parameters.</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> x : (float) The x-coordinate of the center of the ellipse.</span>
+<span class="sd"> y : (float) The y-coordinate of the center of the ellipse.</span>
+<span class="sd"> a : (float) The length of the semi-major axis of the ellipse.</span>
+<span class="sd"> b : (float) The length of the semi-minor axis of the ellipse.</span>
+<span class="sd"> angle : (float) The rotation angle of the ellipse, in radians.</span>
+<span class="sd"> color : (str, optional) The color and line style of the ellipse plot, following matplotlib conventions. Defaults to "-r" (a red solid line).</span>
+<span class="sd"> ax : (matplotlib.axes.Axes, optional) The Axes object to draw the ellipse on. If None (default), a new figure and axes are created.</span>
+<span class="sd"> **kwargs: Additional keyword arguments to pass to plt.plot or ax.plot.</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> ---------</span>
+<span class="sd"> None. This function plots the ellipse based on the specified parameters.</span>
+<span class="sd"> """</span>
+
+ <span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">+</span> <span class="mf">0.1</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
+ <span class="n">px</span> <span class="o">=</span> <span class="p">[</span><span class="n">a</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">it</span><span class="p">)</span> <span class="k">for</span> <span class="n">it</span> <span class="ow">in</span> <span class="n">t</span><span class="p">]</span>
+ <span class="n">py</span> <span class="o">=</span> <span class="p">[</span><span class="n">b</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">it</span><span class="p">)</span> <span class="k">for</span> <span class="n">it</span> <span class="ow">in</span> <span class="n">t</span><span class="p">]</span>
+ <span class="n">fx</span> <span class="o">=</span> <span class="n">rot_mat_2d</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span> <span class="o">@</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">px</span><span class="p">,</span> <span class="n">py</span><span class="p">]))</span>
+ <span class="n">px</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">fx</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:]</span> <span class="o">+</span> <span class="n">x</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
+ <span class="n">py</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">fx</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:]</span> <span class="o">+</span> <span class="n">y</span><span class="p">)</span><span class="o">.</span><span class="n">flatten</span><span class="p">()</span>
+ <span class="k">if</span> <span class="n">ax</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">px</span><span class="p">,</span> <span class="n">py</span><span class="p">,</span> <span class="n">color</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">px</span><span class="p">,</span> <span class="n">py</span><span class="p">,</span> <span class="n">color</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+
+
+<span class="k">def</span> <span class="nf">plot_arrow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">yaw</span><span class="p">,</span> <span class="n">arrow_length</span><span class="o">=</span><span class="mf">1.0</span><span class="p">,</span>
+ <span class="n">origin_point_plot_style</span><span class="o">=</span><span class="s2">"xr"</span><span class="p">,</span>
+ <span class="n">head_width</span><span class="o">=</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">fc</span><span class="o">=</span><span class="s2">"r"</span><span class="p">,</span> <span class="n">ec</span><span class="o">=</span><span class="s2">"k"</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Plot an arrow or arrows based on 2D state (x, y, yaw)</span>
+
+<span class="sd"> All optional settings of matplotlib.pyplot.arrow can be used.</span>
+<span class="sd"> - matplotlib.pyplot.arrow:</span>
+<span class="sd"> https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.arrow.html</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> x : a float or array_like</span>
+<span class="sd"> a value or a list of arrow origin x position.</span>
+<span class="sd"> y : a float or array_like</span>
+<span class="sd"> a value or a list of arrow origin y position.</span>
+<span class="sd"> yaw : a float or array_like</span>
+<span class="sd"> a value or a list of arrow yaw angle (orientation).</span>
+<span class="sd"> arrow_length : a float (optional)</span>
+<span class="sd"> arrow length. default is 1.0</span>
+<span class="sd"> origin_point_plot_style : str (optional)</span>
+<span class="sd"> origin point plot style. If None, not plotting.</span>
+<span class="sd"> head_width : a float (optional)</span>
+<span class="sd"> arrow head width. default is 0.1</span>
+<span class="sd"> fc : string (optional)</span>
+<span class="sd"> face color</span>
+<span class="sd"> ec : string (optional)</span>
+<span class="sd"> edge color</span>
+<span class="sd"> """</span>
+ <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="nb">float</span><span class="p">):</span>
+ <span class="k">for</span> <span class="p">(</span><span class="n">i_x</span><span class="p">,</span> <span class="n">i_y</span><span class="p">,</span> <span class="n">i_yaw</span><span class="p">)</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">yaw</span><span class="p">):</span>
+ <span class="n">plot_arrow</span><span class="p">(</span><span class="n">i_x</span><span class="p">,</span> <span class="n">i_y</span><span class="p">,</span> <span class="n">i_yaw</span><span class="p">,</span> <span class="n">head_width</span><span class="o">=</span><span class="n">head_width</span><span class="p">,</span>
+ <span class="n">fc</span><span class="o">=</span><span class="n">fc</span><span class="p">,</span> <span class="n">ec</span><span class="o">=</span><span class="n">ec</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">arrow</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span>
+ <span class="n">arrow_length</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">yaw</span><span class="p">),</span>
+ <span class="n">arrow_length</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">yaw</span><span class="p">),</span>
+ <span class="n">head_width</span><span class="o">=</span><span class="n">head_width</span><span class="p">,</span>
+ <span class="n">fc</span><span class="o">=</span><span class="n">fc</span><span class="p">,</span> <span class="n">ec</span><span class="o">=</span><span class="n">ec</span><span class="p">,</span>
+ <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+ <span class="k">if</span> <span class="n">origin_point_plot_style</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">origin_point_plot_style</span><span class="p">)</span>
+
+
+<div class="viewcode-block" id="plot_curvature"><a class="viewcode-back" href="../../modules/utils/plot/plot.html#utils.plot.plot_curvature">[docs]</a><span class="k">def</span> <span class="nf">plot_curvature</span><span class="p">(</span><span class="n">x_list</span><span class="p">,</span> <span class="n">y_list</span><span class="p">,</span> <span class="n">heading_list</span><span class="p">,</span> <span class="n">curvature</span><span class="p">,</span>
+ <span class="n">k</span><span class="o">=</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">c</span><span class="o">=</span><span class="s2">"-c"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Curvature"</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Plot curvature on 2D path. This plot is a line from the original path,</span>
+<span class="sd"> the lateral distance from the original path shows curvature magnitude.</span>
+<span class="sd"> Left turning shows right side plot, right turning shows left side plot.</span>
+<span class="sd"> For straight path, the curvature plot will be on the path, because</span>
+<span class="sd"> curvature is 0 on the straight path.</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> x_list : array_like</span>
+<span class="sd"> x position list of the path</span>
+<span class="sd"> y_list : array_like</span>
+<span class="sd"> y position list of the path</span>
+<span class="sd"> heading_list : array_like</span>
+<span class="sd"> heading list of the path</span>
+<span class="sd"> curvature : array_like</span>
+<span class="sd"> curvature list of the path</span>
+<span class="sd"> k : float</span>
+<span class="sd"> curvature scale factor to calculate distance from the original path</span>
+<span class="sd"> c : string</span>
+<span class="sd"> color of the plot</span>
+<span class="sd"> label : string</span>
+<span class="sd"> label of the plot</span>
+<span class="sd"> """</span>
+ <span class="n">cx</span> <span class="o">=</span> <span class="p">[</span><span class="n">x</span> <span class="o">+</span> <span class="n">d</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">yaw</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mf">2.0</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">yaw</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span>
+ <span class="nb">zip</span><span class="p">(</span><span class="n">x_list</span><span class="p">,</span> <span class="n">y_list</span><span class="p">,</span> <span class="n">heading_list</span><span class="p">,</span> <span class="n">curvature</span><span class="p">)]</span>
+ <span class="n">cy</span> <span class="o">=</span> <span class="p">[</span><span class="n">y</span> <span class="o">+</span> <span class="n">d</span> <span class="o">*</span> <span class="n">k</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">yaw</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">pi</span> <span class="o">/</span> <span class="mf">2.0</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">yaw</span><span class="p">,</span> <span class="n">d</span> <span class="ow">in</span>
+ <span class="nb">zip</span><span class="p">(</span><span class="n">x_list</span><span class="p">,</span> <span class="n">y_list</span><span class="p">,</span> <span class="n">heading_list</span><span class="p">,</span> <span class="n">curvature</span><span class="p">)]</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">cx</span><span class="p">,</span> <span class="n">cy</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="n">label</span><span class="p">)</span>
+ <span class="k">for</span> <span class="n">ix</span><span class="p">,</span> <span class="n">iy</span><span class="p">,</span> <span class="n">icx</span><span class="p">,</span> <span class="n">icy</span> <span class="ow">in</span> <span class="nb">zip</span><span class="p">(</span><span class="n">x_list</span><span class="p">,</span> <span class="n">y_list</span><span class="p">,</span> <span class="n">cx</span><span class="p">,</span> <span class="n">cy</span><span class="p">):</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">ix</span><span class="p">,</span> <span class="n">icx</span><span class="p">],</span> <span class="p">[</span><span class="n">iy</span><span class="p">,</span> <span class="n">icy</span><span class="p">],</span> <span class="n">c</span><span class="p">)</span></div>
+
+
+<span class="k">class</span> <span class="nc">Arrow3D</span><span class="p">(</span><span class="n">FancyArrowPatch</span><span class="p">):</span>
+
+ <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">,</span> <span class="n">dz</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+ <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="fm">__init__</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">),</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">_xyz</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">_dxdydz</span> <span class="o">=</span> <span class="p">(</span><span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">,</span> <span class="n">dz</span><span class="p">)</span>
+
+ <span class="k">def</span> <span class="nf">draw</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">renderer</span><span class="p">):</span>
+ <span class="n">x1</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">z1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_xyz</span>
+ <span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">,</span> <span class="n">dz</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_dxdydz</span>
+ <span class="n">x2</span><span class="p">,</span> <span class="n">y2</span><span class="p">,</span> <span class="n">z2</span> <span class="o">=</span> <span class="p">(</span><span class="n">x1</span> <span class="o">+</span> <span class="n">dx</span><span class="p">,</span> <span class="n">y1</span> <span class="o">+</span> <span class="n">dy</span><span class="p">,</span> <span class="n">z1</span> <span class="o">+</span> <span class="n">dz</span><span class="p">)</span>
+
+ <span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">zs</span> <span class="o">=</span> <span class="n">proj_transform</span><span class="p">((</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">),</span> <span class="p">(</span><span class="n">y1</span><span class="p">,</span> <span class="n">y2</span><span class="p">),</span> <span class="p">(</span><span class="n">z1</span><span class="p">,</span> <span class="n">z2</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">axes</span><span class="o">.</span><span class="n">M</span><span class="p">)</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">set_positions</span><span class="p">((</span><span class="n">xs</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ys</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">xs</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">ys</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
+ <span class="nb">super</span><span class="p">()</span><span class="o">.</span><span class="n">draw</span><span class="p">(</span><span class="n">renderer</span><span class="p">)</span>
+
+ <span class="k">def</span> <span class="nf">do_3d_projection</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">renderer</span><span class="o">=</span><span class="kc">None</span><span class="p">):</span>
+ <span class="n">x1</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">z1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_xyz</span>
+ <span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">,</span> <span class="n">dz</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">_dxdydz</span>
+ <span class="n">x2</span><span class="p">,</span> <span class="n">y2</span><span class="p">,</span> <span class="n">z2</span> <span class="o">=</span> <span class="p">(</span><span class="n">x1</span> <span class="o">+</span> <span class="n">dx</span><span class="p">,</span> <span class="n">y1</span> <span class="o">+</span> <span class="n">dy</span><span class="p">,</span> <span class="n">z1</span> <span class="o">+</span> <span class="n">dz</span><span class="p">)</span>
+
+ <span class="n">xs</span><span class="p">,</span> <span class="n">ys</span><span class="p">,</span> <span class="n">zs</span> <span class="o">=</span> <span class="n">proj_transform</span><span class="p">((</span><span class="n">x1</span><span class="p">,</span> <span class="n">x2</span><span class="p">),</span> <span class="p">(</span><span class="n">y1</span><span class="p">,</span> <span class="n">y2</span><span class="p">),</span> <span class="p">(</span><span class="n">z1</span><span class="p">,</span> <span class="n">z2</span><span class="p">),</span> <span class="bp">self</span><span class="o">.</span><span class="n">axes</span><span class="o">.</span><span class="n">M</span><span class="p">)</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">set_positions</span><span class="p">((</span><span class="n">xs</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">ys</span><span class="p">[</span><span class="mi">0</span><span class="p">]),</span> <span class="p">(</span><span class="n">xs</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">ys</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
+
+ <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">zs</span><span class="p">)</span>
+
+
+<span class="k">def</span> <span class="nf">_arrow3D</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">,</span> <span class="n">dz</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">'''Add an 3d arrow to an `Axes3D` instance.'''</span>
+ <span class="n">arrow</span> <span class="o">=</span> <span class="n">Arrow3D</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">dx</span><span class="p">,</span> <span class="n">dy</span><span class="p">,</span> <span class="n">dz</span><span class="p">,</span> <span class="o">*</span><span class="n">args</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">add_artist</span><span class="p">(</span><span class="n">arrow</span><span class="p">)</span>
+
+
+<span class="k">def</span> <span class="nf">plot_3d_vector_arrow</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">):</span>
+ <span class="nb">setattr</span><span class="p">(</span><span class="n">Axes3D</span><span class="p">,</span> <span class="s1">'arrow3D'</span><span class="p">,</span> <span class="n">_arrow3D</span><span class="p">)</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">arrow3D</span><span class="p">(</span><span class="n">p1</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">p1</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">p1</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span>
+ <span class="n">p2</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">-</span><span class="n">p1</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">p2</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">-</span><span class="n">p1</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">p2</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span><span class="o">-</span><span class="n">p1</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span>
+ <span class="n">mutation_scale</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span>
+ <span class="n">arrowstyle</span><span class="o">=</span><span class="s2">"-|>"</span><span class="p">,</span>
+ <span class="p">)</span>
+
+
+<span class="k">def</span> <span class="nf">plot_triangle</span><span class="p">(</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">,</span> <span class="n">ax</span><span class="p">):</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">add_collection3d</span><span class="p">(</span><span class="n">art3d</span><span class="o">.</span><span class="n">Poly3DCollection</span><span class="p">([[</span><span class="n">p1</span><span class="p">,</span> <span class="n">p2</span><span class="p">,</span> <span class="n">p3</span><span class="p">]],</span> <span class="n">color</span><span class="o">=</span><span class="s1">'b'</span><span class="p">))</span>
+
+
+<span class="k">def</span> <span class="nf">set_equal_3d_axis</span><span class="p">(</span><span class="n">ax</span><span class="p">,</span> <span class="n">x_lims</span><span class="p">,</span> <span class="n">y_lims</span><span class="p">,</span> <span class="n">z_lims</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""Helper function to set equal axis</span>
+
+<span class="sd"> Args:</span>
+<span class="sd"> ax (Axes3DSubplot): matplotlib 3D axis, created by</span>
+<span class="sd"> `ax = fig.add_subplot(projection='3d')`</span>
+<span class="sd"> x_lims (np.array): array containing min and max value of x</span>
+<span class="sd"> y_lims (np.array): array containing min and max value of y</span>
+<span class="sd"> z_lims (np.array): array containing min and max value of z</span>
+<span class="sd"> """</span>
+ <span class="n">x_lims</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">x_lims</span><span class="p">)</span>
+ <span class="n">y_lims</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">y_lims</span><span class="p">)</span>
+ <span class="n">z_lims</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">z_lims</span><span class="p">)</span>
+ <span class="c1"># compute max required range</span>
+ <span class="n">max_range</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">x_lims</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">-</span> <span class="n">x_lims</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span>
+ <span class="n">y_lims</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">-</span> <span class="n">y_lims</span><span class="o">.</span><span class="n">min</span><span class="p">(),</span>
+ <span class="n">z_lims</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">-</span> <span class="n">z_lims</span><span class="o">.</span><span class="n">min</span><span class="p">()])</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">/</span> <span class="mf">2.0</span>
+ <span class="c1"># compute mid-point along each axis</span>
+ <span class="n">mid_x</span> <span class="o">=</span> <span class="p">(</span><span class="n">x_lims</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">+</span> <span class="n">x_lims</span><span class="o">.</span><span class="n">min</span><span class="p">())</span> <span class="o">*</span> <span class="mf">0.5</span>
+ <span class="n">mid_y</span> <span class="o">=</span> <span class="p">(</span><span class="n">y_lims</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">+</span> <span class="n">y_lims</span><span class="o">.</span><span class="n">min</span><span class="p">())</span> <span class="o">*</span> <span class="mf">0.5</span>
+ <span class="n">mid_z</span> <span class="o">=</span> <span class="p">(</span><span class="n">z_lims</span><span class="o">.</span><span class="n">max</span><span class="p">()</span> <span class="o">+</span> <span class="n">z_lims</span><span class="o">.</span><span class="n">min</span><span class="p">())</span> <span class="o">*</span> <span class="mf">0.5</span>
+
+ <span class="c1"># set limits to axis</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">set_xlim</span><span class="p">(</span><span class="n">mid_x</span> <span class="o">-</span> <span class="n">max_range</span><span class="p">,</span> <span class="n">mid_x</span> <span class="o">+</span> <span class="n">max_range</span><span class="p">)</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">set_ylim</span><span class="p">(</span><span class="n">mid_y</span> <span class="o">-</span> <span class="n">max_range</span><span class="p">,</span> <span class="n">mid_y</span> <span class="o">+</span> <span class="n">max_range</span><span class="p">)</span>
+ <span class="n">ax</span><span class="o">.</span><span class="n">set_zlim</span><span class="p">(</span><span class="n">mid_z</span> <span class="o">-</span> <span class="n">max_range</span><span class="p">,</span> <span class="n">mid_z</span> <span class="o">+</span> <span class="n">max_range</span><span class="p">)</span>
+
+
+<span class="k">if</span> <span class="vm">__name__</span> <span class="o">==</span> <span class="s1">'__main__'</span><span class="p">:</span>
+ <span class="n">plot_ellipse</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mi">15</span><span class="p">))</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s1">'equal'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+</pre></div>
+
+ </div>
+ </div>
+ <footer>
+
+ <hr/>
+
+ <div role="contentinfo">
+ <p>© Copyright 2018-2021, Atsushi Sakai.</p>
+ </div>
+
+ Built with <a href="https://www.sphinx-doc.org/">Sphinx</a> using a
+ <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
+ provided by <a href="https://readthedocs.org">Read the Docs</a>.
+
+
+</footer>
+ </div>
+ </div>
+ </section>
+ </div>
+ <script>
+ jQuery(function () {
+ SphinxRtdTheme.Navigation.enable(true);
+ });
+ </script>
+
+</body>
+</html>
\ No newline at end of file
diff --git a/_sources/getting_started_main.rst.txt b/_sources/getting_started_main.rst.txt
new file mode 100644
index 00000000000..497b85a23a8
--- /dev/null
+++ b/_sources/getting_started_main.rst.txt
@@ -0,0 +1,85 @@
+.. _`getting started`:
+
+Getting Started
+===============
+
+What is this?
+-------------
+
+This is an Open Source Software (OSS) project: PythonRobotics, which is a Python code collection of robotics algorithms.
+
+The focus of the project is on autonomous navigation, and the goal is for beginners in robotics to understand the basic ideas behind each algorithm.
+
+In this project, the algorithms which are practical and widely used in both academia and industry are selected.
+
+Each sample code is written in Python3 and only depends on some standard modules for readability and ease of use.
+
+It includes intuitive animations to understand the behavior of the simulation.
+
+
+See this paper for more details:
+
+- PythonRobotics: a Python code collection of robotics algorithms: https://arxiv.org/abs/1808.10703
+
+.. _`Requirements`:
+
+Requirements
+-------------
+
+- `Python 3.11.x`_
+- `NumPy`_
+- `SciPy`_
+- `Matplotlib`_
+- `cvxpy`_
+
+For development:
+
+- `pytest`_ (for unit tests)
+- `pytest-xdist`_ (for parallel unit tests)
+- `mypy`_ (for type check)
+- `sphinx`_ (for document generation)
+- `ruff`_ (for code style check)
+
+.. _`Python 3.11.x`: https://www.python.org/
+.. _`NumPy`: https://numpy.org/
+.. _`SciPy`: https://scipy.org/
+.. _`Matplotlib`: https://matplotlib.org/
+.. _`cvxpy`: https://www.cvxpy.org/
+.. _`pytest`: https://docs.pytest.org/en/latest/
+.. _`pytest-xdist`: https://github.com/pytest-dev/pytest-xdist
+.. _`mypy`: https://mypy-lang.org/
+.. _`sphinx`: https://www.sphinx-doc.org/en/master/index.html
+.. _`ruff`: https://github.com/charliermarsh/ruff
+
+
+How to use
+----------
+
+1. Clone this repo and go into dir.
+
+.. code-block::
+
+ >$ git clone https://github.com/AtsushiSakai/PythonRobotics.git
+
+ >$ cd PythonRobotics
+
+
+2. Install the required libraries.
+
+using conda :
+
+.. code-block::
+
+ >$ conda env create -f requirements/environment.yml
+
+using pip :
+
+.. code-block::
+
+ >$ pip install -r requirements/requirements.txt
+
+
+3. Execute python script in each directory.
+
+4. Add star to this repo if you like it 😃.
+
diff --git a/docs/modules/0_getting_started/3_how_to_contribute_main.rst b/_sources/how_to_contribute_main.rst.txt
similarity index 69%
rename from docs/modules/0_getting_started/3_how_to_contribute_main.rst
rename to _sources/how_to_contribute_main.rst.txt
index 1e61760649f..48895d6fdad 100644
--- a/docs/modules/0_getting_started/3_how_to_contribute_main.rst
+++ b/_sources/how_to_contribute_main.rst.txt
@@ -1,39 +1,10 @@
-How to contribute
+How To Contribute
=================
This document describes how to contribute this project.
-There are several ways to contribute to this project as below:
-#. `Adding a new algorithm example`_
-#. `Reporting and fixing a defect`_
-#. `Adding missed documentations for existing examples`_
-#. `Supporting this project`_
-
-Before contributing
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-Please check following items before contributing:
-
-Understanding this project
----------------------------
-
-Please check this :ref:`What is PythonRobotics?` section and this paper
-`PythonRobotics: a Python code collection of robotics algorithms`_
-to understand the philosophies of this project.
-
-.. _`PythonRobotics: a Python code collection of robotics algorithms`: https://arxiv.org/abs/1808.10703
-
-Check your Python version.
----------------------------
-
-We only accept a PR for Python 3.12.x or higher.
-
-We will not accept a PR for Python 2.x.
-
-.. _`Adding a new algorithm example`:
-
-1. Adding a new algorithm example
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+Adding a new algorithm example
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
This is a step by step manual to add a new algorithm example.
@@ -96,16 +67,9 @@ Please check other documents for details.
You can build the doc locally based on `doc README`_.
-For creating a gif animation, you can use this tool: `matplotrecorder`_.
-
-The created gif file should be stored in the `PythonRoboticsGifs`_ repository,
-so please create a PR to add it and refer to it in the doc.
-
-Note that the `reStructuredText`_ based doc should only focus on the
-mathematics and the algorithm of the example.
+Note that the `reStructuredText`_ based doc should only focus on the mathematics and the algorithm of the example.
-Documentations related codes should be in the python script as the header
-comments of the script or docstrings of each function.
+Documentations related codes should be in the python script as the header comments of the script or docstrings of each function.
.. _`submit a pull request`:
@@ -128,12 +92,9 @@ After that, I will start the review.
Note that this is my hobby project; I appreciate your patience during the review process.
-
-.. _`Reporting and fixing a defect`:
-
-2. Reporting and fixing a defect
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+Reporting and fixing a defect
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Reporting and fixing a defect is also great contribution.
@@ -154,24 +115,19 @@ in the test code to show the issue was solved.
This doc `submit a pull request`_ can be helpful to submit a pull request.
-.. _`Adding missed documentations for existing examples`:
-
-3. Adding missed documentations for existing examples
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+Adding missed documentations for existing examples
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Adding the missed documentations for existing examples is also great contribution.
If you check the `Python Robotics Docs`_, you can notice that some of the examples
-only have a simulation gif or short overview descriptions or just TBD.,
+only have a simulation gif or short overview descriptions,
but no detailed algorithm or mathematical description.
-These documents needs to be improved.
This doc `how to write doc`_ can be helpful to write documents.
-.. _`Supporting this project`:
-
-4. Supporting this project
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
+Supporting this project
+^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
Supporting this project financially is also a great contribution!!.
@@ -185,12 +141,10 @@ If you or your company would like to support this project, please consider:
If you would like to support us in some other way, please contact with creating an issue.
-Current Major Sponsors:
-
-#. `GitHub`_ : They are providing a GitHub Copilot Pro license for this OSS development.
-#. `JetBrains`_ : They are providing a free license of their IDEs for this OSS development.
-#. `1Password`_ : They are providing a free license of their 1Password team license for this OSS project.
+Sponsors
+---------
+1. `JetBrains`_ : They are providing a free license of their IDEs for this OSS development.
.. _`Python Robotics Docs`: https://atsushisakai.github.io/PythonRobotics
@@ -203,12 +157,8 @@ Current Major Sponsors:
.. _`doc README`: https://github.com/AtsushiSakai/PythonRobotics/blob/master/docs/README.md
.. _`test_codestyle.py`: https://github.com/AtsushiSakai/PythonRobotics/blob/master/tests/test_codestyle.py
.. _`JetBrains`: https://www.jetbrains.com/
-.. _`GitHub`: https://www.github.com/
.. _`Sponsor @AtsushiSakai on GitHub Sponsors`: https://github.com/sponsors/AtsushiSakai
.. _`Become a backer or sponsor on Patreon`: https://www.patreon.com/myenigma
-.. _`One-time donation via PayPal`: https://www.paypal.com/paypalme/myenigmapay/
-.. _`1Password`: https://github.com/1Password/for-open-source
-.. _`matplotrecorder`: https://github.com/AtsushiSakai/matplotrecorder
-.. _`PythonRoboticsGifs`: https://github.com/AtsushiSakai/PythonRoboticsGifs
+.. _`One-time donation via PayPal`: https://www.paypal.me/myenigmapay/
diff --git a/_sources/index_main.rst.txt b/_sources/index_main.rst.txt
new file mode 100644
index 00000000000..67bd9889f2a
--- /dev/null
+++ b/_sources/index_main.rst.txt
@@ -0,0 +1,57 @@
+.. PythonRobotics documentation master file, created by
+ sphinx-quickstart on Sat Sep 15 13:15:55 2018.
+ You can adapt this file completely to your liking, but it should at least
+ contain the root `toctree` directive.
+
+Welcome to PythonRobotics's documentation!
+==========================================
+
+Python codes for robotics algorithm. The project is on `GitHub`_.
+
+This is a Python code collection of robotics algorithms.
+
+Features:
+
+1. Easy to read for understanding each algorithm's basic idea.
+
+2. Widely used and practical algorithms are selected.
+
+3. Minimum dependency.
+
+See this paper for more details:
+
+- `[1808.10703] PythonRobotics: a Python code collection of robotics
+ algorithms`_ (`BibTeX`_)
+
+
+.. _`[1808.10703] PythonRobotics: a Python code collection of robotics algorithms`: https://arxiv.org/abs/1808.10703
+.. _BibTeX: https://github.com/AtsushiSakai/PythonRoboticsPaper/blob/master/python_robotics.bib
+.. _GitHub: https://github.com/AtsushiSakai/PythonRobotics
+
+
+.. toctree::
+ :maxdepth: 2
+ :caption: Contents
+
+ getting_started
+ modules/introduction
+ modules/localization/localization
+ modules/mapping/mapping
+ modules/slam/slam
+ modules/path_planning/path_planning
+ modules/path_tracking/path_tracking
+ modules/arm_navigation/arm_navigation
+ modules/aerial_navigation/aerial_navigation
+ modules/bipedal/bipedal
+ modules/control/control
+ modules/utils/utils
+ modules/appendix/appendix
+ how_to_contribute
+
+
+Indices and tables
+==================
+
+* :ref:`genindex`
+* :ref:`modindex`
+* :ref:`search`
diff --git a/docs/modules/8_aerial_navigation/aerial_navigation_main.rst b/_sources/modules/aerial_navigation/aerial_navigation_main.rst.txt
similarity index 89%
rename from docs/modules/8_aerial_navigation/aerial_navigation_main.rst
rename to _sources/modules/aerial_navigation/aerial_navigation_main.rst.txt
index 7f766897702..b2ccb071aff 100644
--- a/docs/modules/8_aerial_navigation/aerial_navigation_main.rst
+++ b/_sources/modules/aerial_navigation/aerial_navigation_main.rst.txt
@@ -1,4 +1,4 @@
-.. _`Aerial Navigation`:
+.. _aerial_navigation:
Aerial Navigation
=================
diff --git a/docs/modules/8_aerial_navigation/drone_3d_trajectory_following/drone_3d_trajectory_following_main.rst b/_sources/modules/aerial_navigation/drone_3d_trajectory_following/drone_3d_trajectory_following_main.rst.txt
similarity index 100%
rename from docs/modules/8_aerial_navigation/drone_3d_trajectory_following/drone_3d_trajectory_following_main.rst
rename to _sources/modules/aerial_navigation/drone_3d_trajectory_following/drone_3d_trajectory_following_main.rst.txt
diff --git a/docs/modules/8_aerial_navigation/rocket_powered_landing/rocket_powered_landing_main.rst b/_sources/modules/aerial_navigation/rocket_powered_landing/rocket_powered_landing_main.rst.txt
similarity index 100%
rename from docs/modules/8_aerial_navigation/rocket_powered_landing/rocket_powered_landing_main.rst
rename to _sources/modules/aerial_navigation/rocket_powered_landing/rocket_powered_landing_main.rst.txt
diff --git a/docs/modules/12_appendix/Kalmanfilter_basics_2_main.rst b/_sources/modules/appendix/Kalmanfilter_basics_2_main.rst.txt
similarity index 100%
rename from docs/modules/12_appendix/Kalmanfilter_basics_2_main.rst
rename to _sources/modules/appendix/Kalmanfilter_basics_2_main.rst.txt
diff --git a/docs/modules/12_appendix/Kalmanfilter_basics_main.rst b/_sources/modules/appendix/Kalmanfilter_basics_main.rst.txt
similarity index 100%
rename from docs/modules/12_appendix/Kalmanfilter_basics_main.rst
rename to _sources/modules/appendix/Kalmanfilter_basics_main.rst.txt
diff --git a/docs/modules/12_appendix/appendix_main.rst b/_sources/modules/appendix/appendix_main.rst.txt
similarity index 61%
rename from docs/modules/12_appendix/appendix_main.rst
rename to _sources/modules/appendix/appendix_main.rst.txt
index d0b9eeea3a8..8a29d846764 100644
--- a/docs/modules/12_appendix/appendix_main.rst
+++ b/_sources/modules/appendix/appendix_main.rst.txt
@@ -1,4 +1,4 @@
-.. _`Appendix`:
+.. _appendix:
Appendix
==============
@@ -7,9 +7,6 @@ Appendix
:maxdepth: 2
:caption: Contents
- steering_motion_model
Kalmanfilter_basics
Kalmanfilter_basics_2
- internal_sensors
- external_sensors
diff --git a/docs/modules/7_arm_navigation/arm_navigation_main.rst b/_sources/modules/arm_navigation/arm_navigation_main.rst.txt
similarity index 88%
rename from docs/modules/7_arm_navigation/arm_navigation_main.rst
rename to _sources/modules/arm_navigation/arm_navigation_main.rst.txt
index 7acd3ee7d39..bbbc872c580 100644
--- a/docs/modules/7_arm_navigation/arm_navigation_main.rst
+++ b/_sources/modules/arm_navigation/arm_navigation_main.rst.txt
@@ -1,4 +1,4 @@
-.. _`Arm Navigation`:
+.. _arm_navigation:
Arm Navigation
==============
diff --git a/docs/modules/7_arm_navigation/n_joint_arm_to_point_control_main.rst b/_sources/modules/arm_navigation/n_joint_arm_to_point_control_main.rst.txt
similarity index 100%
rename from docs/modules/7_arm_navigation/n_joint_arm_to_point_control_main.rst
rename to _sources/modules/arm_navigation/n_joint_arm_to_point_control_main.rst.txt
diff --git a/docs/modules/7_arm_navigation/obstacle_avoidance_arm_navigation_main.rst b/_sources/modules/arm_navigation/obstacle_avoidance_arm_navigation_main.rst.txt
similarity index 100%
rename from docs/modules/7_arm_navigation/obstacle_avoidance_arm_navigation_main.rst
rename to _sources/modules/arm_navigation/obstacle_avoidance_arm_navigation_main.rst.txt
diff --git a/docs/modules/7_arm_navigation/planar_two_link_ik_main.rst b/_sources/modules/arm_navigation/planar_two_link_ik_main.rst.txt
similarity index 100%
rename from docs/modules/7_arm_navigation/planar_two_link_ik_main.rst
rename to _sources/modules/arm_navigation/planar_two_link_ik_main.rst.txt
diff --git a/docs/modules/9_bipedal/bipedal_main.rst b/_sources/modules/bipedal/bipedal_main.rst.txt
similarity index 88%
rename from docs/modules/9_bipedal/bipedal_main.rst
rename to _sources/modules/bipedal/bipedal_main.rst.txt
index dc387dc4e83..fc5b9330559 100644
--- a/docs/modules/9_bipedal/bipedal_main.rst
+++ b/_sources/modules/bipedal/bipedal_main.rst.txt
@@ -1,4 +1,4 @@
-.. _`Bipedal`:
+.. _bipedal:
Bipedal
=================
diff --git a/docs/modules/9_bipedal/bipedal_planner/bipedal_planner_main.rst b/_sources/modules/bipedal/bipedal_planner/bipedal_planner_main.rst.txt
similarity index 100%
rename from docs/modules/9_bipedal/bipedal_planner/bipedal_planner_main.rst
rename to _sources/modules/bipedal/bipedal_planner/bipedal_planner_main.rst.txt
diff --git a/_sources/modules/control/control_main.rst.txt b/_sources/modules/control/control_main.rst.txt
new file mode 100644
index 00000000000..cee2aa9e8e4
--- /dev/null
+++ b/_sources/modules/control/control_main.rst.txt
@@ -0,0 +1,12 @@
+.. _control:
+
+Control
+=================
+
+.. toctree::
+ :maxdepth: 2
+ :caption: Contents
+
+ inverted_pendulum_control/inverted_pendulum_control
+ move_to_a_pose_control/move_to_a_pose_control
+
diff --git a/docs/modules/10_inverted_pendulum/inverted_pendulum_main.rst b/_sources/modules/control/inverted_pendulum_control/inverted_pendulum_control_main.rst.txt
similarity index 97%
rename from docs/modules/10_inverted_pendulum/inverted_pendulum_main.rst
rename to _sources/modules/control/inverted_pendulum_control/inverted_pendulum_control_main.rst.txt
index 048cbea9acd..e41729fd61f 100644
--- a/docs/modules/10_inverted_pendulum/inverted_pendulum_main.rst
+++ b/_sources/modules/control/inverted_pendulum_control/inverted_pendulum_control_main.rst.txt
@@ -1,7 +1,5 @@
-.. _`Inverted Pendulum`:
-
-Inverted Pendulum
-------------------
+Inverted Pendulum Control
+-----------------------------
An inverted pendulum on a cart consists of a mass :math:`m` at the top of a pole of length :math:`l` pivoted on a
horizontally moving base as shown in the adjacent.
diff --git a/docs/modules/6_path_tracking/move_to_a_pose_control/move_to_a_pose_control_main.rst b/_sources/modules/control/move_to_a_pose_control/move_to_a_pose_control_main.rst.txt
similarity index 100%
rename from docs/modules/6_path_tracking/move_to_a_pose_control/move_to_a_pose_control_main.rst
rename to _sources/modules/control/move_to_a_pose_control/move_to_a_pose_control_main.rst.txt
diff --git a/_sources/modules/introduction_main.rst.txt b/_sources/modules/introduction_main.rst.txt
new file mode 100644
index 00000000000..f9fb487297d
--- /dev/null
+++ b/_sources/modules/introduction_main.rst.txt
@@ -0,0 +1,42 @@
+
+Introduction
+============
+
+TBD
+
+Definition Of Robotics
+----------------------
+
+TBD
+
+History Of Robotics
+----------------------
+
+TBD
+
+Application Of Robotics
+------------------------
+
+TBD
+
+Software for Robotics
+----------------------
+
+TBD
+
+Software for Robotics
+----------------------
+
+TBD
+
+Python for Robotics
+----------------------
+
+TBD
+
+Learning Robotics Algorithms
+----------------------------
+
+TBD
+
+
diff --git a/docs/modules/2_localization/ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization_main.rst b/_sources/modules/localization/ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization_main.rst.txt
similarity index 100%
rename from docs/modules/2_localization/ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization_main.rst
rename to _sources/modules/localization/ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization_main.rst.txt
diff --git a/docs/modules/2_localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization_main.rst b/_sources/modules/localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization_main.rst.txt
similarity index 51%
rename from docs/modules/2_localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization_main.rst
rename to _sources/modules/localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization_main.rst.txt
index da214b6de58..0ec920c9dfa 100644
--- a/docs/modules/2_localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization_main.rst
+++ b/_sources/modules/localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization_main.rst.txt
@@ -2,9 +2,6 @@
Extended Kalman Filter Localization
-----------------------------------
-Position Estimation Kalman Filter
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
.. image:: extended_kalman_filter_localization_1_0.png
:width: 600px
@@ -12,7 +9,6 @@ Position Estimation Kalman Filter
.. figure:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/extended_kalman_filter/animation.gif
-
This is a sensor fusion localization with Extended Kalman Filter(EKF).
The blue line is true trajectory, the black line is dead reckoning
@@ -26,26 +22,9 @@ The red ellipse is estimated covariance ellipse with EKF.
Code: `PythonRobotics/extended_kalman_filter.py at master ·
AtsushiSakai/PythonRobotics <https://github.com/AtsushiSakai/PythonRobotics/blob/master/Localization/extended_kalman_filter/extended_kalman_filter.py>`__
-Kalman Filter with Speed Scale Factor Correction
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-
-.. image:: ekf_with_velocity_correction_1_0.png
- :width: 600px
-
-This is a Extended kalman filter (EKF) localization with velocity correction.
-
-This is for correcting the vehicle speed measured with scale factor errors due to factors such as wheel wear.
-
-Code: `PythonRobotics/extended_kalman_ekf_with_velocity_correctionfilter.py
-AtsushiSakai/PythonRobotics <https://github.com/AtsushiSakai/PythonRobotics/blob/master/Localization/extended_kalman_filter/extended_kalman_ekf_with_velocity_correctionfilter.py>`__
-
Filter design
~~~~~~~~~~~~~
-Position Estimation Kalman Filter
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
In this simulation, the robot has a state vector includes 4 states at
time :math:`t`.
@@ -82,28 +61,9 @@ In the code, “observation” function generates the input and observation
vector with noise
`code <https://github.com/AtsushiSakai/PythonRobotics/blob/916b4382de090de29f54538b356cef1c811aacce/Localization/extended_kalman_filter/extended_kalman_filter.py#L34-L50>`__
-Kalman Filter with Speed Scale Factor Correction
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-In this simulation, the robot has a state vector includes 5 states at
-time :math:`t`.
-
-.. math:: \textbf{x}_t=[x_t, y_t, \phi_t, v_t, s_t]
-
-x, y are a 2D x-y position, :math:`\phi` is orientation, v is
-velocity, and s is a scale factor of velocity.
-
-In the code, “xEst” means the state vector.
-`code <https://github.com/AtsushiSakai/PythonRobotics/blob/916b4382de090de29f54538b356cef1c811aacce/Localization/extended_kalman_filter/extended_kalman_ekf_with_velocity_correctionfilter.py#L163>`__
-
-The rest is the same as the Position Estimation Kalman Filter.
-
Motion Model
~~~~~~~~~~~~
-Position Estimation Kalman Filter
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
The robot model is
.. math:: \dot{x} = v \cos(\phi)
@@ -137,50 +97,9 @@ Its Jacobian matrix is
:math:`\begin{equation*} = \begin{bmatrix} 1& 0 & -v \sin(\phi) \Delta t & \cos(\phi) \Delta t\\ 0 & 1 & v \cos(\phi) \Delta t & \sin(\phi) \Delta t\\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \end{equation*}`
-
-Kalman Filter with Speed Scale Factor Correction
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-The robot model is
-
-.. math:: \dot{x} = v s \cos(\phi)
-
-.. math:: \dot{y} = v s \sin(\phi)
-
-.. math:: \dot{\phi} = \omega
-
-So, the motion model is
-
-.. math:: \textbf{x}_{t+1} = f(\textbf{x}_t, \textbf{u}_t) = F\textbf{x}_t+B\textbf{u}_t
-
-where
-
-:math:`\begin{equation*} F= \begin{bmatrix} 1 & 0 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 & 0\\ 0 & 0 & 1 & 0 & 0\\ 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 1\\ \end{bmatrix} \end{equation*}`
-
-:math:`\begin{equation*} B= \begin{bmatrix} cos(\phi) \Delta t s & 0\\ sin(\phi) \Delta t s & 0\\ 0 & \Delta t\\ 1 & 0\\ 0 & 0\\ \end{bmatrix} \end{equation*}`
-
-:math:`\Delta t` is a time interval.
-
-This is implemented at
-`code <https://github.com/AtsushiSakai/PythonRobotics/blob/916b4382de090de29f54538b356cef1c811aacce/Localization/extended_kalman_filter/extended_kalman_filter.py#L61-L76>`__
-
-The motion function is that
-
-:math:`\begin{equation*} \begin{bmatrix} x' \\ y' \\ w' \\ v' \end{bmatrix} = f(\textbf{x}, \textbf{u}) = \begin{bmatrix} x + v s \cos(\phi)\Delta t \\ y + v s \sin(\phi)\Delta t \\ \phi + \omega \Delta t \\ v \end{bmatrix} \end{equation*}`
-
-Its Jacobian matrix is
-
-:math:`\begin{equation*} J_f = \begin{bmatrix} \frac{\partial x'}{\partial x}& \frac{\partial x'}{\partial y} & \frac{\partial x'}{\partial \phi} & \frac{\partial x'}{\partial v} & \frac{\partial x'}{\partial s}\\ \frac{\partial y'}{\partial x}& \frac{\partial y'}{\partial y} & \frac{\partial y'}{\partial \phi} & \frac{\partial y'}{\partial v} & \frac{\partial y'}{\partial s}\\ \frac{\partial \phi'}{\partial x}& \frac{\partial \phi'}{\partial y} & \frac{\partial \phi'}{\partial \phi} & \frac{\partial \phi'}{\partial v} & \frac{\partial \phi'}{\partial s}\\ \frac{\partial v'}{\partial x}& \frac{\partial v'}{\partial y} & \frac{\partial v'}{\partial \phi} & \frac{\partial v'}{\partial v} & \frac{\partial v'}{\partial s} \\ \frac{\partial s'}{\partial x}& \frac{\partial s'}{\partial y} & \frac{\partial s'}{\partial \phi} & \frac{\partial s'}{\partial v} & \frac{\partial s'}{\partial s} \end{bmatrix} \end{equation*}`
-
-:math:`\begin{equation*} = \begin{bmatrix} 1& 0 & -v s \sin(\phi) \Delta t & s \cos(\phi) \Delta t & \cos(\phi) v \Delta t\\ 0 & 1 & v s \cos(\phi) \Delta t & s \sin(\phi) \Delta t & v \sin(\phi) \Delta t\\ 0 & 0 & 1 & 0 & 0 \\ 0 & 0 & 0 & 1 & 0 \end{bmatrix} \end{equation*}`
-
-
Observation Model
~~~~~~~~~~~~~~~~~
-Position Estimation Kalman Filter
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
The robot can get x-y position infomation from GPS.
So GPS Observation model is
@@ -201,30 +120,6 @@ Its Jacobian matrix is
:math:`\begin{equation*} = \begin{bmatrix} 1& 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ \end{bmatrix} \end{equation*}`
-Kalman Filter with Speed Scale Factor Correction
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-The robot can get x-y position infomation from GPS.
-
-So GPS Observation model is
-
-.. math:: \textbf{z}_{t} = g(\textbf{x}_t) = H \textbf{x}_t
-
-where
-
-:math:`\begin{equation*} H = \begin{bmatrix} 1 & 0 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 & 0 \\ \end{bmatrix} \end{equation*}`
-
-The observation function states that
-
-:math:`\begin{equation*} \begin{bmatrix} x' \\ y' \end{bmatrix} = g(\textbf{x}) = \begin{bmatrix} x \\ y \end{bmatrix} \end{equation*}`
-
-Its Jacobian matrix is
-
-:math:`\begin{equation*} J_g = \begin{bmatrix} \frac{\partial x'}{\partial x} & \frac{\partial x'}{\partial y} & \frac{\partial x'}{\partial \phi} & \frac{\partial x'}{\partial v} & \frac{\partial x'}{\partial s}\\ \frac{\partial y'}{\partial x}& \frac{\partial y'}{\partial y} & \frac{\partial y'}{\partial \phi} & \frac{\partial y'}{ \partial v} & \frac{\partial y'}{ \partial s}\\ \end{bmatrix} \end{equation*}`
-
-:math:`\begin{equation*} = \begin{bmatrix} 1& 0 & 0 & 0 & 0\\ 0 & 1 & 0 & 0 & 0\\ \end{bmatrix} \end{equation*}`
-
-
Extended Kalman Filter
~~~~~~~~~~~~~~~~~~~~~~
diff --git a/docs/modules/2_localization/histogram_filter_localization/histogram_filter_localization_main.rst b/_sources/modules/localization/histogram_filter_localization/histogram_filter_localization_main.rst.txt
similarity index 100%
rename from docs/modules/2_localization/histogram_filter_localization/histogram_filter_localization_main.rst
rename to _sources/modules/localization/histogram_filter_localization/histogram_filter_localization_main.rst.txt
diff --git a/docs/modules/2_localization/localization_main.rst b/_sources/modules/localization/localization_main.rst.txt
similarity index 55%
rename from docs/modules/2_localization/localization_main.rst
rename to _sources/modules/localization/localization_main.rst.txt
index 770a234b69e..db6651f6b87 100644
--- a/docs/modules/2_localization/localization_main.rst
+++ b/_sources/modules/localization/localization_main.rst.txt
@@ -1,8 +1,7 @@
-.. _`Localization`:
+.. _localization:
Localization
============
-Localization is the ability of a robot to know its position and orientation with sensors such as Global Navigation Satellite System:GNSS etc. In localization, Bayesian filters such as Kalman filters, histogram filter, and particle filter are widely used[31]. Fig.2 shows localization simulations using histogram filter and particle filter.
.. toctree::
:maxdepth: 2
diff --git a/docs/modules/2_localization/particle_filter_localization/particle_filter_localization_main.rst b/_sources/modules/localization/particle_filter_localization/particle_filter_localization_main.rst.txt
similarity index 94%
rename from docs/modules/2_localization/particle_filter_localization/particle_filter_localization_main.rst
rename to _sources/modules/localization/particle_filter_localization/particle_filter_localization_main.rst.txt
index 20a9eb58fc3..c8652ce8a75 100644
--- a/docs/modules/2_localization/particle_filter_localization/particle_filter_localization_main.rst
+++ b/_sources/modules/localization/particle_filter_localization/particle_filter_localization_main.rst.txt
@@ -34,4 +34,4 @@ References:
~~~~~~~~~~~
- `_PROBABILISTIC ROBOTICS: <http://www.probabilistic-robotics.org>`_
-- `Improving the particle filter in high dimensions using conjugate artificial process noise <https://arxiv.org/pdf/1801.07000>`_
+- `Improving the particle filter in high dimensions using conjugate artificial process noise <https://arxiv.org/pdf/1801.07000.pdf>`_
diff --git a/docs/modules/2_localization/unscented_kalman_filter_localization/unscented_kalman_filter_localization_main.rst b/_sources/modules/localization/unscented_kalman_filter_localization/unscented_kalman_filter_localization_main.rst.txt
similarity index 100%
rename from docs/modules/2_localization/unscented_kalman_filter_localization/unscented_kalman_filter_localization_main.rst
rename to _sources/modules/localization/unscented_kalman_filter_localization/unscented_kalman_filter_localization_main.rst.txt
diff --git a/docs/modules/3_mapping/circle_fitting/circle_fitting_main.rst b/_sources/modules/mapping/circle_fitting/circle_fitting_main.rst.txt
similarity index 100%
rename from docs/modules/3_mapping/circle_fitting/circle_fitting_main.rst
rename to _sources/modules/mapping/circle_fitting/circle_fitting_main.rst.txt
diff --git a/docs/modules/3_mapping/gaussian_grid_map/gaussian_grid_map_main.rst b/_sources/modules/mapping/gaussian_grid_map/gaussian_grid_map_main.rst.txt
similarity index 100%
rename from docs/modules/3_mapping/gaussian_grid_map/gaussian_grid_map_main.rst
rename to _sources/modules/mapping/gaussian_grid_map/gaussian_grid_map_main.rst.txt
diff --git a/docs/modules/3_mapping/k_means_object_clustering/k_means_object_clustering_main.rst b/_sources/modules/mapping/k_means_object_clustering/k_means_object_clustering_main.rst.txt
similarity index 100%
rename from docs/modules/3_mapping/k_means_object_clustering/k_means_object_clustering_main.rst
rename to _sources/modules/mapping/k_means_object_clustering/k_means_object_clustering_main.rst.txt
diff --git a/docs/modules/3_mapping/lidar_to_grid_map_tutorial/lidar_to_grid_map_tutorial_main.rst b/_sources/modules/mapping/lidar_to_grid_map_tutorial/lidar_to_grid_map_tutorial_main.rst.txt
similarity index 100%
rename from docs/modules/3_mapping/lidar_to_grid_map_tutorial/lidar_to_grid_map_tutorial_main.rst
rename to _sources/modules/mapping/lidar_to_grid_map_tutorial/lidar_to_grid_map_tutorial_main.rst.txt
diff --git a/docs/modules/3_mapping/mapping_main.rst b/_sources/modules/mapping/mapping_main.rst.txt
similarity index 50%
rename from docs/modules/3_mapping/mapping_main.rst
rename to _sources/modules/mapping/mapping_main.rst.txt
index 34a37448936..a98acaaf503 100644
--- a/docs/modules/3_mapping/mapping_main.rst
+++ b/_sources/modules/mapping/mapping_main.rst.txt
@@ -1,9 +1,7 @@
-.. _`Mapping`:
+.. _mapping:
Mapping
=======
-Mapping is the ability of a robot to understand its surroundings with external sensors such as LIDAR and camera. Robots have to recognize the position and shape of obstacles to avoid them. In mapping, grid mapping and machine learning algorithms are widely used[31][18]. Fig.3 shows mapping simulation results using grid mapping with 2D ray casting and 2D object clustering with k-means algorithm.
-
.. toctree::
:maxdepth: 2
:caption: Contents
@@ -17,4 +15,3 @@ Mapping is the ability of a robot to understand its surroundings with external s
circle_fitting/circle_fitting
rectangle_fitting/rectangle_fitting
normal_vector_estimation/normal_vector_estimation
- distance_map/distance_map
diff --git a/docs/modules/3_mapping/ndt_map/ndt_map_main.rst b/_sources/modules/mapping/ndt_map/ndt_map_main.rst.txt
similarity index 100%
rename from docs/modules/3_mapping/ndt_map/ndt_map_main.rst
rename to _sources/modules/mapping/ndt_map/ndt_map_main.rst.txt
diff --git a/docs/modules/3_mapping/normal_vector_estimation/normal_vector_estimation_main.rst b/_sources/modules/mapping/normal_vector_estimation/normal_vector_estimation_main.rst.txt
similarity index 100%
rename from docs/modules/3_mapping/normal_vector_estimation/normal_vector_estimation_main.rst
rename to _sources/modules/mapping/normal_vector_estimation/normal_vector_estimation_main.rst.txt
diff --git a/docs/modules/3_mapping/point_cloud_sampling/point_cloud_sampling_main.rst b/_sources/modules/mapping/point_cloud_sampling/point_cloud_sampling_main.rst.txt
similarity index 100%
rename from docs/modules/3_mapping/point_cloud_sampling/point_cloud_sampling_main.rst
rename to _sources/modules/mapping/point_cloud_sampling/point_cloud_sampling_main.rst.txt
diff --git a/docs/modules/3_mapping/ray_casting_grid_map/ray_casting_grid_map_main.rst b/_sources/modules/mapping/ray_casting_grid_map/ray_casting_grid_map_main.rst.txt
similarity index 100%
rename from docs/modules/3_mapping/ray_casting_grid_map/ray_casting_grid_map_main.rst
rename to _sources/modules/mapping/ray_casting_grid_map/ray_casting_grid_map_main.rst.txt
diff --git a/docs/modules/3_mapping/rectangle_fitting/rectangle_fitting_main.rst b/_sources/modules/mapping/rectangle_fitting/rectangle_fitting_main.rst.txt
similarity index 97%
rename from docs/modules/3_mapping/rectangle_fitting/rectangle_fitting_main.rst
rename to _sources/modules/mapping/rectangle_fitting/rectangle_fitting_main.rst.txt
index b6ced1dc1d7..50a50141b29 100644
--- a/docs/modules/3_mapping/rectangle_fitting/rectangle_fitting_main.rst
+++ b/_sources/modules/mapping/rectangle_fitting/rectangle_fitting_main.rst.txt
@@ -7,7 +7,7 @@ This is an object shape recognition using rectangle fitting.
This example code is based on this paper algorithm:
-- `Efficient L\-Shape Fitting for Vehicle Detection Using Laser Scanners \- The Robotics Institute Carnegie Mellon University <https://www.ri.cmu.edu/publications/efficient-l-shape-fitting-for-vehicle-detection-using-laser-scanners/>`_
+- `Efficient L\-Shape Fitting for Vehicle Detection Using Laser Scanners \- The Robotics Institute Carnegie Mellon University <https://www.ri.cmu.edu/publications/efficient-l-shape-fitting-for-vehicle-detection-using-laser-scanners>`_
The algorithm consists of 2 steps as below.
@@ -66,4 +66,4 @@ API
References
~~~~~~~~~~
-- `Efficient L\-Shape Fitting for Vehicle Detection Using Laser Scanners \- The Robotics Institute Carnegie Mellon University <https://www.ri.cmu.edu/publications/efficient-l-shape-fitting-for-vehicle-detection-using-laser-scanners/>`_
+- `Efficient L\-Shape Fitting for Vehicle Detection Using Laser Scanners \- The Robotics Institute Carnegie Mellon University <https://www.ri.cmu.edu/publications/efficient-l-shape-fitting-for-vehicle-detection-using-laser-scanners>`_
diff --git a/docs/modules/5_path_planning/bezier_path/bezier_path_main.rst b/_sources/modules/path_planning/bezier_path/bezier_path_main.rst.txt
similarity index 75%
rename from docs/modules/5_path_planning/bezier_path/bezier_path_main.rst
rename to _sources/modules/path_planning/bezier_path/bezier_path_main.rst.txt
index d306a853525..fbba6a4496b 100644
--- a/docs/modules/5_path_planning/bezier_path/bezier_path_main.rst
+++ b/_sources/modules/path_planning/bezier_path/bezier_path_main.rst.txt
@@ -17,4 +17,4 @@ Ref:
- `Continuous Curvature Path Generation Based on Bezier Curves for
Autonomous
- Vehicles <https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=b00b657c3e0e828c589132a14825e7119772003d>`
+ Vehicles <http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.294.6438&rep=rep1&type=pdf>`__
diff --git a/docs/modules/5_path_planning/bspline_path/bspline_path_main.rst b/_sources/modules/path_planning/bspline_path/bspline_path_main.rst.txt
similarity index 100%
rename from docs/modules/5_path_planning/bspline_path/bspline_path_main.rst
rename to _sources/modules/path_planning/bspline_path/bspline_path_main.rst.txt
diff --git a/docs/modules/5_path_planning/bugplanner/bugplanner_main.rst b/_sources/modules/path_planning/bugplanner/bugplanner_main.rst.txt
similarity index 59%
rename from docs/modules/5_path_planning/bugplanner/bugplanner_main.rst
rename to _sources/modules/path_planning/bugplanner/bugplanner_main.rst.txt
index 81c91c0313e..72cc46709f7 100644
--- a/docs/modules/5_path_planning/bugplanner/bugplanner_main.rst
+++ b/_sources/modules/path_planning/bugplanner/bugplanner_main.rst.txt
@@ -5,4 +5,4 @@ This is a 2D planning with Bug algorithm.
.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/BugPlanner/animation.gif
-- `ECE452 Bug Algorithms <https://web.archive.org/web/20201103052224/https://sites.google.com/site/ece452bugalgorithms/>`_
+- `ECE452 Bug Algorithms <https://sites.google.com/site/ece452bugalgorithms/>`_
diff --git a/docs/modules/5_path_planning/clothoid_path/clothoid_path_main.rst b/_sources/modules/path_planning/clothoid_path/clothoid_path_main.rst.txt
similarity index 100%
rename from docs/modules/5_path_planning/clothoid_path/clothoid_path_main.rst
rename to _sources/modules/path_planning/clothoid_path/clothoid_path_main.rst.txt
diff --git a/docs/modules/5_path_planning/coverage_path/coverage_path_main.rst b/_sources/modules/path_planning/coverage_path/coverage_path_main.rst.txt
similarity index 93%
rename from docs/modules/5_path_planning/coverage_path/coverage_path_main.rst
rename to _sources/modules/path_planning/coverage_path/coverage_path_main.rst.txt
index 0a688b5ed27..828342a294c 100644
--- a/docs/modules/5_path_planning/coverage_path/coverage_path_main.rst
+++ b/_sources/modules/path_planning/coverage_path/coverage_path_main.rst.txt
@@ -29,6 +29,6 @@ This is a 2D grid based wavefront coverage path planner simulation:
.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/WavefrontCPP/animation2.gif
.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/WavefrontCPP/animation3.gif
-- `Planning paths of complete coverage of an unstructured environment by a mobile robot <https://pinkwink.kr/attachment/cfile3.uf@1354654A4E8945BD13FE77.pdf>`_
+- `Planning paths of complete coverage of an unstructured environment by a mobile robot <http://pinkwink.kr/attachment/cfile3.uf@1354654A4E8945BD13FE77.pdf>`_
diff --git a/docs/modules/5_path_planning/cubic_spline/cubic_spline_main.rst b/_sources/modules/path_planning/cubic_spline/cubic_spline_main.rst.txt
similarity index 100%
rename from docs/modules/5_path_planning/cubic_spline/cubic_spline_main.rst
rename to _sources/modules/path_planning/cubic_spline/cubic_spline_main.rst.txt
diff --git a/docs/modules/5_path_planning/dubins_path/dubins_path_main.rst b/_sources/modules/path_planning/dubins_path/dubins_path_main.rst.txt
similarity index 97%
rename from docs/modules/5_path_planning/dubins_path/dubins_path_main.rst
rename to _sources/modules/path_planning/dubins_path/dubins_path_main.rst.txt
index 12172fb51e1..516638d83da 100644
--- a/docs/modules/5_path_planning/dubins_path/dubins_path_main.rst
+++ b/_sources/modules/path_planning/dubins_path/dubins_path_main.rst.txt
@@ -72,5 +72,5 @@ Reference
~~~~~~~~~~~~~~~~~~~~
- `On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents <https://www.jstor.org/stable/2372560?origin=crossref>`__
- `Dubins path - Wikipedia <https://en.wikipedia.org/wiki/Dubins_path>`__
-- `15.3.1 Dubins Curves <https://lavalle.pl/planning/node821.html>`__
+- `15.3.1 Dubins Curves <http://planning.cs.uiuc.edu/node821.html>`__
- `A Comprehensive, Step-by-Step Tutorial to Computing Dubin’s Paths <https://gieseanw.wordpress.com/2012/10/21/a-comprehensive-step-by-step-tutorial-to-computing-dubins-paths/>`__
diff --git a/docs/modules/5_path_planning/dynamic_window_approach/dynamic_window_approach_main.rst b/_sources/modules/path_planning/dynamic_window_approach/dynamic_window_approach_main.rst.txt
similarity index 100%
rename from docs/modules/5_path_planning/dynamic_window_approach/dynamic_window_approach_main.rst
rename to _sources/modules/path_planning/dynamic_window_approach/dynamic_window_approach_main.rst.txt
diff --git a/docs/modules/5_path_planning/eta3_spline/eta3_spline_main.rst b/_sources/modules/path_planning/eta3_spline/eta3_spline_main.rst.txt
similarity index 100%
rename from docs/modules/5_path_planning/eta3_spline/eta3_spline_main.rst
rename to _sources/modules/path_planning/eta3_spline/eta3_spline_main.rst.txt
diff --git a/_sources/modules/path_planning/frenet_frame_path/frenet_frame_path_main.rst.txt b/_sources/modules/path_planning/frenet_frame_path/frenet_frame_path_main.rst.txt
new file mode 100644
index 00000000000..e9d9041e0e4
--- /dev/null
+++ b/_sources/modules/path_planning/frenet_frame_path/frenet_frame_path_main.rst.txt
@@ -0,0 +1,20 @@
+Optimal Trajectory in a Frenet Frame
+------------------------------------
+
+.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/FrenetOptimalTrajectory/animation.gif
+
+This is optimal trajectory generation in a Frenet Frame.
+
+The cyan line is the target course and black crosses are obstacles.
+
+The red line is predicted path.
+
+Ref:
+
+- `Optimal Trajectory Generation for Dynamic Street Scenarios in a
+ Frenet
+ Frame <https://www.researchgate.net/profile/Moritz_Werling/publication/224156269_Optimal_Trajectory_Generation_for_Dynamic_Street_Scenarios_in_a_Frenet_Frame/links/54f749df0cf210398e9277af.pdf>`__
+
+- `Optimal trajectory generation for dynamic street scenarios in a
+ Frenet Frame <https://www.youtube.com/watch?v=Cj6tAQe7UCY>`__
+
diff --git a/docs/modules/5_path_planning/grid_base_search/grid_base_search_main.rst b/_sources/modules/path_planning/grid_base_search/grid_base_search_main.rst.txt
similarity index 100%
rename from docs/modules/5_path_planning/grid_base_search/grid_base_search_main.rst
rename to _sources/modules/path_planning/grid_base_search/grid_base_search_main.rst.txt
diff --git a/docs/modules/5_path_planning/hybridastar/hybridastar_main.rst b/_sources/modules/path_planning/hybridastar/hybridastar_main.rst.txt
similarity index 100%
rename from docs/modules/5_path_planning/hybridastar/hybridastar_main.rst
rename to _sources/modules/path_planning/hybridastar/hybridastar_main.rst.txt
diff --git a/docs/modules/5_path_planning/lqr_path/lqr_path_main.rst b/_sources/modules/path_planning/lqr_path/lqr_path_main.rst.txt
similarity index 100%
rename from docs/modules/5_path_planning/lqr_path/lqr_path_main.rst
rename to _sources/modules/path_planning/lqr_path/lqr_path_main.rst.txt
diff --git a/docs/modules/5_path_planning/model_predictive_trajectory_generator/model_predictive_trajectory_generator_main.rst b/_sources/modules/path_planning/model_predictive_trajectory_generator/model_predictive_trajectory_generator_main.rst.txt
similarity index 87%
rename from docs/modules/5_path_planning/model_predictive_trajectory_generator/model_predictive_trajectory_generator_main.rst
rename to _sources/modules/path_planning/model_predictive_trajectory_generator/model_predictive_trajectory_generator_main.rst.txt
index 463363ddcf1..0fc997898ed 100644
--- a/docs/modules/5_path_planning/model_predictive_trajectory_generator/model_predictive_trajectory_generator_main.rst
+++ b/_sources/modules/path_planning/model_predictive_trajectory_generator/model_predictive_trajectory_generator_main.rst.txt
@@ -19,4 +19,4 @@ Lookup table generation sample
Ref:
- `Optimal rough terrain trajectory generation for wheeled mobile
- robots <https://journals.sagepub.com/doi/pdf/10.1177/0278364906075328>`__
+ robots <http://journals.sagepub.com/doi/pdf/10.1177/0278364906075328>`__
diff --git a/docs/modules/5_path_planning/path_planning_main.rst b/_sources/modules/path_planning/path_planning_main.rst.txt
similarity index 57%
rename from docs/modules/5_path_planning/path_planning_main.rst
rename to _sources/modules/path_planning/path_planning_main.rst.txt
index 0c84a19c22f..a3237f16f19 100644
--- a/docs/modules/5_path_planning/path_planning_main.rst
+++ b/_sources/modules/path_planning/path_planning_main.rst.txt
@@ -1,10 +1,8 @@
-.. _`Path Planning`:
+.. _path_planning:
Path Planning
=============
-Path planning is the ability of a robot to search feasible and efficient path to the goal. The path has to satisfy some constraints based on the robot’s motion model and obstacle positions, and optimize some objective functions such as time to goal and distance to obstacle. In path planning, dynamic programming based approaches and sampling based approaches are widely used[22]. Fig.5 shows simulation results of potential field path planning and LQRRRT* path planning[27].
-
.. toctree::
:maxdepth: 2
:caption: Contents
@@ -12,7 +10,6 @@ Path planning is the ability of a robot to search feasible and efficient path to
dynamic_window_approach/dynamic_window_approach
bugplanner/bugplanner
grid_base_search/grid_base_search
- time_based_grid_search/time_based_grid_search
model_predictive_trajectory_generator/model_predictive_trajectory_generator
state_lattice_planner/state_lattice_planner
prm_planner/prm_planner
@@ -21,7 +18,6 @@ Path planning is the ability of a robot to search feasible and efficient path to
rrt/rrt
cubic_spline/cubic_spline
bspline_path/bspline_path
- catmull_rom_spline/catmull_rom_spline
clothoid_path/clothoid_path
eta3_spline/eta3_spline
bezier_path/bezier_path
@@ -32,4 +28,3 @@ Path planning is the ability of a robot to search feasible and efficient path to
hybridastar/hybridastar
frenet_frame_path/frenet_frame_path
coverage_path/coverage_path
- elastic_bands/elastic_bands
\ No newline at end of file
diff --git a/docs/modules/5_path_planning/prm_planner/prm_planner_main.rst b/_sources/modules/path_planning/prm_planner/prm_planner_main.rst.txt
similarity index 100%
rename from docs/modules/5_path_planning/prm_planner/prm_planner_main.rst
rename to _sources/modules/path_planning/prm_planner/prm_planner_main.rst.txt
diff --git a/docs/modules/5_path_planning/quintic_polynomials_planner/quintic_polynomials_planner_main.rst b/_sources/modules/path_planning/quintic_polynomials_planner/quintic_polynomials_planner_main.rst.txt
similarity index 98%
rename from docs/modules/5_path_planning/quintic_polynomials_planner/quintic_polynomials_planner_main.rst
rename to _sources/modules/path_planning/quintic_polynomials_planner/quintic_polynomials_planner_main.rst.txt
index 0412b3c9b3d..feec345bae8 100644
--- a/docs/modules/5_path_planning/quintic_polynomials_planner/quintic_polynomials_planner_main.rst
+++ b/_sources/modules/path_planning/quintic_polynomials_planner/quintic_polynomials_planner_main.rst.txt
@@ -101,6 +101,6 @@ References:
~~~~~~~~~~~
- `Local Path Planning And Motion Control For Agv In
- Positioning <https://ieeexplore.ieee.org/document/637936/>`__
+ Positioning <http://ieeexplore.ieee.org/document/637936/>`__
diff --git a/_sources/modules/path_planning/reeds_shepp_path/reeds_shepp_path_main.rst.txt b/_sources/modules/path_planning/reeds_shepp_path/reeds_shepp_path_main.rst.txt
new file mode 100644
index 00000000000..81e565888ec
--- /dev/null
+++ b/_sources/modules/path_planning/reeds_shepp_path/reeds_shepp_path_main.rst.txt
@@ -0,0 +1,17 @@
+Reeds Shepp planning
+--------------------
+
+A sample code with Reeds Shepp path planning.
+
+.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ReedsSheppPath/animation.gif?raw=true
+
+Ref:
+
+- `15.3.2 Reeds-Shepp
+ Curves <http://planning.cs.uiuc.edu/node822.html>`__
+
+- `optimal paths for a car that goes both forwards and
+ backwards <https://pdfs.semanticscholar.org/932e/c495b1d0018fd59dee12a0bf74434fac7af4.pdf>`__
+
+- `ghliu/pyReedsShepp: Implementation of Reeds Shepp
+ curve. <https://github.com/ghliu/pyReedsShepp>`__
diff --git a/docs/modules/5_path_planning/rrt/rrt_main.rst b/_sources/modules/path_planning/rrt/rrt_main.rst.txt
similarity index 93%
rename from docs/modules/5_path_planning/rrt/rrt_main.rst
rename to _sources/modules/path_planning/rrt/rrt_main.rst.txt
index e5f351a7baf..5a3a30dcff4 100644
--- a/docs/modules/5_path_planning/rrt/rrt_main.rst
+++ b/_sources/modules/path_planning/rrt/rrt_main.rst.txt
@@ -57,7 +57,7 @@ Ref:
- `Informed RRT\*: Optimal Sampling-based Path Planning Focused via
Direct Sampling of an Admissible Ellipsoidal
- Heuristic <https://arxiv.org/pdf/1404.2334>`__
+ Heuristic <https://arxiv.org/pdf/1404.2334.pdf>`__
.. _batch-informed-rrt*:
@@ -90,10 +90,10 @@ PID is used for speed control.
Ref:
- `Motion Planning in Complex Environments using Closed-loop
- Prediction <https://acl.mit.edu/papers/KuwataGNC08.pdf>`__
+ Prediction <http://acl.mit.edu/papers/KuwataGNC08.pdf>`__
- `Real-time Motion Planning with Applications to Autonomous Urban
- Driving <https://acl.mit.edu/papers/KuwataTCST09.pdf>`__
+ Driving <http://acl.mit.edu/papers/KuwataTCST09.pdf>`__
- `[1601.06326] Sampling-based Algorithms for Optimal Motion Planning
Using Closed-loop Prediction <https://arxiv.org/abs/1601.06326>`__
@@ -113,6 +113,6 @@ Ref:
- `LQR-RRT\*: Optimal Sampling-Based Motion Planning with Automatically
Derived Extension
- Heuristics <https://lis.csail.mit.edu/pubs/perez-icra12.pdf>`__
+ Heuristics <http://lis.csail.mit.edu/pubs/perez-icra12.pdf>`__
- `MahanFathi/LQR-RRTstar: LQR-RRT\* method is used for random motion planning of a simple pendulum in its phase plot <https://github.com/MahanFathi/LQR-RRTstar>`__
\ No newline at end of file
diff --git a/docs/modules/5_path_planning/state_lattice_planner/state_lattice_planner_main.rst b/_sources/modules/path_planning/state_lattice_planner/state_lattice_planner_main.rst.txt
similarity index 84%
rename from docs/modules/5_path_planning/state_lattice_planner/state_lattice_planner_main.rst
rename to _sources/modules/path_planning/state_lattice_planner/state_lattice_planner_main.rst.txt
index d5e7ed17d14..3ef0c7eca21 100644
--- a/docs/modules/5_path_planning/state_lattice_planner/state_lattice_planner_main.rst
+++ b/_sources/modules/path_planning/state_lattice_planner/state_lattice_planner_main.rst.txt
@@ -25,9 +25,9 @@ Lane sampling
Ref:
- `Optimal rough terrain trajectory generation for wheeled mobile
- robots <https://journals.sagepub.com/doi/pdf/10.1177/0278364906075328>`__
+ robots <http://journals.sagepub.com/doi/pdf/10.1177/0278364906075328>`__
- `State Space Sampling of Feasible Motions for High-Performance Mobile
Robot Navigation in Complex
- Environments <https://www.frc.ri.cmu.edu/~alonzo/pubs/papers/JFR_08_SS_Sampling.pdf>`__
+ Environments <http://www.frc.ri.cmu.edu/~alonzo/pubs/papers/JFR_08_SS_Sampling.pdf>`__
diff --git a/docs/modules/5_path_planning/visibility_road_map_planner/visibility_road_map_planner_main.rst b/_sources/modules/path_planning/visibility_road_map_planner/visibility_road_map_planner_main.rst.txt
similarity index 100%
rename from docs/modules/5_path_planning/visibility_road_map_planner/visibility_road_map_planner_main.rst
rename to _sources/modules/path_planning/visibility_road_map_planner/visibility_road_map_planner_main.rst.txt
diff --git a/docs/modules/5_path_planning/vrm_planner/vrm_planner_main.rst b/_sources/modules/path_planning/vrm_planner/vrm_planner_main.rst.txt
similarity index 100%
rename from docs/modules/5_path_planning/vrm_planner/vrm_planner_main.rst
rename to _sources/modules/path_planning/vrm_planner/vrm_planner_main.rst.txt
diff --git a/docs/modules/6_path_tracking/cgmres_nmpc/cgmres_nmpc_main.rst b/_sources/modules/path_tracking/cgmres_nmpc/cgmres_nmpc_main.rst.txt
similarity index 96%
rename from docs/modules/6_path_tracking/cgmres_nmpc/cgmres_nmpc_main.rst
rename to _sources/modules/path_tracking/cgmres_nmpc/cgmres_nmpc_main.rst.txt
index 23f1218a947..a1980ba17ea 100644
--- a/docs/modules/6_path_tracking/cgmres_nmpc/cgmres_nmpc_main.rst
+++ b/_sources/modules/path_tracking/cgmres_nmpc/cgmres_nmpc_main.rst.txt
@@ -60,7 +60,7 @@ Ref
- `Shunichi09/nonlinear_control: Implementing the nonlinear model
predictive control, sliding mode
- control <https://github.com/Shunichi09/PythonLinearNonlinearControl>`__
+ control <https://github.com/Shunichi09/nonlinear_control>`__
- `非線形モデル予測制御におけるCGMRES法をpythonで実装する -
Qiita <https://qiita.com/MENDY/items/4108190a579395053924>`__
diff --git a/_sources/modules/path_tracking/lqr_speed_and_steering_control/lqr_speed_and_steering_control_main.rst.txt b/_sources/modules/path_tracking/lqr_speed_and_steering_control/lqr_speed_and_steering_control_main.rst.txt
new file mode 100644
index 00000000000..68ea9c88b2a
--- /dev/null
+++ b/_sources/modules/path_tracking/lqr_speed_and_steering_control/lqr_speed_and_steering_control_main.rst.txt
@@ -0,0 +1,13 @@
+.. _linearquadratic-regulator-(lqr)-speed-and-steering-control:
+
+Linear–quadratic regulator (LQR) speed and steering control
+-----------------------------------------------------------
+
+Path tracking simulation with LQR speed and steering control.
+
+.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/lqr_speed_steer_control/animation.gif
+
+References:
+~~~~~~~~~~~
+
+- `Towards fully autonomous driving: Systems and algorithms <http://ieeexplore.ieee.org/document/5940562/>`__
diff --git a/_sources/modules/path_tracking/lqr_steering_control/lqr_steering_control_main.rst.txt b/_sources/modules/path_tracking/lqr_steering_control/lqr_steering_control_main.rst.txt
new file mode 100644
index 00000000000..bf6d6b5854c
--- /dev/null
+++ b/_sources/modules/path_tracking/lqr_steering_control/lqr_steering_control_main.rst.txt
@@ -0,0 +1,14 @@
+.. _linearquadratic-regulator-(lqr)-steering-control:
+
+Linear–quadratic regulator (LQR) steering control
+-------------------------------------------------
+
+Path tracking simulation with LQR steering control and PID speed
+control.
+
+.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/lqr_steer_control/animation.gif
+
+References:
+~~~~~~~~~~~
+- `ApolloAuto/apollo: An open autonomous driving platform <https://github.com/ApolloAuto/apollo>`_
+
diff --git a/docs/modules/6_path_tracking/model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control_main.rst b/_sources/modules/path_tracking/model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control_main.rst.txt
similarity index 98%
rename from docs/modules/6_path_tracking/model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control_main.rst
rename to _sources/modules/path_tracking/model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control_main.rst.txt
index de55b545ba3..59a71666746 100644
--- a/docs/modules/6_path_tracking/model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control_main.rst
+++ b/_sources/modules/path_tracking/model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control_main.rst.txt
@@ -133,5 +133,5 @@ Reference
- `Vehicle Dynamics and Control \| Rajesh Rajamani \|
Springer <http://www.springer.com/us/book/9781461414322>`__
-- `MPC Book - MPC Lab @
- UC-Berkeley <https://sites.google.com/berkeley.edu/mpc-lab/mpc-course-material>`__
+- `MPC Course Material - MPC Lab @
+ UC-Berkeley <http://www.mpc.berkeley.edu/mpc-course-material>`__
diff --git a/_sources/modules/path_tracking/path_tracking_main.rst.txt b/_sources/modules/path_tracking/path_tracking_main.rst.txt
new file mode 100644
index 00000000000..504ba087952
--- /dev/null
+++ b/_sources/modules/path_tracking/path_tracking_main.rst.txt
@@ -0,0 +1,16 @@
+.. _path_tracking:
+
+Path Tracking
+=============
+
+.. toctree::
+ :maxdepth: 2
+ :caption: Contents
+
+ pure_pursuit_tracking/pure_pursuit_tracking
+ stanley_control/stanley_control
+ rear_wheel_feedback_control/rear_wheel_feedback_control
+ lqr_steering_control/lqr_steering_control
+ lqr_speed_and_steering_control/lqr_speed_and_steering_control
+ model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control
+ cgmres_nmpc/cgmres_nmpc
diff --git a/docs/modules/6_path_tracking/pure_pursuit_tracking/pure_pursuit_tracking_main.rst b/_sources/modules/path_tracking/pure_pursuit_tracking/pure_pursuit_tracking_main.rst.txt
similarity index 100%
rename from docs/modules/6_path_tracking/pure_pursuit_tracking/pure_pursuit_tracking_main.rst
rename to _sources/modules/path_tracking/pure_pursuit_tracking/pure_pursuit_tracking_main.rst.txt
diff --git a/docs/modules/6_path_tracking/rear_wheel_feedback_control/rear_wheel_feedback_control_main.rst b/_sources/modules/path_tracking/rear_wheel_feedback_control/rear_wheel_feedback_control_main.rst.txt
similarity index 100%
rename from docs/modules/6_path_tracking/rear_wheel_feedback_control/rear_wheel_feedback_control_main.rst
rename to _sources/modules/path_tracking/rear_wheel_feedback_control/rear_wheel_feedback_control_main.rst.txt
diff --git a/docs/modules/6_path_tracking/stanley_control/stanley_control_main.rst b/_sources/modules/path_tracking/stanley_control/stanley_control_main.rst.txt
similarity index 100%
rename from docs/modules/6_path_tracking/stanley_control/stanley_control_main.rst
rename to _sources/modules/path_tracking/stanley_control/stanley_control_main.rst.txt
diff --git a/docs/modules/4_slam/FastSLAM1/FastSLAM1_main.rst b/_sources/modules/slam/FastSLAM1/FastSLAM1_main.rst.txt
similarity index 100%
rename from docs/modules/4_slam/FastSLAM1/FastSLAM1_main.rst
rename to _sources/modules/slam/FastSLAM1/FastSLAM1_main.rst.txt
diff --git a/docs/modules/4_slam/FastSLAM2/FastSLAM2_main.rst b/_sources/modules/slam/FastSLAM2/FastSLAM2_main.rst.txt
similarity index 100%
rename from docs/modules/4_slam/FastSLAM2/FastSLAM2_main.rst
rename to _sources/modules/slam/FastSLAM2/FastSLAM2_main.rst.txt
diff --git a/docs/modules/4_slam/ekf_slam/ekf_slam_main.rst b/_sources/modules/slam/ekf_slam/ekf_slam_main.rst.txt
similarity index 95%
rename from docs/modules/4_slam/ekf_slam/ekf_slam_main.rst
rename to _sources/modules/slam/ekf_slam/ekf_slam_main.rst.txt
index b27971225ec..70a7d131aee 100644
--- a/docs/modules/4_slam/ekf_slam/ekf_slam_main.rst
+++ b/_sources/modules/slam/ekf_slam/ekf_slam_main.rst.txt
@@ -63,27 +63,27 @@ Take care to note the difference between :math:`X` (state) and :math:`x`
original author: Atsushi Sakai (@Atsushi_twi)
notebook author: Andrew Tu (drewtu2)
"""
-
+
import math
import numpy as np
%matplotlib notebook
import matplotlib.pyplot as plt
-
-
+
+
# EKF state covariance
Cx = np.diag([0.5, 0.5, np.deg2rad(30.0)])**2 # Change in covariance
-
+
# Simulation parameter
Qsim = np.diag([0.2, np.deg2rad(1.0)])**2 # Sensor Noise
Rsim = np.diag([1.0, np.deg2rad(10.0)])**2 # Process Noise
-
+
DT = 0.1 # time tick [s]
SIM_TIME = 50.0 # simulation time [s]
MAX_RANGE = 20.0 # maximum observation range
M_DIST_TH = 2.0 # Threshold of Mahalanobis distance for data association.
STATE_SIZE = 3 # State size [x,y,yaw]
LM_SIZE = 2 # LM state size [x,y]
-
+
show_animation = True
Algorithm Walk through
@@ -97,22 +97,23 @@ the estimated state and measurements
def ekf_slam(xEst, PEst, u, z):
"""
- Performs an iteration of EKF SLAM from the available information.
-
+ Performs an iteration of EKF SLAM from the available information.
+
:param xEst: the belief in last position
:param PEst: the uncertainty in last position
- :param u: the control function applied to the last position
+ :param u: the control function applied to the last position
:param z: measurements at this step
:returns: the next estimated position and associated covariance
"""
-
+ S = STATE_SIZE
+
# Predict
- xEst, PEst = predict(xEst, PEst, u)
+ xEst, PEst, G, Fx = predict(xEst, PEst, u)
initP = np.eye(2)
-
+
# Update
- xEst, PEst = update(xEst, PEst, z, initP)
-
+ xEst, PEst = update(xEst, PEst, u, z, initP)
+
return xEst, PEst
@@ -169,25 +170,26 @@ the landmarks.
def predict(xEst, PEst, u):
"""
Performs the prediction step of EKF SLAM
-
+
:param xEst: nx1 state vector
:param PEst: nxn covariance matrix
:param u: 2x1 control vector
:returns: predicted state vector, predicted covariance, jacobian of control vector, transition fx
"""
- G, Fx = jacob_motion(xEst, u)
- xEst[0:STATE_SIZE] = motion_model(xEst[0:STATE_SIZE], u)
+ S = STATE_SIZE
+ G, Fx = jacob_motion(xEst[0:S], u)
+ xEst[0:S] = motion_model(xEst[0:S], u)
# Fx is an an identity matrix of size (STATE_SIZE)
# sigma = G*sigma*G.T + Noise
- PEst = G.T @ PEst @ G + Fx.T @ Cx @ Fx
- return xEst, PEst
+ PEst[0:S, 0:S] = G.T @ PEst[0:S, 0:S] @ G + Fx.T @ Cx @ Fx
+ return xEst, PEst, G, Fx
.. code:: ipython3
def motion_model(x, u):
"""
Computes the motion model based on current state and input function.
-
+
:param x: 3x1 pose estimation
:param u: 2x1 control input [v; w]
:returns: the resulting state after the control function is applied
@@ -195,11 +197,11 @@ the landmarks.
F = np.array([[1.0, 0, 0],
[0, 1.0, 0],
[0, 0, 1.0]])
-
+
B = np.array([[DT * math.cos(x[2, 0]), 0],
[DT * math.sin(x[2, 0]), 0],
[0.0, DT]])
-
+
x = (F @ x) + (B @ u)
return x
@@ -259,21 +261,22 @@ the changing uncertainty.
.. code:: ipython3
- def update(xEst, PEst, z, initP):
+ def update(xEst, PEst, u, z, initP):
"""
Performs the update step of EKF SLAM
-
+
:param xEst: nx1 the predicted pose of the system and the pose of the landmarks
:param PEst: nxn the predicted covariance
+ :param u: 2x1 the control function
:param z: the measurements read at new position
:param initP: 2x2 an identity matrix acting as the initial covariance
:returns: the updated state and covariance for the system
"""
for iz in range(len(z[:, 0])): # for each observation
minid = search_correspond_LM_ID(xEst, PEst, z[iz, 0:2]) # associate to a known landmark
-
+
nLM = calc_n_LM(xEst) # number of landmarks we currently know about
-
+
if minid == nLM: # Landmark is a NEW landmark
print("New LM")
# Extend state and covariance matrix
@@ -282,14 +285,14 @@ the changing uncertainty.
np.hstack((np.zeros((LM_SIZE, len(xEst))), initP))))
xEst = xAug
PEst = PAug
-
+
lm = get_LM_Pos_from_state(xEst, minid)
y, S, H = calc_innovation(lm, xEst, PEst, z[iz, 0:2], minid)
-
+
K = (PEst @ H.T) @ np.linalg.inv(S) # Calculate Kalman Gain
xEst = xEst + (K @ y)
PEst = (np.eye(len(xEst)) - (K @ H)) @ PEst
-
+
xEst[2] = pi_2_pi(xEst[2])
return xEst, PEst
@@ -299,7 +302,7 @@ the changing uncertainty.
def calc_innovation(lm, xEst, PEst, z, LMid):
"""
Calculates the innovation based on expected position and landmark position
-
+
:param lm: landmark position
:param xEst: estimated position/state
:param PEst: estimated covariance
@@ -312,19 +315,19 @@ the changing uncertainty.
zangle = math.atan2(delta[1, 0], delta[0, 0]) - xEst[2, 0]
zp = np.array([[math.sqrt(q), pi_2_pi(zangle)]])
# zp is the expected measurement based on xEst and the expected landmark position
-
+
y = (z - zp).T # y = innovation
y[1] = pi_2_pi(y[1])
-
+
H = jacobH(q, delta, xEst, LMid + 1)
S = H @ PEst @ H.T + Cx[0:2, 0:2]
-
+
return y, S, H
-
+
def jacobH(q, delta, x, i):
"""
Calculates the jacobian of the measurement function
-
+
:param q: the range from the system pose to the landmark
:param delta: the difference between a landmark position and the estimated system position
:param x: the state, including the estimated system position
@@ -334,17 +337,17 @@ the changing uncertainty.
sq = math.sqrt(q)
G = np.array([[-sq * delta[0, 0], - sq * delta[1, 0], 0, sq * delta[0, 0], sq * delta[1, 0]],
[delta[1, 0], - delta[0, 0], - q, - delta[1, 0], delta[0, 0]]])
-
+
G = G / q
nLM = calc_n_LM(x)
F1 = np.hstack((np.eye(3), np.zeros((3, 2 * nLM))))
F2 = np.hstack((np.zeros((2, 3)), np.zeros((2, 2 * (i - 1))),
np.eye(2), np.zeros((2, 2 * nLM - 2 * i))))
-
+
F = np.vstack((F1, F2))
-
+
H = G @ F
-
+
return H
Observation Step
@@ -367,17 +370,17 @@ reckoning and control functions are passed along here as well.
:param xd: the current noisy estimate of the system
:param u: the current control input
:param RFID: the true position of the landmarks
-
- :returns: Computes the true position, observations, dead reckoning (noisy) position,
+
+ :returns: Computes the true position, observations, dead reckoning (noisy) position,
and noisy control function
"""
xTrue = motion_model(xTrue, u)
-
+
# add noise to gps x-y
z = np.zeros((0, 3))
-
+
for i in range(len(RFID[:, 0])): # Test all beacons, only add the ones we can see (within MAX_RANGE)
-
+
dx = RFID[i, 0] - xTrue[0, 0]
dy = RFID[i, 1] - xTrue[1, 0]
d = math.sqrt(dx**2 + dy**2)
@@ -387,12 +390,12 @@ reckoning and control functions are passed along here as well.
anglen = angle + np.random.randn() * Qsim[1, 1] # add noise
zi = np.array([dn, anglen, i])
z = np.vstack((z, zi))
-
+
# add noise to input
ud = np.array([[
u[0, 0] + np.random.randn() * Rsim[0, 0],
u[1, 0] + np.random.randn() * Rsim[1, 1]]]).T
-
+
xd = motion_model(xd, ud)
return xTrue, z, xd, ud
@@ -406,30 +409,32 @@ reckoning and control functions are passed along here as well.
"""
n = int((len(x) - STATE_SIZE) / LM_SIZE)
return n
-
-
+
+
def jacob_motion(x, u):
"""
- Calculates the jacobian of motion model.
-
+ Calculates the jacobian of motion model.
+
:param x: The state, including the estimated position of the system
:param u: The control function
:returns: G: Jacobian
Fx: STATE_SIZE x (STATE_SIZE + 2 * num_landmarks) matrix where the left side is an identity matrix
"""
-
+
# [eye(3) [0 x y; 0 x y; 0 x y]]
Fx = np.hstack((np.eye(STATE_SIZE), np.zeros(
(STATE_SIZE, LM_SIZE * calc_n_LM(x)))))
-
+
jF = np.array([[0.0, 0.0, -DT * u[0] * math.sin(x[2, 0])],
[0.0, 0.0, DT * u[0] * math.cos(x[2, 0])],
[0.0, 0.0, 0.0]],dtype=object)
-
+
G = np.eye(STATE_SIZE) + Fx.T @ jF @ Fx
if calc_n_LM(x) > 0:
print(Fx.shape)
return G, Fx,
+
+
.. code:: ipython3
@@ -437,68 +442,68 @@ reckoning and control functions are passed along here as well.
def calc_LM_Pos(x, z):
"""
Calculates the pose in the world coordinate frame of a landmark at the given measurement.
-
+
:param x: [x; y; theta]
:param z: [range; bearing]
:returns: [x; y] for given measurement
"""
zp = np.zeros((2, 1))
-
+
zp[0, 0] = x[0, 0] + z[0] * math.cos(x[2, 0] + z[1])
zp[1, 0] = x[1, 0] + z[0] * math.sin(x[2, 0] + z[1])
#zp[0, 0] = x[0, 0] + z[0, 0] * math.cos(x[2, 0] + z[0, 1])
#zp[1, 0] = x[1, 0] + z[0, 0] * math.sin(x[2, 0] + z[0, 1])
-
+
return zp
-
-
+
+
def get_LM_Pos_from_state(x, ind):
"""
Returns the position of a given landmark
-
+
:param x: The state containing all landmark positions
:param ind: landmark id
:returns: The position of the landmark
"""
lm = x[STATE_SIZE + LM_SIZE * ind: STATE_SIZE + LM_SIZE * (ind + 1), :]
-
+
return lm
-
-
+
+
def search_correspond_LM_ID(xAug, PAug, zi):
"""
Landmark association with Mahalanobis distance.
-
- If this landmark is at least M_DIST_TH units away from all known landmarks,
+
+ If this landmark is at least M_DIST_TH units away from all known landmarks,
it is a NEW landmark.
-
+
:param xAug: The estimated state
:param PAug: The estimated covariance
:param zi: the read measurements of specific landmark
:returns: landmark id
"""
-
+
nLM = calc_n_LM(xAug)
-
+
mdist = []
-
+
for i in range(nLM):
lm = get_LM_Pos_from_state(xAug, i)
y, S, H = calc_innovation(lm, xAug, PAug, zi, i)
mdist.append(y.T @ np.linalg.inv(S) @ y)
-
+
mdist.append(M_DIST_TH) # new landmark
-
+
minid = mdist.index(min(mdist))
-
+
return minid
-
+
def calc_input():
v = 1.0 # [m/s]
yawrate = 0.1 # [rad/s]
u = np.array([[v, yawrate]]).T
return u
-
+
def pi_2_pi(angle):
return (angle + math.pi) % (2 * math.pi) - math.pi
@@ -506,53 +511,53 @@ reckoning and control functions are passed along here as well.
def main():
print(" start!!")
-
+
time = 0.0
-
+
# RFID positions [x, y]
RFID = np.array([[10.0, -2.0],
[15.0, 10.0],
[3.0, 15.0],
[-5.0, 20.0]])
-
+
# State Vector [x y yaw v]'
xEst = np.zeros((STATE_SIZE, 1))
xTrue = np.zeros((STATE_SIZE, 1))
PEst = np.eye(STATE_SIZE)
-
+
xDR = np.zeros((STATE_SIZE, 1)) # Dead reckoning
-
+
# history
hxEst = xEst
hxTrue = xTrue
hxDR = xTrue
-
+
while SIM_TIME >= time:
time += DT
u = calc_input()
-
+
xTrue, z, xDR, ud = observation(xTrue, xDR, u, RFID)
-
+
xEst, PEst = ekf_slam(xEst, PEst, ud, z)
-
+
x_state = xEst[0:STATE_SIZE]
-
+
# store data history
hxEst = np.hstack((hxEst, x_state))
hxDR = np.hstack((hxDR, xDR))
hxTrue = np.hstack((hxTrue, xTrue))
-
+
if show_animation: # pragma: no cover
plt.cla()
-
+
plt.plot(RFID[:, 0], RFID[:, 1], "*k")
plt.plot(xEst[0], xEst[1], ".r")
-
+
# plot landmark
for i in range(calc_n_LM(xEst)):
plt.plot(xEst[STATE_SIZE + i * 2],
xEst[STATE_SIZE + i * 2 + 1], "xg")
-
+
plt.plot(hxTrue[0, :],
hxTrue[1, :], "-b")
plt.plot(hxDR[0, :],
@@ -582,3 +587,5 @@ References:
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
- `PROBABILISTIC ROBOTICS <http://www.probabilistic-robotics.org/>`_
+
+
diff --git a/docs/modules/4_slam/graph_slam/graph_slam_main.rst b/_sources/modules/slam/graph_slam/graph_slam_main.rst.txt
similarity index 100%
rename from docs/modules/4_slam/graph_slam/graph_slam_main.rst
rename to _sources/modules/slam/graph_slam/graph_slam_main.rst.txt
diff --git a/docs/modules/4_slam/iterative_closest_point_matching/iterative_closest_point_matching_main.rst b/_sources/modules/slam/iterative_closest_point_matching/iterative_closest_point_matching_main.rst.txt
similarity index 100%
rename from docs/modules/4_slam/iterative_closest_point_matching/iterative_closest_point_matching_main.rst
rename to _sources/modules/slam/iterative_closest_point_matching/iterative_closest_point_matching_main.rst.txt
diff --git a/_sources/modules/slam/slam_main.rst.txt b/_sources/modules/slam/slam_main.rst.txt
new file mode 100644
index 00000000000..86befa6e357
--- /dev/null
+++ b/_sources/modules/slam/slam_main.rst.txt
@@ -0,0 +1,16 @@
+.. _slam:
+
+SLAM
+====
+
+Simultaneous Localization and Mapping(SLAM) examples
+
+.. toctree::
+ :maxdepth: 2
+ :caption: Contents
+
+ iterative_closest_point_matching/iterative_closest_point_matching
+ ekf_slam/ekf_slam
+ FastSLAM1/FastSLAM1
+ FastSLAM2/FastSLAM2
+ graph_slam/graph_slam
diff --git a/docs/modules/11_utils/plot/plot_main.rst b/_sources/modules/utils/plot/plot_main.rst.txt
similarity index 100%
rename from docs/modules/11_utils/plot/plot_main.rst
rename to _sources/modules/utils/plot/plot_main.rst.txt
diff --git a/docs/modules/11_utils/utils_main.rst b/_sources/modules/utils/utils_main.rst.txt
similarity index 90%
rename from docs/modules/11_utils/utils_main.rst
rename to _sources/modules/utils/utils_main.rst.txt
index 95c982b077f..ff79a262053 100644
--- a/docs/modules/11_utils/utils_main.rst
+++ b/_sources/modules/utils/utils_main.rst.txt
@@ -1,4 +1,4 @@
-.. _`utils`:
+.. _utils:
Utilities
==========
diff --git a/_static/basic.css b/_static/basic.css
new file mode 100644
index 00000000000..603f6a8798e
--- /dev/null
+++ b/_static/basic.css
@@ -0,0 +1,905 @@
+/*
+ * basic.css
+ * ~~~~~~~~~
+ *
+ * Sphinx stylesheet -- basic theme.
+ *
+ * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+/* -- main layout ----------------------------------------------------------- */
+
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+ clear: both;
+}
+
+div.section::after {
+ display: block;
+ content: '';
+ clear: left;
+}
+
+/* -- relbar ---------------------------------------------------------------- */
+
+div.related {
+ width: 100%;
+ font-size: 90%;
+}
+
+div.related h3 {
+ display: none;
+}
+
+div.related ul {
+ margin: 0;
+ padding: 0 0 0 10px;
+ list-style: none;
+}
+
+div.related li {
+ display: inline;
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+ float: right;
+ margin-right: 5px;
+}
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+ padding: 10px 5px 0 10px;
+}
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+ width: 230px;
+ margin-left: -100%;
+ font-size: 90%;
+ word-wrap: break-word;
+ overflow-wrap : break-word;
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+div.sphinxsidebar ul.want-points {
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+ margin-top: 10px;
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+ font-size: 1em;
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+ width: 80%;
+ padding: 0.25em;
+ box-sizing: border-box;
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+ float: left;
+ width: 20%;
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+ box-sizing: border-box;
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+ border: 0;
+ max-width: 100%;
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+ margin: 10px 0 0 20px;
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+ padding: 5px 0 5px 20px;
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+ background-position: 0 7px;
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+ font-weight: bold;
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+ color: #888;
+ margin: 2px 0 0 30px;
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+ height: 10px;
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+ margin-top: 10px;
+ background-color: #f2f2f2;
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+
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+ margin-right: 3px;
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+}
+
+div.modindex-jumpbox {
+ border-top: 1px solid #ddd;
+ border-bottom: 1px solid #ddd;
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+ font-weight: bold;
+}
+
+h1 code, h2 code, h3 code, h4 code, h5 code, h6 code {
+ background-color: transparent;
+}
+
+.viewcode-link {
+ float: right;
+}
+
+.viewcode-back {
+ float: right;
+ font-family: sans-serif;
+}
+
+div.viewcode-block:target {
+ margin: -1px -10px;
+ padding: 0 10px;
+}
+
+/* -- math display ---------------------------------------------------------- */
+
+img.math {
+ vertical-align: middle;
+}
+
+div.body div.math p {
+ text-align: center;
+}
+
+span.eqno {
+ float: right;
+}
+
+span.eqno a.headerlink {
+ position: absolute;
+ z-index: 1;
+}
+
+div.math:hover a.headerlink {
+ visibility: visible;
+}
+
+/* -- printout stylesheet --------------------------------------------------- */
+
+@media print {
+ div.document,
+ div.documentwrapper,
+ div.bodywrapper {
+ margin: 0 !important;
+ width: 100%;
+ }
+
+ div.sphinxsidebar,
+ div.related,
+ div.footer,
+ #top-link {
+ display: none;
+ }
+}
\ No newline at end of file
diff --git a/_static/check-solid.svg b/_static/check-solid.svg
new file mode 100644
index 00000000000..92fad4b5c0b
--- /dev/null
+++ b/_static/check-solid.svg
@@ -0,0 +1,4 @@
+<svg xmlns="http://www.w3.org/2000/svg" class="icon icon-tabler icon-tabler-check" width="44" height="44" viewBox="0 0 24 24" stroke-width="2" stroke="#22863a" fill="none" stroke-linecap="round" stroke-linejoin="round">
+ <path stroke="none" d="M0 0h24v24H0z" fill="none"/>
+ <path d="M5 12l5 5l10 -10" />
+</svg>
diff --git a/_static/clipboard.min.js b/_static/clipboard.min.js
new file mode 100644
index 00000000000..54b3c463811
--- /dev/null
+++ b/_static/clipboard.min.js
@@ -0,0 +1,7 @@
+/*!
+ * clipboard.js v2.0.8
+ * https://clipboardjs.com/
+ *
+ * Licensed MIT © Zeno Rocha
+ */
+!function(t,e){"object"==typeof exports&&"object"==typeof module?module.exports=e():"function"==typeof define&&define.amd?define([],e):"object"==typeof exports?exports.ClipboardJS=e():t.ClipboardJS=e()}(this,function(){return n={686:function(t,e,n){"use strict";n.d(e,{default:function(){return o}});var e=n(279),i=n.n(e),e=n(370),u=n.n(e),e=n(817),c=n.n(e);function a(t){try{return document.execCommand(t)}catch(t){return}}var f=function(t){t=c()(t);return a("cut"),t};var l=function(t){var e,n,o,r=1<arguments.length&&void 0!==arguments[1]?arguments[1]:{container:document.body},i="";return"string"==typeof t?(e=t,n="rtl"===document.documentElement.getAttribute("dir"),(o=document.createElement("textarea")).style.fontSize="12pt",o.style.border="0",o.style.padding="0",o.style.margin="0",o.style.position="absolute",o.style[n?"right":"left"]="-9999px",n=window.pageYOffset||document.documentElement.scrollTop,o.style.top="".concat(n,"px"),o.setAttribute("readonly",""),o.value=e,o=o,r.container.appendChild(o),i=c()(o),a("copy"),o.remove()):(i=c()(t),a("copy")),i};function r(t){return(r="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(t){return typeof t}:function(t){return t&&"function"==typeof Symbol&&t.constructor===Symbol&&t!==Symbol.prototype?"symbol":typeof t})(t)}var s=function(){var t=0<arguments.length&&void 0!==arguments[0]?arguments[0]:{},e=t.action,n=void 0===e?"copy":e,o=t.container,e=t.target,t=t.text;if("copy"!==n&&"cut"!==n)throw new Error('Invalid "action" value, use either "copy" or "cut"');if(void 0!==e){if(!e||"object"!==r(e)||1!==e.nodeType)throw new Error('Invalid "target" value, use a valid Element');if("copy"===n&&e.hasAttribute("disabled"))throw new Error('Invalid "target" attribute. Please use "readonly" instead of "disabled" attribute');if("cut"===n&&(e.hasAttribute("readonly")||e.hasAttribute("disabled")))throw new Error('Invalid "target" attribute. You can\'t cut text from elements with "readonly" or "disabled" attributes')}return t?l(t,{container:o}):e?"cut"===n?f(e):l(e,{container:o}):void 0};function d(t){return(d="function"==typeof Symbol&&"symbol"==typeof Symbol.iterator?function(t){return typeof t}:function(t){return t&&"function"==typeof Symbol&&t.constructor===Symbol&&t!==Symbol.prototype?"symbol":typeof t})(t)}function p(t,e){for(var n=0;n<e.length;n++){var o=e[n];o.enumerable=o.enumerable||!1,o.configurable=!0,"value"in o&&(o.writable=!0),Object.defineProperty(t,o.key,o)}}function y(t,e){return(y=Object.setPrototypeOf||function(t,e){return t.__proto__=e,t})(t,e)}function h(n){var o=function(){if("undefined"==typeof Reflect||!Reflect.construct)return!1;if(Reflect.construct.sham)return!1;if("function"==typeof Proxy)return!0;try{return Date.prototype.toString.call(Reflect.construct(Date,[],function(){})),!0}catch(t){return!1}}();return function(){var t,e=m(n);return t=o?(t=m(this).constructor,Reflect.construct(e,arguments,t)):e.apply(this,arguments),e=this,!(t=t)||"object"!==d(t)&&"function"!=typeof t?function(t){if(void 0!==t)return t;throw new ReferenceError("this hasn't been initialised - super() hasn't been called")}(e):t}}function m(t){return(m=Object.setPrototypeOf?Object.getPrototypeOf:function(t){return t.__proto__||Object.getPrototypeOf(t)})(t)}function v(t,e){t="data-clipboard-".concat(t);if(e.hasAttribute(t))return e.getAttribute(t)}var o=function(){!function(t,e){if("function"!=typeof e&&null!==e)throw new TypeError("Super expression must either be null or a function");t.prototype=Object.create(e&&e.prototype,{constructor:{value:t,writable:!0,configurable:!0}}),e&&y(t,e)}(r,i());var t,e,n,o=h(r);function r(t,e){var n;return function(t){if(!(t instanceof r))throw new TypeError("Cannot call a class as a function")}(this),(n=o.call(this)).resolveOptions(e),n.listenClick(t),n}return t=r,n=[{key:"copy",value:function(t){var e=1<arguments.length&&void 0!==arguments[1]?arguments[1]:{container:document.body};return l(t,e)}},{key:"cut",value:function(t){return f(t)}},{key:"isSupported",value:function(){var t=0<arguments.length&&void 0!==arguments[0]?arguments[0]:["copy","cut"],t="string"==typeof t?[t]:t,e=!!document.queryCommandSupported;return t.forEach(function(t){e=e&&!!document.queryCommandSupported(t)}),e}}],(e=[{key:"resolveOptions",value:function(){var t=0<arguments.length&&void 0!==arguments[0]?arguments[0]:{};this.action="function"==typeof t.action?t.action:this.defaultAction,this.target="function"==typeof t.target?t.target:this.defaultTarget,this.text="function"==typeof t.text?t.text:this.defaultText,this.container="object"===d(t.container)?t.container:document.body}},{key:"listenClick",value:function(t){var e=this;this.listener=u()(t,"click",function(t){return e.onClick(t)})}},{key:"onClick",value:function(t){var e=t.delegateTarget||t.currentTarget,t=s({action:this.action(e),container:this.container,target:this.target(e),text:this.text(e)});this.emit(t?"success":"error",{action:this.action,text:t,trigger:e,clearSelection:function(){e&&e.focus(),document.activeElement.blur(),window.getSelection().removeAllRanges()}})}},{key:"defaultAction",value:function(t){return v("action",t)}},{key:"defaultTarget",value:function(t){t=v("target",t);if(t)return document.querySelector(t)}},{key:"defaultText",value:function(t){return v("text",t)}},{key:"destroy",value:function(){this.listener.destroy()}}])&&p(t.prototype,e),n&&p(t,n),r}()},828:function(t){var e;"undefined"==typeof Element||Element.prototype.matches||((e=Element.prototype).matches=e.matchesSelector||e.mozMatchesSelector||e.msMatchesSelector||e.oMatchesSelector||e.webkitMatchesSelector),t.exports=function(t,e){for(;t&&9!==t.nodeType;){if("function"==typeof t.matches&&t.matches(e))return t;t=t.parentNode}}},438:function(t,e,n){var u=n(828);function i(t,e,n,o,r){var i=function(e,n,t,o){return function(t){t.delegateTarget=u(t.target,n),t.delegateTarget&&o.call(e,t)}}.apply(this,arguments);return t.addEventListener(n,i,r),{destroy:function(){t.removeEventListener(n,i,r)}}}t.exports=function(t,e,n,o,r){return"function"==typeof t.addEventListener?i.apply(null,arguments):"function"==typeof n?i.bind(null,document).apply(null,arguments):("string"==typeof t&&(t=document.querySelectorAll(t)),Array.prototype.map.call(t,function(t){return i(t,e,n,o,r)}))}},879:function(t,n){n.node=function(t){return void 0!==t&&t instanceof HTMLElement&&1===t.nodeType},n.nodeList=function(t){var e=Object.prototype.toString.call(t);return void 0!==t&&("[object NodeList]"===e||"[object HTMLCollection]"===e)&&"length"in t&&(0===t.length||n.node(t[0]))},n.string=function(t){return"string"==typeof t||t instanceof String},n.fn=function(t){return"[object Function]"===Object.prototype.toString.call(t)}},370:function(t,e,n){var f=n(879),l=n(438);t.exports=function(t,e,n){if(!t&&!e&&!n)throw new Error("Missing required arguments");if(!f.string(e))throw new TypeError("Second argument must be a String");if(!f.fn(n))throw new TypeError("Third argument must be a Function");if(f.node(t))return c=e,a=n,(u=t).addEventListener(c,a),{destroy:function(){u.removeEventListener(c,a)}};if(f.nodeList(t))return o=t,r=e,i=n,Array.prototype.forEach.call(o,function(t){t.addEventListener(r,i)}),{destroy:function(){Array.prototype.forEach.call(o,function(t){t.removeEventListener(r,i)})}};if(f.string(t))return t=t,e=e,n=n,l(document.body,t,e,n);throw new TypeError("First argument must be a String, HTMLElement, HTMLCollection, or NodeList");var o,r,i,u,c,a}},817:function(t){t.exports=function(t){var e,n="SELECT"===t.nodeName?(t.focus(),t.value):"INPUT"===t.nodeName||"TEXTAREA"===t.nodeName?((e=t.hasAttribute("readonly"))||t.setAttribute("readonly",""),t.select(),t.setSelectionRange(0,t.value.length),e||t.removeAttribute("readonly"),t.value):(t.hasAttribute("contenteditable")&&t.focus(),n=window.getSelection(),(e=document.createRange()).selectNodeContents(t),n.removeAllRanges(),n.addRange(e),n.toString());return n}},279:function(t){function e(){}e.prototype={on:function(t,e,n){var o=this.e||(this.e={});return(o[t]||(o[t]=[])).push({fn:e,ctx:n}),this},once:function(t,e,n){var o=this;function r(){o.off(t,r),e.apply(n,arguments)}return r._=e,this.on(t,r,n)},emit:function(t){for(var e=[].slice.call(arguments,1),n=((this.e||(this.e={}))[t]||[]).slice(),o=0,r=n.length;o<r;o++)n[o].fn.apply(n[o].ctx,e);return this},off:function(t,e){var n=this.e||(this.e={}),o=n[t],r=[];if(o&&e)for(var i=0,u=o.length;i<u;i++)o[i].fn!==e&&o[i].fn._!==e&&r.push(o[i]);return r.length?n[t]=r:delete n[t],this}},t.exports=e,t.exports.TinyEmitter=e}},r={},o.n=function(t){var e=t&&t.__esModule?function(){return t.default}:function(){return t};return o.d(e,{a:e}),e},o.d=function(t,e){for(var n in e)o.o(e,n)&&!o.o(t,n)&&Object.defineProperty(t,n,{enumerable:!0,get:e[n]})},o.o=function(t,e){return Object.prototype.hasOwnProperty.call(t,e)},o(686).default;function o(t){if(r[t])return r[t].exports;var e=r[t]={exports:{}};return n[t](e,e.exports,o),e.exports}var n,r});
\ No newline at end of file
diff --git a/_static/copy-button.svg b/_static/copy-button.svg
new file mode 100644
index 00000000000..9c074dae528
--- /dev/null
+++ b/_static/copy-button.svg
@@ -0,0 +1,5 @@
+<svg xmlns="http://www.w3.org/2000/svg" class="icon icon-tabler icon-tabler-copy" width="44" height="44" viewBox="0 0 24 24" stroke-width="1.5" stroke="#000000" fill="none" stroke-linecap="round" stroke-linejoin="round">
+ <path stroke="none" d="M0 0h24v24H0z" fill="none"/>
+ <rect x="8" y="8" width="12" height="12" rx="2" />
+ <path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2" />
+</svg>
diff --git a/_static/copybutton.css b/_static/copybutton.css
new file mode 100644
index 00000000000..f1916ec7d1b
--- /dev/null
+++ b/_static/copybutton.css
@@ -0,0 +1,94 @@
+/* Copy buttons */
+button.copybtn {
+ position: absolute;
+ display: flex;
+ top: .3em;
+ right: .3em;
+ width: 1.7em;
+ height: 1.7em;
+ opacity: 0;
+ transition: opacity 0.3s, border .3s, background-color .3s;
+ user-select: none;
+ padding: 0;
+ border: none;
+ outline: none;
+ border-radius: 0.4em;
+ /* The colors that GitHub uses */
+ border: #1b1f2426 1px solid;
+ background-color: #f6f8fa;
+ color: #57606a;
+}
+
+button.copybtn.success {
+ border-color: #22863a;
+ color: #22863a;
+}
+
+button.copybtn svg {
+ stroke: currentColor;
+ width: 1.5em;
+ height: 1.5em;
+ padding: 0.1em;
+}
+
+div.highlight {
+ position: relative;
+}
+
+/* Show the copybutton */
+.highlight:hover button.copybtn, button.copybtn.success {
+ opacity: 1;
+}
+
+.highlight button.copybtn:hover {
+ background-color: rgb(235, 235, 235);
+}
+
+.highlight button.copybtn:active {
+ background-color: rgb(187, 187, 187);
+}
+
+/**
+ * A minimal CSS-only tooltip copied from:
+ * https://codepen.io/mildrenben/pen/rVBrpK
+ *
+ * To use, write HTML like the following:
+ *
+ * <p class="o-tooltip--left" data-tooltip="Hey">Short</p>
+ */
+ .o-tooltip--left {
+ position: relative;
+ }
+
+ .o-tooltip--left:after {
+ opacity: 0;
+ visibility: hidden;
+ position: absolute;
+ content: attr(data-tooltip);
+ padding: .2em;
+ font-size: .8em;
+ left: -.2em;
+ background: grey;
+ color: white;
+ white-space: nowrap;
+ z-index: 2;
+ border-radius: 2px;
+ transform: translateX(-102%) translateY(0);
+ transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1);
+}
+
+.o-tooltip--left:hover:after {
+ display: block;
+ opacity: 1;
+ visibility: visible;
+ transform: translateX(-100%) translateY(0);
+ transition: opacity 0.2s cubic-bezier(0.64, 0.09, 0.08, 1), transform 0.2s cubic-bezier(0.64, 0.09, 0.08, 1);
+ transition-delay: .5s;
+}
+
+/* By default the copy button shouldn't show up when printing a page */
+@media print {
+ button.copybtn {
+ display: none;
+ }
+}
diff --git a/_static/copybutton.js b/_static/copybutton.js
new file mode 100644
index 00000000000..2ea7ff3e217
--- /dev/null
+++ b/_static/copybutton.js
@@ -0,0 +1,248 @@
+// Localization support
+const messages = {
+ 'en': {
+ 'copy': 'Copy',
+ 'copy_to_clipboard': 'Copy to clipboard',
+ 'copy_success': 'Copied!',
+ 'copy_failure': 'Failed to copy',
+ },
+ 'es' : {
+ 'copy': 'Copiar',
+ 'copy_to_clipboard': 'Copiar al portapapeles',
+ 'copy_success': '¡Copiado!',
+ 'copy_failure': 'Error al copiar',
+ },
+ 'de' : {
+ 'copy': 'Kopieren',
+ 'copy_to_clipboard': 'In die Zwischenablage kopieren',
+ 'copy_success': 'Kopiert!',
+ 'copy_failure': 'Fehler beim Kopieren',
+ },
+ 'fr' : {
+ 'copy': 'Copier',
+ 'copy_to_clipboard': 'Copier dans le presse-papier',
+ 'copy_success': 'Copié !',
+ 'copy_failure': 'Échec de la copie',
+ },
+ 'ru': {
+ 'copy': 'Скопировать',
+ 'copy_to_clipboard': 'Скопировать в буфер',
+ 'copy_success': 'Скопировано!',
+ 'copy_failure': 'Не удалось скопировать',
+ },
+ 'zh-CN': {
+ 'copy': '复制',
+ 'copy_to_clipboard': '复制到剪贴板',
+ 'copy_success': '复制成功!',
+ 'copy_failure': '复制失败',
+ },
+ 'it' : {
+ 'copy': 'Copiare',
+ 'copy_to_clipboard': 'Copiato negli appunti',
+ 'copy_success': 'Copiato!',
+ 'copy_failure': 'Errore durante la copia',
+ }
+}
+
+let locale = 'en'
+if( document.documentElement.lang !== undefined
+ && messages[document.documentElement.lang] !== undefined ) {
+ locale = document.documentElement.lang
+}
+
+let doc_url_root = DOCUMENTATION_OPTIONS.URL_ROOT;
+if (doc_url_root == '#') {
+ doc_url_root = '';
+}
+
+/**
+ * SVG files for our copy buttons
+ */
+let iconCheck = `<svg xmlns="http://www.w3.org/2000/svg" class="icon icon-tabler icon-tabler-check" width="44" height="44" viewBox="0 0 24 24" stroke-width="2" stroke="#22863a" fill="none" stroke-linecap="round" stroke-linejoin="round">
+ <title>${messages[locale]['copy_success']}</title>
+ <path stroke="none" d="M0 0h24v24H0z" fill="none"/>
+ <path d="M5 12l5 5l10 -10" />
+</svg>`
+
+// If the user specified their own SVG use that, otherwise use the default
+let iconCopy = ``;
+if (!iconCopy) {
+ iconCopy = `<svg xmlns="http://www.w3.org/2000/svg" class="icon icon-tabler icon-tabler-copy" width="44" height="44" viewBox="0 0 24 24" stroke-width="1.5" stroke="#000000" fill="none" stroke-linecap="round" stroke-linejoin="round">
+ <title>${messages[locale]['copy_to_clipboard']}</title>
+ <path stroke="none" d="M0 0h24v24H0z" fill="none"/>
+ <rect x="8" y="8" width="12" height="12" rx="2" />
+ <path d="M16 8v-2a2 2 0 0 0 -2 -2h-8a2 2 0 0 0 -2 2v8a2 2 0 0 0 2 2h2" />
+</svg>`
+}
+
+/**
+ * Set up copy/paste for code blocks
+ */
+
+const runWhenDOMLoaded = cb => {
+ if (document.readyState != 'loading') {
+ cb()
+ } else if (document.addEventListener) {
+ document.addEventListener('DOMContentLoaded', cb)
+ } else {
+ document.attachEvent('onreadystatechange', function() {
+ if (document.readyState == 'complete') cb()
+ })
+ }
+}
+
+const codeCellId = index => `codecell${index}`
+
+// Clears selected text since ClipboardJS will select the text when copying
+const clearSelection = () => {
+ if (window.getSelection) {
+ window.getSelection().removeAllRanges()
+ } else if (document.selection) {
+ document.selection.empty()
+ }
+}
+
+// Changes tooltip text for a moment, then changes it back
+// We want the timeout of our `success` class to be a bit shorter than the
+// tooltip and icon change, so that we can hide the icon before changing back.
+var timeoutIcon = 2000;
+var timeoutSuccessClass = 1500;
+
+const temporarilyChangeTooltip = (el, oldText, newText) => {
+ el.setAttribute('data-tooltip', newText)
+ el.classList.add('success')
+ // Remove success a little bit sooner than we change the tooltip
+ // So that we can use CSS to hide the copybutton first
+ setTimeout(() => el.classList.remove('success'), timeoutSuccessClass)
+ setTimeout(() => el.setAttribute('data-tooltip', oldText), timeoutIcon)
+}
+
+// Changes the copy button icon for two seconds, then changes it back
+const temporarilyChangeIcon = (el) => {
+ el.innerHTML = iconCheck;
+ setTimeout(() => {el.innerHTML = iconCopy}, timeoutIcon)
+}
+
+const addCopyButtonToCodeCells = () => {
+ // If ClipboardJS hasn't loaded, wait a bit and try again. This
+ // happens because we load ClipboardJS asynchronously.
+ if (window.ClipboardJS === undefined) {
+ setTimeout(addCopyButtonToCodeCells, 250)
+ return
+ }
+
+ // Add copybuttons to all of our code cells
+ const COPYBUTTON_SELECTOR = 'div.highlight pre';
+ const codeCells = document.querySelectorAll(COPYBUTTON_SELECTOR)
+ codeCells.forEach((codeCell, index) => {
+ const id = codeCellId(index)
+ codeCell.setAttribute('id', id)
+
+ const clipboardButton = id =>
+ `<button class="copybtn o-tooltip--left" data-tooltip="${messages[locale]['copy']}" data-clipboard-target="#${id}">
+ ${iconCopy}
+ </button>`
+ codeCell.insertAdjacentHTML('afterend', clipboardButton(id))
+ })
+
+function escapeRegExp(string) {
+ return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
+}
+
+/**
+ * Removes excluded text from a Node.
+ *
+ * @param {Node} target Node to filter.
+ * @param {string} exclude CSS selector of nodes to exclude.
+ * @returns {DOMString} Text from `target` with text removed.
+ */
+function filterText(target, exclude) {
+ const clone = target.cloneNode(true); // clone as to not modify the live DOM
+ if (exclude) {
+ // remove excluded nodes
+ clone.querySelectorAll(exclude).forEach(node => node.remove());
+ }
+ return clone.innerText;
+}
+
+// Callback when a copy button is clicked. Will be passed the node that was clicked
+// should then grab the text and replace pieces of text that shouldn't be used in output
+function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") {
+ var regexp;
+ var match;
+
+ // Do we check for line continuation characters and "HERE-documents"?
+ var useLineCont = !!lineContinuationChar
+ var useHereDoc = !!hereDocDelim
+
+ // create regexp to capture prompt and remaining line
+ if (isRegexp) {
+ regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)')
+ } else {
+ regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)')
+ }
+
+ const outputLines = [];
+ var promptFound = false;
+ var gotLineCont = false;
+ var gotHereDoc = false;
+ const lineGotPrompt = [];
+ for (const line of textContent.split('\n')) {
+ match = line.match(regexp)
+ if (match || gotLineCont || gotHereDoc) {
+ promptFound = regexp.test(line)
+ lineGotPrompt.push(promptFound)
+ if (removePrompts && promptFound) {
+ outputLines.push(match[2])
+ } else {
+ outputLines.push(line)
+ }
+ gotLineCont = line.endsWith(lineContinuationChar) & useLineCont
+ if (line.includes(hereDocDelim) & useHereDoc)
+ gotHereDoc = !gotHereDoc
+ } else if (!onlyCopyPromptLines) {
+ outputLines.push(line)
+ } else if (copyEmptyLines && line.trim() === '') {
+ outputLines.push(line)
+ }
+ }
+
+ // If no lines with the prompt were found then just use original lines
+ if (lineGotPrompt.some(v => v === true)) {
+ textContent = outputLines.join('\n');
+ }
+
+ // Remove a trailing newline to avoid auto-running when pasting
+ if (textContent.endsWith("\n")) {
+ textContent = textContent.slice(0, -1)
+ }
+ return textContent
+}
+
+
+var copyTargetText = (trigger) => {
+ var target = document.querySelector(trigger.attributes['data-clipboard-target'].value);
+
+ // get filtered text
+ let exclude = '.linenos';
+
+ let text = filterText(target, exclude);
+ return formatCopyText(text, '', false, true, true, true, '', '')
+}
+
+ // Initialize with a callback so we can modify the text before copy
+ const clipboard = new ClipboardJS('.copybtn', {text: copyTargetText})
+
+ // Update UI with error/success messages
+ clipboard.on('success', event => {
+ clearSelection()
+ temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_success'])
+ temporarilyChangeIcon(event.trigger)
+ })
+
+ clipboard.on('error', event => {
+ temporarilyChangeTooltip(event.trigger, messages[locale]['copy'], messages[locale]['copy_failure'])
+ })
+}
+
+runWhenDOMLoaded(addCopyButtonToCodeCells)
\ No newline at end of file
diff --git a/_static/copybutton_funcs.js b/_static/copybutton_funcs.js
new file mode 100644
index 00000000000..dbe1aaad79c
--- /dev/null
+++ b/_static/copybutton_funcs.js
@@ -0,0 +1,73 @@
+function escapeRegExp(string) {
+ return string.replace(/[.*+?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
+}
+
+/**
+ * Removes excluded text from a Node.
+ *
+ * @param {Node} target Node to filter.
+ * @param {string} exclude CSS selector of nodes to exclude.
+ * @returns {DOMString} Text from `target` with text removed.
+ */
+export function filterText(target, exclude) {
+ const clone = target.cloneNode(true); // clone as to not modify the live DOM
+ if (exclude) {
+ // remove excluded nodes
+ clone.querySelectorAll(exclude).forEach(node => node.remove());
+ }
+ return clone.innerText;
+}
+
+// Callback when a copy button is clicked. Will be passed the node that was clicked
+// should then grab the text and replace pieces of text that shouldn't be used in output
+export function formatCopyText(textContent, copybuttonPromptText, isRegexp = false, onlyCopyPromptLines = true, removePrompts = true, copyEmptyLines = true, lineContinuationChar = "", hereDocDelim = "") {
+ var regexp;
+ var match;
+
+ // Do we check for line continuation characters and "HERE-documents"?
+ var useLineCont = !!lineContinuationChar
+ var useHereDoc = !!hereDocDelim
+
+ // create regexp to capture prompt and remaining line
+ if (isRegexp) {
+ regexp = new RegExp('^(' + copybuttonPromptText + ')(.*)')
+ } else {
+ regexp = new RegExp('^(' + escapeRegExp(copybuttonPromptText) + ')(.*)')
+ }
+
+ const outputLines = [];
+ var promptFound = false;
+ var gotLineCont = false;
+ var gotHereDoc = false;
+ const lineGotPrompt = [];
+ for (const line of textContent.split('\n')) {
+ match = line.match(regexp)
+ if (match || gotLineCont || gotHereDoc) {
+ promptFound = regexp.test(line)
+ lineGotPrompt.push(promptFound)
+ if (removePrompts && promptFound) {
+ outputLines.push(match[2])
+ } else {
+ outputLines.push(line)
+ }
+ gotLineCont = line.endsWith(lineContinuationChar) & useLineCont
+ if (line.includes(hereDocDelim) & useHereDoc)
+ gotHereDoc = !gotHereDoc
+ } else if (!onlyCopyPromptLines) {
+ outputLines.push(line)
+ } else if (copyEmptyLines && line.trim() === '') {
+ outputLines.push(line)
+ }
+ }
+
+ // If no lines with the prompt were found then just use original lines
+ if (lineGotPrompt.some(v => v === true)) {
+ textContent = outputLines.join('\n');
+ }
+
+ // Remove a trailing newline to avoid auto-running when pasting
+ if (textContent.endsWith("\n")) {
+ textContent = textContent.slice(0, -1)
+ }
+ return textContent
+}
diff --git a/_static/css/badge_only.css b/_static/css/badge_only.css
new file mode 100644
index 00000000000..e380325bc6e
--- /dev/null
+++ b/_static/css/badge_only.css
@@ -0,0 +1 @@
+.fa:before{-webkit-font-smoothing:antialiased}.clearfix{*zoom:1}.clearfix:after,.clearfix:before{display:table;content:""}.clearfix:after{clear:both}@font-face{font-family:FontAwesome;font-style:normal;font-weight:400;src:url(fonts/fontawesome-webfont.eot?674f50d287a8c48dc19ba404d20fe713?#iefix) format("embedded-opentype"),url(fonts/fontawesome-webfont.woff2?af7ae505a9eed503f8b8e6982036873e) format("woff2"),url(fonts/fontawesome-webfont.woff?fee66e712a8a08eef5805a46892932ad) format("woff"),url(fonts/fontawesome-webfont.ttf?b06871f281fee6b241d60582ae9369b9) format("truetype"),url(fonts/fontawesome-webfont.svg?912ec66d7572ff821749319396470bde#FontAwesome) format("svg")}.fa:before{font-family:FontAwesome;font-style:normal;font-weight:400;line-height:1}.fa:before,a .fa{text-decoration:inherit}.fa:before,a .fa,li .fa{display:inline-block}li .fa-large:before{width:1.875em}ul.fas{list-style-type:none;margin-left:2em;text-indent:-.8em}ul.fas li .fa{width:.8em}ul.fas li .fa-large:before{vertical-align:baseline}.fa-book:before,.icon-book:before{content:"\f02d"}.fa-caret-down:before,.icon-caret-down:before{content:"\f0d7"}.fa-caret-up:before,.icon-caret-up:before{content:"\f0d8"}.fa-caret-left:before,.icon-caret-left:before{content:"\f0d9"}.fa-caret-right:before,.icon-caret-right:before{content:"\f0da"}.rst-versions{position:fixed;bottom:0;left:0;width:300px;color:#fcfcfc;background:#1f1d1d;font-family:Lato,proxima-nova,Helvetica Neue,Arial,sans-serif;z-index:400}.rst-versions a{color:#2980b9;text-decoration:none}.rst-versions .rst-badge-small{display:none}.rst-versions .rst-current-version{padding:12px;background-color:#272525;display:block;text-align:right;font-size:90%;cursor:pointer;color:#27ae60}.rst-versions .rst-current-version:after{clear:both;content:"";display:block}.rst-versions .rst-current-version .fa{color:#fcfcfc}.rst-versions .rst-current-version .fa-book,.rst-versions .rst-current-version .icon-book{float:left}.rst-versions .rst-current-version.rst-out-of-date{background-color:#e74c3c;color:#fff}.rst-versions .rst-current-version.rst-active-old-version{background-color:#f1c40f;color:#000}.rst-versions.shift-up{height:auto;max-height:100%;overflow-y:scroll}.rst-versions.shift-up .rst-other-versions{display:block}.rst-versions .rst-other-versions{font-size:90%;padding:12px;color:grey;display:none}.rst-versions .rst-other-versions hr{display:block;height:1px;border:0;margin:20px 0;padding:0;border-top:1px solid #413d3d}.rst-versions .rst-other-versions dd{display:inline-block;margin:0}.rst-versions .rst-other-versions dd a{display:inline-block;padding:6px;color:#fcfcfc}.rst-versions.rst-badge{width:auto;bottom:20px;right:20px;left:auto;border:none;max-width:300px;max-height:90%}.rst-versions.rst-badge .fa-book,.rst-versions.rst-badge .icon-book{float:none;line-height:30px}.rst-versions.rst-badge.shift-up .rst-current-version{text-align:right}.rst-versions.rst-badge.shift-up .rst-current-version .fa-book,.rst-versions.rst-badge.shift-up .rst-current-version .icon-book{float:left}.rst-versions.rst-badge>.rst-current-version{width:auto;height:30px;line-height:30px;padding:0 6px;display:block;text-align:center}@media screen and (max-width:768px){.rst-versions{width:85%;display:none}.rst-versions.shift{display:block}}
\ No newline at end of file
diff --git a/_static/css/fonts/Roboto-Slab-Bold.woff b/_static/css/fonts/Roboto-Slab-Bold.woff
new file mode 100644
index 00000000000..6cb60000181
Binary files /dev/null and b/_static/css/fonts/Roboto-Slab-Bold.woff differ
diff --git a/_static/css/fonts/Roboto-Slab-Bold.woff2 b/_static/css/fonts/Roboto-Slab-Bold.woff2
new file mode 100644
index 00000000000..7059e23142a
Binary files /dev/null and b/_static/css/fonts/Roboto-Slab-Bold.woff2 differ
diff --git a/_static/css/fonts/Roboto-Slab-Regular.woff b/_static/css/fonts/Roboto-Slab-Regular.woff
new file mode 100644
index 00000000000..f815f63f99d
Binary files /dev/null and b/_static/css/fonts/Roboto-Slab-Regular.woff differ
diff --git a/_static/css/fonts/Roboto-Slab-Regular.woff2 b/_static/css/fonts/Roboto-Slab-Regular.woff2
new file mode 100644
index 00000000000..f2c76e5bda1
Binary files /dev/null and b/_static/css/fonts/Roboto-Slab-Regular.woff2 differ
diff --git a/_static/css/fonts/fontawesome-webfont.eot b/_static/css/fonts/fontawesome-webfont.eot
new file mode 100644
index 00000000000..e9f60ca953f
Binary files /dev/null and b/_static/css/fonts/fontawesome-webfont.eot differ
diff --git a/_static/css/fonts/fontawesome-webfont.svg b/_static/css/fonts/fontawesome-webfont.svg
new file mode 100644
index 00000000000..855c845e538
--- /dev/null
+++ b/_static/css/fonts/fontawesome-webfont.svg
@@ -0,0 +1,2671 @@
+<?xml version="1.0" standalone="no"?>
+<!DOCTYPE svg PUBLIC "-//W3C//DTD SVG 1.1//EN" "http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd" >
+<svg>
+<metadata>
+Created by FontForge 20120731 at Mon Oct 24 17:37:40 2016
+ By ,,,
+Copyright Dave Gandy 2016. All rights reserved.
+</metadata>
+<defs>
+<font id="FontAwesome" horiz-adv-x="1536" >
+ <font-face
+ font-family="FontAwesome"
+ font-weight="400"
+ font-stretch="normal"
+ units-per-em="1792"
+ panose-1="0 0 0 0 0 0 0 0 0 0"
+ ascent="1536"
+ descent="-256"
+ bbox="-1.02083 -256.962 2304.6 1537.02"
+ underline-thickness="0"
+ underline-position="0"
+ unicode-range="U+0020-F500"
+ />
+<missing-glyph horiz-adv-x="896"
+d="M224 112h448v1312h-448v-1312zM112 0v1536h672v-1536h-672z" />
+ <glyph glyph-name=".notdef" horiz-adv-x="896"
+d="M224 112h448v1312h-448v-1312zM112 0v1536h672v-1536h-672z" />
+ <glyph glyph-name=".null" horiz-adv-x="0"
+ />
+ <glyph glyph-name="nonmarkingreturn" horiz-adv-x="597"
+ />
+ <glyph glyph-name="space" unicode=" " horiz-adv-x="448"
+ />
+ <glyph glyph-name="dieresis" unicode="¨" horiz-adv-x="1792"
+ />
+ <glyph glyph-name="copyright" unicode="©" horiz-adv-x="1792"
+ />
+ <glyph glyph-name="registered" unicode="®" horiz-adv-x="1792"
+ />
+ <glyph glyph-name="acute" unicode="´" horiz-adv-x="1792"
+ />
+ <glyph glyph-name="AE" unicode="Æ" horiz-adv-x="1792"
+ />
+ <glyph glyph-name="Oslash" unicode="Ø" horiz-adv-x="1792"
+ />
+ <glyph glyph-name="trademark" unicode="™" horiz-adv-x="1792"
+ />
+ <glyph glyph-name="infinity" unicode="∞" horiz-adv-x="1792"
+ />
+ <glyph glyph-name="notequal" unicode="≠" horiz-adv-x="1792"
+ />
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diff --git a/docs/_static/custom.css b/_static/custom.css
similarity index 100%
rename from docs/_static/custom.css
rename to _static/custom.css
diff --git a/_static/dark_mode_css/custom.css b/_static/dark_mode_css/custom.css
new file mode 100644
index 00000000000..989c2ada1eb
--- /dev/null
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+html.writer-html5
+ .rst-content
+ dl[class]:not(.option-list):not(.field-list):not(.footnote):not(.glossary):not(.simple)
+ > dt,
+.rst-content code,
+.rst-content tt,
+html.writer-html4 .rst-content dl:not(.docutils) dl:not(.field-list) > dt,
+html.writer-html5
+ .rst-content
+ dl[class]:not(.option-list):not(.field-list):not(.footnote):not(.glossary):not(.simple)
+ dl:not(.field-list)
+ > dt,
+code,
+.rst-content code.xref,
+.rst-content tt.xref {
+ transition: all 0.2s ease-in-out;
+}
diff --git a/_static/dark_mode_css/dark.css b/_static/dark_mode_css/dark.css
new file mode 100644
index 00000000000..fb8802d7e71
--- /dev/null
+++ b/_static/dark_mode_css/dark.css
@@ -0,0 +1,501 @@
+:root {
+ --dark-text-color: #c1c1c1;
+ --dark-link-color: #249ee8;
+}
+
+html[data-theme='dark'] body {
+ color: #bfbfbf;
+}
+
+html[data-theme='dark'] .wy-nav-content-wrap {
+ background-color: #101010;
+}
+
+html[data-theme='dark'] .wy-nav-content {
+ background-color: #141414;
+}
+
+html[data-theme='dark'] .section {
+ color: var(--dark-text-color);
+}
+
+html[data-theme='dark'] .highlight {
+ background-color: #17181c;
+}
+
+html[data-theme='dark'] .highlight .nn {
+ color: var(--dark-text-color);
+}
+
+html[data-theme='dark'] .highlight .nb {
+ color: #8bb8df;
+}
+
+html[data-theme='dark'] .highlight .kn,
+html[data-theme='dark'] .highlight .kc,
+html[data-theme='dark'] .highlight .k {
+ color: #41c2ea;
+}
+
+html[data-theme='dark'] .highlight .s1,
+html[data-theme='dark'] .highlight .s2 {
+ color: #b3e87f;
+}
+
+html[data-theme='dark'] .highlight .nt {
+ color: #ccb350;
+}
+
+html[data-theme='dark'] .highlight .c1 {
+ color: #686868;
+}
+
+html[data-theme='dark'] .rst-content div[class^='highlight'] {
+ border-color: #1a1a1a;
+}
+
+html[data-theme='dark'] .wy-nav-content a,
+html[data-theme='dark'] .wy-nav-content a:visited {
+ color: var(--dark-link-color);
+}
+
+html[data-theme='dark'] .btn-neutral {
+ background-color: #17181c !important;
+}
+
+html[data-theme='dark'] .btn-neutral:hover {
+ background-color: #101114 !important;
+}
+
+html[data-theme='dark'] .btn-neutral:visited {
+ color: #c1c1c1 !important;
+}
+
+html[data-theme='dark'] .btn {
+ box-shadow: none;
+}
+
+html[data-theme='dark'] footer {
+ color: #bdbdbd;
+}
+
+html[data-theme='dark'] .wy-nav-side {
+ background-color: #0d0d0d;
+}
+
+html[data-theme='dark'] .wy-menu-vertical li.current {
+ background-color: #141414;
+}
+
+html[data-theme='dark'] .wy-menu-vertical li.current > a,
+html[data-theme='dark'] .wy-menu-vertical li.on a {
+ background-color: #141415;
+ color: var(--dark-text-color);
+}
+
+html[data-theme='dark'] .wy-menu-vertical li.toctree-l1.current > a,
+html[data-theme='dark'] .wy-menu-vertical li.current a {
+ border-color: #0b0c0d;
+}
+
+html[data-theme='dark'] .wy-menu-vertical li.current a {
+ color: #bbb;
+}
+
+html[data-theme='dark'] .wy-menu-vertical li.current a:hover {
+ background-color: #222;
+}
+
+html[data-theme='dark'] .wy-menu-vertical a:hover,
+html[data-theme='dark'] .wy-menu-vertical li.current > a:hover,
+html[data-theme='dark'] .wy-menu-vertical li.on a:hover {
+ background-color: #1e1e1e;
+}
+
+html[data-theme='dark'] .wy-menu-vertical li.toctree-l2.current > a,
+html[data-theme='dark']
+ .wy-menu-vertical
+ li.toctree-l2.current
+ li.toctree-l3
+ > a {
+ background-color: #18181a;
+}
+
+html[data-theme='dark'] .wy-side-nav-search {
+ background-color: #0b152d;
+}
+
+html[data-theme='dark'] .wy-side-nav-search .wy-dropdown > a,
+html[data-theme='dark'] .wy-side-nav-search > a {
+ color: #ddd;
+}
+
+html[data-theme='dark'] .wy-side-nav-search input[type='text'] {
+ border-color: #111;
+ background-color: #141414;
+ color: var(--dark-text-color);
+}
+
+html[data-theme='dark'] .theme-switcher {
+ background-color: #0b0c0d;
+ color: var(--dark-text-color);
+}
+
+html[data-theme='dark'].writer-html4 .rst-content dl:not(.docutils) > dt,
+html[data-theme='dark'].writer-html5
+ .rst-content
+ dl[class]:not(.option-list):not(.field-list):not(.footnote):not(.glossary):not(.simple)
+ > dt {
+ background-color: #0b0b0b;
+ color: #007dce;
+ border-color: #282828;
+}
+
+html[data-theme='dark'] .rst-content code,
+html[data-theme='dark'] .rst-content tt {
+ color: var(--dark-text-color);
+}
+
+html[data-theme='dark'].writer-html4
+ .rst-content
+ dl:not(.docutils)
+ dl:not(.field-list)
+ > dt,
+html[data-theme='dark'].writer-html5
+ .rst-content
+ dl[class]:not(.option-list):not(.field-list):not(.footnote):not(.glossary):not(.simple)
+ dl:not(.field-list)
+ > dt {
+ background-color: #0f0f0f;
+ color: #959595;
+ border-color: #2b2b2b;
+}
+
+html[data-theme='dark'] .rst-content code,
+html[data-theme='dark'] .rst-content tt,
+html[data-theme='dark'] code {
+ background-color: #2d2d2d;
+ border-color: #1c1c1c;
+}
+
+html[data-theme='dark'] .rst-content code.xref,
+html[data-theme='dark'] .rst-content tt.xref,
+html[data-theme='dark'] a .rst-content code,
+html[data-theme='dark'] a .rst-content tt {
+ color: #cecece;
+}
+
+html[data-theme='dark'] .rst-content .hint,
+html[data-theme='dark'] .rst-content .important,
+html[data-theme='dark'] .rst-content .tip,
+html[data-theme='dark'] .rst-content .wy-alert-success.admonition,
+html[data-theme='dark'] .rst-content .wy-alert-success.admonition-todo,
+html[data-theme='dark'] .rst-content .wy-alert-success.attention,
+html[data-theme='dark'] .rst-content .wy-alert-success.caution,
+html[data-theme='dark'] .rst-content .wy-alert-success.danger,
+html[data-theme='dark'] .rst-content .wy-alert-success.error,
+html[data-theme='dark'] .rst-content .wy-alert-success.note,
+html[data-theme='dark'] .rst-content .wy-alert-success.seealso,
+html[data-theme='dark'] .rst-content .wy-alert-success.warning,
+html[data-theme='dark'] .wy-alert.wy-alert-success {
+ background-color: #00392e;
+}
+
+html[data-theme='dark'] .rst-content .hint .admonition-title,
+html[data-theme='dark'] .rst-content .hint .wy-alert-title,
+html[data-theme='dark'] .rst-content .important .admonition-title,
+html[data-theme='dark'] .rst-content .important .wy-alert-title,
+html[data-theme='dark'] .rst-content .tip .admonition-title,
+html[data-theme='dark'] .rst-content .tip .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-success.admonition-todo
+ .admonition-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-success.admonition-todo
+ .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-success.admonition
+ .admonition-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-success.admonition
+ .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-success.attention
+ .admonition-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-success.attention
+ .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-success.caution
+ .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-success.caution .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-success.danger .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-success.danger .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-success.error .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-success.error .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-success.note .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-success.note .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-success.seealso
+ .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-success.seealso .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-success.warning
+ .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-success.warning .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert.wy-alert-success
+ .admonition-title,
+html[data-theme='dark']
+ .wy-alert.wy-alert-success
+ .rst-content
+ .admonition-title,
+html[data-theme='dark'] .wy-alert.wy-alert-success .wy-alert-title {
+ background-color: #006a56;
+}
+
+html[data-theme='dark'] .rst-content .note,
+html[data-theme='dark'] .rst-content .seealso,
+html[data-theme='dark'] .rst-content .wy-alert-info.admonition,
+html[data-theme='dark'] .rst-content .wy-alert-info.admonition-todo,
+html[data-theme='dark'] .rst-content .wy-alert-info.attention,
+html[data-theme='dark'] .rst-content .wy-alert-info.caution,
+html[data-theme='dark'] .rst-content .wy-alert-info.danger,
+html[data-theme='dark'] .rst-content .wy-alert-info.error,
+html[data-theme='dark'] .rst-content .wy-alert-info.hint,
+html[data-theme='dark'] .rst-content .wy-alert-info.important,
+html[data-theme='dark'] .rst-content .wy-alert-info.tip,
+html[data-theme='dark'] .rst-content .wy-alert-info.warning,
+html[data-theme='dark'] .wy-alert.wy-alert-info {
+ background-color: #002c4d;
+}
+
+html[data-theme='dark'] .rst-content .note .admonition-title,
+html[data-theme='dark'] .rst-content .note .wy-alert-title,
+html[data-theme='dark'] .rst-content .seealso .admonition-title,
+html[data-theme='dark'] .rst-content .seealso .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-info.admonition-todo
+ .admonition-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-info.admonition-todo
+ .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-info.admonition
+ .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.admonition .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.attention .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.attention .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.caution .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.caution .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.danger .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.danger .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.error .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.error .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.hint .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.hint .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.important .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.important .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.tip .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.tip .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.warning .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-info.warning .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert.wy-alert-info .admonition-title,
+html[data-theme='dark'] .wy-alert.wy-alert-info .rst-content .admonition-title,
+html[data-theme='dark'] .wy-alert.wy-alert-info .wy-alert-title {
+ background-color: #004a7b;
+}
+
+html[data-theme='dark'] .rst-content .admonition-todo,
+html[data-theme='dark'] .rst-content .attention,
+html[data-theme='dark'] .rst-content .caution,
+html[data-theme='dark'] .rst-content .warning,
+html[data-theme='dark'] .rst-content .wy-alert-warning.admonition,
+html[data-theme='dark'] .rst-content .wy-alert-warning.danger,
+html[data-theme='dark'] .rst-content .wy-alert-warning.error,
+html[data-theme='dark'] .rst-content .wy-alert-warning.hint,
+html[data-theme='dark'] .rst-content .wy-alert-warning.important,
+html[data-theme='dark'] .rst-content .wy-alert-warning.note,
+html[data-theme='dark'] .rst-content .wy-alert-warning.seealso,
+html[data-theme='dark'] .rst-content .wy-alert-warning.tip,
+html[data-theme='dark'] .wy-alert.wy-alert-warning {
+ background-color: #533500;
+}
+
+html[data-theme='dark'] .rst-content .admonition-todo .admonition-title,
+html[data-theme='dark'] .rst-content .admonition-todo .wy-alert-title,
+html[data-theme='dark'] .rst-content .attention .admonition-title,
+html[data-theme='dark'] .rst-content .attention .wy-alert-title,
+html[data-theme='dark'] .rst-content .caution .admonition-title,
+html[data-theme='dark'] .rst-content .caution .wy-alert-title,
+html[data-theme='dark'] .rst-content .warning .admonition-title,
+html[data-theme='dark'] .rst-content .warning .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-warning.admonition
+ .admonition-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-warning.admonition
+ .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-warning.danger .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-warning.danger .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-warning.error .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-warning.error .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-warning.hint .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-warning.hint .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-warning.important
+ .admonition-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-warning.important
+ .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-warning.note .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-warning.note .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-warning.seealso
+ .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-warning.seealso .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-warning.tip .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-warning.tip .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert.wy-alert-warning
+ .admonition-title,
+html[data-theme='dark']
+ .wy-alert.wy-alert-warning
+ .rst-content
+ .admonition-title,
+html[data-theme='dark'] .wy-alert.wy-alert-warning .wy-alert-title {
+ background-color: #803b00;
+}
+
+html[data-theme='dark'] .rst-content .danger,
+html[data-theme='dark'] .rst-content .error,
+html[data-theme='dark'] .rst-content .wy-alert-danger.admonition,
+html[data-theme='dark'] .rst-content .wy-alert-danger.admonition-todo,
+html[data-theme='dark'] .rst-content .wy-alert-danger.attention,
+html[data-theme='dark'] .rst-content .wy-alert-danger.caution,
+html[data-theme='dark'] .rst-content .wy-alert-danger.hint,
+html[data-theme='dark'] .rst-content .wy-alert-danger.important,
+html[data-theme='dark'] .rst-content .wy-alert-danger.note,
+html[data-theme='dark'] .rst-content .wy-alert-danger.seealso,
+html[data-theme='dark'] .rst-content .wy-alert-danger.tip,
+html[data-theme='dark'] .rst-content .wy-alert-danger.warning,
+html[data-theme='dark'] .wy-alert.wy-alert-danger {
+ background-color: #82231a;
+}
+
+html[data-theme='dark'] .rst-content .danger .admonition-title,
+html[data-theme='dark'] .rst-content .danger .wy-alert-title,
+html[data-theme='dark'] .rst-content .error .admonition-title,
+html[data-theme='dark'] .rst-content .error .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-danger.admonition-todo
+ .admonition-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-danger.admonition-todo
+ .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-danger.admonition
+ .admonition-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-danger.admonition
+ .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-danger.attention
+ .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.attention .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.caution .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.caution .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.hint .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.hint .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert-danger.important
+ .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.important .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.note .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.note .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.seealso .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.seealso .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.tip .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.tip .wy-alert-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.warning .admonition-title,
+html[data-theme='dark'] .rst-content .wy-alert-danger.warning .wy-alert-title,
+html[data-theme='dark']
+ .rst-content
+ .wy-alert.wy-alert-danger
+ .admonition-title,
+html[data-theme='dark']
+ .wy-alert.wy-alert-danger
+ .rst-content
+ .admonition-title,
+html[data-theme='dark'] .wy-alert.wy-alert-danger .wy-alert-title {
+ background-color: #b9372b;
+}
+
+html[data-theme='dark'] .wy-nav-top {
+ background-color: #0b152d;
+}
+
+html[data-theme='dark'] .rst-content table.docutils thead,
+html[data-theme='dark'] .rst-content table.field-list thead,
+html[data-theme='dark'] .wy-table thead {
+ color: var(--dark-text-color);
+}
+
+html[data-theme='dark']
+ .rst-content
+ table.docutils:not(.field-list)
+ tr:nth-child(2n-1)
+ td,
+html[data-theme='dark'] .wy-table-backed,
+html[data-theme='dark'] html[data-theme='dark'] .wy-table-odd td,
+html[data-theme='dark'] .wy-table-striped tr:nth-child(2n-1) td {
+ background-color: #181818;
+}
+
+html[data-theme='dark'] .rst-content table.docutils td,
+html[data-theme='dark'] .wy-table-bordered-all td,
+html[data-theme='dark'].writer-html5 .rst-content table.docutils th,
+html[data-theme='dark'] .rst-content table.docutils,
+html[data-theme='dark'] .wy-table-bordered-all {
+ border-color: #262626;
+}
+
+html[data-theme='dark'] .rst-content table.docutils caption,
+html[data-theme='dark'] .rst-content table.field-list caption,
+html[data-theme='dark'] .wy-table caption {
+ color: var(--dark-text-color);
+}
+
+html[data-theme='dark'] .wy-menu-vertical li.toctree-l3.current > a,
+html[data-theme='dark']
+ .wy-menu-vertical
+ li.toctree-l3.current
+ li.toctree-l4
+ > a {
+ background-color: #18181a;
+}
diff --git a/_static/dark_mode_css/general.css b/_static/dark_mode_css/general.css
new file mode 100644
index 00000000000..aa614f8178e
--- /dev/null
+++ b/_static/dark_mode_css/general.css
@@ -0,0 +1,68 @@
+input[type='color'],
+input[type='date'],
+input[type='datetime-local'],
+input[type='datetime'],
+input[type='email'],
+input[type='month'],
+input[type='number'],
+input[type='password'],
+input[type='search'],
+input[type='tel'],
+input[type='text'],
+input[type='time'],
+input[type='url'],
+input[type='week'] {
+ box-shadow: none;
+}
+
+.theme-switcher {
+ border-radius: 50%;
+ position: fixed;
+ right: 1.6em;
+ bottom: 1.4em;
+ z-index: 3;
+ border: none;
+ height: 2.2em;
+ width: 2.2em;
+ background-color: #fcfcfc;
+ font-size: 20px;
+ -webkit-box-shadow: 0px 3px 14px 4px rgba(0, 0, 0, 0.62);
+ box-shadow: 0px 3px 14px 4px rgba(0, 0, 0, 0.62);
+ color: #404040;
+ transition: all 0.3s ease-in-out;
+}
+
+body,
+.wy-nav-content-wrap,
+.wy-nav-content,
+.section,
+.highlight,
+.rst-content div[class^='highlight'],
+.wy-nav-content a,
+.btn-neutral,
+.btn,
+footer,
+.wy-nav-side,
+.wy-menu-vertical li,
+.wy-menu-vertical a,
+.wy-side-nav-search .wy-dropdown,
+.wy-side-nav-search a,
+.wy-side-nav-search input,
+html.writer-html4 .rst-content dl:not(.docutils) > dt,
+html.writer-html5
+ .rst-content
+ dl[class]:not(.option-list):not(.field-list):not(.footnote):not(.glossary):not(.simple)
+ > dt,
+.rst-content code,
+.rst-content tt,
+html.writer-html4 .rst-content dl:not(.docutils) dl:not(.field-list) > dt,
+html.writer-html5
+ .rst-content
+ dl[class]:not(.option-list):not(.field-list):not(.footnote):not(.glossary):not(.simple)
+ dl:not(.field-list)
+ > dt,
+code,
+.rst-content code.xref,
+.rst-content tt.xref {
+ transition: all 0.2s ease-in-out;
+}
diff --git a/_static/dark_mode_js/default_dark.js b/_static/dark_mode_js/default_dark.js
new file mode 100644
index 00000000000..ea63e07258e
--- /dev/null
+++ b/_static/dark_mode_js/default_dark.js
@@ -0,0 +1,13 @@
+const loadTheme = () => {
+ let theme = localStorage.getItem('theme');
+
+ if (theme !== null) {
+ if (theme === 'dark')
+ document.documentElement.setAttribute('data-theme', 'dark');
+ } else {
+ localStorage.setItem('theme', 'dark');
+ document.documentElement.setAttribute('data-theme', 'dark');
+ }
+};
+
+loadTheme();
diff --git a/_static/dark_mode_js/default_light.js b/_static/dark_mode_js/default_light.js
new file mode 100644
index 00000000000..2b19f92eab9
--- /dev/null
+++ b/_static/dark_mode_js/default_light.js
@@ -0,0 +1,13 @@
+const loadTheme = () => {
+ let theme = localStorage.getItem('theme');
+
+ if (theme !== null) {
+ if (theme === 'dark')
+ document.documentElement.setAttribute('data-theme', 'dark');
+ } else {
+ localStorage.setItem('theme', 'light');
+ document.documentElement.setAttribute('data-theme', 'light');
+ }
+};
+
+loadTheme();
diff --git a/_static/dark_mode_js/theme_switcher.js b/_static/dark_mode_js/theme_switcher.js
new file mode 100644
index 00000000000..860bd5d7e04
--- /dev/null
+++ b/_static/dark_mode_js/theme_switcher.js
@@ -0,0 +1,39 @@
+const createThemeSwitcher = () => {
+ let btn = document.createElement('BUTTON');
+ btn.className = 'theme-switcher';
+ btn.id = 'themeSwitcher';
+ btn.innerHTML =
+ '<i id=themeMoon class="fa fa-moon-o"></i><i id=themeSun class="fa fa-sun-o"></i>';
+ document.body.appendChild(btn);
+
+ if (localStorage.getItem('theme') === 'dark') $('#themeMoon').hide(0);
+ else $('#themeSun').hide(0);
+};
+
+$(document).ready(() => {
+ createThemeSwitcher();
+ $('#themeSwitcher').click(switchTheme);
+
+ $('footer').html(
+ $('footer').html() +
+ 'Dark theme provided by <a href="http://mrdogebro.com">MrDogeBro</a>.'
+ );
+});
+
+const switchTheme = () => {
+ if (localStorage.getItem('theme') === 'dark') {
+ localStorage.setItem('theme', 'light');
+ document.documentElement.setAttribute('data-theme', 'light');
+
+ $('#themeSun').fadeOut(200, () => {
+ $('#themeMoon').fadeIn(200);
+ });
+ } else {
+ localStorage.setItem('theme', 'dark');
+ document.documentElement.setAttribute('data-theme', 'dark');
+
+ $('#themeMoon').fadeOut(200, () => {
+ $('#themeSun').fadeIn(200);
+ });
+ }
+};
diff --git a/_static/doctools.js b/_static/doctools.js
new file mode 100644
index 00000000000..8cbf1b161a6
--- /dev/null
+++ b/_static/doctools.js
@@ -0,0 +1,323 @@
+/*
+ * doctools.js
+ * ~~~~~~~~~~~
+ *
+ * Sphinx JavaScript utilities for all documentation.
+ *
+ * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+/**
+ * select a different prefix for underscore
+ */
+$u = _.noConflict();
+
+/**
+ * make the code below compatible with browsers without
+ * an installed firebug like debugger
+if (!window.console || !console.firebug) {
+ var names = ["log", "debug", "info", "warn", "error", "assert", "dir",
+ "dirxml", "group", "groupEnd", "time", "timeEnd", "count", "trace",
+ "profile", "profileEnd"];
+ window.console = {};
+ for (var i = 0; i < names.length; ++i)
+ window.console[names[i]] = function() {};
+}
+ */
+
+/**
+ * small helper function to urldecode strings
+ *
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/decodeURIComponent#Decoding_query_parameters_from_a_URL
+ */
+jQuery.urldecode = function(x) {
+ if (!x) {
+ return x
+ }
+ return decodeURIComponent(x.replace(/\+/g, ' '));
+};
+
+/**
+ * small helper function to urlencode strings
+ */
+jQuery.urlencode = encodeURIComponent;
+
+/**
+ * This function returns the parsed url parameters of the
+ * current request. Multiple values per key are supported,
+ * it will always return arrays of strings for the value parts.
+ */
+jQuery.getQueryParameters = function(s) {
+ if (typeof s === 'undefined')
+ s = document.location.search;
+ var parts = s.substr(s.indexOf('?') + 1).split('&');
+ var result = {};
+ for (var i = 0; i < parts.length; i++) {
+ var tmp = parts[i].split('=', 2);
+ var key = jQuery.urldecode(tmp[0]);
+ var value = jQuery.urldecode(tmp[1]);
+ if (key in result)
+ result[key].push(value);
+ else
+ result[key] = [value];
+ }
+ return result;
+};
+
+/**
+ * highlight a given string on a jquery object by wrapping it in
+ * span elements with the given class name.
+ */
+jQuery.fn.highlightText = function(text, className) {
+ function highlight(node, addItems) {
+ if (node.nodeType === 3) {
+ var val = node.nodeValue;
+ var pos = val.toLowerCase().indexOf(text);
+ if (pos >= 0 &&
+ !jQuery(node.parentNode).hasClass(className) &&
+ !jQuery(node.parentNode).hasClass("nohighlight")) {
+ var span;
+ var isInSVG = jQuery(node).closest("body, svg, foreignObject").is("svg");
+ if (isInSVG) {
+ span = document.createElementNS("http://www.w3.org/2000/svg", "tspan");
+ } else {
+ span = document.createElement("span");
+ span.className = className;
+ }
+ span.appendChild(document.createTextNode(val.substr(pos, text.length)));
+ node.parentNode.insertBefore(span, node.parentNode.insertBefore(
+ document.createTextNode(val.substr(pos + text.length)),
+ node.nextSibling));
+ node.nodeValue = val.substr(0, pos);
+ if (isInSVG) {
+ var rect = document.createElementNS("http://www.w3.org/2000/svg", "rect");
+ var bbox = node.parentElement.getBBox();
+ rect.x.baseVal.value = bbox.x;
+ rect.y.baseVal.value = bbox.y;
+ rect.width.baseVal.value = bbox.width;
+ rect.height.baseVal.value = bbox.height;
+ rect.setAttribute('class', className);
+ addItems.push({
+ "parent": node.parentNode,
+ "target": rect});
+ }
+ }
+ }
+ else if (!jQuery(node).is("button, select, textarea")) {
+ jQuery.each(node.childNodes, function() {
+ highlight(this, addItems);
+ });
+ }
+ }
+ var addItems = [];
+ var result = this.each(function() {
+ highlight(this, addItems);
+ });
+ for (var i = 0; i < addItems.length; ++i) {
+ jQuery(addItems[i].parent).before(addItems[i].target);
+ }
+ return result;
+};
+
+/*
+ * backward compatibility for jQuery.browser
+ * This will be supported until firefox bug is fixed.
+ */
+if (!jQuery.browser) {
+ jQuery.uaMatch = function(ua) {
+ ua = ua.toLowerCase();
+
+ var match = /(chrome)[ \/]([\w.]+)/.exec(ua) ||
+ /(webkit)[ \/]([\w.]+)/.exec(ua) ||
+ /(opera)(?:.*version|)[ \/]([\w.]+)/.exec(ua) ||
+ /(msie) ([\w.]+)/.exec(ua) ||
+ ua.indexOf("compatible") < 0 && /(mozilla)(?:.*? rv:([\w.]+)|)/.exec(ua) ||
+ [];
+
+ return {
+ browser: match[ 1 ] || "",
+ version: match[ 2 ] || "0"
+ };
+ };
+ jQuery.browser = {};
+ jQuery.browser[jQuery.uaMatch(navigator.userAgent).browser] = true;
+}
+
+/**
+ * Small JavaScript module for the documentation.
+ */
+var Documentation = {
+
+ init : function() {
+ this.fixFirefoxAnchorBug();
+ this.highlightSearchWords();
+ this.initIndexTable();
+ if (DOCUMENTATION_OPTIONS.NAVIGATION_WITH_KEYS) {
+ this.initOnKeyListeners();
+ }
+ },
+
+ /**
+ * i18n support
+ */
+ TRANSLATIONS : {},
+ PLURAL_EXPR : function(n) { return n === 1 ? 0 : 1; },
+ LOCALE : 'unknown',
+
+ // gettext and ngettext don't access this so that the functions
+ // can safely bound to a different name (_ = Documentation.gettext)
+ gettext : function(string) {
+ var translated = Documentation.TRANSLATIONS[string];
+ if (typeof translated === 'undefined')
+ return string;
+ return (typeof translated === 'string') ? translated : translated[0];
+ },
+
+ ngettext : function(singular, plural, n) {
+ var translated = Documentation.TRANSLATIONS[singular];
+ if (typeof translated === 'undefined')
+ return (n == 1) ? singular : plural;
+ return translated[Documentation.PLURALEXPR(n)];
+ },
+
+ addTranslations : function(catalog) {
+ for (var key in catalog.messages)
+ this.TRANSLATIONS[key] = catalog.messages[key];
+ this.PLURAL_EXPR = new Function('n', 'return +(' + catalog.plural_expr + ')');
+ this.LOCALE = catalog.locale;
+ },
+
+ /**
+ * add context elements like header anchor links
+ */
+ addContextElements : function() {
+ $('div[id] > :header:first').each(function() {
+ $('<a class="headerlink">\u00B6</a>').
+ attr('href', '#' + this.id).
+ attr('title', _('Permalink to this headline')).
+ appendTo(this);
+ });
+ $('dt[id]').each(function() {
+ $('<a class="headerlink">\u00B6</a>').
+ attr('href', '#' + this.id).
+ attr('title', _('Permalink to this definition')).
+ appendTo(this);
+ });
+ },
+
+ /**
+ * workaround a firefox stupidity
+ * see: https://bugzilla.mozilla.org/show_bug.cgi?id=645075
+ */
+ fixFirefoxAnchorBug : function() {
+ if (document.location.hash && $.browser.mozilla)
+ window.setTimeout(function() {
+ document.location.href += '';
+ }, 10);
+ },
+
+ /**
+ * highlight the search words provided in the url in the text
+ */
+ highlightSearchWords : function() {
+ var params = $.getQueryParameters();
+ var terms = (params.highlight) ? params.highlight[0].split(/\s+/) : [];
+ if (terms.length) {
+ var body = $('div.body');
+ if (!body.length) {
+ body = $('body');
+ }
+ window.setTimeout(function() {
+ $.each(terms, function() {
+ body.highlightText(this.toLowerCase(), 'highlighted');
+ });
+ }, 10);
+ $('<p class="highlight-link"><a href="javascript:Documentation.' +
+ 'hideSearchWords()">' + _('Hide Search Matches') + '</a></p>')
+ .appendTo($('#searchbox'));
+ }
+ },
+
+ /**
+ * init the domain index toggle buttons
+ */
+ initIndexTable : function() {
+ var togglers = $('img.toggler').click(function() {
+ var src = $(this).attr('src');
+ var idnum = $(this).attr('id').substr(7);
+ $('tr.cg-' + idnum).toggle();
+ if (src.substr(-9) === 'minus.png')
+ $(this).attr('src', src.substr(0, src.length-9) + 'plus.png');
+ else
+ $(this).attr('src', src.substr(0, src.length-8) + 'minus.png');
+ }).css('display', '');
+ if (DOCUMENTATION_OPTIONS.COLLAPSE_INDEX) {
+ togglers.click();
+ }
+ },
+
+ /**
+ * helper function to hide the search marks again
+ */
+ hideSearchWords : function() {
+ $('#searchbox .highlight-link').fadeOut(300);
+ $('span.highlighted').removeClass('highlighted');
+ },
+
+ /**
+ * make the url absolute
+ */
+ makeURL : function(relativeURL) {
+ return DOCUMENTATION_OPTIONS.URL_ROOT + '/' + relativeURL;
+ },
+
+ /**
+ * get the current relative url
+ */
+ getCurrentURL : function() {
+ var path = document.location.pathname;
+ var parts = path.split(/\//);
+ $.each(DOCUMENTATION_OPTIONS.URL_ROOT.split(/\//), function() {
+ if (this === '..')
+ parts.pop();
+ });
+ var url = parts.join('/');
+ return path.substring(url.lastIndexOf('/') + 1, path.length - 1);
+ },
+
+ initOnKeyListeners: function() {
+ $(document).keydown(function(event) {
+ var activeElementType = document.activeElement.tagName;
+ // don't navigate when in search box, textarea, dropdown or button
+ if (activeElementType !== 'TEXTAREA' && activeElementType !== 'INPUT' && activeElementType !== 'SELECT'
+ && activeElementType !== 'BUTTON' && !event.altKey && !event.ctrlKey && !event.metaKey
+ && !event.shiftKey) {
+ switch (event.keyCode) {
+ case 37: // left
+ var prevHref = $('link[rel="prev"]').prop('href');
+ if (prevHref) {
+ window.location.href = prevHref;
+ return false;
+ }
+ break;
+ case 39: // right
+ var nextHref = $('link[rel="next"]').prop('href');
+ if (nextHref) {
+ window.location.href = nextHref;
+ return false;
+ }
+ break;
+ }
+ }
+ });
+ }
+};
+
+// quick alias for translations
+_ = Documentation.gettext;
+
+$(document).ready(function() {
+ Documentation.init();
+});
diff --git a/_static/documentation_options.js b/_static/documentation_options.js
new file mode 100644
index 00000000000..4daa6b50bdf
--- /dev/null
+++ b/_static/documentation_options.js
@@ -0,0 +1,12 @@
+var DOCUMENTATION_OPTIONS = {
+ URL_ROOT: document.getElementById("documentation_options").getAttribute('data-url_root'),
+ VERSION: '',
+ LANGUAGE: 'en',
+ COLLAPSE_INDEX: false,
+ BUILDER: 'html',
+ FILE_SUFFIX: '.html',
+ LINK_SUFFIX: '.html',
+ HAS_SOURCE: true,
+ SOURCELINK_SUFFIX: '.txt',
+ NAVIGATION_WITH_KEYS: false
+};
\ No newline at end of file
diff --git a/_static/file.png b/_static/file.png
new file mode 100644
index 00000000000..a858a410e4f
Binary files /dev/null and b/_static/file.png differ
diff --git a/icon.png b/_static/icon.png
similarity index 100%
rename from icon.png
rename to _static/icon.png
diff --git a/_static/img/doc_ci.png b/_static/img/doc_ci.png
new file mode 100644
index 00000000000..a9a73f7e927
Binary files /dev/null and b/_static/img/doc_ci.png differ
diff --git a/_static/jquery-3.5.1.js b/_static/jquery-3.5.1.js
new file mode 100644
index 00000000000..50937333b99
--- /dev/null
+++ b/_static/jquery-3.5.1.js
@@ -0,0 +1,10872 @@
+/*!
+ * jQuery JavaScript Library v3.5.1
+ * https://jquery.com/
+ *
+ * Includes Sizzle.js
+ * https://sizzlejs.com/
+ *
+ * Copyright JS Foundation and other contributors
+ * Released under the MIT license
+ * https://jquery.org/license
+ *
+ * Date: 2020-05-04T22:49Z
+ */
+( function( global, factory ) {
+
+ "use strict";
+
+ if ( typeof module === "object" && typeof module.exports === "object" ) {
+
+ // For CommonJS and CommonJS-like environments where a proper `window`
+ // is present, execute the factory and get jQuery.
+ // For environments that do not have a `window` with a `document`
+ // (such as Node.js), expose a factory as module.exports.
+ // This accentuates the need for the creation of a real `window`.
+ // e.g. var jQuery = require("jquery")(window);
+ // See ticket #14549 for more info.
+ module.exports = global.document ?
+ factory( global, true ) :
+ function( w ) {
+ if ( !w.document ) {
+ throw new Error( "jQuery requires a window with a document" );
+ }
+ return factory( w );
+ };
+ } else {
+ factory( global );
+ }
+
+// Pass this if window is not defined yet
+} )( typeof window !== "undefined" ? window : this, function( window, noGlobal ) {
+
+// Edge <= 12 - 13+, Firefox <=18 - 45+, IE 10 - 11, Safari 5.1 - 9+, iOS 6 - 9.1
+// throw exceptions when non-strict code (e.g., ASP.NET 4.5) accesses strict mode
+// arguments.callee.caller (trac-13335). But as of jQuery 3.0 (2016), strict mode should be common
+// enough that all such attempts are guarded in a try block.
+"use strict";
+
+var arr = [];
+
+var getProto = Object.getPrototypeOf;
+
+var slice = arr.slice;
+
+var flat = arr.flat ? function( array ) {
+ return arr.flat.call( array );
+} : function( array ) {
+ return arr.concat.apply( [], array );
+};
+
+
+var push = arr.push;
+
+var indexOf = arr.indexOf;
+
+var class2type = {};
+
+var toString = class2type.toString;
+
+var hasOwn = class2type.hasOwnProperty;
+
+var fnToString = hasOwn.toString;
+
+var ObjectFunctionString = fnToString.call( Object );
+
+var support = {};
+
+var isFunction = function isFunction( obj ) {
+
+ // Support: Chrome <=57, Firefox <=52
+ // In some browsers, typeof returns "function" for HTML <object> elements
+ // (i.e., `typeof document.createElement( "object" ) === "function"`).
+ // We don't want to classify *any* DOM node as a function.
+ return typeof obj === "function" && typeof obj.nodeType !== "number";
+ };
+
+
+var isWindow = function isWindow( obj ) {
+ return obj != null && obj === obj.window;
+ };
+
+
+var document = window.document;
+
+
+
+ var preservedScriptAttributes = {
+ type: true,
+ src: true,
+ nonce: true,
+ noModule: true
+ };
+
+ function DOMEval( code, node, doc ) {
+ doc = doc || document;
+
+ var i, val,
+ script = doc.createElement( "script" );
+
+ script.text = code;
+ if ( node ) {
+ for ( i in preservedScriptAttributes ) {
+
+ // Support: Firefox 64+, Edge 18+
+ // Some browsers don't support the "nonce" property on scripts.
+ // On the other hand, just using `getAttribute` is not enough as
+ // the `nonce` attribute is reset to an empty string whenever it
+ // becomes browsing-context connected.
+ // See https://github.com/whatwg/html/issues/2369
+ // See https://html.spec.whatwg.org/#nonce-attributes
+ // The `node.getAttribute` check was added for the sake of
+ // `jQuery.globalEval` so that it can fake a nonce-containing node
+ // via an object.
+ val = node[ i ] || node.getAttribute && node.getAttribute( i );
+ if ( val ) {
+ script.setAttribute( i, val );
+ }
+ }
+ }
+ doc.head.appendChild( script ).parentNode.removeChild( script );
+ }
+
+
+function toType( obj ) {
+ if ( obj == null ) {
+ return obj + "";
+ }
+
+ // Support: Android <=2.3 only (functionish RegExp)
+ return typeof obj === "object" || typeof obj === "function" ?
+ class2type[ toString.call( obj ) ] || "object" :
+ typeof obj;
+}
+/* global Symbol */
+// Defining this global in .eslintrc.json would create a danger of using the global
+// unguarded in another place, it seems safer to define global only for this module
+
+
+
+var
+ version = "3.5.1",
+
+ // Define a local copy of jQuery
+ jQuery = function( selector, context ) {
+
+ // The jQuery object is actually just the init constructor 'enhanced'
+ // Need init if jQuery is called (just allow error to be thrown if not included)
+ return new jQuery.fn.init( selector, context );
+ };
+
+jQuery.fn = jQuery.prototype = {
+
+ // The current version of jQuery being used
+ jquery: version,
+
+ constructor: jQuery,
+
+ // The default length of a jQuery object is 0
+ length: 0,
+
+ toArray: function() {
+ return slice.call( this );
+ },
+
+ // Get the Nth element in the matched element set OR
+ // Get the whole matched element set as a clean array
+ get: function( num ) {
+
+ // Return all the elements in a clean array
+ if ( num == null ) {
+ return slice.call( this );
+ }
+
+ // Return just the one element from the set
+ return num < 0 ? this[ num + this.length ] : this[ num ];
+ },
+
+ // Take an array of elements and push it onto the stack
+ // (returning the new matched element set)
+ pushStack: function( elems ) {
+
+ // Build a new jQuery matched element set
+ var ret = jQuery.merge( this.constructor(), elems );
+
+ // Add the old object onto the stack (as a reference)
+ ret.prevObject = this;
+
+ // Return the newly-formed element set
+ return ret;
+ },
+
+ // Execute a callback for every element in the matched set.
+ each: function( callback ) {
+ return jQuery.each( this, callback );
+ },
+
+ map: function( callback ) {
+ return this.pushStack( jQuery.map( this, function( elem, i ) {
+ return callback.call( elem, i, elem );
+ } ) );
+ },
+
+ slice: function() {
+ return this.pushStack( slice.apply( this, arguments ) );
+ },
+
+ first: function() {
+ return this.eq( 0 );
+ },
+
+ last: function() {
+ return this.eq( -1 );
+ },
+
+ even: function() {
+ return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+ return ( i + 1 ) % 2;
+ } ) );
+ },
+
+ odd: function() {
+ return this.pushStack( jQuery.grep( this, function( _elem, i ) {
+ return i % 2;
+ } ) );
+ },
+
+ eq: function( i ) {
+ var len = this.length,
+ j = +i + ( i < 0 ? len : 0 );
+ return this.pushStack( j >= 0 && j < len ? [ this[ j ] ] : [] );
+ },
+
+ end: function() {
+ return this.prevObject || this.constructor();
+ },
+
+ // For internal use only.
+ // Behaves like an Array's method, not like a jQuery method.
+ push: push,
+ sort: arr.sort,
+ splice: arr.splice
+};
+
+jQuery.extend = jQuery.fn.extend = function() {
+ var options, name, src, copy, copyIsArray, clone,
+ target = arguments[ 0 ] || {},
+ i = 1,
+ length = arguments.length,
+ deep = false;
+
+ // Handle a deep copy situation
+ if ( typeof target === "boolean" ) {
+ deep = target;
+
+ // Skip the boolean and the target
+ target = arguments[ i ] || {};
+ i++;
+ }
+
+ // Handle case when target is a string or something (possible in deep copy)
+ if ( typeof target !== "object" && !isFunction( target ) ) {
+ target = {};
+ }
+
+ // Extend jQuery itself if only one argument is passed
+ if ( i === length ) {
+ target = this;
+ i--;
+ }
+
+ for ( ; i < length; i++ ) {
+
+ // Only deal with non-null/undefined values
+ if ( ( options = arguments[ i ] ) != null ) {
+
+ // Extend the base object
+ for ( name in options ) {
+ copy = options[ name ];
+
+ // Prevent Object.prototype pollution
+ // Prevent never-ending loop
+ if ( name === "__proto__" || target === copy ) {
+ continue;
+ }
+
+ // Recurse if we're merging plain objects or arrays
+ if ( deep && copy && ( jQuery.isPlainObject( copy ) ||
+ ( copyIsArray = Array.isArray( copy ) ) ) ) {
+ src = target[ name ];
+
+ // Ensure proper type for the source value
+ if ( copyIsArray && !Array.isArray( src ) ) {
+ clone = [];
+ } else if ( !copyIsArray && !jQuery.isPlainObject( src ) ) {
+ clone = {};
+ } else {
+ clone = src;
+ }
+ copyIsArray = false;
+
+ // Never move original objects, clone them
+ target[ name ] = jQuery.extend( deep, clone, copy );
+
+ // Don't bring in undefined values
+ } else if ( copy !== undefined ) {
+ target[ name ] = copy;
+ }
+ }
+ }
+ }
+
+ // Return the modified object
+ return target;
+};
+
+jQuery.extend( {
+
+ // Unique for each copy of jQuery on the page
+ expando: "jQuery" + ( version + Math.random() ).replace( /\D/g, "" ),
+
+ // Assume jQuery is ready without the ready module
+ isReady: true,
+
+ error: function( msg ) {
+ throw new Error( msg );
+ },
+
+ noop: function() {},
+
+ isPlainObject: function( obj ) {
+ var proto, Ctor;
+
+ // Detect obvious negatives
+ // Use toString instead of jQuery.type to catch host objects
+ if ( !obj || toString.call( obj ) !== "[object Object]" ) {
+ return false;
+ }
+
+ proto = getProto( obj );
+
+ // Objects with no prototype (e.g., `Object.create( null )`) are plain
+ if ( !proto ) {
+ return true;
+ }
+
+ // Objects with prototype are plain iff they were constructed by a global Object function
+ Ctor = hasOwn.call( proto, "constructor" ) && proto.constructor;
+ return typeof Ctor === "function" && fnToString.call( Ctor ) === ObjectFunctionString;
+ },
+
+ isEmptyObject: function( obj ) {
+ var name;
+
+ for ( name in obj ) {
+ return false;
+ }
+ return true;
+ },
+
+ // Evaluates a script in a provided context; falls back to the global one
+ // if not specified.
+ globalEval: function( code, options, doc ) {
+ DOMEval( code, { nonce: options && options.nonce }, doc );
+ },
+
+ each: function( obj, callback ) {
+ var length, i = 0;
+
+ if ( isArrayLike( obj ) ) {
+ length = obj.length;
+ for ( ; i < length; i++ ) {
+ if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+ break;
+ }
+ }
+ } else {
+ for ( i in obj ) {
+ if ( callback.call( obj[ i ], i, obj[ i ] ) === false ) {
+ break;
+ }
+ }
+ }
+
+ return obj;
+ },
+
+ // results is for internal usage only
+ makeArray: function( arr, results ) {
+ var ret = results || [];
+
+ if ( arr != null ) {
+ if ( isArrayLike( Object( arr ) ) ) {
+ jQuery.merge( ret,
+ typeof arr === "string" ?
+ [ arr ] : arr
+ );
+ } else {
+ push.call( ret, arr );
+ }
+ }
+
+ return ret;
+ },
+
+ inArray: function( elem, arr, i ) {
+ return arr == null ? -1 : indexOf.call( arr, elem, i );
+ },
+
+ // Support: Android <=4.0 only, PhantomJS 1 only
+ // push.apply(_, arraylike) throws on ancient WebKit
+ merge: function( first, second ) {
+ var len = +second.length,
+ j = 0,
+ i = first.length;
+
+ for ( ; j < len; j++ ) {
+ first[ i++ ] = second[ j ];
+ }
+
+ first.length = i;
+
+ return first;
+ },
+
+ grep: function( elems, callback, invert ) {
+ var callbackInverse,
+ matches = [],
+ i = 0,
+ length = elems.length,
+ callbackExpect = !invert;
+
+ // Go through the array, only saving the items
+ // that pass the validator function
+ for ( ; i < length; i++ ) {
+ callbackInverse = !callback( elems[ i ], i );
+ if ( callbackInverse !== callbackExpect ) {
+ matches.push( elems[ i ] );
+ }
+ }
+
+ return matches;
+ },
+
+ // arg is for internal usage only
+ map: function( elems, callback, arg ) {
+ var length, value,
+ i = 0,
+ ret = [];
+
+ // Go through the array, translating each of the items to their new values
+ if ( isArrayLike( elems ) ) {
+ length = elems.length;
+ for ( ; i < length; i++ ) {
+ value = callback( elems[ i ], i, arg );
+
+ if ( value != null ) {
+ ret.push( value );
+ }
+ }
+
+ // Go through every key on the object,
+ } else {
+ for ( i in elems ) {
+ value = callback( elems[ i ], i, arg );
+
+ if ( value != null ) {
+ ret.push( value );
+ }
+ }
+ }
+
+ // Flatten any nested arrays
+ return flat( ret );
+ },
+
+ // A global GUID counter for objects
+ guid: 1,
+
+ // jQuery.support is not used in Core but other projects attach their
+ // properties to it so it needs to exist.
+ support: support
+} );
+
+if ( typeof Symbol === "function" ) {
+ jQuery.fn[ Symbol.iterator ] = arr[ Symbol.iterator ];
+}
+
+// Populate the class2type map
+jQuery.each( "Boolean Number String Function Array Date RegExp Object Error Symbol".split( " " ),
+function( _i, name ) {
+ class2type[ "[object " + name + "]" ] = name.toLowerCase();
+} );
+
+function isArrayLike( obj ) {
+
+ // Support: real iOS 8.2 only (not reproducible in simulator)
+ // `in` check used to prevent JIT error (gh-2145)
+ // hasOwn isn't used here due to false negatives
+ // regarding Nodelist length in IE
+ var length = !!obj && "length" in obj && obj.length,
+ type = toType( obj );
+
+ if ( isFunction( obj ) || isWindow( obj ) ) {
+ return false;
+ }
+
+ return type === "array" || length === 0 ||
+ typeof length === "number" && length > 0 && ( length - 1 ) in obj;
+}
+var Sizzle =
+/*!
+ * Sizzle CSS Selector Engine v2.3.5
+ * https://sizzlejs.com/
+ *
+ * Copyright JS Foundation and other contributors
+ * Released under the MIT license
+ * https://js.foundation/
+ *
+ * Date: 2020-03-14
+ */
+( function( window ) {
+var i,
+ support,
+ Expr,
+ getText,
+ isXML,
+ tokenize,
+ compile,
+ select,
+ outermostContext,
+ sortInput,
+ hasDuplicate,
+
+ // Local document vars
+ setDocument,
+ document,
+ docElem,
+ documentIsHTML,
+ rbuggyQSA,
+ rbuggyMatches,
+ matches,
+ contains,
+
+ // Instance-specific data
+ expando = "sizzle" + 1 * new Date(),
+ preferredDoc = window.document,
+ dirruns = 0,
+ done = 0,
+ classCache = createCache(),
+ tokenCache = createCache(),
+ compilerCache = createCache(),
+ nonnativeSelectorCache = createCache(),
+ sortOrder = function( a, b ) {
+ if ( a === b ) {
+ hasDuplicate = true;
+ }
+ return 0;
+ },
+
+ // Instance methods
+ hasOwn = ( {} ).hasOwnProperty,
+ arr = [],
+ pop = arr.pop,
+ pushNative = arr.push,
+ push = arr.push,
+ slice = arr.slice,
+
+ // Use a stripped-down indexOf as it's faster than native
+ // https://jsperf.com/thor-indexof-vs-for/5
+ indexOf = function( list, elem ) {
+ var i = 0,
+ len = list.length;
+ for ( ; i < len; i++ ) {
+ if ( list[ i ] === elem ) {
+ return i;
+ }
+ }
+ return -1;
+ },
+
+ booleans = "checked|selected|async|autofocus|autoplay|controls|defer|disabled|hidden|" +
+ "ismap|loop|multiple|open|readonly|required|scoped",
+
+ // Regular expressions
+
+ // http://www.w3.org/TR/css3-selectors/#whitespace
+ whitespace = "[\\x20\\t\\r\\n\\f]",
+
+ // https://www.w3.org/TR/css-syntax-3/#ident-token-diagram
+ identifier = "(?:\\\\[\\da-fA-F]{1,6}" + whitespace +
+ "?|\\\\[^\\r\\n\\f]|[\\w-]|[^\0-\\x7f])+",
+
+ // Attribute selectors: http://www.w3.org/TR/selectors/#attribute-selectors
+ attributes = "\\[" + whitespace + "*(" + identifier + ")(?:" + whitespace +
+
+ // Operator (capture 2)
+ "*([*^$|!~]?=)" + whitespace +
+
+ // "Attribute values must be CSS identifiers [capture 5]
+ // or strings [capture 3 or capture 4]"
+ "*(?:'((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\"|(" + identifier + "))|)" +
+ whitespace + "*\\]",
+
+ pseudos = ":(" + identifier + ")(?:\\((" +
+
+ // To reduce the number of selectors needing tokenize in the preFilter, prefer arguments:
+ // 1. quoted (capture 3; capture 4 or capture 5)
+ "('((?:\\\\.|[^\\\\'])*)'|\"((?:\\\\.|[^\\\\\"])*)\")|" +
+
+ // 2. simple (capture 6)
+ "((?:\\\\.|[^\\\\()[\\]]|" + attributes + ")*)|" +
+
+ // 3. anything else (capture 2)
+ ".*" +
+ ")\\)|)",
+
+ // Leading and non-escaped trailing whitespace, capturing some non-whitespace characters preceding the latter
+ rwhitespace = new RegExp( whitespace + "+", "g" ),
+ rtrim = new RegExp( "^" + whitespace + "+|((?:^|[^\\\\])(?:\\\\.)*)" +
+ whitespace + "+$", "g" ),
+
+ rcomma = new RegExp( "^" + whitespace + "*," + whitespace + "*" ),
+ rcombinators = new RegExp( "^" + whitespace + "*([>+~]|" + whitespace + ")" + whitespace +
+ "*" ),
+ rdescend = new RegExp( whitespace + "|>" ),
+
+ rpseudo = new RegExp( pseudos ),
+ ridentifier = new RegExp( "^" + identifier + "$" ),
+
+ matchExpr = {
+ "ID": new RegExp( "^#(" + identifier + ")" ),
+ "CLASS": new RegExp( "^\\.(" + identifier + ")" ),
+ "TAG": new RegExp( "^(" + identifier + "|[*])" ),
+ "ATTR": new RegExp( "^" + attributes ),
+ "PSEUDO": new RegExp( "^" + pseudos ),
+ "CHILD": new RegExp( "^:(only|first|last|nth|nth-last)-(child|of-type)(?:\\(" +
+ whitespace + "*(even|odd|(([+-]|)(\\d*)n|)" + whitespace + "*(?:([+-]|)" +
+ whitespace + "*(\\d+)|))" + whitespace + "*\\)|)", "i" ),
+ "bool": new RegExp( "^(?:" + booleans + ")$", "i" ),
+
+ // For use in libraries implementing .is()
+ // We use this for POS matching in `select`
+ "needsContext": new RegExp( "^" + whitespace +
+ "*[>+~]|:(even|odd|eq|gt|lt|nth|first|last)(?:\\(" + whitespace +
+ "*((?:-\\d)?\\d*)" + whitespace + "*\\)|)(?=[^-]|$)", "i" )
+ },
+
+ rhtml = /HTML$/i,
+ rinputs = /^(?:input|select|textarea|button)$/i,
+ rheader = /^h\d$/i,
+
+ rnative = /^[^{]+\{\s*\[native \w/,
+
+ // Easily-parseable/retrievable ID or TAG or CLASS selectors
+ rquickExpr = /^(?:#([\w-]+)|(\w+)|\.([\w-]+))$/,
+
+ rsibling = /[+~]/,
+
+ // CSS escapes
+ // http://www.w3.org/TR/CSS21/syndata.html#escaped-characters
+ runescape = new RegExp( "\\\\[\\da-fA-F]{1,6}" + whitespace + "?|\\\\([^\\r\\n\\f])", "g" ),
+ funescape = function( escape, nonHex ) {
+ var high = "0x" + escape.slice( 1 ) - 0x10000;
+
+ return nonHex ?
+
+ // Strip the backslash prefix from a non-hex escape sequence
+ nonHex :
+
+ // Replace a hexadecimal escape sequence with the encoded Unicode code point
+ // Support: IE <=11+
+ // For values outside the Basic Multilingual Plane (BMP), manually construct a
+ // surrogate pair
+ high < 0 ?
+ String.fromCharCode( high + 0x10000 ) :
+ String.fromCharCode( high >> 10 | 0xD800, high & 0x3FF | 0xDC00 );
+ },
+
+ // CSS string/identifier serialization
+ // https://drafts.csswg.org/cssom/#common-serializing-idioms
+ rcssescape = /([\0-\x1f\x7f]|^-?\d)|^-$|[^\0-\x1f\x7f-\uFFFF\w-]/g,
+ fcssescape = function( ch, asCodePoint ) {
+ if ( asCodePoint ) {
+
+ // U+0000 NULL becomes U+FFFD REPLACEMENT CHARACTER
+ if ( ch === "\0" ) {
+ return "\uFFFD";
+ }
+
+ // Control characters and (dependent upon position) numbers get escaped as code points
+ return ch.slice( 0, -1 ) + "\\" +
+ ch.charCodeAt( ch.length - 1 ).toString( 16 ) + " ";
+ }
+
+ // Other potentially-special ASCII characters get backslash-escaped
+ return "\\" + ch;
+ },
+
+ // Used for iframes
+ // See setDocument()
+ // Removing the function wrapper causes a "Permission Denied"
+ // error in IE
+ unloadHandler = function() {
+ setDocument();
+ },
+
+ inDisabledFieldset = addCombinator(
+ function( elem ) {
+ return elem.disabled === true && elem.nodeName.toLowerCase() === "fieldset";
+ },
+ { dir: "parentNode", next: "legend" }
+ );
+
+// Optimize for push.apply( _, NodeList )
+try {
+ push.apply(
+ ( arr = slice.call( preferredDoc.childNodes ) ),
+ preferredDoc.childNodes
+ );
+
+ // Support: Android<4.0
+ // Detect silently failing push.apply
+ // eslint-disable-next-line no-unused-expressions
+ arr[ preferredDoc.childNodes.length ].nodeType;
+} catch ( e ) {
+ push = { apply: arr.length ?
+
+ // Leverage slice if possible
+ function( target, els ) {
+ pushNative.apply( target, slice.call( els ) );
+ } :
+
+ // Support: IE<9
+ // Otherwise append directly
+ function( target, els ) {
+ var j = target.length,
+ i = 0;
+
+ // Can't trust NodeList.length
+ while ( ( target[ j++ ] = els[ i++ ] ) ) {}
+ target.length = j - 1;
+ }
+ };
+}
+
+function Sizzle( selector, context, results, seed ) {
+ var m, i, elem, nid, match, groups, newSelector,
+ newContext = context && context.ownerDocument,
+
+ // nodeType defaults to 9, since context defaults to document
+ nodeType = context ? context.nodeType : 9;
+
+ results = results || [];
+
+ // Return early from calls with invalid selector or context
+ if ( typeof selector !== "string" || !selector ||
+ nodeType !== 1 && nodeType !== 9 && nodeType !== 11 ) {
+
+ return results;
+ }
+
+ // Try to shortcut find operations (as opposed to filters) in HTML documents
+ if ( !seed ) {
+ setDocument( context );
+ context = context || document;
+
+ if ( documentIsHTML ) {
+
+ // If the selector is sufficiently simple, try using a "get*By*" DOM method
+ // (excepting DocumentFragment context, where the methods don't exist)
+ if ( nodeType !== 11 && ( match = rquickExpr.exec( selector ) ) ) {
+
+ // ID selector
+ if ( ( m = match[ 1 ] ) ) {
+
+ // Document context
+ if ( nodeType === 9 ) {
+ if ( ( elem = context.getElementById( m ) ) ) {
+
+ // Support: IE, Opera, Webkit
+ // TODO: identify versions
+ // getElementById can match elements by name instead of ID
+ if ( elem.id === m ) {
+ results.push( elem );
+ return results;
+ }
+ } else {
+ return results;
+ }
+
+ // Element context
+ } else {
+
+ // Support: IE, Opera, Webkit
+ // TODO: identify versions
+ // getElementById can match elements by name instead of ID
+ if ( newContext && ( elem = newContext.getElementById( m ) ) &&
+ contains( context, elem ) &&
+ elem.id === m ) {
+
+ results.push( elem );
+ return results;
+ }
+ }
+
+ // Type selector
+ } else if ( match[ 2 ] ) {
+ push.apply( results, context.getElementsByTagName( selector ) );
+ return results;
+
+ // Class selector
+ } else if ( ( m = match[ 3 ] ) && support.getElementsByClassName &&
+ context.getElementsByClassName ) {
+
+ push.apply( results, context.getElementsByClassName( m ) );
+ return results;
+ }
+ }
+
+ // Take advantage of querySelectorAll
+ if ( support.qsa &&
+ !nonnativeSelectorCache[ selector + " " ] &&
+ ( !rbuggyQSA || !rbuggyQSA.test( selector ) ) &&
+
+ // Support: IE 8 only
+ // Exclude object elements
+ ( nodeType !== 1 || context.nodeName.toLowerCase() !== "object" ) ) {
+
+ newSelector = selector;
+ newContext = context;
+
+ // qSA considers elements outside a scoping root when evaluating child or
+ // descendant combinators, which is not what we want.
+ // In such cases, we work around the behavior by prefixing every selector in the
+ // list with an ID selector referencing the scope context.
+ // The technique has to be used as well when a leading combinator is used
+ // as such selectors are not recognized by querySelectorAll.
+ // Thanks to Andrew Dupont for this technique.
+ if ( nodeType === 1 &&
+ ( rdescend.test( selector ) || rcombinators.test( selector ) ) ) {
+
+ // Expand context for sibling selectors
+ newContext = rsibling.test( selector ) && testContext( context.parentNode ) ||
+ context;
+
+ // We can use :scope instead of the ID hack if the browser
+ // supports it & if we're not changing the context.
+ if ( newContext !== context || !support.scope ) {
+
+ // Capture the context ID, setting it first if necessary
+ if ( ( nid = context.getAttribute( "id" ) ) ) {
+ nid = nid.replace( rcssescape, fcssescape );
+ } else {
+ context.setAttribute( "id", ( nid = expando ) );
+ }
+ }
+
+ // Prefix every selector in the list
+ groups = tokenize( selector );
+ i = groups.length;
+ while ( i-- ) {
+ groups[ i ] = ( nid ? "#" + nid : ":scope" ) + " " +
+ toSelector( groups[ i ] );
+ }
+ newSelector = groups.join( "," );
+ }
+
+ try {
+ push.apply( results,
+ newContext.querySelectorAll( newSelector )
+ );
+ return results;
+ } catch ( qsaError ) {
+ nonnativeSelectorCache( selector, true );
+ } finally {
+ if ( nid === expando ) {
+ context.removeAttribute( "id" );
+ }
+ }
+ }
+ }
+ }
+
+ // All others
+ return select( selector.replace( rtrim, "$1" ), context, results, seed );
+}
+
+/**
+ * Create key-value caches of limited size
+ * @returns {function(string, object)} Returns the Object data after storing it on itself with
+ * property name the (space-suffixed) string and (if the cache is larger than Expr.cacheLength)
+ * deleting the oldest entry
+ */
+function createCache() {
+ var keys = [];
+
+ function cache( key, value ) {
+
+ // Use (key + " ") to avoid collision with native prototype properties (see Issue #157)
+ if ( keys.push( key + " " ) > Expr.cacheLength ) {
+
+ // Only keep the most recent entries
+ delete cache[ keys.shift() ];
+ }
+ return ( cache[ key + " " ] = value );
+ }
+ return cache;
+}
+
+/**
+ * Mark a function for special use by Sizzle
+ * @param {Function} fn The function to mark
+ */
+function markFunction( fn ) {
+ fn[ expando ] = true;
+ return fn;
+}
+
+/**
+ * Support testing using an element
+ * @param {Function} fn Passed the created element and returns a boolean result
+ */
+function assert( fn ) {
+ var el = document.createElement( "fieldset" );
+
+ try {
+ return !!fn( el );
+ } catch ( e ) {
+ return false;
+ } finally {
+
+ // Remove from its parent by default
+ if ( el.parentNode ) {
+ el.parentNode.removeChild( el );
+ }
+
+ // release memory in IE
+ el = null;
+ }
+}
+
+/**
+ * Adds the same handler for all of the specified attrs
+ * @param {String} attrs Pipe-separated list of attributes
+ * @param {Function} handler The method that will be applied
+ */
+function addHandle( attrs, handler ) {
+ var arr = attrs.split( "|" ),
+ i = arr.length;
+
+ while ( i-- ) {
+ Expr.attrHandle[ arr[ i ] ] = handler;
+ }
+}
+
+/**
+ * Checks document order of two siblings
+ * @param {Element} a
+ * @param {Element} b
+ * @returns {Number} Returns less than 0 if a precedes b, greater than 0 if a follows b
+ */
+function siblingCheck( a, b ) {
+ var cur = b && a,
+ diff = cur && a.nodeType === 1 && b.nodeType === 1 &&
+ a.sourceIndex - b.sourceIndex;
+
+ // Use IE sourceIndex if available on both nodes
+ if ( diff ) {
+ return diff;
+ }
+
+ // Check if b follows a
+ if ( cur ) {
+ while ( ( cur = cur.nextSibling ) ) {
+ if ( cur === b ) {
+ return -1;
+ }
+ }
+ }
+
+ return a ? 1 : -1;
+}
+
+/**
+ * Returns a function to use in pseudos for input types
+ * @param {String} type
+ */
+function createInputPseudo( type ) {
+ return function( elem ) {
+ var name = elem.nodeName.toLowerCase();
+ return name === "input" && elem.type === type;
+ };
+}
+
+/**
+ * Returns a function to use in pseudos for buttons
+ * @param {String} type
+ */
+function createButtonPseudo( type ) {
+ return function( elem ) {
+ var name = elem.nodeName.toLowerCase();
+ return ( name === "input" || name === "button" ) && elem.type === type;
+ };
+}
+
+/**
+ * Returns a function to use in pseudos for :enabled/:disabled
+ * @param {Boolean} disabled true for :disabled; false for :enabled
+ */
+function createDisabledPseudo( disabled ) {
+
+ // Known :disabled false positives: fieldset[disabled] > legend:nth-of-type(n+2) :can-disable
+ return function( elem ) {
+
+ // Only certain elements can match :enabled or :disabled
+ // https://html.spec.whatwg.org/multipage/scripting.html#selector-enabled
+ // https://html.spec.whatwg.org/multipage/scripting.html#selector-disabled
+ if ( "form" in elem ) {
+
+ // Check for inherited disabledness on relevant non-disabled elements:
+ // * listed form-associated elements in a disabled fieldset
+ // https://html.spec.whatwg.org/multipage/forms.html#category-listed
+ // https://html.spec.whatwg.org/multipage/forms.html#concept-fe-disabled
+ // * option elements in a disabled optgroup
+ // https://html.spec.whatwg.org/multipage/forms.html#concept-option-disabled
+ // All such elements have a "form" property.
+ if ( elem.parentNode && elem.disabled === false ) {
+
+ // Option elements defer to a parent optgroup if present
+ if ( "label" in elem ) {
+ if ( "label" in elem.parentNode ) {
+ return elem.parentNode.disabled === disabled;
+ } else {
+ return elem.disabled === disabled;
+ }
+ }
+
+ // Support: IE 6 - 11
+ // Use the isDisabled shortcut property to check for disabled fieldset ancestors
+ return elem.isDisabled === disabled ||
+
+ // Where there is no isDisabled, check manually
+ /* jshint -W018 */
+ elem.isDisabled !== !disabled &&
+ inDisabledFieldset( elem ) === disabled;
+ }
+
+ return elem.disabled === disabled;
+
+ // Try to winnow out elements that can't be disabled before trusting the disabled property.
+ // Some victims get caught in our net (label, legend, menu, track), but it shouldn't
+ // even exist on them, let alone have a boolean value.
+ } else if ( "label" in elem ) {
+ return elem.disabled === disabled;
+ }
+
+ // Remaining elements are neither :enabled nor :disabled
+ return false;
+ };
+}
+
+/**
+ * Returns a function to use in pseudos for positionals
+ * @param {Function} fn
+ */
+function createPositionalPseudo( fn ) {
+ return markFunction( function( argument ) {
+ argument = +argument;
+ return markFunction( function( seed, matches ) {
+ var j,
+ matchIndexes = fn( [], seed.length, argument ),
+ i = matchIndexes.length;
+
+ // Match elements found at the specified indexes
+ while ( i-- ) {
+ if ( seed[ ( j = matchIndexes[ i ] ) ] ) {
+ seed[ j ] = !( matches[ j ] = seed[ j ] );
+ }
+ }
+ } );
+ } );
+}
+
+/**
+ * Checks a node for validity as a Sizzle context
+ * @param {Element|Object=} context
+ * @returns {Element|Object|Boolean} The input node if acceptable, otherwise a falsy value
+ */
+function testContext( context ) {
+ return context && typeof context.getElementsByTagName !== "undefined" && context;
+}
+
+// Expose support vars for convenience
+support = Sizzle.support = {};
+
+/**
+ * Detects XML nodes
+ * @param {Element|Object} elem An element or a document
+ * @returns {Boolean} True iff elem is a non-HTML XML node
+ */
+isXML = Sizzle.isXML = function( elem ) {
+ var namespace = elem.namespaceURI,
+ docElem = ( elem.ownerDocument || elem ).documentElement;
+
+ // Support: IE <=8
+ // Assume HTML when documentElement doesn't yet exist, such as inside loading iframes
+ // https://bugs.jquery.com/ticket/4833
+ return !rhtml.test( namespace || docElem && docElem.nodeName || "HTML" );
+};
+
+/**
+ * Sets document-related variables once based on the current document
+ * @param {Element|Object} [doc] An element or document object to use to set the document
+ * @returns {Object} Returns the current document
+ */
+setDocument = Sizzle.setDocument = function( node ) {
+ var hasCompare, subWindow,
+ doc = node ? node.ownerDocument || node : preferredDoc;
+
+ // Return early if doc is invalid or already selected
+ // Support: IE 11+, Edge 17 - 18+
+ // IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+ // two documents; shallow comparisons work.
+ // eslint-disable-next-line eqeqeq
+ if ( doc == document || doc.nodeType !== 9 || !doc.documentElement ) {
+ return document;
+ }
+
+ // Update global variables
+ document = doc;
+ docElem = document.documentElement;
+ documentIsHTML = !isXML( document );
+
+ // Support: IE 9 - 11+, Edge 12 - 18+
+ // Accessing iframe documents after unload throws "permission denied" errors (jQuery #13936)
+ // Support: IE 11+, Edge 17 - 18+
+ // IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+ // two documents; shallow comparisons work.
+ // eslint-disable-next-line eqeqeq
+ if ( preferredDoc != document &&
+ ( subWindow = document.defaultView ) && subWindow.top !== subWindow ) {
+
+ // Support: IE 11, Edge
+ if ( subWindow.addEventListener ) {
+ subWindow.addEventListener( "unload", unloadHandler, false );
+
+ // Support: IE 9 - 10 only
+ } else if ( subWindow.attachEvent ) {
+ subWindow.attachEvent( "onunload", unloadHandler );
+ }
+ }
+
+ // Support: IE 8 - 11+, Edge 12 - 18+, Chrome <=16 - 25 only, Firefox <=3.6 - 31 only,
+ // Safari 4 - 5 only, Opera <=11.6 - 12.x only
+ // IE/Edge & older browsers don't support the :scope pseudo-class.
+ // Support: Safari 6.0 only
+ // Safari 6.0 supports :scope but it's an alias of :root there.
+ support.scope = assert( function( el ) {
+ docElem.appendChild( el ).appendChild( document.createElement( "div" ) );
+ return typeof el.querySelectorAll !== "undefined" &&
+ !el.querySelectorAll( ":scope fieldset div" ).length;
+ } );
+
+ /* Attributes
+ ---------------------------------------------------------------------- */
+
+ // Support: IE<8
+ // Verify that getAttribute really returns attributes and not properties
+ // (excepting IE8 booleans)
+ support.attributes = assert( function( el ) {
+ el.className = "i";
+ return !el.getAttribute( "className" );
+ } );
+
+ /* getElement(s)By*
+ ---------------------------------------------------------------------- */
+
+ // Check if getElementsByTagName("*") returns only elements
+ support.getElementsByTagName = assert( function( el ) {
+ el.appendChild( document.createComment( "" ) );
+ return !el.getElementsByTagName( "*" ).length;
+ } );
+
+ // Support: IE<9
+ support.getElementsByClassName = rnative.test( document.getElementsByClassName );
+
+ // Support: IE<10
+ // Check if getElementById returns elements by name
+ // The broken getElementById methods don't pick up programmatically-set names,
+ // so use a roundabout getElementsByName test
+ support.getById = assert( function( el ) {
+ docElem.appendChild( el ).id = expando;
+ return !document.getElementsByName || !document.getElementsByName( expando ).length;
+ } );
+
+ // ID filter and find
+ if ( support.getById ) {
+ Expr.filter[ "ID" ] = function( id ) {
+ var attrId = id.replace( runescape, funescape );
+ return function( elem ) {
+ return elem.getAttribute( "id" ) === attrId;
+ };
+ };
+ Expr.find[ "ID" ] = function( id, context ) {
+ if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+ var elem = context.getElementById( id );
+ return elem ? [ elem ] : [];
+ }
+ };
+ } else {
+ Expr.filter[ "ID" ] = function( id ) {
+ var attrId = id.replace( runescape, funescape );
+ return function( elem ) {
+ var node = typeof elem.getAttributeNode !== "undefined" &&
+ elem.getAttributeNode( "id" );
+ return node && node.value === attrId;
+ };
+ };
+
+ // Support: IE 6 - 7 only
+ // getElementById is not reliable as a find shortcut
+ Expr.find[ "ID" ] = function( id, context ) {
+ if ( typeof context.getElementById !== "undefined" && documentIsHTML ) {
+ var node, i, elems,
+ elem = context.getElementById( id );
+
+ if ( elem ) {
+
+ // Verify the id attribute
+ node = elem.getAttributeNode( "id" );
+ if ( node && node.value === id ) {
+ return [ elem ];
+ }
+
+ // Fall back on getElementsByName
+ elems = context.getElementsByName( id );
+ i = 0;
+ while ( ( elem = elems[ i++ ] ) ) {
+ node = elem.getAttributeNode( "id" );
+ if ( node && node.value === id ) {
+ return [ elem ];
+ }
+ }
+ }
+
+ return [];
+ }
+ };
+ }
+
+ // Tag
+ Expr.find[ "TAG" ] = support.getElementsByTagName ?
+ function( tag, context ) {
+ if ( typeof context.getElementsByTagName !== "undefined" ) {
+ return context.getElementsByTagName( tag );
+
+ // DocumentFragment nodes don't have gEBTN
+ } else if ( support.qsa ) {
+ return context.querySelectorAll( tag );
+ }
+ } :
+
+ function( tag, context ) {
+ var elem,
+ tmp = [],
+ i = 0,
+
+ // By happy coincidence, a (broken) gEBTN appears on DocumentFragment nodes too
+ results = context.getElementsByTagName( tag );
+
+ // Filter out possible comments
+ if ( tag === "*" ) {
+ while ( ( elem = results[ i++ ] ) ) {
+ if ( elem.nodeType === 1 ) {
+ tmp.push( elem );
+ }
+ }
+
+ return tmp;
+ }
+ return results;
+ };
+
+ // Class
+ Expr.find[ "CLASS" ] = support.getElementsByClassName && function( className, context ) {
+ if ( typeof context.getElementsByClassName !== "undefined" && documentIsHTML ) {
+ return context.getElementsByClassName( className );
+ }
+ };
+
+ /* QSA/matchesSelector
+ ---------------------------------------------------------------------- */
+
+ // QSA and matchesSelector support
+
+ // matchesSelector(:active) reports false when true (IE9/Opera 11.5)
+ rbuggyMatches = [];
+
+ // qSa(:focus) reports false when true (Chrome 21)
+ // We allow this because of a bug in IE8/9 that throws an error
+ // whenever `document.activeElement` is accessed on an iframe
+ // So, we allow :focus to pass through QSA all the time to avoid the IE error
+ // See https://bugs.jquery.com/ticket/13378
+ rbuggyQSA = [];
+
+ if ( ( support.qsa = rnative.test( document.querySelectorAll ) ) ) {
+
+ // Build QSA regex
+ // Regex strategy adopted from Diego Perini
+ assert( function( el ) {
+
+ var input;
+
+ // Select is set to empty string on purpose
+ // This is to test IE's treatment of not explicitly
+ // setting a boolean content attribute,
+ // since its presence should be enough
+ // https://bugs.jquery.com/ticket/12359
+ docElem.appendChild( el ).innerHTML = "<a id='" + expando + "'></a>" +
+ "<select id='" + expando + "-\r\\' msallowcapture=''>" +
+ "<option selected=''></option></select>";
+
+ // Support: IE8, Opera 11-12.16
+ // Nothing should be selected when empty strings follow ^= or $= or *=
+ // The test attribute must be unknown in Opera but "safe" for WinRT
+ // https://msdn.microsoft.com/en-us/library/ie/hh465388.aspx#attribute_section
+ if ( el.querySelectorAll( "[msallowcapture^='']" ).length ) {
+ rbuggyQSA.push( "[*^$]=" + whitespace + "*(?:''|\"\")" );
+ }
+
+ // Support: IE8
+ // Boolean attributes and "value" are not treated correctly
+ if ( !el.querySelectorAll( "[selected]" ).length ) {
+ rbuggyQSA.push( "\\[" + whitespace + "*(?:value|" + booleans + ")" );
+ }
+
+ // Support: Chrome<29, Android<4.4, Safari<7.0+, iOS<7.0+, PhantomJS<1.9.8+
+ if ( !el.querySelectorAll( "[id~=" + expando + "-]" ).length ) {
+ rbuggyQSA.push( "~=" );
+ }
+
+ // Support: IE 11+, Edge 15 - 18+
+ // IE 11/Edge don't find elements on a `[name='']` query in some cases.
+ // Adding a temporary attribute to the document before the selection works
+ // around the issue.
+ // Interestingly, IE 10 & older don't seem to have the issue.
+ input = document.createElement( "input" );
+ input.setAttribute( "name", "" );
+ el.appendChild( input );
+ if ( !el.querySelectorAll( "[name='']" ).length ) {
+ rbuggyQSA.push( "\\[" + whitespace + "*name" + whitespace + "*=" +
+ whitespace + "*(?:''|\"\")" );
+ }
+
+ // Webkit/Opera - :checked should return selected option elements
+ // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+ // IE8 throws error here and will not see later tests
+ if ( !el.querySelectorAll( ":checked" ).length ) {
+ rbuggyQSA.push( ":checked" );
+ }
+
+ // Support: Safari 8+, iOS 8+
+ // https://bugs.webkit.org/show_bug.cgi?id=136851
+ // In-page `selector#id sibling-combinator selector` fails
+ if ( !el.querySelectorAll( "a#" + expando + "+*" ).length ) {
+ rbuggyQSA.push( ".#.+[+~]" );
+ }
+
+ // Support: Firefox <=3.6 - 5 only
+ // Old Firefox doesn't throw on a badly-escaped identifier.
+ el.querySelectorAll( "\\\f" );
+ rbuggyQSA.push( "[\\r\\n\\f]" );
+ } );
+
+ assert( function( el ) {
+ el.innerHTML = "<a href='' disabled='disabled'></a>" +
+ "<select disabled='disabled'><option/></select>";
+
+ // Support: Windows 8 Native Apps
+ // The type and name attributes are restricted during .innerHTML assignment
+ var input = document.createElement( "input" );
+ input.setAttribute( "type", "hidden" );
+ el.appendChild( input ).setAttribute( "name", "D" );
+
+ // Support: IE8
+ // Enforce case-sensitivity of name attribute
+ if ( el.querySelectorAll( "[name=d]" ).length ) {
+ rbuggyQSA.push( "name" + whitespace + "*[*^$|!~]?=" );
+ }
+
+ // FF 3.5 - :enabled/:disabled and hidden elements (hidden elements are still enabled)
+ // IE8 throws error here and will not see later tests
+ if ( el.querySelectorAll( ":enabled" ).length !== 2 ) {
+ rbuggyQSA.push( ":enabled", ":disabled" );
+ }
+
+ // Support: IE9-11+
+ // IE's :disabled selector does not pick up the children of disabled fieldsets
+ docElem.appendChild( el ).disabled = true;
+ if ( el.querySelectorAll( ":disabled" ).length !== 2 ) {
+ rbuggyQSA.push( ":enabled", ":disabled" );
+ }
+
+ // Support: Opera 10 - 11 only
+ // Opera 10-11 does not throw on post-comma invalid pseudos
+ el.querySelectorAll( "*,:x" );
+ rbuggyQSA.push( ",.*:" );
+ } );
+ }
+
+ if ( ( support.matchesSelector = rnative.test( ( matches = docElem.matches ||
+ docElem.webkitMatchesSelector ||
+ docElem.mozMatchesSelector ||
+ docElem.oMatchesSelector ||
+ docElem.msMatchesSelector ) ) ) ) {
+
+ assert( function( el ) {
+
+ // Check to see if it's possible to do matchesSelector
+ // on a disconnected node (IE 9)
+ support.disconnectedMatch = matches.call( el, "*" );
+
+ // This should fail with an exception
+ // Gecko does not error, returns false instead
+ matches.call( el, "[s!='']:x" );
+ rbuggyMatches.push( "!=", pseudos );
+ } );
+ }
+
+ rbuggyQSA = rbuggyQSA.length && new RegExp( rbuggyQSA.join( "|" ) );
+ rbuggyMatches = rbuggyMatches.length && new RegExp( rbuggyMatches.join( "|" ) );
+
+ /* Contains
+ ---------------------------------------------------------------------- */
+ hasCompare = rnative.test( docElem.compareDocumentPosition );
+
+ // Element contains another
+ // Purposefully self-exclusive
+ // As in, an element does not contain itself
+ contains = hasCompare || rnative.test( docElem.contains ) ?
+ function( a, b ) {
+ var adown = a.nodeType === 9 ? a.documentElement : a,
+ bup = b && b.parentNode;
+ return a === bup || !!( bup && bup.nodeType === 1 && (
+ adown.contains ?
+ adown.contains( bup ) :
+ a.compareDocumentPosition && a.compareDocumentPosition( bup ) & 16
+ ) );
+ } :
+ function( a, b ) {
+ if ( b ) {
+ while ( ( b = b.parentNode ) ) {
+ if ( b === a ) {
+ return true;
+ }
+ }
+ }
+ return false;
+ };
+
+ /* Sorting
+ ---------------------------------------------------------------------- */
+
+ // Document order sorting
+ sortOrder = hasCompare ?
+ function( a, b ) {
+
+ // Flag for duplicate removal
+ if ( a === b ) {
+ hasDuplicate = true;
+ return 0;
+ }
+
+ // Sort on method existence if only one input has compareDocumentPosition
+ var compare = !a.compareDocumentPosition - !b.compareDocumentPosition;
+ if ( compare ) {
+ return compare;
+ }
+
+ // Calculate position if both inputs belong to the same document
+ // Support: IE 11+, Edge 17 - 18+
+ // IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+ // two documents; shallow comparisons work.
+ // eslint-disable-next-line eqeqeq
+ compare = ( a.ownerDocument || a ) == ( b.ownerDocument || b ) ?
+ a.compareDocumentPosition( b ) :
+
+ // Otherwise we know they are disconnected
+ 1;
+
+ // Disconnected nodes
+ if ( compare & 1 ||
+ ( !support.sortDetached && b.compareDocumentPosition( a ) === compare ) ) {
+
+ // Choose the first element that is related to our preferred document
+ // Support: IE 11+, Edge 17 - 18+
+ // IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+ // two documents; shallow comparisons work.
+ // eslint-disable-next-line eqeqeq
+ if ( a == document || a.ownerDocument == preferredDoc &&
+ contains( preferredDoc, a ) ) {
+ return -1;
+ }
+
+ // Support: IE 11+, Edge 17 - 18+
+ // IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+ // two documents; shallow comparisons work.
+ // eslint-disable-next-line eqeqeq
+ if ( b == document || b.ownerDocument == preferredDoc &&
+ contains( preferredDoc, b ) ) {
+ return 1;
+ }
+
+ // Maintain original order
+ return sortInput ?
+ ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+ 0;
+ }
+
+ return compare & 4 ? -1 : 1;
+ } :
+ function( a, b ) {
+
+ // Exit early if the nodes are identical
+ if ( a === b ) {
+ hasDuplicate = true;
+ return 0;
+ }
+
+ var cur,
+ i = 0,
+ aup = a.parentNode,
+ bup = b.parentNode,
+ ap = [ a ],
+ bp = [ b ];
+
+ // Parentless nodes are either documents or disconnected
+ if ( !aup || !bup ) {
+
+ // Support: IE 11+, Edge 17 - 18+
+ // IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+ // two documents; shallow comparisons work.
+ /* eslint-disable eqeqeq */
+ return a == document ? -1 :
+ b == document ? 1 :
+ /* eslint-enable eqeqeq */
+ aup ? -1 :
+ bup ? 1 :
+ sortInput ?
+ ( indexOf( sortInput, a ) - indexOf( sortInput, b ) ) :
+ 0;
+
+ // If the nodes are siblings, we can do a quick check
+ } else if ( aup === bup ) {
+ return siblingCheck( a, b );
+ }
+
+ // Otherwise we need full lists of their ancestors for comparison
+ cur = a;
+ while ( ( cur = cur.parentNode ) ) {
+ ap.unshift( cur );
+ }
+ cur = b;
+ while ( ( cur = cur.parentNode ) ) {
+ bp.unshift( cur );
+ }
+
+ // Walk down the tree looking for a discrepancy
+ while ( ap[ i ] === bp[ i ] ) {
+ i++;
+ }
+
+ return i ?
+
+ // Do a sibling check if the nodes have a common ancestor
+ siblingCheck( ap[ i ], bp[ i ] ) :
+
+ // Otherwise nodes in our document sort first
+ // Support: IE 11+, Edge 17 - 18+
+ // IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+ // two documents; shallow comparisons work.
+ /* eslint-disable eqeqeq */
+ ap[ i ] == preferredDoc ? -1 :
+ bp[ i ] == preferredDoc ? 1 :
+ /* eslint-enable eqeqeq */
+ 0;
+ };
+
+ return document;
+};
+
+Sizzle.matches = function( expr, elements ) {
+ return Sizzle( expr, null, null, elements );
+};
+
+Sizzle.matchesSelector = function( elem, expr ) {
+ setDocument( elem );
+
+ if ( support.matchesSelector && documentIsHTML &&
+ !nonnativeSelectorCache[ expr + " " ] &&
+ ( !rbuggyMatches || !rbuggyMatches.test( expr ) ) &&
+ ( !rbuggyQSA || !rbuggyQSA.test( expr ) ) ) {
+
+ try {
+ var ret = matches.call( elem, expr );
+
+ // IE 9's matchesSelector returns false on disconnected nodes
+ if ( ret || support.disconnectedMatch ||
+
+ // As well, disconnected nodes are said to be in a document
+ // fragment in IE 9
+ elem.document && elem.document.nodeType !== 11 ) {
+ return ret;
+ }
+ } catch ( e ) {
+ nonnativeSelectorCache( expr, true );
+ }
+ }
+
+ return Sizzle( expr, document, null, [ elem ] ).length > 0;
+};
+
+Sizzle.contains = function( context, elem ) {
+
+ // Set document vars if needed
+ // Support: IE 11+, Edge 17 - 18+
+ // IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+ // two documents; shallow comparisons work.
+ // eslint-disable-next-line eqeqeq
+ if ( ( context.ownerDocument || context ) != document ) {
+ setDocument( context );
+ }
+ return contains( context, elem );
+};
+
+Sizzle.attr = function( elem, name ) {
+
+ // Set document vars if needed
+ // Support: IE 11+, Edge 17 - 18+
+ // IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+ // two documents; shallow comparisons work.
+ // eslint-disable-next-line eqeqeq
+ if ( ( elem.ownerDocument || elem ) != document ) {
+ setDocument( elem );
+ }
+
+ var fn = Expr.attrHandle[ name.toLowerCase() ],
+
+ // Don't get fooled by Object.prototype properties (jQuery #13807)
+ val = fn && hasOwn.call( Expr.attrHandle, name.toLowerCase() ) ?
+ fn( elem, name, !documentIsHTML ) :
+ undefined;
+
+ return val !== undefined ?
+ val :
+ support.attributes || !documentIsHTML ?
+ elem.getAttribute( name ) :
+ ( val = elem.getAttributeNode( name ) ) && val.specified ?
+ val.value :
+ null;
+};
+
+Sizzle.escape = function( sel ) {
+ return ( sel + "" ).replace( rcssescape, fcssescape );
+};
+
+Sizzle.error = function( msg ) {
+ throw new Error( "Syntax error, unrecognized expression: " + msg );
+};
+
+/**
+ * Document sorting and removing duplicates
+ * @param {ArrayLike} results
+ */
+Sizzle.uniqueSort = function( results ) {
+ var elem,
+ duplicates = [],
+ j = 0,
+ i = 0;
+
+ // Unless we *know* we can detect duplicates, assume their presence
+ hasDuplicate = !support.detectDuplicates;
+ sortInput = !support.sortStable && results.slice( 0 );
+ results.sort( sortOrder );
+
+ if ( hasDuplicate ) {
+ while ( ( elem = results[ i++ ] ) ) {
+ if ( elem === results[ i ] ) {
+ j = duplicates.push( i );
+ }
+ }
+ while ( j-- ) {
+ results.splice( duplicates[ j ], 1 );
+ }
+ }
+
+ // Clear input after sorting to release objects
+ // See https://github.com/jquery/sizzle/pull/225
+ sortInput = null;
+
+ return results;
+};
+
+/**
+ * Utility function for retrieving the text value of an array of DOM nodes
+ * @param {Array|Element} elem
+ */
+getText = Sizzle.getText = function( elem ) {
+ var node,
+ ret = "",
+ i = 0,
+ nodeType = elem.nodeType;
+
+ if ( !nodeType ) {
+
+ // If no nodeType, this is expected to be an array
+ while ( ( node = elem[ i++ ] ) ) {
+
+ // Do not traverse comment nodes
+ ret += getText( node );
+ }
+ } else if ( nodeType === 1 || nodeType === 9 || nodeType === 11 ) {
+
+ // Use textContent for elements
+ // innerText usage removed for consistency of new lines (jQuery #11153)
+ if ( typeof elem.textContent === "string" ) {
+ return elem.textContent;
+ } else {
+
+ // Traverse its children
+ for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+ ret += getText( elem );
+ }
+ }
+ } else if ( nodeType === 3 || nodeType === 4 ) {
+ return elem.nodeValue;
+ }
+
+ // Do not include comment or processing instruction nodes
+
+ return ret;
+};
+
+Expr = Sizzle.selectors = {
+
+ // Can be adjusted by the user
+ cacheLength: 50,
+
+ createPseudo: markFunction,
+
+ match: matchExpr,
+
+ attrHandle: {},
+
+ find: {},
+
+ relative: {
+ ">": { dir: "parentNode", first: true },
+ " ": { dir: "parentNode" },
+ "+": { dir: "previousSibling", first: true },
+ "~": { dir: "previousSibling" }
+ },
+
+ preFilter: {
+ "ATTR": function( match ) {
+ match[ 1 ] = match[ 1 ].replace( runescape, funescape );
+
+ // Move the given value to match[3] whether quoted or unquoted
+ match[ 3 ] = ( match[ 3 ] || match[ 4 ] ||
+ match[ 5 ] || "" ).replace( runescape, funescape );
+
+ if ( match[ 2 ] === "~=" ) {
+ match[ 3 ] = " " + match[ 3 ] + " ";
+ }
+
+ return match.slice( 0, 4 );
+ },
+
+ "CHILD": function( match ) {
+
+ /* matches from matchExpr["CHILD"]
+ 1 type (only|nth|...)
+ 2 what (child|of-type)
+ 3 argument (even|odd|\d*|\d*n([+-]\d+)?|...)
+ 4 xn-component of xn+y argument ([+-]?\d*n|)
+ 5 sign of xn-component
+ 6 x of xn-component
+ 7 sign of y-component
+ 8 y of y-component
+ */
+ match[ 1 ] = match[ 1 ].toLowerCase();
+
+ if ( match[ 1 ].slice( 0, 3 ) === "nth" ) {
+
+ // nth-* requires argument
+ if ( !match[ 3 ] ) {
+ Sizzle.error( match[ 0 ] );
+ }
+
+ // numeric x and y parameters for Expr.filter.CHILD
+ // remember that false/true cast respectively to 0/1
+ match[ 4 ] = +( match[ 4 ] ?
+ match[ 5 ] + ( match[ 6 ] || 1 ) :
+ 2 * ( match[ 3 ] === "even" || match[ 3 ] === "odd" ) );
+ match[ 5 ] = +( ( match[ 7 ] + match[ 8 ] ) || match[ 3 ] === "odd" );
+
+ // other types prohibit arguments
+ } else if ( match[ 3 ] ) {
+ Sizzle.error( match[ 0 ] );
+ }
+
+ return match;
+ },
+
+ "PSEUDO": function( match ) {
+ var excess,
+ unquoted = !match[ 6 ] && match[ 2 ];
+
+ if ( matchExpr[ "CHILD" ].test( match[ 0 ] ) ) {
+ return null;
+ }
+
+ // Accept quoted arguments as-is
+ if ( match[ 3 ] ) {
+ match[ 2 ] = match[ 4 ] || match[ 5 ] || "";
+
+ // Strip excess characters from unquoted arguments
+ } else if ( unquoted && rpseudo.test( unquoted ) &&
+
+ // Get excess from tokenize (recursively)
+ ( excess = tokenize( unquoted, true ) ) &&
+
+ // advance to the next closing parenthesis
+ ( excess = unquoted.indexOf( ")", unquoted.length - excess ) - unquoted.length ) ) {
+
+ // excess is a negative index
+ match[ 0 ] = match[ 0 ].slice( 0, excess );
+ match[ 2 ] = unquoted.slice( 0, excess );
+ }
+
+ // Return only captures needed by the pseudo filter method (type and argument)
+ return match.slice( 0, 3 );
+ }
+ },
+
+ filter: {
+
+ "TAG": function( nodeNameSelector ) {
+ var nodeName = nodeNameSelector.replace( runescape, funescape ).toLowerCase();
+ return nodeNameSelector === "*" ?
+ function() {
+ return true;
+ } :
+ function( elem ) {
+ return elem.nodeName && elem.nodeName.toLowerCase() === nodeName;
+ };
+ },
+
+ "CLASS": function( className ) {
+ var pattern = classCache[ className + " " ];
+
+ return pattern ||
+ ( pattern = new RegExp( "(^|" + whitespace +
+ ")" + className + "(" + whitespace + "|$)" ) ) && classCache(
+ className, function( elem ) {
+ return pattern.test(
+ typeof elem.className === "string" && elem.className ||
+ typeof elem.getAttribute !== "undefined" &&
+ elem.getAttribute( "class" ) ||
+ ""
+ );
+ } );
+ },
+
+ "ATTR": function( name, operator, check ) {
+ return function( elem ) {
+ var result = Sizzle.attr( elem, name );
+
+ if ( result == null ) {
+ return operator === "!=";
+ }
+ if ( !operator ) {
+ return true;
+ }
+
+ result += "";
+
+ /* eslint-disable max-len */
+
+ return operator === "=" ? result === check :
+ operator === "!=" ? result !== check :
+ operator === "^=" ? check && result.indexOf( check ) === 0 :
+ operator === "*=" ? check && result.indexOf( check ) > -1 :
+ operator === "$=" ? check && result.slice( -check.length ) === check :
+ operator === "~=" ? ( " " + result.replace( rwhitespace, " " ) + " " ).indexOf( check ) > -1 :
+ operator === "|=" ? result === check || result.slice( 0, check.length + 1 ) === check + "-" :
+ false;
+ /* eslint-enable max-len */
+
+ };
+ },
+
+ "CHILD": function( type, what, _argument, first, last ) {
+ var simple = type.slice( 0, 3 ) !== "nth",
+ forward = type.slice( -4 ) !== "last",
+ ofType = what === "of-type";
+
+ return first === 1 && last === 0 ?
+
+ // Shortcut for :nth-*(n)
+ function( elem ) {
+ return !!elem.parentNode;
+ } :
+
+ function( elem, _context, xml ) {
+ var cache, uniqueCache, outerCache, node, nodeIndex, start,
+ dir = simple !== forward ? "nextSibling" : "previousSibling",
+ parent = elem.parentNode,
+ name = ofType && elem.nodeName.toLowerCase(),
+ useCache = !xml && !ofType,
+ diff = false;
+
+ if ( parent ) {
+
+ // :(first|last|only)-(child|of-type)
+ if ( simple ) {
+ while ( dir ) {
+ node = elem;
+ while ( ( node = node[ dir ] ) ) {
+ if ( ofType ?
+ node.nodeName.toLowerCase() === name :
+ node.nodeType === 1 ) {
+
+ return false;
+ }
+ }
+
+ // Reverse direction for :only-* (if we haven't yet done so)
+ start = dir = type === "only" && !start && "nextSibling";
+ }
+ return true;
+ }
+
+ start = [ forward ? parent.firstChild : parent.lastChild ];
+
+ // non-xml :nth-child(...) stores cache data on `parent`
+ if ( forward && useCache ) {
+
+ // Seek `elem` from a previously-cached index
+
+ // ...in a gzip-friendly way
+ node = parent;
+ outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+ // Support: IE <9 only
+ // Defend against cloned attroperties (jQuery gh-1709)
+ uniqueCache = outerCache[ node.uniqueID ] ||
+ ( outerCache[ node.uniqueID ] = {} );
+
+ cache = uniqueCache[ type ] || [];
+ nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+ diff = nodeIndex && cache[ 2 ];
+ node = nodeIndex && parent.childNodes[ nodeIndex ];
+
+ while ( ( node = ++nodeIndex && node && node[ dir ] ||
+
+ // Fallback to seeking `elem` from the start
+ ( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+ // When found, cache indexes on `parent` and break
+ if ( node.nodeType === 1 && ++diff && node === elem ) {
+ uniqueCache[ type ] = [ dirruns, nodeIndex, diff ];
+ break;
+ }
+ }
+
+ } else {
+
+ // Use previously-cached element index if available
+ if ( useCache ) {
+
+ // ...in a gzip-friendly way
+ node = elem;
+ outerCache = node[ expando ] || ( node[ expando ] = {} );
+
+ // Support: IE <9 only
+ // Defend against cloned attroperties (jQuery gh-1709)
+ uniqueCache = outerCache[ node.uniqueID ] ||
+ ( outerCache[ node.uniqueID ] = {} );
+
+ cache = uniqueCache[ type ] || [];
+ nodeIndex = cache[ 0 ] === dirruns && cache[ 1 ];
+ diff = nodeIndex;
+ }
+
+ // xml :nth-child(...)
+ // or :nth-last-child(...) or :nth(-last)?-of-type(...)
+ if ( diff === false ) {
+
+ // Use the same loop as above to seek `elem` from the start
+ while ( ( node = ++nodeIndex && node && node[ dir ] ||
+ ( diff = nodeIndex = 0 ) || start.pop() ) ) {
+
+ if ( ( ofType ?
+ node.nodeName.toLowerCase() === name :
+ node.nodeType === 1 ) &&
+ ++diff ) {
+
+ // Cache the index of each encountered element
+ if ( useCache ) {
+ outerCache = node[ expando ] ||
+ ( node[ expando ] = {} );
+
+ // Support: IE <9 only
+ // Defend against cloned attroperties (jQuery gh-1709)
+ uniqueCache = outerCache[ node.uniqueID ] ||
+ ( outerCache[ node.uniqueID ] = {} );
+
+ uniqueCache[ type ] = [ dirruns, diff ];
+ }
+
+ if ( node === elem ) {
+ break;
+ }
+ }
+ }
+ }
+ }
+
+ // Incorporate the offset, then check against cycle size
+ diff -= last;
+ return diff === first || ( diff % first === 0 && diff / first >= 0 );
+ }
+ };
+ },
+
+ "PSEUDO": function( pseudo, argument ) {
+
+ // pseudo-class names are case-insensitive
+ // http://www.w3.org/TR/selectors/#pseudo-classes
+ // Prioritize by case sensitivity in case custom pseudos are added with uppercase letters
+ // Remember that setFilters inherits from pseudos
+ var args,
+ fn = Expr.pseudos[ pseudo ] || Expr.setFilters[ pseudo.toLowerCase() ] ||
+ Sizzle.error( "unsupported pseudo: " + pseudo );
+
+ // The user may use createPseudo to indicate that
+ // arguments are needed to create the filter function
+ // just as Sizzle does
+ if ( fn[ expando ] ) {
+ return fn( argument );
+ }
+
+ // But maintain support for old signatures
+ if ( fn.length > 1 ) {
+ args = [ pseudo, pseudo, "", argument ];
+ return Expr.setFilters.hasOwnProperty( pseudo.toLowerCase() ) ?
+ markFunction( function( seed, matches ) {
+ var idx,
+ matched = fn( seed, argument ),
+ i = matched.length;
+ while ( i-- ) {
+ idx = indexOf( seed, matched[ i ] );
+ seed[ idx ] = !( matches[ idx ] = matched[ i ] );
+ }
+ } ) :
+ function( elem ) {
+ return fn( elem, 0, args );
+ };
+ }
+
+ return fn;
+ }
+ },
+
+ pseudos: {
+
+ // Potentially complex pseudos
+ "not": markFunction( function( selector ) {
+
+ // Trim the selector passed to compile
+ // to avoid treating leading and trailing
+ // spaces as combinators
+ var input = [],
+ results = [],
+ matcher = compile( selector.replace( rtrim, "$1" ) );
+
+ return matcher[ expando ] ?
+ markFunction( function( seed, matches, _context, xml ) {
+ var elem,
+ unmatched = matcher( seed, null, xml, [] ),
+ i = seed.length;
+
+ // Match elements unmatched by `matcher`
+ while ( i-- ) {
+ if ( ( elem = unmatched[ i ] ) ) {
+ seed[ i ] = !( matches[ i ] = elem );
+ }
+ }
+ } ) :
+ function( elem, _context, xml ) {
+ input[ 0 ] = elem;
+ matcher( input, null, xml, results );
+
+ // Don't keep the element (issue #299)
+ input[ 0 ] = null;
+ return !results.pop();
+ };
+ } ),
+
+ "has": markFunction( function( selector ) {
+ return function( elem ) {
+ return Sizzle( selector, elem ).length > 0;
+ };
+ } ),
+
+ "contains": markFunction( function( text ) {
+ text = text.replace( runescape, funescape );
+ return function( elem ) {
+ return ( elem.textContent || getText( elem ) ).indexOf( text ) > -1;
+ };
+ } ),
+
+ // "Whether an element is represented by a :lang() selector
+ // is based solely on the element's language value
+ // being equal to the identifier C,
+ // or beginning with the identifier C immediately followed by "-".
+ // The matching of C against the element's language value is performed case-insensitively.
+ // The identifier C does not have to be a valid language name."
+ // http://www.w3.org/TR/selectors/#lang-pseudo
+ "lang": markFunction( function( lang ) {
+
+ // lang value must be a valid identifier
+ if ( !ridentifier.test( lang || "" ) ) {
+ Sizzle.error( "unsupported lang: " + lang );
+ }
+ lang = lang.replace( runescape, funescape ).toLowerCase();
+ return function( elem ) {
+ var elemLang;
+ do {
+ if ( ( elemLang = documentIsHTML ?
+ elem.lang :
+ elem.getAttribute( "xml:lang" ) || elem.getAttribute( "lang" ) ) ) {
+
+ elemLang = elemLang.toLowerCase();
+ return elemLang === lang || elemLang.indexOf( lang + "-" ) === 0;
+ }
+ } while ( ( elem = elem.parentNode ) && elem.nodeType === 1 );
+ return false;
+ };
+ } ),
+
+ // Miscellaneous
+ "target": function( elem ) {
+ var hash = window.location && window.location.hash;
+ return hash && hash.slice( 1 ) === elem.id;
+ },
+
+ "root": function( elem ) {
+ return elem === docElem;
+ },
+
+ "focus": function( elem ) {
+ return elem === document.activeElement &&
+ ( !document.hasFocus || document.hasFocus() ) &&
+ !!( elem.type || elem.href || ~elem.tabIndex );
+ },
+
+ // Boolean properties
+ "enabled": createDisabledPseudo( false ),
+ "disabled": createDisabledPseudo( true ),
+
+ "checked": function( elem ) {
+
+ // In CSS3, :checked should return both checked and selected elements
+ // http://www.w3.org/TR/2011/REC-css3-selectors-20110929/#checked
+ var nodeName = elem.nodeName.toLowerCase();
+ return ( nodeName === "input" && !!elem.checked ) ||
+ ( nodeName === "option" && !!elem.selected );
+ },
+
+ "selected": function( elem ) {
+
+ // Accessing this property makes selected-by-default
+ // options in Safari work properly
+ if ( elem.parentNode ) {
+ // eslint-disable-next-line no-unused-expressions
+ elem.parentNode.selectedIndex;
+ }
+
+ return elem.selected === true;
+ },
+
+ // Contents
+ "empty": function( elem ) {
+
+ // http://www.w3.org/TR/selectors/#empty-pseudo
+ // :empty is negated by element (1) or content nodes (text: 3; cdata: 4; entity ref: 5),
+ // but not by others (comment: 8; processing instruction: 7; etc.)
+ // nodeType < 6 works because attributes (2) do not appear as children
+ for ( elem = elem.firstChild; elem; elem = elem.nextSibling ) {
+ if ( elem.nodeType < 6 ) {
+ return false;
+ }
+ }
+ return true;
+ },
+
+ "parent": function( elem ) {
+ return !Expr.pseudos[ "empty" ]( elem );
+ },
+
+ // Element/input types
+ "header": function( elem ) {
+ return rheader.test( elem.nodeName );
+ },
+
+ "input": function( elem ) {
+ return rinputs.test( elem.nodeName );
+ },
+
+ "button": function( elem ) {
+ var name = elem.nodeName.toLowerCase();
+ return name === "input" && elem.type === "button" || name === "button";
+ },
+
+ "text": function( elem ) {
+ var attr;
+ return elem.nodeName.toLowerCase() === "input" &&
+ elem.type === "text" &&
+
+ // Support: IE<8
+ // New HTML5 attribute values (e.g., "search") appear with elem.type === "text"
+ ( ( attr = elem.getAttribute( "type" ) ) == null ||
+ attr.toLowerCase() === "text" );
+ },
+
+ // Position-in-collection
+ "first": createPositionalPseudo( function() {
+ return [ 0 ];
+ } ),
+
+ "last": createPositionalPseudo( function( _matchIndexes, length ) {
+ return [ length - 1 ];
+ } ),
+
+ "eq": createPositionalPseudo( function( _matchIndexes, length, argument ) {
+ return [ argument < 0 ? argument + length : argument ];
+ } ),
+
+ "even": createPositionalPseudo( function( matchIndexes, length ) {
+ var i = 0;
+ for ( ; i < length; i += 2 ) {
+ matchIndexes.push( i );
+ }
+ return matchIndexes;
+ } ),
+
+ "odd": createPositionalPseudo( function( matchIndexes, length ) {
+ var i = 1;
+ for ( ; i < length; i += 2 ) {
+ matchIndexes.push( i );
+ }
+ return matchIndexes;
+ } ),
+
+ "lt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+ var i = argument < 0 ?
+ argument + length :
+ argument > length ?
+ length :
+ argument;
+ for ( ; --i >= 0; ) {
+ matchIndexes.push( i );
+ }
+ return matchIndexes;
+ } ),
+
+ "gt": createPositionalPseudo( function( matchIndexes, length, argument ) {
+ var i = argument < 0 ? argument + length : argument;
+ for ( ; ++i < length; ) {
+ matchIndexes.push( i );
+ }
+ return matchIndexes;
+ } )
+ }
+};
+
+Expr.pseudos[ "nth" ] = Expr.pseudos[ "eq" ];
+
+// Add button/input type pseudos
+for ( i in { radio: true, checkbox: true, file: true, password: true, image: true } ) {
+ Expr.pseudos[ i ] = createInputPseudo( i );
+}
+for ( i in { submit: true, reset: true } ) {
+ Expr.pseudos[ i ] = createButtonPseudo( i );
+}
+
+// Easy API for creating new setFilters
+function setFilters() {}
+setFilters.prototype = Expr.filters = Expr.pseudos;
+Expr.setFilters = new setFilters();
+
+tokenize = Sizzle.tokenize = function( selector, parseOnly ) {
+ var matched, match, tokens, type,
+ soFar, groups, preFilters,
+ cached = tokenCache[ selector + " " ];
+
+ if ( cached ) {
+ return parseOnly ? 0 : cached.slice( 0 );
+ }
+
+ soFar = selector;
+ groups = [];
+ preFilters = Expr.preFilter;
+
+ while ( soFar ) {
+
+ // Comma and first run
+ if ( !matched || ( match = rcomma.exec( soFar ) ) ) {
+ if ( match ) {
+
+ // Don't consume trailing commas as valid
+ soFar = soFar.slice( match[ 0 ].length ) || soFar;
+ }
+ groups.push( ( tokens = [] ) );
+ }
+
+ matched = false;
+
+ // Combinators
+ if ( ( match = rcombinators.exec( soFar ) ) ) {
+ matched = match.shift();
+ tokens.push( {
+ value: matched,
+
+ // Cast descendant combinators to space
+ type: match[ 0 ].replace( rtrim, " " )
+ } );
+ soFar = soFar.slice( matched.length );
+ }
+
+ // Filters
+ for ( type in Expr.filter ) {
+ if ( ( match = matchExpr[ type ].exec( soFar ) ) && ( !preFilters[ type ] ||
+ ( match = preFilters[ type ]( match ) ) ) ) {
+ matched = match.shift();
+ tokens.push( {
+ value: matched,
+ type: type,
+ matches: match
+ } );
+ soFar = soFar.slice( matched.length );
+ }
+ }
+
+ if ( !matched ) {
+ break;
+ }
+ }
+
+ // Return the length of the invalid excess
+ // if we're just parsing
+ // Otherwise, throw an error or return tokens
+ return parseOnly ?
+ soFar.length :
+ soFar ?
+ Sizzle.error( selector ) :
+
+ // Cache the tokens
+ tokenCache( selector, groups ).slice( 0 );
+};
+
+function toSelector( tokens ) {
+ var i = 0,
+ len = tokens.length,
+ selector = "";
+ for ( ; i < len; i++ ) {
+ selector += tokens[ i ].value;
+ }
+ return selector;
+}
+
+function addCombinator( matcher, combinator, base ) {
+ var dir = combinator.dir,
+ skip = combinator.next,
+ key = skip || dir,
+ checkNonElements = base && key === "parentNode",
+ doneName = done++;
+
+ return combinator.first ?
+
+ // Check against closest ancestor/preceding element
+ function( elem, context, xml ) {
+ while ( ( elem = elem[ dir ] ) ) {
+ if ( elem.nodeType === 1 || checkNonElements ) {
+ return matcher( elem, context, xml );
+ }
+ }
+ return false;
+ } :
+
+ // Check against all ancestor/preceding elements
+ function( elem, context, xml ) {
+ var oldCache, uniqueCache, outerCache,
+ newCache = [ dirruns, doneName ];
+
+ // We can't set arbitrary data on XML nodes, so they don't benefit from combinator caching
+ if ( xml ) {
+ while ( ( elem = elem[ dir ] ) ) {
+ if ( elem.nodeType === 1 || checkNonElements ) {
+ if ( matcher( elem, context, xml ) ) {
+ return true;
+ }
+ }
+ }
+ } else {
+ while ( ( elem = elem[ dir ] ) ) {
+ if ( elem.nodeType === 1 || checkNonElements ) {
+ outerCache = elem[ expando ] || ( elem[ expando ] = {} );
+
+ // Support: IE <9 only
+ // Defend against cloned attroperties (jQuery gh-1709)
+ uniqueCache = outerCache[ elem.uniqueID ] ||
+ ( outerCache[ elem.uniqueID ] = {} );
+
+ if ( skip && skip === elem.nodeName.toLowerCase() ) {
+ elem = elem[ dir ] || elem;
+ } else if ( ( oldCache = uniqueCache[ key ] ) &&
+ oldCache[ 0 ] === dirruns && oldCache[ 1 ] === doneName ) {
+
+ // Assign to newCache so results back-propagate to previous elements
+ return ( newCache[ 2 ] = oldCache[ 2 ] );
+ } else {
+
+ // Reuse newcache so results back-propagate to previous elements
+ uniqueCache[ key ] = newCache;
+
+ // A match means we're done; a fail means we have to keep checking
+ if ( ( newCache[ 2 ] = matcher( elem, context, xml ) ) ) {
+ return true;
+ }
+ }
+ }
+ }
+ }
+ return false;
+ };
+}
+
+function elementMatcher( matchers ) {
+ return matchers.length > 1 ?
+ function( elem, context, xml ) {
+ var i = matchers.length;
+ while ( i-- ) {
+ if ( !matchers[ i ]( elem, context, xml ) ) {
+ return false;
+ }
+ }
+ return true;
+ } :
+ matchers[ 0 ];
+}
+
+function multipleContexts( selector, contexts, results ) {
+ var i = 0,
+ len = contexts.length;
+ for ( ; i < len; i++ ) {
+ Sizzle( selector, contexts[ i ], results );
+ }
+ return results;
+}
+
+function condense( unmatched, map, filter, context, xml ) {
+ var elem,
+ newUnmatched = [],
+ i = 0,
+ len = unmatched.length,
+ mapped = map != null;
+
+ for ( ; i < len; i++ ) {
+ if ( ( elem = unmatched[ i ] ) ) {
+ if ( !filter || filter( elem, context, xml ) ) {
+ newUnmatched.push( elem );
+ if ( mapped ) {
+ map.push( i );
+ }
+ }
+ }
+ }
+
+ return newUnmatched;
+}
+
+function setMatcher( preFilter, selector, matcher, postFilter, postFinder, postSelector ) {
+ if ( postFilter && !postFilter[ expando ] ) {
+ postFilter = setMatcher( postFilter );
+ }
+ if ( postFinder && !postFinder[ expando ] ) {
+ postFinder = setMatcher( postFinder, postSelector );
+ }
+ return markFunction( function( seed, results, context, xml ) {
+ var temp, i, elem,
+ preMap = [],
+ postMap = [],
+ preexisting = results.length,
+
+ // Get initial elements from seed or context
+ elems = seed || multipleContexts(
+ selector || "*",
+ context.nodeType ? [ context ] : context,
+ []
+ ),
+
+ // Prefilter to get matcher input, preserving a map for seed-results synchronization
+ matcherIn = preFilter && ( seed || !selector ) ?
+ condense( elems, preMap, preFilter, context, xml ) :
+ elems,
+
+ matcherOut = matcher ?
+
+ // If we have a postFinder, or filtered seed, or non-seed postFilter or preexisting results,
+ postFinder || ( seed ? preFilter : preexisting || postFilter ) ?
+
+ // ...intermediate processing is necessary
+ [] :
+
+ // ...otherwise use results directly
+ results :
+ matcherIn;
+
+ // Find primary matches
+ if ( matcher ) {
+ matcher( matcherIn, matcherOut, context, xml );
+ }
+
+ // Apply postFilter
+ if ( postFilter ) {
+ temp = condense( matcherOut, postMap );
+ postFilter( temp, [], context, xml );
+
+ // Un-match failing elements by moving them back to matcherIn
+ i = temp.length;
+ while ( i-- ) {
+ if ( ( elem = temp[ i ] ) ) {
+ matcherOut[ postMap[ i ] ] = !( matcherIn[ postMap[ i ] ] = elem );
+ }
+ }
+ }
+
+ if ( seed ) {
+ if ( postFinder || preFilter ) {
+ if ( postFinder ) {
+
+ // Get the final matcherOut by condensing this intermediate into postFinder contexts
+ temp = [];
+ i = matcherOut.length;
+ while ( i-- ) {
+ if ( ( elem = matcherOut[ i ] ) ) {
+
+ // Restore matcherIn since elem is not yet a final match
+ temp.push( ( matcherIn[ i ] = elem ) );
+ }
+ }
+ postFinder( null, ( matcherOut = [] ), temp, xml );
+ }
+
+ // Move matched elements from seed to results to keep them synchronized
+ i = matcherOut.length;
+ while ( i-- ) {
+ if ( ( elem = matcherOut[ i ] ) &&
+ ( temp = postFinder ? indexOf( seed, elem ) : preMap[ i ] ) > -1 ) {
+
+ seed[ temp ] = !( results[ temp ] = elem );
+ }
+ }
+ }
+
+ // Add elements to results, through postFinder if defined
+ } else {
+ matcherOut = condense(
+ matcherOut === results ?
+ matcherOut.splice( preexisting, matcherOut.length ) :
+ matcherOut
+ );
+ if ( postFinder ) {
+ postFinder( null, results, matcherOut, xml );
+ } else {
+ push.apply( results, matcherOut );
+ }
+ }
+ } );
+}
+
+function matcherFromTokens( tokens ) {
+ var checkContext, matcher, j,
+ len = tokens.length,
+ leadingRelative = Expr.relative[ tokens[ 0 ].type ],
+ implicitRelative = leadingRelative || Expr.relative[ " " ],
+ i = leadingRelative ? 1 : 0,
+
+ // The foundational matcher ensures that elements are reachable from top-level context(s)
+ matchContext = addCombinator( function( elem ) {
+ return elem === checkContext;
+ }, implicitRelative, true ),
+ matchAnyContext = addCombinator( function( elem ) {
+ return indexOf( checkContext, elem ) > -1;
+ }, implicitRelative, true ),
+ matchers = [ function( elem, context, xml ) {
+ var ret = ( !leadingRelative && ( xml || context !== outermostContext ) ) || (
+ ( checkContext = context ).nodeType ?
+ matchContext( elem, context, xml ) :
+ matchAnyContext( elem, context, xml ) );
+
+ // Avoid hanging onto element (issue #299)
+ checkContext = null;
+ return ret;
+ } ];
+
+ for ( ; i < len; i++ ) {
+ if ( ( matcher = Expr.relative[ tokens[ i ].type ] ) ) {
+ matchers = [ addCombinator( elementMatcher( matchers ), matcher ) ];
+ } else {
+ matcher = Expr.filter[ tokens[ i ].type ].apply( null, tokens[ i ].matches );
+
+ // Return special upon seeing a positional matcher
+ if ( matcher[ expando ] ) {
+
+ // Find the next relative operator (if any) for proper handling
+ j = ++i;
+ for ( ; j < len; j++ ) {
+ if ( Expr.relative[ tokens[ j ].type ] ) {
+ break;
+ }
+ }
+ return setMatcher(
+ i > 1 && elementMatcher( matchers ),
+ i > 1 && toSelector(
+
+ // If the preceding token was a descendant combinator, insert an implicit any-element `*`
+ tokens
+ .slice( 0, i - 1 )
+ .concat( { value: tokens[ i - 2 ].type === " " ? "*" : "" } )
+ ).replace( rtrim, "$1" ),
+ matcher,
+ i < j && matcherFromTokens( tokens.slice( i, j ) ),
+ j < len && matcherFromTokens( ( tokens = tokens.slice( j ) ) ),
+ j < len && toSelector( tokens )
+ );
+ }
+ matchers.push( matcher );
+ }
+ }
+
+ return elementMatcher( matchers );
+}
+
+function matcherFromGroupMatchers( elementMatchers, setMatchers ) {
+ var bySet = setMatchers.length > 0,
+ byElement = elementMatchers.length > 0,
+ superMatcher = function( seed, context, xml, results, outermost ) {
+ var elem, j, matcher,
+ matchedCount = 0,
+ i = "0",
+ unmatched = seed && [],
+ setMatched = [],
+ contextBackup = outermostContext,
+
+ // We must always have either seed elements or outermost context
+ elems = seed || byElement && Expr.find[ "TAG" ]( "*", outermost ),
+
+ // Use integer dirruns iff this is the outermost matcher
+ dirrunsUnique = ( dirruns += contextBackup == null ? 1 : Math.random() || 0.1 ),
+ len = elems.length;
+
+ if ( outermost ) {
+
+ // Support: IE 11+, Edge 17 - 18+
+ // IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+ // two documents; shallow comparisons work.
+ // eslint-disable-next-line eqeqeq
+ outermostContext = context == document || context || outermost;
+ }
+
+ // Add elements passing elementMatchers directly to results
+ // Support: IE<9, Safari
+ // Tolerate NodeList properties (IE: "length"; Safari: <number>) matching elements by id
+ for ( ; i !== len && ( elem = elems[ i ] ) != null; i++ ) {
+ if ( byElement && elem ) {
+ j = 0;
+
+ // Support: IE 11+, Edge 17 - 18+
+ // IE/Edge sometimes throw a "Permission denied" error when strict-comparing
+ // two documents; shallow comparisons work.
+ // eslint-disable-next-line eqeqeq
+ if ( !context && elem.ownerDocument != document ) {
+ setDocument( elem );
+ xml = !documentIsHTML;
+ }
+ while ( ( matcher = elementMatchers[ j++ ] ) ) {
+ if ( matcher( elem, context || document, xml ) ) {
+ results.push( elem );
+ break;
+ }
+ }
+ if ( outermost ) {
+ dirruns = dirrunsUnique;
+ }
+ }
+
+ // Track unmatched elements for set filters
+ if ( bySet ) {
+
+ // They will have gone through all possible matchers
+ if ( ( elem = !matcher && elem ) ) {
+ matchedCount--;
+ }
+
+ // Lengthen the array for every element, matched or not
+ if ( seed ) {
+ unmatched.push( elem );
+ }
+ }
+ }
+
+ // `i` is now the count of elements visited above, and adding it to `matchedCount`
+ // makes the latter nonnegative.
+ matchedCount += i;
+
+ // Apply set filters to unmatched elements
+ // NOTE: This can be skipped if there are no unmatched elements (i.e., `matchedCount`
+ // equals `i`), unless we didn't visit _any_ elements in the above loop because we have
+ // no element matchers and no seed.
+ // Incrementing an initially-string "0" `i` allows `i` to remain a string only in that
+ // case, which will result in a "00" `matchedCount` that differs from `i` but is also
+ // numerically zero.
+ if ( bySet && i !== matchedCount ) {
+ j = 0;
+ while ( ( matcher = setMatchers[ j++ ] ) ) {
+ matcher( unmatched, setMatched, context, xml );
+ }
+
+ if ( seed ) {
+
+ // Reintegrate element matches to eliminate the need for sorting
+ if ( matchedCount > 0 ) {
+ while ( i-- ) {
+ if ( !( unmatched[ i ] || setMatched[ i ] ) ) {
+ setMatched[ i ] = pop.call( results );
+ }
+ }
+ }
+
+ // Discard index placeholder values to get only actual matches
+ setMatched = condense( setMatched );
+ }
+
+ // Add matches to results
+ push.apply( results, setMatched );
+
+ // Seedless set matches succeeding multiple successful matchers stipulate sorting
+ if ( outermost && !seed && setMatched.length > 0 &&
+ ( matchedCount + setMatchers.length ) > 1 ) {
+
+ Sizzle.uniqueSort( results );
+ }
+ }
+
+ // Override manipulation of globals by nested matchers
+ if ( outermost ) {
+ dirruns = dirrunsUnique;
+ outermostContext = contextBackup;
+ }
+
+ return unmatched;
+ };
+
+ return bySet ?
+ markFunction( superMatcher ) :
+ superMatcher;
+}
+
+compile = Sizzle.compile = function( selector, match /* Internal Use Only */ ) {
+ var i,
+ setMatchers = [],
+ elementMatchers = [],
+ cached = compilerCache[ selector + " " ];
+
+ if ( !cached ) {
+
+ // Generate a function of recursive functions that can be used to check each element
+ if ( !match ) {
+ match = tokenize( selector );
+ }
+ i = match.length;
+ while ( i-- ) {
+ cached = matcherFromTokens( match[ i ] );
+ if ( cached[ expando ] ) {
+ setMatchers.push( cached );
+ } else {
+ elementMatchers.push( cached );
+ }
+ }
+
+ // Cache the compiled function
+ cached = compilerCache(
+ selector,
+ matcherFromGroupMatchers( elementMatchers, setMatchers )
+ );
+
+ // Save selector and tokenization
+ cached.selector = selector;
+ }
+ return cached;
+};
+
+/**
+ * A low-level selection function that works with Sizzle's compiled
+ * selector functions
+ * @param {String|Function} selector A selector or a pre-compiled
+ * selector function built with Sizzle.compile
+ * @param {Element} context
+ * @param {Array} [results]
+ * @param {Array} [seed] A set of elements to match against
+ */
+select = Sizzle.select = function( selector, context, results, seed ) {
+ var i, tokens, token, type, find,
+ compiled = typeof selector === "function" && selector,
+ match = !seed && tokenize( ( selector = compiled.selector || selector ) );
+
+ results = results || [];
+
+ // Try to minimize operations if there is only one selector in the list and no seed
+ // (the latter of which guarantees us context)
+ if ( match.length === 1 ) {
+
+ // Reduce context if the leading compound selector is an ID
+ tokens = match[ 0 ] = match[ 0 ].slice( 0 );
+ if ( tokens.length > 2 && ( token = tokens[ 0 ] ).type === "ID" &&
+ context.nodeType === 9 && documentIsHTML && Expr.relative[ tokens[ 1 ].type ] ) {
+
+ context = ( Expr.find[ "ID" ]( token.matches[ 0 ]
+ .replace( runescape, funescape ), context ) || [] )[ 0 ];
+ if ( !context ) {
+ return results;
+
+ // Precompiled matchers will still verify ancestry, so step up a level
+ } else if ( compiled ) {
+ context = context.parentNode;
+ }
+
+ selector = selector.slice( tokens.shift().value.length );
+ }
+
+ // Fetch a seed set for right-to-left matching
+ i = matchExpr[ "needsContext" ].test( selector ) ? 0 : tokens.length;
+ while ( i-- ) {
+ token = tokens[ i ];
+
+ // Abort if we hit a combinator
+ if ( Expr.relative[ ( type = token.type ) ] ) {
+ break;
+ }
+ if ( ( find = Expr.find[ type ] ) ) {
+
+ // Search, expanding context for leading sibling combinators
+ if ( ( seed = find(
+ token.matches[ 0 ].replace( runescape, funescape ),
+ rsibling.test( tokens[ 0 ].type ) && testContext( context.parentNode ) ||
+ context
+ ) ) ) {
+
+ // If seed is empty or no tokens remain, we can return early
+ tokens.splice( i, 1 );
+ selector = seed.length && toSelector( tokens );
+ if ( !selector ) {
+ push.apply( results, seed );
+ return results;
+ }
+
+ break;
+ }
+ }
+ }
+ }
+
+ // Compile and execute a filtering function if one is not provided
+ // Provide `match` to avoid retokenization if we modified the selector above
+ ( compiled || compile( selector, match ) )(
+ seed,
+ context,
+ !documentIsHTML,
+ results,
+ !context || rsibling.test( selector ) && testContext( context.parentNode ) || context
+ );
+ return results;
+};
+
+// One-time assignments
+
+// Sort stability
+support.sortStable = expando.split( "" ).sort( sortOrder ).join( "" ) === expando;
+
+// Support: Chrome 14-35+
+// Always assume duplicates if they aren't passed to the comparison function
+support.detectDuplicates = !!hasDuplicate;
+
+// Initialize against the default document
+setDocument();
+
+// Support: Webkit<537.32 - Safari 6.0.3/Chrome 25 (fixed in Chrome 27)
+// Detached nodes confoundingly follow *each other*
+support.sortDetached = assert( function( el ) {
+
+ // Should return 1, but returns 4 (following)
+ return el.compareDocumentPosition( document.createElement( "fieldset" ) ) & 1;
+} );
+
+// Support: IE<8
+// Prevent attribute/property "interpolation"
+// https://msdn.microsoft.com/en-us/library/ms536429%28VS.85%29.aspx
+if ( !assert( function( el ) {
+ el.innerHTML = "<a href='#'></a>";
+ return el.firstChild.getAttribute( "href" ) === "#";
+} ) ) {
+ addHandle( "type|href|height|width", function( elem, name, isXML ) {
+ if ( !isXML ) {
+ return elem.getAttribute( name, name.toLowerCase() === "type" ? 1 : 2 );
+ }
+ } );
+}
+
+// Support: IE<9
+// Use defaultValue in place of getAttribute("value")
+if ( !support.attributes || !assert( function( el ) {
+ el.innerHTML = "<input/>";
+ el.firstChild.setAttribute( "value", "" );
+ return el.firstChild.getAttribute( "value" ) === "";
+} ) ) {
+ addHandle( "value", function( elem, _name, isXML ) {
+ if ( !isXML && elem.nodeName.toLowerCase() === "input" ) {
+ return elem.defaultValue;
+ }
+ } );
+}
+
+// Support: IE<9
+// Use getAttributeNode to fetch booleans when getAttribute lies
+if ( !assert( function( el ) {
+ return el.getAttribute( "disabled" ) == null;
+} ) ) {
+ addHandle( booleans, function( elem, name, isXML ) {
+ var val;
+ if ( !isXML ) {
+ return elem[ name ] === true ? name.toLowerCase() :
+ ( val = elem.getAttributeNode( name ) ) && val.specified ?
+ val.value :
+ null;
+ }
+ } );
+}
+
+return Sizzle;
+
+} )( window );
+
+
+
+jQuery.find = Sizzle;
+jQuery.expr = Sizzle.selectors;
+
+// Deprecated
+jQuery.expr[ ":" ] = jQuery.expr.pseudos;
+jQuery.uniqueSort = jQuery.unique = Sizzle.uniqueSort;
+jQuery.text = Sizzle.getText;
+jQuery.isXMLDoc = Sizzle.isXML;
+jQuery.contains = Sizzle.contains;
+jQuery.escapeSelector = Sizzle.escape;
+
+
+
+
+var dir = function( elem, dir, until ) {
+ var matched = [],
+ truncate = until !== undefined;
+
+ while ( ( elem = elem[ dir ] ) && elem.nodeType !== 9 ) {
+ if ( elem.nodeType === 1 ) {
+ if ( truncate && jQuery( elem ).is( until ) ) {
+ break;
+ }
+ matched.push( elem );
+ }
+ }
+ return matched;
+};
+
+
+var siblings = function( n, elem ) {
+ var matched = [];
+
+ for ( ; n; n = n.nextSibling ) {
+ if ( n.nodeType === 1 && n !== elem ) {
+ matched.push( n );
+ }
+ }
+
+ return matched;
+};
+
+
+var rneedsContext = jQuery.expr.match.needsContext;
+
+
+
+function nodeName( elem, name ) {
+
+ return elem.nodeName && elem.nodeName.toLowerCase() === name.toLowerCase();
+
+};
+var rsingleTag = ( /^<([a-z][^\/\0>:\x20\t\r\n\f]*)[\x20\t\r\n\f]*\/?>(?:<\/\1>|)$/i );
+
+
+
+// Implement the identical functionality for filter and not
+function winnow( elements, qualifier, not ) {
+ if ( isFunction( qualifier ) ) {
+ return jQuery.grep( elements, function( elem, i ) {
+ return !!qualifier.call( elem, i, elem ) !== not;
+ } );
+ }
+
+ // Single element
+ if ( qualifier.nodeType ) {
+ return jQuery.grep( elements, function( elem ) {
+ return ( elem === qualifier ) !== not;
+ } );
+ }
+
+ // Arraylike of elements (jQuery, arguments, Array)
+ if ( typeof qualifier !== "string" ) {
+ return jQuery.grep( elements, function( elem ) {
+ return ( indexOf.call( qualifier, elem ) > -1 ) !== not;
+ } );
+ }
+
+ // Filtered directly for both simple and complex selectors
+ return jQuery.filter( qualifier, elements, not );
+}
+
+jQuery.filter = function( expr, elems, not ) {
+ var elem = elems[ 0 ];
+
+ if ( not ) {
+ expr = ":not(" + expr + ")";
+ }
+
+ if ( elems.length === 1 && elem.nodeType === 1 ) {
+ return jQuery.find.matchesSelector( elem, expr ) ? [ elem ] : [];
+ }
+
+ return jQuery.find.matches( expr, jQuery.grep( elems, function( elem ) {
+ return elem.nodeType === 1;
+ } ) );
+};
+
+jQuery.fn.extend( {
+ find: function( selector ) {
+ var i, ret,
+ len = this.length,
+ self = this;
+
+ if ( typeof selector !== "string" ) {
+ return this.pushStack( jQuery( selector ).filter( function() {
+ for ( i = 0; i < len; i++ ) {
+ if ( jQuery.contains( self[ i ], this ) ) {
+ return true;
+ }
+ }
+ } ) );
+ }
+
+ ret = this.pushStack( [] );
+
+ for ( i = 0; i < len; i++ ) {
+ jQuery.find( selector, self[ i ], ret );
+ }
+
+ return len > 1 ? jQuery.uniqueSort( ret ) : ret;
+ },
+ filter: function( selector ) {
+ return this.pushStack( winnow( this, selector || [], false ) );
+ },
+ not: function( selector ) {
+ return this.pushStack( winnow( this, selector || [], true ) );
+ },
+ is: function( selector ) {
+ return !!winnow(
+ this,
+
+ // If this is a positional/relative selector, check membership in the returned set
+ // so $("p:first").is("p:last") won't return true for a doc with two "p".
+ typeof selector === "string" && rneedsContext.test( selector ) ?
+ jQuery( selector ) :
+ selector || [],
+ false
+ ).length;
+ }
+} );
+
+
+// Initialize a jQuery object
+
+
+// A central reference to the root jQuery(document)
+var rootjQuery,
+
+ // A simple way to check for HTML strings
+ // Prioritize #id over <tag> to avoid XSS via location.hash (#9521)
+ // Strict HTML recognition (#11290: must start with <)
+ // Shortcut simple #id case for speed
+ rquickExpr = /^(?:\s*(<[\w\W]+>)[^>]*|#([\w-]+))$/,
+
+ init = jQuery.fn.init = function( selector, context, root ) {
+ var match, elem;
+
+ // HANDLE: $(""), $(null), $(undefined), $(false)
+ if ( !selector ) {
+ return this;
+ }
+
+ // Method init() accepts an alternate rootjQuery
+ // so migrate can support jQuery.sub (gh-2101)
+ root = root || rootjQuery;
+
+ // Handle HTML strings
+ if ( typeof selector === "string" ) {
+ if ( selector[ 0 ] === "<" &&
+ selector[ selector.length - 1 ] === ">" &&
+ selector.length >= 3 ) {
+
+ // Assume that strings that start and end with <> are HTML and skip the regex check
+ match = [ null, selector, null ];
+
+ } else {
+ match = rquickExpr.exec( selector );
+ }
+
+ // Match html or make sure no context is specified for #id
+ if ( match && ( match[ 1 ] || !context ) ) {
+
+ // HANDLE: $(html) -> $(array)
+ if ( match[ 1 ] ) {
+ context = context instanceof jQuery ? context[ 0 ] : context;
+
+ // Option to run scripts is true for back-compat
+ // Intentionally let the error be thrown if parseHTML is not present
+ jQuery.merge( this, jQuery.parseHTML(
+ match[ 1 ],
+ context && context.nodeType ? context.ownerDocument || context : document,
+ true
+ ) );
+
+ // HANDLE: $(html, props)
+ if ( rsingleTag.test( match[ 1 ] ) && jQuery.isPlainObject( context ) ) {
+ for ( match in context ) {
+
+ // Properties of context are called as methods if possible
+ if ( isFunction( this[ match ] ) ) {
+ this[ match ]( context[ match ] );
+
+ // ...and otherwise set as attributes
+ } else {
+ this.attr( match, context[ match ] );
+ }
+ }
+ }
+
+ return this;
+
+ // HANDLE: $(#id)
+ } else {
+ elem = document.getElementById( match[ 2 ] );
+
+ if ( elem ) {
+
+ // Inject the element directly into the jQuery object
+ this[ 0 ] = elem;
+ this.length = 1;
+ }
+ return this;
+ }
+
+ // HANDLE: $(expr, $(...))
+ } else if ( !context || context.jquery ) {
+ return ( context || root ).find( selector );
+
+ // HANDLE: $(expr, context)
+ // (which is just equivalent to: $(context).find(expr)
+ } else {
+ return this.constructor( context ).find( selector );
+ }
+
+ // HANDLE: $(DOMElement)
+ } else if ( selector.nodeType ) {
+ this[ 0 ] = selector;
+ this.length = 1;
+ return this;
+
+ // HANDLE: $(function)
+ // Shortcut for document ready
+ } else if ( isFunction( selector ) ) {
+ return root.ready !== undefined ?
+ root.ready( selector ) :
+
+ // Execute immediately if ready is not present
+ selector( jQuery );
+ }
+
+ return jQuery.makeArray( selector, this );
+ };
+
+// Give the init function the jQuery prototype for later instantiation
+init.prototype = jQuery.fn;
+
+// Initialize central reference
+rootjQuery = jQuery( document );
+
+
+var rparentsprev = /^(?:parents|prev(?:Until|All))/,
+
+ // Methods guaranteed to produce a unique set when starting from a unique set
+ guaranteedUnique = {
+ children: true,
+ contents: true,
+ next: true,
+ prev: true
+ };
+
+jQuery.fn.extend( {
+ has: function( target ) {
+ var targets = jQuery( target, this ),
+ l = targets.length;
+
+ return this.filter( function() {
+ var i = 0;
+ for ( ; i < l; i++ ) {
+ if ( jQuery.contains( this, targets[ i ] ) ) {
+ return true;
+ }
+ }
+ } );
+ },
+
+ closest: function( selectors, context ) {
+ var cur,
+ i = 0,
+ l = this.length,
+ matched = [],
+ targets = typeof selectors !== "string" && jQuery( selectors );
+
+ // Positional selectors never match, since there's no _selection_ context
+ if ( !rneedsContext.test( selectors ) ) {
+ for ( ; i < l; i++ ) {
+ for ( cur = this[ i ]; cur && cur !== context; cur = cur.parentNode ) {
+
+ // Always skip document fragments
+ if ( cur.nodeType < 11 && ( targets ?
+ targets.index( cur ) > -1 :
+
+ // Don't pass non-elements to Sizzle
+ cur.nodeType === 1 &&
+ jQuery.find.matchesSelector( cur, selectors ) ) ) {
+
+ matched.push( cur );
+ break;
+ }
+ }
+ }
+ }
+
+ return this.pushStack( matched.length > 1 ? jQuery.uniqueSort( matched ) : matched );
+ },
+
+ // Determine the position of an element within the set
+ index: function( elem ) {
+
+ // No argument, return index in parent
+ if ( !elem ) {
+ return ( this[ 0 ] && this[ 0 ].parentNode ) ? this.first().prevAll().length : -1;
+ }
+
+ // Index in selector
+ if ( typeof elem === "string" ) {
+ return indexOf.call( jQuery( elem ), this[ 0 ] );
+ }
+
+ // Locate the position of the desired element
+ return indexOf.call( this,
+
+ // If it receives a jQuery object, the first element is used
+ elem.jquery ? elem[ 0 ] : elem
+ );
+ },
+
+ add: function( selector, context ) {
+ return this.pushStack(
+ jQuery.uniqueSort(
+ jQuery.merge( this.get(), jQuery( selector, context ) )
+ )
+ );
+ },
+
+ addBack: function( selector ) {
+ return this.add( selector == null ?
+ this.prevObject : this.prevObject.filter( selector )
+ );
+ }
+} );
+
+function sibling( cur, dir ) {
+ while ( ( cur = cur[ dir ] ) && cur.nodeType !== 1 ) {}
+ return cur;
+}
+
+jQuery.each( {
+ parent: function( elem ) {
+ var parent = elem.parentNode;
+ return parent && parent.nodeType !== 11 ? parent : null;
+ },
+ parents: function( elem ) {
+ return dir( elem, "parentNode" );
+ },
+ parentsUntil: function( elem, _i, until ) {
+ return dir( elem, "parentNode", until );
+ },
+ next: function( elem ) {
+ return sibling( elem, "nextSibling" );
+ },
+ prev: function( elem ) {
+ return sibling( elem, "previousSibling" );
+ },
+ nextAll: function( elem ) {
+ return dir( elem, "nextSibling" );
+ },
+ prevAll: function( elem ) {
+ return dir( elem, "previousSibling" );
+ },
+ nextUntil: function( elem, _i, until ) {
+ return dir( elem, "nextSibling", until );
+ },
+ prevUntil: function( elem, _i, until ) {
+ return dir( elem, "previousSibling", until );
+ },
+ siblings: function( elem ) {
+ return siblings( ( elem.parentNode || {} ).firstChild, elem );
+ },
+ children: function( elem ) {
+ return siblings( elem.firstChild );
+ },
+ contents: function( elem ) {
+ if ( elem.contentDocument != null &&
+
+ // Support: IE 11+
+ // <object> elements with no `data` attribute has an object
+ // `contentDocument` with a `null` prototype.
+ getProto( elem.contentDocument ) ) {
+
+ return elem.contentDocument;
+ }
+
+ // Support: IE 9 - 11 only, iOS 7 only, Android Browser <=4.3 only
+ // Treat the template element as a regular one in browsers that
+ // don't support it.
+ if ( nodeName( elem, "template" ) ) {
+ elem = elem.content || elem;
+ }
+
+ return jQuery.merge( [], elem.childNodes );
+ }
+}, function( name, fn ) {
+ jQuery.fn[ name ] = function( until, selector ) {
+ var matched = jQuery.map( this, fn, until );
+
+ if ( name.slice( -5 ) !== "Until" ) {
+ selector = until;
+ }
+
+ if ( selector && typeof selector === "string" ) {
+ matched = jQuery.filter( selector, matched );
+ }
+
+ if ( this.length > 1 ) {
+
+ // Remove duplicates
+ if ( !guaranteedUnique[ name ] ) {
+ jQuery.uniqueSort( matched );
+ }
+
+ // Reverse order for parents* and prev-derivatives
+ if ( rparentsprev.test( name ) ) {
+ matched.reverse();
+ }
+ }
+
+ return this.pushStack( matched );
+ };
+} );
+var rnothtmlwhite = ( /[^\x20\t\r\n\f]+/g );
+
+
+
+// Convert String-formatted options into Object-formatted ones
+function createOptions( options ) {
+ var object = {};
+ jQuery.each( options.match( rnothtmlwhite ) || [], function( _, flag ) {
+ object[ flag ] = true;
+ } );
+ return object;
+}
+
+/*
+ * Create a callback list using the following parameters:
+ *
+ * options: an optional list of space-separated options that will change how
+ * the callback list behaves or a more traditional option object
+ *
+ * By default a callback list will act like an event callback list and can be
+ * "fired" multiple times.
+ *
+ * Possible options:
+ *
+ * once: will ensure the callback list can only be fired once (like a Deferred)
+ *
+ * memory: will keep track of previous values and will call any callback added
+ * after the list has been fired right away with the latest "memorized"
+ * values (like a Deferred)
+ *
+ * unique: will ensure a callback can only be added once (no duplicate in the list)
+ *
+ * stopOnFalse: interrupt callings when a callback returns false
+ *
+ */
+jQuery.Callbacks = function( options ) {
+
+ // Convert options from String-formatted to Object-formatted if needed
+ // (we check in cache first)
+ options = typeof options === "string" ?
+ createOptions( options ) :
+ jQuery.extend( {}, options );
+
+ var // Flag to know if list is currently firing
+ firing,
+
+ // Last fire value for non-forgettable lists
+ memory,
+
+ // Flag to know if list was already fired
+ fired,
+
+ // Flag to prevent firing
+ locked,
+
+ // Actual callback list
+ list = [],
+
+ // Queue of execution data for repeatable lists
+ queue = [],
+
+ // Index of currently firing callback (modified by add/remove as needed)
+ firingIndex = -1,
+
+ // Fire callbacks
+ fire = function() {
+
+ // Enforce single-firing
+ locked = locked || options.once;
+
+ // Execute callbacks for all pending executions,
+ // respecting firingIndex overrides and runtime changes
+ fired = firing = true;
+ for ( ; queue.length; firingIndex = -1 ) {
+ memory = queue.shift();
+ while ( ++firingIndex < list.length ) {
+
+ // Run callback and check for early termination
+ if ( list[ firingIndex ].apply( memory[ 0 ], memory[ 1 ] ) === false &&
+ options.stopOnFalse ) {
+
+ // Jump to end and forget the data so .add doesn't re-fire
+ firingIndex = list.length;
+ memory = false;
+ }
+ }
+ }
+
+ // Forget the data if we're done with it
+ if ( !options.memory ) {
+ memory = false;
+ }
+
+ firing = false;
+
+ // Clean up if we're done firing for good
+ if ( locked ) {
+
+ // Keep an empty list if we have data for future add calls
+ if ( memory ) {
+ list = [];
+
+ // Otherwise, this object is spent
+ } else {
+ list = "";
+ }
+ }
+ },
+
+ // Actual Callbacks object
+ self = {
+
+ // Add a callback or a collection of callbacks to the list
+ add: function() {
+ if ( list ) {
+
+ // If we have memory from a past run, we should fire after adding
+ if ( memory && !firing ) {
+ firingIndex = list.length - 1;
+ queue.push( memory );
+ }
+
+ ( function add( args ) {
+ jQuery.each( args, function( _, arg ) {
+ if ( isFunction( arg ) ) {
+ if ( !options.unique || !self.has( arg ) ) {
+ list.push( arg );
+ }
+ } else if ( arg && arg.length && toType( arg ) !== "string" ) {
+
+ // Inspect recursively
+ add( arg );
+ }
+ } );
+ } )( arguments );
+
+ if ( memory && !firing ) {
+ fire();
+ }
+ }
+ return this;
+ },
+
+ // Remove a callback from the list
+ remove: function() {
+ jQuery.each( arguments, function( _, arg ) {
+ var index;
+ while ( ( index = jQuery.inArray( arg, list, index ) ) > -1 ) {
+ list.splice( index, 1 );
+
+ // Handle firing indexes
+ if ( index <= firingIndex ) {
+ firingIndex--;
+ }
+ }
+ } );
+ return this;
+ },
+
+ // Check if a given callback is in the list.
+ // If no argument is given, return whether or not list has callbacks attached.
+ has: function( fn ) {
+ return fn ?
+ jQuery.inArray( fn, list ) > -1 :
+ list.length > 0;
+ },
+
+ // Remove all callbacks from the list
+ empty: function() {
+ if ( list ) {
+ list = [];
+ }
+ return this;
+ },
+
+ // Disable .fire and .add
+ // Abort any current/pending executions
+ // Clear all callbacks and values
+ disable: function() {
+ locked = queue = [];
+ list = memory = "";
+ return this;
+ },
+ disabled: function() {
+ return !list;
+ },
+
+ // Disable .fire
+ // Also disable .add unless we have memory (since it would have no effect)
+ // Abort any pending executions
+ lock: function() {
+ locked = queue = [];
+ if ( !memory && !firing ) {
+ list = memory = "";
+ }
+ return this;
+ },
+ locked: function() {
+ return !!locked;
+ },
+
+ // Call all callbacks with the given context and arguments
+ fireWith: function( context, args ) {
+ if ( !locked ) {
+ args = args || [];
+ args = [ context, args.slice ? args.slice() : args ];
+ queue.push( args );
+ if ( !firing ) {
+ fire();
+ }
+ }
+ return this;
+ },
+
+ // Call all the callbacks with the given arguments
+ fire: function() {
+ self.fireWith( this, arguments );
+ return this;
+ },
+
+ // To know if the callbacks have already been called at least once
+ fired: function() {
+ return !!fired;
+ }
+ };
+
+ return self;
+};
+
+
+function Identity( v ) {
+ return v;
+}
+function Thrower( ex ) {
+ throw ex;
+}
+
+function adoptValue( value, resolve, reject, noValue ) {
+ var method;
+
+ try {
+
+ // Check for promise aspect first to privilege synchronous behavior
+ if ( value && isFunction( ( method = value.promise ) ) ) {
+ method.call( value ).done( resolve ).fail( reject );
+
+ // Other thenables
+ } else if ( value && isFunction( ( method = value.then ) ) ) {
+ method.call( value, resolve, reject );
+
+ // Other non-thenables
+ } else {
+
+ // Control `resolve` arguments by letting Array#slice cast boolean `noValue` to integer:
+ // * false: [ value ].slice( 0 ) => resolve( value )
+ // * true: [ value ].slice( 1 ) => resolve()
+ resolve.apply( undefined, [ value ].slice( noValue ) );
+ }
+
+ // For Promises/A+, convert exceptions into rejections
+ // Since jQuery.when doesn't unwrap thenables, we can skip the extra checks appearing in
+ // Deferred#then to conditionally suppress rejection.
+ } catch ( value ) {
+
+ // Support: Android 4.0 only
+ // Strict mode functions invoked without .call/.apply get global-object context
+ reject.apply( undefined, [ value ] );
+ }
+}
+
+jQuery.extend( {
+
+ Deferred: function( func ) {
+ var tuples = [
+
+ // action, add listener, callbacks,
+ // ... .then handlers, argument index, [final state]
+ [ "notify", "progress", jQuery.Callbacks( "memory" ),
+ jQuery.Callbacks( "memory" ), 2 ],
+ [ "resolve", "done", jQuery.Callbacks( "once memory" ),
+ jQuery.Callbacks( "once memory" ), 0, "resolved" ],
+ [ "reject", "fail", jQuery.Callbacks( "once memory" ),
+ jQuery.Callbacks( "once memory" ), 1, "rejected" ]
+ ],
+ state = "pending",
+ promise = {
+ state: function() {
+ return state;
+ },
+ always: function() {
+ deferred.done( arguments ).fail( arguments );
+ return this;
+ },
+ "catch": function( fn ) {
+ return promise.then( null, fn );
+ },
+
+ // Keep pipe for back-compat
+ pipe: function( /* fnDone, fnFail, fnProgress */ ) {
+ var fns = arguments;
+
+ return jQuery.Deferred( function( newDefer ) {
+ jQuery.each( tuples, function( _i, tuple ) {
+
+ // Map tuples (progress, done, fail) to arguments (done, fail, progress)
+ var fn = isFunction( fns[ tuple[ 4 ] ] ) && fns[ tuple[ 4 ] ];
+
+ // deferred.progress(function() { bind to newDefer or newDefer.notify })
+ // deferred.done(function() { bind to newDefer or newDefer.resolve })
+ // deferred.fail(function() { bind to newDefer or newDefer.reject })
+ deferred[ tuple[ 1 ] ]( function() {
+ var returned = fn && fn.apply( this, arguments );
+ if ( returned && isFunction( returned.promise ) ) {
+ returned.promise()
+ .progress( newDefer.notify )
+ .done( newDefer.resolve )
+ .fail( newDefer.reject );
+ } else {
+ newDefer[ tuple[ 0 ] + "With" ](
+ this,
+ fn ? [ returned ] : arguments
+ );
+ }
+ } );
+ } );
+ fns = null;
+ } ).promise();
+ },
+ then: function( onFulfilled, onRejected, onProgress ) {
+ var maxDepth = 0;
+ function resolve( depth, deferred, handler, special ) {
+ return function() {
+ var that = this,
+ args = arguments,
+ mightThrow = function() {
+ var returned, then;
+
+ // Support: Promises/A+ section 2.3.3.3.3
+ // https://promisesaplus.com/#point-59
+ // Ignore double-resolution attempts
+ if ( depth < maxDepth ) {
+ return;
+ }
+
+ returned = handler.apply( that, args );
+
+ // Support: Promises/A+ section 2.3.1
+ // https://promisesaplus.com/#point-48
+ if ( returned === deferred.promise() ) {
+ throw new TypeError( "Thenable self-resolution" );
+ }
+
+ // Support: Promises/A+ sections 2.3.3.1, 3.5
+ // https://promisesaplus.com/#point-54
+ // https://promisesaplus.com/#point-75
+ // Retrieve `then` only once
+ then = returned &&
+
+ // Support: Promises/A+ section 2.3.4
+ // https://promisesaplus.com/#point-64
+ // Only check objects and functions for thenability
+ ( typeof returned === "object" ||
+ typeof returned === "function" ) &&
+ returned.then;
+
+ // Handle a returned thenable
+ if ( isFunction( then ) ) {
+
+ // Special processors (notify) just wait for resolution
+ if ( special ) {
+ then.call(
+ returned,
+ resolve( maxDepth, deferred, Identity, special ),
+ resolve( maxDepth, deferred, Thrower, special )
+ );
+
+ // Normal processors (resolve) also hook into progress
+ } else {
+
+ // ...and disregard older resolution values
+ maxDepth++;
+
+ then.call(
+ returned,
+ resolve( maxDepth, deferred, Identity, special ),
+ resolve( maxDepth, deferred, Thrower, special ),
+ resolve( maxDepth, deferred, Identity,
+ deferred.notifyWith )
+ );
+ }
+
+ // Handle all other returned values
+ } else {
+
+ // Only substitute handlers pass on context
+ // and multiple values (non-spec behavior)
+ if ( handler !== Identity ) {
+ that = undefined;
+ args = [ returned ];
+ }
+
+ // Process the value(s)
+ // Default process is resolve
+ ( special || deferred.resolveWith )( that, args );
+ }
+ },
+
+ // Only normal processors (resolve) catch and reject exceptions
+ process = special ?
+ mightThrow :
+ function() {
+ try {
+ mightThrow();
+ } catch ( e ) {
+
+ if ( jQuery.Deferred.exceptionHook ) {
+ jQuery.Deferred.exceptionHook( e,
+ process.stackTrace );
+ }
+
+ // Support: Promises/A+ section 2.3.3.3.4.1
+ // https://promisesaplus.com/#point-61
+ // Ignore post-resolution exceptions
+ if ( depth + 1 >= maxDepth ) {
+
+ // Only substitute handlers pass on context
+ // and multiple values (non-spec behavior)
+ if ( handler !== Thrower ) {
+ that = undefined;
+ args = [ e ];
+ }
+
+ deferred.rejectWith( that, args );
+ }
+ }
+ };
+
+ // Support: Promises/A+ section 2.3.3.3.1
+ // https://promisesaplus.com/#point-57
+ // Re-resolve promises immediately to dodge false rejection from
+ // subsequent errors
+ if ( depth ) {
+ process();
+ } else {
+
+ // Call an optional hook to record the stack, in case of exception
+ // since it's otherwise lost when execution goes async
+ if ( jQuery.Deferred.getStackHook ) {
+ process.stackTrace = jQuery.Deferred.getStackHook();
+ }
+ window.setTimeout( process );
+ }
+ };
+ }
+
+ return jQuery.Deferred( function( newDefer ) {
+
+ // progress_handlers.add( ... )
+ tuples[ 0 ][ 3 ].add(
+ resolve(
+ 0,
+ newDefer,
+ isFunction( onProgress ) ?
+ onProgress :
+ Identity,
+ newDefer.notifyWith
+ )
+ );
+
+ // fulfilled_handlers.add( ... )
+ tuples[ 1 ][ 3 ].add(
+ resolve(
+ 0,
+ newDefer,
+ isFunction( onFulfilled ) ?
+ onFulfilled :
+ Identity
+ )
+ );
+
+ // rejected_handlers.add( ... )
+ tuples[ 2 ][ 3 ].add(
+ resolve(
+ 0,
+ newDefer,
+ isFunction( onRejected ) ?
+ onRejected :
+ Thrower
+ )
+ );
+ } ).promise();
+ },
+
+ // Get a promise for this deferred
+ // If obj is provided, the promise aspect is added to the object
+ promise: function( obj ) {
+ return obj != null ? jQuery.extend( obj, promise ) : promise;
+ }
+ },
+ deferred = {};
+
+ // Add list-specific methods
+ jQuery.each( tuples, function( i, tuple ) {
+ var list = tuple[ 2 ],
+ stateString = tuple[ 5 ];
+
+ // promise.progress = list.add
+ // promise.done = list.add
+ // promise.fail = list.add
+ promise[ tuple[ 1 ] ] = list.add;
+
+ // Handle state
+ if ( stateString ) {
+ list.add(
+ function() {
+
+ // state = "resolved" (i.e., fulfilled)
+ // state = "rejected"
+ state = stateString;
+ },
+
+ // rejected_callbacks.disable
+ // fulfilled_callbacks.disable
+ tuples[ 3 - i ][ 2 ].disable,
+
+ // rejected_handlers.disable
+ // fulfilled_handlers.disable
+ tuples[ 3 - i ][ 3 ].disable,
+
+ // progress_callbacks.lock
+ tuples[ 0 ][ 2 ].lock,
+
+ // progress_handlers.lock
+ tuples[ 0 ][ 3 ].lock
+ );
+ }
+
+ // progress_handlers.fire
+ // fulfilled_handlers.fire
+ // rejected_handlers.fire
+ list.add( tuple[ 3 ].fire );
+
+ // deferred.notify = function() { deferred.notifyWith(...) }
+ // deferred.resolve = function() { deferred.resolveWith(...) }
+ // deferred.reject = function() { deferred.rejectWith(...) }
+ deferred[ tuple[ 0 ] ] = function() {
+ deferred[ tuple[ 0 ] + "With" ]( this === deferred ? undefined : this, arguments );
+ return this;
+ };
+
+ // deferred.notifyWith = list.fireWith
+ // deferred.resolveWith = list.fireWith
+ // deferred.rejectWith = list.fireWith
+ deferred[ tuple[ 0 ] + "With" ] = list.fireWith;
+ } );
+
+ // Make the deferred a promise
+ promise.promise( deferred );
+
+ // Call given func if any
+ if ( func ) {
+ func.call( deferred, deferred );
+ }
+
+ // All done!
+ return deferred;
+ },
+
+ // Deferred helper
+ when: function( singleValue ) {
+ var
+
+ // count of uncompleted subordinates
+ remaining = arguments.length,
+
+ // count of unprocessed arguments
+ i = remaining,
+
+ // subordinate fulfillment data
+ resolveContexts = Array( i ),
+ resolveValues = slice.call( arguments ),
+
+ // the master Deferred
+ master = jQuery.Deferred(),
+
+ // subordinate callback factory
+ updateFunc = function( i ) {
+ return function( value ) {
+ resolveContexts[ i ] = this;
+ resolveValues[ i ] = arguments.length > 1 ? slice.call( arguments ) : value;
+ if ( !( --remaining ) ) {
+ master.resolveWith( resolveContexts, resolveValues );
+ }
+ };
+ };
+
+ // Single- and empty arguments are adopted like Promise.resolve
+ if ( remaining <= 1 ) {
+ adoptValue( singleValue, master.done( updateFunc( i ) ).resolve, master.reject,
+ !remaining );
+
+ // Use .then() to unwrap secondary thenables (cf. gh-3000)
+ if ( master.state() === "pending" ||
+ isFunction( resolveValues[ i ] && resolveValues[ i ].then ) ) {
+
+ return master.then();
+ }
+ }
+
+ // Multiple arguments are aggregated like Promise.all array elements
+ while ( i-- ) {
+ adoptValue( resolveValues[ i ], updateFunc( i ), master.reject );
+ }
+
+ return master.promise();
+ }
+} );
+
+
+// These usually indicate a programmer mistake during development,
+// warn about them ASAP rather than swallowing them by default.
+var rerrorNames = /^(Eval|Internal|Range|Reference|Syntax|Type|URI)Error$/;
+
+jQuery.Deferred.exceptionHook = function( error, stack ) {
+
+ // Support: IE 8 - 9 only
+ // Console exists when dev tools are open, which can happen at any time
+ if ( window.console && window.console.warn && error && rerrorNames.test( error.name ) ) {
+ window.console.warn( "jQuery.Deferred exception: " + error.message, error.stack, stack );
+ }
+};
+
+
+
+
+jQuery.readyException = function( error ) {
+ window.setTimeout( function() {
+ throw error;
+ } );
+};
+
+
+
+
+// The deferred used on DOM ready
+var readyList = jQuery.Deferred();
+
+jQuery.fn.ready = function( fn ) {
+
+ readyList
+ .then( fn )
+
+ // Wrap jQuery.readyException in a function so that the lookup
+ // happens at the time of error handling instead of callback
+ // registration.
+ .catch( function( error ) {
+ jQuery.readyException( error );
+ } );
+
+ return this;
+};
+
+jQuery.extend( {
+
+ // Is the DOM ready to be used? Set to true once it occurs.
+ isReady: false,
+
+ // A counter to track how many items to wait for before
+ // the ready event fires. See #6781
+ readyWait: 1,
+
+ // Handle when the DOM is ready
+ ready: function( wait ) {
+
+ // Abort if there are pending holds or we're already ready
+ if ( wait === true ? --jQuery.readyWait : jQuery.isReady ) {
+ return;
+ }
+
+ // Remember that the DOM is ready
+ jQuery.isReady = true;
+
+ // If a normal DOM Ready event fired, decrement, and wait if need be
+ if ( wait !== true && --jQuery.readyWait > 0 ) {
+ return;
+ }
+
+ // If there are functions bound, to execute
+ readyList.resolveWith( document, [ jQuery ] );
+ }
+} );
+
+jQuery.ready.then = readyList.then;
+
+// The ready event handler and self cleanup method
+function completed() {
+ document.removeEventListener( "DOMContentLoaded", completed );
+ window.removeEventListener( "load", completed );
+ jQuery.ready();
+}
+
+// Catch cases where $(document).ready() is called
+// after the browser event has already occurred.
+// Support: IE <=9 - 10 only
+// Older IE sometimes signals "interactive" too soon
+if ( document.readyState === "complete" ||
+ ( document.readyState !== "loading" && !document.documentElement.doScroll ) ) {
+
+ // Handle it asynchronously to allow scripts the opportunity to delay ready
+ window.setTimeout( jQuery.ready );
+
+} else {
+
+ // Use the handy event callback
+ document.addEventListener( "DOMContentLoaded", completed );
+
+ // A fallback to window.onload, that will always work
+ window.addEventListener( "load", completed );
+}
+
+
+
+
+// Multifunctional method to get and set values of a collection
+// The value/s can optionally be executed if it's a function
+var access = function( elems, fn, key, value, chainable, emptyGet, raw ) {
+ var i = 0,
+ len = elems.length,
+ bulk = key == null;
+
+ // Sets many values
+ if ( toType( key ) === "object" ) {
+ chainable = true;
+ for ( i in key ) {
+ access( elems, fn, i, key[ i ], true, emptyGet, raw );
+ }
+
+ // Sets one value
+ } else if ( value !== undefined ) {
+ chainable = true;
+
+ if ( !isFunction( value ) ) {
+ raw = true;
+ }
+
+ if ( bulk ) {
+
+ // Bulk operations run against the entire set
+ if ( raw ) {
+ fn.call( elems, value );
+ fn = null;
+
+ // ...except when executing function values
+ } else {
+ bulk = fn;
+ fn = function( elem, _key, value ) {
+ return bulk.call( jQuery( elem ), value );
+ };
+ }
+ }
+
+ if ( fn ) {
+ for ( ; i < len; i++ ) {
+ fn(
+ elems[ i ], key, raw ?
+ value :
+ value.call( elems[ i ], i, fn( elems[ i ], key ) )
+ );
+ }
+ }
+ }
+
+ if ( chainable ) {
+ return elems;
+ }
+
+ // Gets
+ if ( bulk ) {
+ return fn.call( elems );
+ }
+
+ return len ? fn( elems[ 0 ], key ) : emptyGet;
+};
+
+
+// Matches dashed string for camelizing
+var rmsPrefix = /^-ms-/,
+ rdashAlpha = /-([a-z])/g;
+
+// Used by camelCase as callback to replace()
+function fcamelCase( _all, letter ) {
+ return letter.toUpperCase();
+}
+
+// Convert dashed to camelCase; used by the css and data modules
+// Support: IE <=9 - 11, Edge 12 - 15
+// Microsoft forgot to hump their vendor prefix (#9572)
+function camelCase( string ) {
+ return string.replace( rmsPrefix, "ms-" ).replace( rdashAlpha, fcamelCase );
+}
+var acceptData = function( owner ) {
+
+ // Accepts only:
+ // - Node
+ // - Node.ELEMENT_NODE
+ // - Node.DOCUMENT_NODE
+ // - Object
+ // - Any
+ return owner.nodeType === 1 || owner.nodeType === 9 || !( +owner.nodeType );
+};
+
+
+
+
+function Data() {
+ this.expando = jQuery.expando + Data.uid++;
+}
+
+Data.uid = 1;
+
+Data.prototype = {
+
+ cache: function( owner ) {
+
+ // Check if the owner object already has a cache
+ var value = owner[ this.expando ];
+
+ // If not, create one
+ if ( !value ) {
+ value = {};
+
+ // We can accept data for non-element nodes in modern browsers,
+ // but we should not, see #8335.
+ // Always return an empty object.
+ if ( acceptData( owner ) ) {
+
+ // If it is a node unlikely to be stringify-ed or looped over
+ // use plain assignment
+ if ( owner.nodeType ) {
+ owner[ this.expando ] = value;
+
+ // Otherwise secure it in a non-enumerable property
+ // configurable must be true to allow the property to be
+ // deleted when data is removed
+ } else {
+ Object.defineProperty( owner, this.expando, {
+ value: value,
+ configurable: true
+ } );
+ }
+ }
+ }
+
+ return value;
+ },
+ set: function( owner, data, value ) {
+ var prop,
+ cache = this.cache( owner );
+
+ // Handle: [ owner, key, value ] args
+ // Always use camelCase key (gh-2257)
+ if ( typeof data === "string" ) {
+ cache[ camelCase( data ) ] = value;
+
+ // Handle: [ owner, { properties } ] args
+ } else {
+
+ // Copy the properties one-by-one to the cache object
+ for ( prop in data ) {
+ cache[ camelCase( prop ) ] = data[ prop ];
+ }
+ }
+ return cache;
+ },
+ get: function( owner, key ) {
+ return key === undefined ?
+ this.cache( owner ) :
+
+ // Always use camelCase key (gh-2257)
+ owner[ this.expando ] && owner[ this.expando ][ camelCase( key ) ];
+ },
+ access: function( owner, key, value ) {
+
+ // In cases where either:
+ //
+ // 1. No key was specified
+ // 2. A string key was specified, but no value provided
+ //
+ // Take the "read" path and allow the get method to determine
+ // which value to return, respectively either:
+ //
+ // 1. The entire cache object
+ // 2. The data stored at the key
+ //
+ if ( key === undefined ||
+ ( ( key && typeof key === "string" ) && value === undefined ) ) {
+
+ return this.get( owner, key );
+ }
+
+ // When the key is not a string, or both a key and value
+ // are specified, set or extend (existing objects) with either:
+ //
+ // 1. An object of properties
+ // 2. A key and value
+ //
+ this.set( owner, key, value );
+
+ // Since the "set" path can have two possible entry points
+ // return the expected data based on which path was taken[*]
+ return value !== undefined ? value : key;
+ },
+ remove: function( owner, key ) {
+ var i,
+ cache = owner[ this.expando ];
+
+ if ( cache === undefined ) {
+ return;
+ }
+
+ if ( key !== undefined ) {
+
+ // Support array or space separated string of keys
+ if ( Array.isArray( key ) ) {
+
+ // If key is an array of keys...
+ // We always set camelCase keys, so remove that.
+ key = key.map( camelCase );
+ } else {
+ key = camelCase( key );
+
+ // If a key with the spaces exists, use it.
+ // Otherwise, create an array by matching non-whitespace
+ key = key in cache ?
+ [ key ] :
+ ( key.match( rnothtmlwhite ) || [] );
+ }
+
+ i = key.length;
+
+ while ( i-- ) {
+ delete cache[ key[ i ] ];
+ }
+ }
+
+ // Remove the expando if there's no more data
+ if ( key === undefined || jQuery.isEmptyObject( cache ) ) {
+
+ // Support: Chrome <=35 - 45
+ // Webkit & Blink performance suffers when deleting properties
+ // from DOM nodes, so set to undefined instead
+ // https://bugs.chromium.org/p/chromium/issues/detail?id=378607 (bug restricted)
+ if ( owner.nodeType ) {
+ owner[ this.expando ] = undefined;
+ } else {
+ delete owner[ this.expando ];
+ }
+ }
+ },
+ hasData: function( owner ) {
+ var cache = owner[ this.expando ];
+ return cache !== undefined && !jQuery.isEmptyObject( cache );
+ }
+};
+var dataPriv = new Data();
+
+var dataUser = new Data();
+
+
+
+// Implementation Summary
+//
+// 1. Enforce API surface and semantic compatibility with 1.9.x branch
+// 2. Improve the module's maintainability by reducing the storage
+// paths to a single mechanism.
+// 3. Use the same single mechanism to support "private" and "user" data.
+// 4. _Never_ expose "private" data to user code (TODO: Drop _data, _removeData)
+// 5. Avoid exposing implementation details on user objects (eg. expando properties)
+// 6. Provide a clear path for implementation upgrade to WeakMap in 2014
+
+var rbrace = /^(?:\{[\w\W]*\}|\[[\w\W]*\])$/,
+ rmultiDash = /[A-Z]/g;
+
+function getData( data ) {
+ if ( data === "true" ) {
+ return true;
+ }
+
+ if ( data === "false" ) {
+ return false;
+ }
+
+ if ( data === "null" ) {
+ return null;
+ }
+
+ // Only convert to a number if it doesn't change the string
+ if ( data === +data + "" ) {
+ return +data;
+ }
+
+ if ( rbrace.test( data ) ) {
+ return JSON.parse( data );
+ }
+
+ return data;
+}
+
+function dataAttr( elem, key, data ) {
+ var name;
+
+ // If nothing was found internally, try to fetch any
+ // data from the HTML5 data-* attribute
+ if ( data === undefined && elem.nodeType === 1 ) {
+ name = "data-" + key.replace( rmultiDash, "-$&" ).toLowerCase();
+ data = elem.getAttribute( name );
+
+ if ( typeof data === "string" ) {
+ try {
+ data = getData( data );
+ } catch ( e ) {}
+
+ // Make sure we set the data so it isn't changed later
+ dataUser.set( elem, key, data );
+ } else {
+ data = undefined;
+ }
+ }
+ return data;
+}
+
+jQuery.extend( {
+ hasData: function( elem ) {
+ return dataUser.hasData( elem ) || dataPriv.hasData( elem );
+ },
+
+ data: function( elem, name, data ) {
+ return dataUser.access( elem, name, data );
+ },
+
+ removeData: function( elem, name ) {
+ dataUser.remove( elem, name );
+ },
+
+ // TODO: Now that all calls to _data and _removeData have been replaced
+ // with direct calls to dataPriv methods, these can be deprecated.
+ _data: function( elem, name, data ) {
+ return dataPriv.access( elem, name, data );
+ },
+
+ _removeData: function( elem, name ) {
+ dataPriv.remove( elem, name );
+ }
+} );
+
+jQuery.fn.extend( {
+ data: function( key, value ) {
+ var i, name, data,
+ elem = this[ 0 ],
+ attrs = elem && elem.attributes;
+
+ // Gets all values
+ if ( key === undefined ) {
+ if ( this.length ) {
+ data = dataUser.get( elem );
+
+ if ( elem.nodeType === 1 && !dataPriv.get( elem, "hasDataAttrs" ) ) {
+ i = attrs.length;
+ while ( i-- ) {
+
+ // Support: IE 11 only
+ // The attrs elements can be null (#14894)
+ if ( attrs[ i ] ) {
+ name = attrs[ i ].name;
+ if ( name.indexOf( "data-" ) === 0 ) {
+ name = camelCase( name.slice( 5 ) );
+ dataAttr( elem, name, data[ name ] );
+ }
+ }
+ }
+ dataPriv.set( elem, "hasDataAttrs", true );
+ }
+ }
+
+ return data;
+ }
+
+ // Sets multiple values
+ if ( typeof key === "object" ) {
+ return this.each( function() {
+ dataUser.set( this, key );
+ } );
+ }
+
+ return access( this, function( value ) {
+ var data;
+
+ // The calling jQuery object (element matches) is not empty
+ // (and therefore has an element appears at this[ 0 ]) and the
+ // `value` parameter was not undefined. An empty jQuery object
+ // will result in `undefined` for elem = this[ 0 ] which will
+ // throw an exception if an attempt to read a data cache is made.
+ if ( elem && value === undefined ) {
+
+ // Attempt to get data from the cache
+ // The key will always be camelCased in Data
+ data = dataUser.get( elem, key );
+ if ( data !== undefined ) {
+ return data;
+ }
+
+ // Attempt to "discover" the data in
+ // HTML5 custom data-* attrs
+ data = dataAttr( elem, key );
+ if ( data !== undefined ) {
+ return data;
+ }
+
+ // We tried really hard, but the data doesn't exist.
+ return;
+ }
+
+ // Set the data...
+ this.each( function() {
+
+ // We always store the camelCased key
+ dataUser.set( this, key, value );
+ } );
+ }, null, value, arguments.length > 1, null, true );
+ },
+
+ removeData: function( key ) {
+ return this.each( function() {
+ dataUser.remove( this, key );
+ } );
+ }
+} );
+
+
+jQuery.extend( {
+ queue: function( elem, type, data ) {
+ var queue;
+
+ if ( elem ) {
+ type = ( type || "fx" ) + "queue";
+ queue = dataPriv.get( elem, type );
+
+ // Speed up dequeue by getting out quickly if this is just a lookup
+ if ( data ) {
+ if ( !queue || Array.isArray( data ) ) {
+ queue = dataPriv.access( elem, type, jQuery.makeArray( data ) );
+ } else {
+ queue.push( data );
+ }
+ }
+ return queue || [];
+ }
+ },
+
+ dequeue: function( elem, type ) {
+ type = type || "fx";
+
+ var queue = jQuery.queue( elem, type ),
+ startLength = queue.length,
+ fn = queue.shift(),
+ hooks = jQuery._queueHooks( elem, type ),
+ next = function() {
+ jQuery.dequeue( elem, type );
+ };
+
+ // If the fx queue is dequeued, always remove the progress sentinel
+ if ( fn === "inprogress" ) {
+ fn = queue.shift();
+ startLength--;
+ }
+
+ if ( fn ) {
+
+ // Add a progress sentinel to prevent the fx queue from being
+ // automatically dequeued
+ if ( type === "fx" ) {
+ queue.unshift( "inprogress" );
+ }
+
+ // Clear up the last queue stop function
+ delete hooks.stop;
+ fn.call( elem, next, hooks );
+ }
+
+ if ( !startLength && hooks ) {
+ hooks.empty.fire();
+ }
+ },
+
+ // Not public - generate a queueHooks object, or return the current one
+ _queueHooks: function( elem, type ) {
+ var key = type + "queueHooks";
+ return dataPriv.get( elem, key ) || dataPriv.access( elem, key, {
+ empty: jQuery.Callbacks( "once memory" ).add( function() {
+ dataPriv.remove( elem, [ type + "queue", key ] );
+ } )
+ } );
+ }
+} );
+
+jQuery.fn.extend( {
+ queue: function( type, data ) {
+ var setter = 2;
+
+ if ( typeof type !== "string" ) {
+ data = type;
+ type = "fx";
+ setter--;
+ }
+
+ if ( arguments.length < setter ) {
+ return jQuery.queue( this[ 0 ], type );
+ }
+
+ return data === undefined ?
+ this :
+ this.each( function() {
+ var queue = jQuery.queue( this, type, data );
+
+ // Ensure a hooks for this queue
+ jQuery._queueHooks( this, type );
+
+ if ( type === "fx" && queue[ 0 ] !== "inprogress" ) {
+ jQuery.dequeue( this, type );
+ }
+ } );
+ },
+ dequeue: function( type ) {
+ return this.each( function() {
+ jQuery.dequeue( this, type );
+ } );
+ },
+ clearQueue: function( type ) {
+ return this.queue( type || "fx", [] );
+ },
+
+ // Get a promise resolved when queues of a certain type
+ // are emptied (fx is the type by default)
+ promise: function( type, obj ) {
+ var tmp,
+ count = 1,
+ defer = jQuery.Deferred(),
+ elements = this,
+ i = this.length,
+ resolve = function() {
+ if ( !( --count ) ) {
+ defer.resolveWith( elements, [ elements ] );
+ }
+ };
+
+ if ( typeof type !== "string" ) {
+ obj = type;
+ type = undefined;
+ }
+ type = type || "fx";
+
+ while ( i-- ) {
+ tmp = dataPriv.get( elements[ i ], type + "queueHooks" );
+ if ( tmp && tmp.empty ) {
+ count++;
+ tmp.empty.add( resolve );
+ }
+ }
+ resolve();
+ return defer.promise( obj );
+ }
+} );
+var pnum = ( /[+-]?(?:\d*\.|)\d+(?:[eE][+-]?\d+|)/ ).source;
+
+var rcssNum = new RegExp( "^(?:([+-])=|)(" + pnum + ")([a-z%]*)$", "i" );
+
+
+var cssExpand = [ "Top", "Right", "Bottom", "Left" ];
+
+var documentElement = document.documentElement;
+
+
+
+ var isAttached = function( elem ) {
+ return jQuery.contains( elem.ownerDocument, elem );
+ },
+ composed = { composed: true };
+
+ // Support: IE 9 - 11+, Edge 12 - 18+, iOS 10.0 - 10.2 only
+ // Check attachment across shadow DOM boundaries when possible (gh-3504)
+ // Support: iOS 10.0-10.2 only
+ // Early iOS 10 versions support `attachShadow` but not `getRootNode`,
+ // leading to errors. We need to check for `getRootNode`.
+ if ( documentElement.getRootNode ) {
+ isAttached = function( elem ) {
+ return jQuery.contains( elem.ownerDocument, elem ) ||
+ elem.getRootNode( composed ) === elem.ownerDocument;
+ };
+ }
+var isHiddenWithinTree = function( elem, el ) {
+
+ // isHiddenWithinTree might be called from jQuery#filter function;
+ // in that case, element will be second argument
+ elem = el || elem;
+
+ // Inline style trumps all
+ return elem.style.display === "none" ||
+ elem.style.display === "" &&
+
+ // Otherwise, check computed style
+ // Support: Firefox <=43 - 45
+ // Disconnected elements can have computed display: none, so first confirm that elem is
+ // in the document.
+ isAttached( elem ) &&
+
+ jQuery.css( elem, "display" ) === "none";
+ };
+
+
+
+function adjustCSS( elem, prop, valueParts, tween ) {
+ var adjusted, scale,
+ maxIterations = 20,
+ currentValue = tween ?
+ function() {
+ return tween.cur();
+ } :
+ function() {
+ return jQuery.css( elem, prop, "" );
+ },
+ initial = currentValue(),
+ unit = valueParts && valueParts[ 3 ] || ( jQuery.cssNumber[ prop ] ? "" : "px" ),
+
+ // Starting value computation is required for potential unit mismatches
+ initialInUnit = elem.nodeType &&
+ ( jQuery.cssNumber[ prop ] || unit !== "px" && +initial ) &&
+ rcssNum.exec( jQuery.css( elem, prop ) );
+
+ if ( initialInUnit && initialInUnit[ 3 ] !== unit ) {
+
+ // Support: Firefox <=54
+ // Halve the iteration target value to prevent interference from CSS upper bounds (gh-2144)
+ initial = initial / 2;
+
+ // Trust units reported by jQuery.css
+ unit = unit || initialInUnit[ 3 ];
+
+ // Iteratively approximate from a nonzero starting point
+ initialInUnit = +initial || 1;
+
+ while ( maxIterations-- ) {
+
+ // Evaluate and update our best guess (doubling guesses that zero out).
+ // Finish if the scale equals or crosses 1 (making the old*new product non-positive).
+ jQuery.style( elem, prop, initialInUnit + unit );
+ if ( ( 1 - scale ) * ( 1 - ( scale = currentValue() / initial || 0.5 ) ) <= 0 ) {
+ maxIterations = 0;
+ }
+ initialInUnit = initialInUnit / scale;
+
+ }
+
+ initialInUnit = initialInUnit * 2;
+ jQuery.style( elem, prop, initialInUnit + unit );
+
+ // Make sure we update the tween properties later on
+ valueParts = valueParts || [];
+ }
+
+ if ( valueParts ) {
+ initialInUnit = +initialInUnit || +initial || 0;
+
+ // Apply relative offset (+=/-=) if specified
+ adjusted = valueParts[ 1 ] ?
+ initialInUnit + ( valueParts[ 1 ] + 1 ) * valueParts[ 2 ] :
+ +valueParts[ 2 ];
+ if ( tween ) {
+ tween.unit = unit;
+ tween.start = initialInUnit;
+ tween.end = adjusted;
+ }
+ }
+ return adjusted;
+}
+
+
+var defaultDisplayMap = {};
+
+function getDefaultDisplay( elem ) {
+ var temp,
+ doc = elem.ownerDocument,
+ nodeName = elem.nodeName,
+ display = defaultDisplayMap[ nodeName ];
+
+ if ( display ) {
+ return display;
+ }
+
+ temp = doc.body.appendChild( doc.createElement( nodeName ) );
+ display = jQuery.css( temp, "display" );
+
+ temp.parentNode.removeChild( temp );
+
+ if ( display === "none" ) {
+ display = "block";
+ }
+ defaultDisplayMap[ nodeName ] = display;
+
+ return display;
+}
+
+function showHide( elements, show ) {
+ var display, elem,
+ values = [],
+ index = 0,
+ length = elements.length;
+
+ // Determine new display value for elements that need to change
+ for ( ; index < length; index++ ) {
+ elem = elements[ index ];
+ if ( !elem.style ) {
+ continue;
+ }
+
+ display = elem.style.display;
+ if ( show ) {
+
+ // Since we force visibility upon cascade-hidden elements, an immediate (and slow)
+ // check is required in this first loop unless we have a nonempty display value (either
+ // inline or about-to-be-restored)
+ if ( display === "none" ) {
+ values[ index ] = dataPriv.get( elem, "display" ) || null;
+ if ( !values[ index ] ) {
+ elem.style.display = "";
+ }
+ }
+ if ( elem.style.display === "" && isHiddenWithinTree( elem ) ) {
+ values[ index ] = getDefaultDisplay( elem );
+ }
+ } else {
+ if ( display !== "none" ) {
+ values[ index ] = "none";
+
+ // Remember what we're overwriting
+ dataPriv.set( elem, "display", display );
+ }
+ }
+ }
+
+ // Set the display of the elements in a second loop to avoid constant reflow
+ for ( index = 0; index < length; index++ ) {
+ if ( values[ index ] != null ) {
+ elements[ index ].style.display = values[ index ];
+ }
+ }
+
+ return elements;
+}
+
+jQuery.fn.extend( {
+ show: function() {
+ return showHide( this, true );
+ },
+ hide: function() {
+ return showHide( this );
+ },
+ toggle: function( state ) {
+ if ( typeof state === "boolean" ) {
+ return state ? this.show() : this.hide();
+ }
+
+ return this.each( function() {
+ if ( isHiddenWithinTree( this ) ) {
+ jQuery( this ).show();
+ } else {
+ jQuery( this ).hide();
+ }
+ } );
+ }
+} );
+var rcheckableType = ( /^(?:checkbox|radio)$/i );
+
+var rtagName = ( /<([a-z][^\/\0>\x20\t\r\n\f]*)/i );
+
+var rscriptType = ( /^$|^module$|\/(?:java|ecma)script/i );
+
+
+
+( function() {
+ var fragment = document.createDocumentFragment(),
+ div = fragment.appendChild( document.createElement( "div" ) ),
+ input = document.createElement( "input" );
+
+ // Support: Android 4.0 - 4.3 only
+ // Check state lost if the name is set (#11217)
+ // Support: Windows Web Apps (WWA)
+ // `name` and `type` must use .setAttribute for WWA (#14901)
+ input.setAttribute( "type", "radio" );
+ input.setAttribute( "checked", "checked" );
+ input.setAttribute( "name", "t" );
+
+ div.appendChild( input );
+
+ // Support: Android <=4.1 only
+ // Older WebKit doesn't clone checked state correctly in fragments
+ support.checkClone = div.cloneNode( true ).cloneNode( true ).lastChild.checked;
+
+ // Support: IE <=11 only
+ // Make sure textarea (and checkbox) defaultValue is properly cloned
+ div.innerHTML = "<textarea>x</textarea>";
+ support.noCloneChecked = !!div.cloneNode( true ).lastChild.defaultValue;
+
+ // Support: IE <=9 only
+ // IE <=9 replaces <option> tags with their contents when inserted outside of
+ // the select element.
+ div.innerHTML = "<option></option>";
+ support.option = !!div.lastChild;
+} )();
+
+
+// We have to close these tags to support XHTML (#13200)
+var wrapMap = {
+
+ // XHTML parsers do not magically insert elements in the
+ // same way that tag soup parsers do. So we cannot shorten
+ // this by omitting <tbody> or other required elements.
+ thead: [ 1, "<table>", "</table>" ],
+ col: [ 2, "<table><colgroup>", "</colgroup></table>" ],
+ tr: [ 2, "<table><tbody>", "</tbody></table>" ],
+ td: [ 3, "<table><tbody><tr>", "</tr></tbody></table>" ],
+
+ _default: [ 0, "", "" ]
+};
+
+wrapMap.tbody = wrapMap.tfoot = wrapMap.colgroup = wrapMap.caption = wrapMap.thead;
+wrapMap.th = wrapMap.td;
+
+// Support: IE <=9 only
+if ( !support.option ) {
+ wrapMap.optgroup = wrapMap.option = [ 1, "<select multiple='multiple'>", "</select>" ];
+}
+
+
+function getAll( context, tag ) {
+
+ // Support: IE <=9 - 11 only
+ // Use typeof to avoid zero-argument method invocation on host objects (#15151)
+ var ret;
+
+ if ( typeof context.getElementsByTagName !== "undefined" ) {
+ ret = context.getElementsByTagName( tag || "*" );
+
+ } else if ( typeof context.querySelectorAll !== "undefined" ) {
+ ret = context.querySelectorAll( tag || "*" );
+
+ } else {
+ ret = [];
+ }
+
+ if ( tag === undefined || tag && nodeName( context, tag ) ) {
+ return jQuery.merge( [ context ], ret );
+ }
+
+ return ret;
+}
+
+
+// Mark scripts as having already been evaluated
+function setGlobalEval( elems, refElements ) {
+ var i = 0,
+ l = elems.length;
+
+ for ( ; i < l; i++ ) {
+ dataPriv.set(
+ elems[ i ],
+ "globalEval",
+ !refElements || dataPriv.get( refElements[ i ], "globalEval" )
+ );
+ }
+}
+
+
+var rhtml = /<|&#?\w+;/;
+
+function buildFragment( elems, context, scripts, selection, ignored ) {
+ var elem, tmp, tag, wrap, attached, j,
+ fragment = context.createDocumentFragment(),
+ nodes = [],
+ i = 0,
+ l = elems.length;
+
+ for ( ; i < l; i++ ) {
+ elem = elems[ i ];
+
+ if ( elem || elem === 0 ) {
+
+ // Add nodes directly
+ if ( toType( elem ) === "object" ) {
+
+ // Support: Android <=4.0 only, PhantomJS 1 only
+ // push.apply(_, arraylike) throws on ancient WebKit
+ jQuery.merge( nodes, elem.nodeType ? [ elem ] : elem );
+
+ // Convert non-html into a text node
+ } else if ( !rhtml.test( elem ) ) {
+ nodes.push( context.createTextNode( elem ) );
+
+ // Convert html into DOM nodes
+ } else {
+ tmp = tmp || fragment.appendChild( context.createElement( "div" ) );
+
+ // Deserialize a standard representation
+ tag = ( rtagName.exec( elem ) || [ "", "" ] )[ 1 ].toLowerCase();
+ wrap = wrapMap[ tag ] || wrapMap._default;
+ tmp.innerHTML = wrap[ 1 ] + jQuery.htmlPrefilter( elem ) + wrap[ 2 ];
+
+ // Descend through wrappers to the right content
+ j = wrap[ 0 ];
+ while ( j-- ) {
+ tmp = tmp.lastChild;
+ }
+
+ // Support: Android <=4.0 only, PhantomJS 1 only
+ // push.apply(_, arraylike) throws on ancient WebKit
+ jQuery.merge( nodes, tmp.childNodes );
+
+ // Remember the top-level container
+ tmp = fragment.firstChild;
+
+ // Ensure the created nodes are orphaned (#12392)
+ tmp.textContent = "";
+ }
+ }
+ }
+
+ // Remove wrapper from fragment
+ fragment.textContent = "";
+
+ i = 0;
+ while ( ( elem = nodes[ i++ ] ) ) {
+
+ // Skip elements already in the context collection (trac-4087)
+ if ( selection && jQuery.inArray( elem, selection ) > -1 ) {
+ if ( ignored ) {
+ ignored.push( elem );
+ }
+ continue;
+ }
+
+ attached = isAttached( elem );
+
+ // Append to fragment
+ tmp = getAll( fragment.appendChild( elem ), "script" );
+
+ // Preserve script evaluation history
+ if ( attached ) {
+ setGlobalEval( tmp );
+ }
+
+ // Capture executables
+ if ( scripts ) {
+ j = 0;
+ while ( ( elem = tmp[ j++ ] ) ) {
+ if ( rscriptType.test( elem.type || "" ) ) {
+ scripts.push( elem );
+ }
+ }
+ }
+ }
+
+ return fragment;
+}
+
+
+var
+ rkeyEvent = /^key/,
+ rmouseEvent = /^(?:mouse|pointer|contextmenu|drag|drop)|click/,
+ rtypenamespace = /^([^.]*)(?:\.(.+)|)/;
+
+function returnTrue() {
+ return true;
+}
+
+function returnFalse() {
+ return false;
+}
+
+// Support: IE <=9 - 11+
+// focus() and blur() are asynchronous, except when they are no-op.
+// So expect focus to be synchronous when the element is already active,
+// and blur to be synchronous when the element is not already active.
+// (focus and blur are always synchronous in other supported browsers,
+// this just defines when we can count on it).
+function expectSync( elem, type ) {
+ return ( elem === safeActiveElement() ) === ( type === "focus" );
+}
+
+// Support: IE <=9 only
+// Accessing document.activeElement can throw unexpectedly
+// https://bugs.jquery.com/ticket/13393
+function safeActiveElement() {
+ try {
+ return document.activeElement;
+ } catch ( err ) { }
+}
+
+function on( elem, types, selector, data, fn, one ) {
+ var origFn, type;
+
+ // Types can be a map of types/handlers
+ if ( typeof types === "object" ) {
+
+ // ( types-Object, selector, data )
+ if ( typeof selector !== "string" ) {
+
+ // ( types-Object, data )
+ data = data || selector;
+ selector = undefined;
+ }
+ for ( type in types ) {
+ on( elem, type, selector, data, types[ type ], one );
+ }
+ return elem;
+ }
+
+ if ( data == null && fn == null ) {
+
+ // ( types, fn )
+ fn = selector;
+ data = selector = undefined;
+ } else if ( fn == null ) {
+ if ( typeof selector === "string" ) {
+
+ // ( types, selector, fn )
+ fn = data;
+ data = undefined;
+ } else {
+
+ // ( types, data, fn )
+ fn = data;
+ data = selector;
+ selector = undefined;
+ }
+ }
+ if ( fn === false ) {
+ fn = returnFalse;
+ } else if ( !fn ) {
+ return elem;
+ }
+
+ if ( one === 1 ) {
+ origFn = fn;
+ fn = function( event ) {
+
+ // Can use an empty set, since event contains the info
+ jQuery().off( event );
+ return origFn.apply( this, arguments );
+ };
+
+ // Use same guid so caller can remove using origFn
+ fn.guid = origFn.guid || ( origFn.guid = jQuery.guid++ );
+ }
+ return elem.each( function() {
+ jQuery.event.add( this, types, fn, data, selector );
+ } );
+}
+
+/*
+ * Helper functions for managing events -- not part of the public interface.
+ * Props to Dean Edwards' addEvent library for many of the ideas.
+ */
+jQuery.event = {
+
+ global: {},
+
+ add: function( elem, types, handler, data, selector ) {
+
+ var handleObjIn, eventHandle, tmp,
+ events, t, handleObj,
+ special, handlers, type, namespaces, origType,
+ elemData = dataPriv.get( elem );
+
+ // Only attach events to objects that accept data
+ if ( !acceptData( elem ) ) {
+ return;
+ }
+
+ // Caller can pass in an object of custom data in lieu of the handler
+ if ( handler.handler ) {
+ handleObjIn = handler;
+ handler = handleObjIn.handler;
+ selector = handleObjIn.selector;
+ }
+
+ // Ensure that invalid selectors throw exceptions at attach time
+ // Evaluate against documentElement in case elem is a non-element node (e.g., document)
+ if ( selector ) {
+ jQuery.find.matchesSelector( documentElement, selector );
+ }
+
+ // Make sure that the handler has a unique ID, used to find/remove it later
+ if ( !handler.guid ) {
+ handler.guid = jQuery.guid++;
+ }
+
+ // Init the element's event structure and main handler, if this is the first
+ if ( !( events = elemData.events ) ) {
+ events = elemData.events = Object.create( null );
+ }
+ if ( !( eventHandle = elemData.handle ) ) {
+ eventHandle = elemData.handle = function( e ) {
+
+ // Discard the second event of a jQuery.event.trigger() and
+ // when an event is called after a page has unloaded
+ return typeof jQuery !== "undefined" && jQuery.event.triggered !== e.type ?
+ jQuery.event.dispatch.apply( elem, arguments ) : undefined;
+ };
+ }
+
+ // Handle multiple events separated by a space
+ types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+ t = types.length;
+ while ( t-- ) {
+ tmp = rtypenamespace.exec( types[ t ] ) || [];
+ type = origType = tmp[ 1 ];
+ namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+ // There *must* be a type, no attaching namespace-only handlers
+ if ( !type ) {
+ continue;
+ }
+
+ // If event changes its type, use the special event handlers for the changed type
+ special = jQuery.event.special[ type ] || {};
+
+ // If selector defined, determine special event api type, otherwise given type
+ type = ( selector ? special.delegateType : special.bindType ) || type;
+
+ // Update special based on newly reset type
+ special = jQuery.event.special[ type ] || {};
+
+ // handleObj is passed to all event handlers
+ handleObj = jQuery.extend( {
+ type: type,
+ origType: origType,
+ data: data,
+ handler: handler,
+ guid: handler.guid,
+ selector: selector,
+ needsContext: selector && jQuery.expr.match.needsContext.test( selector ),
+ namespace: namespaces.join( "." )
+ }, handleObjIn );
+
+ // Init the event handler queue if we're the first
+ if ( !( handlers = events[ type ] ) ) {
+ handlers = events[ type ] = [];
+ handlers.delegateCount = 0;
+
+ // Only use addEventListener if the special events handler returns false
+ if ( !special.setup ||
+ special.setup.call( elem, data, namespaces, eventHandle ) === false ) {
+
+ if ( elem.addEventListener ) {
+ elem.addEventListener( type, eventHandle );
+ }
+ }
+ }
+
+ if ( special.add ) {
+ special.add.call( elem, handleObj );
+
+ if ( !handleObj.handler.guid ) {
+ handleObj.handler.guid = handler.guid;
+ }
+ }
+
+ // Add to the element's handler list, delegates in front
+ if ( selector ) {
+ handlers.splice( handlers.delegateCount++, 0, handleObj );
+ } else {
+ handlers.push( handleObj );
+ }
+
+ // Keep track of which events have ever been used, for event optimization
+ jQuery.event.global[ type ] = true;
+ }
+
+ },
+
+ // Detach an event or set of events from an element
+ remove: function( elem, types, handler, selector, mappedTypes ) {
+
+ var j, origCount, tmp,
+ events, t, handleObj,
+ special, handlers, type, namespaces, origType,
+ elemData = dataPriv.hasData( elem ) && dataPriv.get( elem );
+
+ if ( !elemData || !( events = elemData.events ) ) {
+ return;
+ }
+
+ // Once for each type.namespace in types; type may be omitted
+ types = ( types || "" ).match( rnothtmlwhite ) || [ "" ];
+ t = types.length;
+ while ( t-- ) {
+ tmp = rtypenamespace.exec( types[ t ] ) || [];
+ type = origType = tmp[ 1 ];
+ namespaces = ( tmp[ 2 ] || "" ).split( "." ).sort();
+
+ // Unbind all events (on this namespace, if provided) for the element
+ if ( !type ) {
+ for ( type in events ) {
+ jQuery.event.remove( elem, type + types[ t ], handler, selector, true );
+ }
+ continue;
+ }
+
+ special = jQuery.event.special[ type ] || {};
+ type = ( selector ? special.delegateType : special.bindType ) || type;
+ handlers = events[ type ] || [];
+ tmp = tmp[ 2 ] &&
+ new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" );
+
+ // Remove matching events
+ origCount = j = handlers.length;
+ while ( j-- ) {
+ handleObj = handlers[ j ];
+
+ if ( ( mappedTypes || origType === handleObj.origType ) &&
+ ( !handler || handler.guid === handleObj.guid ) &&
+ ( !tmp || tmp.test( handleObj.namespace ) ) &&
+ ( !selector || selector === handleObj.selector ||
+ selector === "**" && handleObj.selector ) ) {
+ handlers.splice( j, 1 );
+
+ if ( handleObj.selector ) {
+ handlers.delegateCount--;
+ }
+ if ( special.remove ) {
+ special.remove.call( elem, handleObj );
+ }
+ }
+ }
+
+ // Remove generic event handler if we removed something and no more handlers exist
+ // (avoids potential for endless recursion during removal of special event handlers)
+ if ( origCount && !handlers.length ) {
+ if ( !special.teardown ||
+ special.teardown.call( elem, namespaces, elemData.handle ) === false ) {
+
+ jQuery.removeEvent( elem, type, elemData.handle );
+ }
+
+ delete events[ type ];
+ }
+ }
+
+ // Remove data and the expando if it's no longer used
+ if ( jQuery.isEmptyObject( events ) ) {
+ dataPriv.remove( elem, "handle events" );
+ }
+ },
+
+ dispatch: function( nativeEvent ) {
+
+ var i, j, ret, matched, handleObj, handlerQueue,
+ args = new Array( arguments.length ),
+
+ // Make a writable jQuery.Event from the native event object
+ event = jQuery.event.fix( nativeEvent ),
+
+ handlers = (
+ dataPriv.get( this, "events" ) || Object.create( null )
+ )[ event.type ] || [],
+ special = jQuery.event.special[ event.type ] || {};
+
+ // Use the fix-ed jQuery.Event rather than the (read-only) native event
+ args[ 0 ] = event;
+
+ for ( i = 1; i < arguments.length; i++ ) {
+ args[ i ] = arguments[ i ];
+ }
+
+ event.delegateTarget = this;
+
+ // Call the preDispatch hook for the mapped type, and let it bail if desired
+ if ( special.preDispatch && special.preDispatch.call( this, event ) === false ) {
+ return;
+ }
+
+ // Determine handlers
+ handlerQueue = jQuery.event.handlers.call( this, event, handlers );
+
+ // Run delegates first; they may want to stop propagation beneath us
+ i = 0;
+ while ( ( matched = handlerQueue[ i++ ] ) && !event.isPropagationStopped() ) {
+ event.currentTarget = matched.elem;
+
+ j = 0;
+ while ( ( handleObj = matched.handlers[ j++ ] ) &&
+ !event.isImmediatePropagationStopped() ) {
+
+ // If the event is namespaced, then each handler is only invoked if it is
+ // specially universal or its namespaces are a superset of the event's.
+ if ( !event.rnamespace || handleObj.namespace === false ||
+ event.rnamespace.test( handleObj.namespace ) ) {
+
+ event.handleObj = handleObj;
+ event.data = handleObj.data;
+
+ ret = ( ( jQuery.event.special[ handleObj.origType ] || {} ).handle ||
+ handleObj.handler ).apply( matched.elem, args );
+
+ if ( ret !== undefined ) {
+ if ( ( event.result = ret ) === false ) {
+ event.preventDefault();
+ event.stopPropagation();
+ }
+ }
+ }
+ }
+ }
+
+ // Call the postDispatch hook for the mapped type
+ if ( special.postDispatch ) {
+ special.postDispatch.call( this, event );
+ }
+
+ return event.result;
+ },
+
+ handlers: function( event, handlers ) {
+ var i, handleObj, sel, matchedHandlers, matchedSelectors,
+ handlerQueue = [],
+ delegateCount = handlers.delegateCount,
+ cur = event.target;
+
+ // Find delegate handlers
+ if ( delegateCount &&
+
+ // Support: IE <=9
+ // Black-hole SVG <use> instance trees (trac-13180)
+ cur.nodeType &&
+
+ // Support: Firefox <=42
+ // Suppress spec-violating clicks indicating a non-primary pointer button (trac-3861)
+ // https://www.w3.org/TR/DOM-Level-3-Events/#event-type-click
+ // Support: IE 11 only
+ // ...but not arrow key "clicks" of radio inputs, which can have `button` -1 (gh-2343)
+ !( event.type === "click" && event.button >= 1 ) ) {
+
+ for ( ; cur !== this; cur = cur.parentNode || this ) {
+
+ // Don't check non-elements (#13208)
+ // Don't process clicks on disabled elements (#6911, #8165, #11382, #11764)
+ if ( cur.nodeType === 1 && !( event.type === "click" && cur.disabled === true ) ) {
+ matchedHandlers = [];
+ matchedSelectors = {};
+ for ( i = 0; i < delegateCount; i++ ) {
+ handleObj = handlers[ i ];
+
+ // Don't conflict with Object.prototype properties (#13203)
+ sel = handleObj.selector + " ";
+
+ if ( matchedSelectors[ sel ] === undefined ) {
+ matchedSelectors[ sel ] = handleObj.needsContext ?
+ jQuery( sel, this ).index( cur ) > -1 :
+ jQuery.find( sel, this, null, [ cur ] ).length;
+ }
+ if ( matchedSelectors[ sel ] ) {
+ matchedHandlers.push( handleObj );
+ }
+ }
+ if ( matchedHandlers.length ) {
+ handlerQueue.push( { elem: cur, handlers: matchedHandlers } );
+ }
+ }
+ }
+ }
+
+ // Add the remaining (directly-bound) handlers
+ cur = this;
+ if ( delegateCount < handlers.length ) {
+ handlerQueue.push( { elem: cur, handlers: handlers.slice( delegateCount ) } );
+ }
+
+ return handlerQueue;
+ },
+
+ addProp: function( name, hook ) {
+ Object.defineProperty( jQuery.Event.prototype, name, {
+ enumerable: true,
+ configurable: true,
+
+ get: isFunction( hook ) ?
+ function() {
+ if ( this.originalEvent ) {
+ return hook( this.originalEvent );
+ }
+ } :
+ function() {
+ if ( this.originalEvent ) {
+ return this.originalEvent[ name ];
+ }
+ },
+
+ set: function( value ) {
+ Object.defineProperty( this, name, {
+ enumerable: true,
+ configurable: true,
+ writable: true,
+ value: value
+ } );
+ }
+ } );
+ },
+
+ fix: function( originalEvent ) {
+ return originalEvent[ jQuery.expando ] ?
+ originalEvent :
+ new jQuery.Event( originalEvent );
+ },
+
+ special: {
+ load: {
+
+ // Prevent triggered image.load events from bubbling to window.load
+ noBubble: true
+ },
+ click: {
+
+ // Utilize native event to ensure correct state for checkable inputs
+ setup: function( data ) {
+
+ // For mutual compressibility with _default, replace `this` access with a local var.
+ // `|| data` is dead code meant only to preserve the variable through minification.
+ var el = this || data;
+
+ // Claim the first handler
+ if ( rcheckableType.test( el.type ) &&
+ el.click && nodeName( el, "input" ) ) {
+
+ // dataPriv.set( el, "click", ... )
+ leverageNative( el, "click", returnTrue );
+ }
+
+ // Return false to allow normal processing in the caller
+ return false;
+ },
+ trigger: function( data ) {
+
+ // For mutual compressibility with _default, replace `this` access with a local var.
+ // `|| data` is dead code meant only to preserve the variable through minification.
+ var el = this || data;
+
+ // Force setup before triggering a click
+ if ( rcheckableType.test( el.type ) &&
+ el.click && nodeName( el, "input" ) ) {
+
+ leverageNative( el, "click" );
+ }
+
+ // Return non-false to allow normal event-path propagation
+ return true;
+ },
+
+ // For cross-browser consistency, suppress native .click() on links
+ // Also prevent it if we're currently inside a leveraged native-event stack
+ _default: function( event ) {
+ var target = event.target;
+ return rcheckableType.test( target.type ) &&
+ target.click && nodeName( target, "input" ) &&
+ dataPriv.get( target, "click" ) ||
+ nodeName( target, "a" );
+ }
+ },
+
+ beforeunload: {
+ postDispatch: function( event ) {
+
+ // Support: Firefox 20+
+ // Firefox doesn't alert if the returnValue field is not set.
+ if ( event.result !== undefined && event.originalEvent ) {
+ event.originalEvent.returnValue = event.result;
+ }
+ }
+ }
+ }
+};
+
+// Ensure the presence of an event listener that handles manually-triggered
+// synthetic events by interrupting progress until reinvoked in response to
+// *native* events that it fires directly, ensuring that state changes have
+// already occurred before other listeners are invoked.
+function leverageNative( el, type, expectSync ) {
+
+ // Missing expectSync indicates a trigger call, which must force setup through jQuery.event.add
+ if ( !expectSync ) {
+ if ( dataPriv.get( el, type ) === undefined ) {
+ jQuery.event.add( el, type, returnTrue );
+ }
+ return;
+ }
+
+ // Register the controller as a special universal handler for all event namespaces
+ dataPriv.set( el, type, false );
+ jQuery.event.add( el, type, {
+ namespace: false,
+ handler: function( event ) {
+ var notAsync, result,
+ saved = dataPriv.get( this, type );
+
+ if ( ( event.isTrigger & 1 ) && this[ type ] ) {
+
+ // Interrupt processing of the outer synthetic .trigger()ed event
+ // Saved data should be false in such cases, but might be a leftover capture object
+ // from an async native handler (gh-4350)
+ if ( !saved.length ) {
+
+ // Store arguments for use when handling the inner native event
+ // There will always be at least one argument (an event object), so this array
+ // will not be confused with a leftover capture object.
+ saved = slice.call( arguments );
+ dataPriv.set( this, type, saved );
+
+ // Trigger the native event and capture its result
+ // Support: IE <=9 - 11+
+ // focus() and blur() are asynchronous
+ notAsync = expectSync( this, type );
+ this[ type ]();
+ result = dataPriv.get( this, type );
+ if ( saved !== result || notAsync ) {
+ dataPriv.set( this, type, false );
+ } else {
+ result = {};
+ }
+ if ( saved !== result ) {
+
+ // Cancel the outer synthetic event
+ event.stopImmediatePropagation();
+ event.preventDefault();
+ return result.value;
+ }
+
+ // If this is an inner synthetic event for an event with a bubbling surrogate
+ // (focus or blur), assume that the surrogate already propagated from triggering the
+ // native event and prevent that from happening again here.
+ // This technically gets the ordering wrong w.r.t. to `.trigger()` (in which the
+ // bubbling surrogate propagates *after* the non-bubbling base), but that seems
+ // less bad than duplication.
+ } else if ( ( jQuery.event.special[ type ] || {} ).delegateType ) {
+ event.stopPropagation();
+ }
+
+ // If this is a native event triggered above, everything is now in order
+ // Fire an inner synthetic event with the original arguments
+ } else if ( saved.length ) {
+
+ // ...and capture the result
+ dataPriv.set( this, type, {
+ value: jQuery.event.trigger(
+
+ // Support: IE <=9 - 11+
+ // Extend with the prototype to reset the above stopImmediatePropagation()
+ jQuery.extend( saved[ 0 ], jQuery.Event.prototype ),
+ saved.slice( 1 ),
+ this
+ )
+ } );
+
+ // Abort handling of the native event
+ event.stopImmediatePropagation();
+ }
+ }
+ } );
+}
+
+jQuery.removeEvent = function( elem, type, handle ) {
+
+ // This "if" is needed for plain objects
+ if ( elem.removeEventListener ) {
+ elem.removeEventListener( type, handle );
+ }
+};
+
+jQuery.Event = function( src, props ) {
+
+ // Allow instantiation without the 'new' keyword
+ if ( !( this instanceof jQuery.Event ) ) {
+ return new jQuery.Event( src, props );
+ }
+
+ // Event object
+ if ( src && src.type ) {
+ this.originalEvent = src;
+ this.type = src.type;
+
+ // Events bubbling up the document may have been marked as prevented
+ // by a handler lower down the tree; reflect the correct value.
+ this.isDefaultPrevented = src.defaultPrevented ||
+ src.defaultPrevented === undefined &&
+
+ // Support: Android <=2.3 only
+ src.returnValue === false ?
+ returnTrue :
+ returnFalse;
+
+ // Create target properties
+ // Support: Safari <=6 - 7 only
+ // Target should not be a text node (#504, #13143)
+ this.target = ( src.target && src.target.nodeType === 3 ) ?
+ src.target.parentNode :
+ src.target;
+
+ this.currentTarget = src.currentTarget;
+ this.relatedTarget = src.relatedTarget;
+
+ // Event type
+ } else {
+ this.type = src;
+ }
+
+ // Put explicitly provided properties onto the event object
+ if ( props ) {
+ jQuery.extend( this, props );
+ }
+
+ // Create a timestamp if incoming event doesn't have one
+ this.timeStamp = src && src.timeStamp || Date.now();
+
+ // Mark it as fixed
+ this[ jQuery.expando ] = true;
+};
+
+// jQuery.Event is based on DOM3 Events as specified by the ECMAScript Language Binding
+// https://www.w3.org/TR/2003/WD-DOM-Level-3-Events-20030331/ecma-script-binding.html
+jQuery.Event.prototype = {
+ constructor: jQuery.Event,
+ isDefaultPrevented: returnFalse,
+ isPropagationStopped: returnFalse,
+ isImmediatePropagationStopped: returnFalse,
+ isSimulated: false,
+
+ preventDefault: function() {
+ var e = this.originalEvent;
+
+ this.isDefaultPrevented = returnTrue;
+
+ if ( e && !this.isSimulated ) {
+ e.preventDefault();
+ }
+ },
+ stopPropagation: function() {
+ var e = this.originalEvent;
+
+ this.isPropagationStopped = returnTrue;
+
+ if ( e && !this.isSimulated ) {
+ e.stopPropagation();
+ }
+ },
+ stopImmediatePropagation: function() {
+ var e = this.originalEvent;
+
+ this.isImmediatePropagationStopped = returnTrue;
+
+ if ( e && !this.isSimulated ) {
+ e.stopImmediatePropagation();
+ }
+
+ this.stopPropagation();
+ }
+};
+
+// Includes all common event props including KeyEvent and MouseEvent specific props
+jQuery.each( {
+ altKey: true,
+ bubbles: true,
+ cancelable: true,
+ changedTouches: true,
+ ctrlKey: true,
+ detail: true,
+ eventPhase: true,
+ metaKey: true,
+ pageX: true,
+ pageY: true,
+ shiftKey: true,
+ view: true,
+ "char": true,
+ code: true,
+ charCode: true,
+ key: true,
+ keyCode: true,
+ button: true,
+ buttons: true,
+ clientX: true,
+ clientY: true,
+ offsetX: true,
+ offsetY: true,
+ pointerId: true,
+ pointerType: true,
+ screenX: true,
+ screenY: true,
+ targetTouches: true,
+ toElement: true,
+ touches: true,
+
+ which: function( event ) {
+ var button = event.button;
+
+ // Add which for key events
+ if ( event.which == null && rkeyEvent.test( event.type ) ) {
+ return event.charCode != null ? event.charCode : event.keyCode;
+ }
+
+ // Add which for click: 1 === left; 2 === middle; 3 === right
+ if ( !event.which && button !== undefined && rmouseEvent.test( event.type ) ) {
+ if ( button & 1 ) {
+ return 1;
+ }
+
+ if ( button & 2 ) {
+ return 3;
+ }
+
+ if ( button & 4 ) {
+ return 2;
+ }
+
+ return 0;
+ }
+
+ return event.which;
+ }
+}, jQuery.event.addProp );
+
+jQuery.each( { focus: "focusin", blur: "focusout" }, function( type, delegateType ) {
+ jQuery.event.special[ type ] = {
+
+ // Utilize native event if possible so blur/focus sequence is correct
+ setup: function() {
+
+ // Claim the first handler
+ // dataPriv.set( this, "focus", ... )
+ // dataPriv.set( this, "blur", ... )
+ leverageNative( this, type, expectSync );
+
+ // Return false to allow normal processing in the caller
+ return false;
+ },
+ trigger: function() {
+
+ // Force setup before trigger
+ leverageNative( this, type );
+
+ // Return non-false to allow normal event-path propagation
+ return true;
+ },
+
+ delegateType: delegateType
+ };
+} );
+
+// Create mouseenter/leave events using mouseover/out and event-time checks
+// so that event delegation works in jQuery.
+// Do the same for pointerenter/pointerleave and pointerover/pointerout
+//
+// Support: Safari 7 only
+// Safari sends mouseenter too often; see:
+// https://bugs.chromium.org/p/chromium/issues/detail?id=470258
+// for the description of the bug (it existed in older Chrome versions as well).
+jQuery.each( {
+ mouseenter: "mouseover",
+ mouseleave: "mouseout",
+ pointerenter: "pointerover",
+ pointerleave: "pointerout"
+}, function( orig, fix ) {
+ jQuery.event.special[ orig ] = {
+ delegateType: fix,
+ bindType: fix,
+
+ handle: function( event ) {
+ var ret,
+ target = this,
+ related = event.relatedTarget,
+ handleObj = event.handleObj;
+
+ // For mouseenter/leave call the handler if related is outside the target.
+ // NB: No relatedTarget if the mouse left/entered the browser window
+ if ( !related || ( related !== target && !jQuery.contains( target, related ) ) ) {
+ event.type = handleObj.origType;
+ ret = handleObj.handler.apply( this, arguments );
+ event.type = fix;
+ }
+ return ret;
+ }
+ };
+} );
+
+jQuery.fn.extend( {
+
+ on: function( types, selector, data, fn ) {
+ return on( this, types, selector, data, fn );
+ },
+ one: function( types, selector, data, fn ) {
+ return on( this, types, selector, data, fn, 1 );
+ },
+ off: function( types, selector, fn ) {
+ var handleObj, type;
+ if ( types && types.preventDefault && types.handleObj ) {
+
+ // ( event ) dispatched jQuery.Event
+ handleObj = types.handleObj;
+ jQuery( types.delegateTarget ).off(
+ handleObj.namespace ?
+ handleObj.origType + "." + handleObj.namespace :
+ handleObj.origType,
+ handleObj.selector,
+ handleObj.handler
+ );
+ return this;
+ }
+ if ( typeof types === "object" ) {
+
+ // ( types-object [, selector] )
+ for ( type in types ) {
+ this.off( type, selector, types[ type ] );
+ }
+ return this;
+ }
+ if ( selector === false || typeof selector === "function" ) {
+
+ // ( types [, fn] )
+ fn = selector;
+ selector = undefined;
+ }
+ if ( fn === false ) {
+ fn = returnFalse;
+ }
+ return this.each( function() {
+ jQuery.event.remove( this, types, fn, selector );
+ } );
+ }
+} );
+
+
+var
+
+ // Support: IE <=10 - 11, Edge 12 - 13 only
+ // In IE/Edge using regex groups here causes severe slowdowns.
+ // See https://connect.microsoft.com/IE/feedback/details/1736512/
+ rnoInnerhtml = /<script|<style|<link/i,
+
+ // checked="checked" or checked
+ rchecked = /checked\s*(?:[^=]|=\s*.checked.)/i,
+ rcleanScript = /^\s*<!(?:\[CDATA\[|--)|(?:\]\]|--)>\s*$/g;
+
+// Prefer a tbody over its parent table for containing new rows
+function manipulationTarget( elem, content ) {
+ if ( nodeName( elem, "table" ) &&
+ nodeName( content.nodeType !== 11 ? content : content.firstChild, "tr" ) ) {
+
+ return jQuery( elem ).children( "tbody" )[ 0 ] || elem;
+ }
+
+ return elem;
+}
+
+// Replace/restore the type attribute of script elements for safe DOM manipulation
+function disableScript( elem ) {
+ elem.type = ( elem.getAttribute( "type" ) !== null ) + "/" + elem.type;
+ return elem;
+}
+function restoreScript( elem ) {
+ if ( ( elem.type || "" ).slice( 0, 5 ) === "true/" ) {
+ elem.type = elem.type.slice( 5 );
+ } else {
+ elem.removeAttribute( "type" );
+ }
+
+ return elem;
+}
+
+function cloneCopyEvent( src, dest ) {
+ var i, l, type, pdataOld, udataOld, udataCur, events;
+
+ if ( dest.nodeType !== 1 ) {
+ return;
+ }
+
+ // 1. Copy private data: events, handlers, etc.
+ if ( dataPriv.hasData( src ) ) {
+ pdataOld = dataPriv.get( src );
+ events = pdataOld.events;
+
+ if ( events ) {
+ dataPriv.remove( dest, "handle events" );
+
+ for ( type in events ) {
+ for ( i = 0, l = events[ type ].length; i < l; i++ ) {
+ jQuery.event.add( dest, type, events[ type ][ i ] );
+ }
+ }
+ }
+ }
+
+ // 2. Copy user data
+ if ( dataUser.hasData( src ) ) {
+ udataOld = dataUser.access( src );
+ udataCur = jQuery.extend( {}, udataOld );
+
+ dataUser.set( dest, udataCur );
+ }
+}
+
+// Fix IE bugs, see support tests
+function fixInput( src, dest ) {
+ var nodeName = dest.nodeName.toLowerCase();
+
+ // Fails to persist the checked state of a cloned checkbox or radio button.
+ if ( nodeName === "input" && rcheckableType.test( src.type ) ) {
+ dest.checked = src.checked;
+
+ // Fails to return the selected option to the default selected state when cloning options
+ } else if ( nodeName === "input" || nodeName === "textarea" ) {
+ dest.defaultValue = src.defaultValue;
+ }
+}
+
+function domManip( collection, args, callback, ignored ) {
+
+ // Flatten any nested arrays
+ args = flat( args );
+
+ var fragment, first, scripts, hasScripts, node, doc,
+ i = 0,
+ l = collection.length,
+ iNoClone = l - 1,
+ value = args[ 0 ],
+ valueIsFunction = isFunction( value );
+
+ // We can't cloneNode fragments that contain checked, in WebKit
+ if ( valueIsFunction ||
+ ( l > 1 && typeof value === "string" &&
+ !support.checkClone && rchecked.test( value ) ) ) {
+ return collection.each( function( index ) {
+ var self = collection.eq( index );
+ if ( valueIsFunction ) {
+ args[ 0 ] = value.call( this, index, self.html() );
+ }
+ domManip( self, args, callback, ignored );
+ } );
+ }
+
+ if ( l ) {
+ fragment = buildFragment( args, collection[ 0 ].ownerDocument, false, collection, ignored );
+ first = fragment.firstChild;
+
+ if ( fragment.childNodes.length === 1 ) {
+ fragment = first;
+ }
+
+ // Require either new content or an interest in ignored elements to invoke the callback
+ if ( first || ignored ) {
+ scripts = jQuery.map( getAll( fragment, "script" ), disableScript );
+ hasScripts = scripts.length;
+
+ // Use the original fragment for the last item
+ // instead of the first because it can end up
+ // being emptied incorrectly in certain situations (#8070).
+ for ( ; i < l; i++ ) {
+ node = fragment;
+
+ if ( i !== iNoClone ) {
+ node = jQuery.clone( node, true, true );
+
+ // Keep references to cloned scripts for later restoration
+ if ( hasScripts ) {
+
+ // Support: Android <=4.0 only, PhantomJS 1 only
+ // push.apply(_, arraylike) throws on ancient WebKit
+ jQuery.merge( scripts, getAll( node, "script" ) );
+ }
+ }
+
+ callback.call( collection[ i ], node, i );
+ }
+
+ if ( hasScripts ) {
+ doc = scripts[ scripts.length - 1 ].ownerDocument;
+
+ // Reenable scripts
+ jQuery.map( scripts, restoreScript );
+
+ // Evaluate executable scripts on first document insertion
+ for ( i = 0; i < hasScripts; i++ ) {
+ node = scripts[ i ];
+ if ( rscriptType.test( node.type || "" ) &&
+ !dataPriv.access( node, "globalEval" ) &&
+ jQuery.contains( doc, node ) ) {
+
+ if ( node.src && ( node.type || "" ).toLowerCase() !== "module" ) {
+
+ // Optional AJAX dependency, but won't run scripts if not present
+ if ( jQuery._evalUrl && !node.noModule ) {
+ jQuery._evalUrl( node.src, {
+ nonce: node.nonce || node.getAttribute( "nonce" )
+ }, doc );
+ }
+ } else {
+ DOMEval( node.textContent.replace( rcleanScript, "" ), node, doc );
+ }
+ }
+ }
+ }
+ }
+ }
+
+ return collection;
+}
+
+function remove( elem, selector, keepData ) {
+ var node,
+ nodes = selector ? jQuery.filter( selector, elem ) : elem,
+ i = 0;
+
+ for ( ; ( node = nodes[ i ] ) != null; i++ ) {
+ if ( !keepData && node.nodeType === 1 ) {
+ jQuery.cleanData( getAll( node ) );
+ }
+
+ if ( node.parentNode ) {
+ if ( keepData && isAttached( node ) ) {
+ setGlobalEval( getAll( node, "script" ) );
+ }
+ node.parentNode.removeChild( node );
+ }
+ }
+
+ return elem;
+}
+
+jQuery.extend( {
+ htmlPrefilter: function( html ) {
+ return html;
+ },
+
+ clone: function( elem, dataAndEvents, deepDataAndEvents ) {
+ var i, l, srcElements, destElements,
+ clone = elem.cloneNode( true ),
+ inPage = isAttached( elem );
+
+ // Fix IE cloning issues
+ if ( !support.noCloneChecked && ( elem.nodeType === 1 || elem.nodeType === 11 ) &&
+ !jQuery.isXMLDoc( elem ) ) {
+
+ // We eschew Sizzle here for performance reasons: https://jsperf.com/getall-vs-sizzle/2
+ destElements = getAll( clone );
+ srcElements = getAll( elem );
+
+ for ( i = 0, l = srcElements.length; i < l; i++ ) {
+ fixInput( srcElements[ i ], destElements[ i ] );
+ }
+ }
+
+ // Copy the events from the original to the clone
+ if ( dataAndEvents ) {
+ if ( deepDataAndEvents ) {
+ srcElements = srcElements || getAll( elem );
+ destElements = destElements || getAll( clone );
+
+ for ( i = 0, l = srcElements.length; i < l; i++ ) {
+ cloneCopyEvent( srcElements[ i ], destElements[ i ] );
+ }
+ } else {
+ cloneCopyEvent( elem, clone );
+ }
+ }
+
+ // Preserve script evaluation history
+ destElements = getAll( clone, "script" );
+ if ( destElements.length > 0 ) {
+ setGlobalEval( destElements, !inPage && getAll( elem, "script" ) );
+ }
+
+ // Return the cloned set
+ return clone;
+ },
+
+ cleanData: function( elems ) {
+ var data, elem, type,
+ special = jQuery.event.special,
+ i = 0;
+
+ for ( ; ( elem = elems[ i ] ) !== undefined; i++ ) {
+ if ( acceptData( elem ) ) {
+ if ( ( data = elem[ dataPriv.expando ] ) ) {
+ if ( data.events ) {
+ for ( type in data.events ) {
+ if ( special[ type ] ) {
+ jQuery.event.remove( elem, type );
+
+ // This is a shortcut to avoid jQuery.event.remove's overhead
+ } else {
+ jQuery.removeEvent( elem, type, data.handle );
+ }
+ }
+ }
+
+ // Support: Chrome <=35 - 45+
+ // Assign undefined instead of using delete, see Data#remove
+ elem[ dataPriv.expando ] = undefined;
+ }
+ if ( elem[ dataUser.expando ] ) {
+
+ // Support: Chrome <=35 - 45+
+ // Assign undefined instead of using delete, see Data#remove
+ elem[ dataUser.expando ] = undefined;
+ }
+ }
+ }
+ }
+} );
+
+jQuery.fn.extend( {
+ detach: function( selector ) {
+ return remove( this, selector, true );
+ },
+
+ remove: function( selector ) {
+ return remove( this, selector );
+ },
+
+ text: function( value ) {
+ return access( this, function( value ) {
+ return value === undefined ?
+ jQuery.text( this ) :
+ this.empty().each( function() {
+ if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+ this.textContent = value;
+ }
+ } );
+ }, null, value, arguments.length );
+ },
+
+ append: function() {
+ return domManip( this, arguments, function( elem ) {
+ if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+ var target = manipulationTarget( this, elem );
+ target.appendChild( elem );
+ }
+ } );
+ },
+
+ prepend: function() {
+ return domManip( this, arguments, function( elem ) {
+ if ( this.nodeType === 1 || this.nodeType === 11 || this.nodeType === 9 ) {
+ var target = manipulationTarget( this, elem );
+ target.insertBefore( elem, target.firstChild );
+ }
+ } );
+ },
+
+ before: function() {
+ return domManip( this, arguments, function( elem ) {
+ if ( this.parentNode ) {
+ this.parentNode.insertBefore( elem, this );
+ }
+ } );
+ },
+
+ after: function() {
+ return domManip( this, arguments, function( elem ) {
+ if ( this.parentNode ) {
+ this.parentNode.insertBefore( elem, this.nextSibling );
+ }
+ } );
+ },
+
+ empty: function() {
+ var elem,
+ i = 0;
+
+ for ( ; ( elem = this[ i ] ) != null; i++ ) {
+ if ( elem.nodeType === 1 ) {
+
+ // Prevent memory leaks
+ jQuery.cleanData( getAll( elem, false ) );
+
+ // Remove any remaining nodes
+ elem.textContent = "";
+ }
+ }
+
+ return this;
+ },
+
+ clone: function( dataAndEvents, deepDataAndEvents ) {
+ dataAndEvents = dataAndEvents == null ? false : dataAndEvents;
+ deepDataAndEvents = deepDataAndEvents == null ? dataAndEvents : deepDataAndEvents;
+
+ return this.map( function() {
+ return jQuery.clone( this, dataAndEvents, deepDataAndEvents );
+ } );
+ },
+
+ html: function( value ) {
+ return access( this, function( value ) {
+ var elem = this[ 0 ] || {},
+ i = 0,
+ l = this.length;
+
+ if ( value === undefined && elem.nodeType === 1 ) {
+ return elem.innerHTML;
+ }
+
+ // See if we can take a shortcut and just use innerHTML
+ if ( typeof value === "string" && !rnoInnerhtml.test( value ) &&
+ !wrapMap[ ( rtagName.exec( value ) || [ "", "" ] )[ 1 ].toLowerCase() ] ) {
+
+ value = jQuery.htmlPrefilter( value );
+
+ try {
+ for ( ; i < l; i++ ) {
+ elem = this[ i ] || {};
+
+ // Remove element nodes and prevent memory leaks
+ if ( elem.nodeType === 1 ) {
+ jQuery.cleanData( getAll( elem, false ) );
+ elem.innerHTML = value;
+ }
+ }
+
+ elem = 0;
+
+ // If using innerHTML throws an exception, use the fallback method
+ } catch ( e ) {}
+ }
+
+ if ( elem ) {
+ this.empty().append( value );
+ }
+ }, null, value, arguments.length );
+ },
+
+ replaceWith: function() {
+ var ignored = [];
+
+ // Make the changes, replacing each non-ignored context element with the new content
+ return domManip( this, arguments, function( elem ) {
+ var parent = this.parentNode;
+
+ if ( jQuery.inArray( this, ignored ) < 0 ) {
+ jQuery.cleanData( getAll( this ) );
+ if ( parent ) {
+ parent.replaceChild( elem, this );
+ }
+ }
+
+ // Force callback invocation
+ }, ignored );
+ }
+} );
+
+jQuery.each( {
+ appendTo: "append",
+ prependTo: "prepend",
+ insertBefore: "before",
+ insertAfter: "after",
+ replaceAll: "replaceWith"
+}, function( name, original ) {
+ jQuery.fn[ name ] = function( selector ) {
+ var elems,
+ ret = [],
+ insert = jQuery( selector ),
+ last = insert.length - 1,
+ i = 0;
+
+ for ( ; i <= last; i++ ) {
+ elems = i === last ? this : this.clone( true );
+ jQuery( insert[ i ] )[ original ]( elems );
+
+ // Support: Android <=4.0 only, PhantomJS 1 only
+ // .get() because push.apply(_, arraylike) throws on ancient WebKit
+ push.apply( ret, elems.get() );
+ }
+
+ return this.pushStack( ret );
+ };
+} );
+var rnumnonpx = new RegExp( "^(" + pnum + ")(?!px)[a-z%]+$", "i" );
+
+var getStyles = function( elem ) {
+
+ // Support: IE <=11 only, Firefox <=30 (#15098, #14150)
+ // IE throws on elements created in popups
+ // FF meanwhile throws on frame elements through "defaultView.getComputedStyle"
+ var view = elem.ownerDocument.defaultView;
+
+ if ( !view || !view.opener ) {
+ view = window;
+ }
+
+ return view.getComputedStyle( elem );
+ };
+
+var swap = function( elem, options, callback ) {
+ var ret, name,
+ old = {};
+
+ // Remember the old values, and insert the new ones
+ for ( name in options ) {
+ old[ name ] = elem.style[ name ];
+ elem.style[ name ] = options[ name ];
+ }
+
+ ret = callback.call( elem );
+
+ // Revert the old values
+ for ( name in options ) {
+ elem.style[ name ] = old[ name ];
+ }
+
+ return ret;
+};
+
+
+var rboxStyle = new RegExp( cssExpand.join( "|" ), "i" );
+
+
+
+( function() {
+
+ // Executing both pixelPosition & boxSizingReliable tests require only one layout
+ // so they're executed at the same time to save the second computation.
+ function computeStyleTests() {
+
+ // This is a singleton, we need to execute it only once
+ if ( !div ) {
+ return;
+ }
+
+ container.style.cssText = "position:absolute;left:-11111px;width:60px;" +
+ "margin-top:1px;padding:0;border:0";
+ div.style.cssText =
+ "position:relative;display:block;box-sizing:border-box;overflow:scroll;" +
+ "margin:auto;border:1px;padding:1px;" +
+ "width:60%;top:1%";
+ documentElement.appendChild( container ).appendChild( div );
+
+ var divStyle = window.getComputedStyle( div );
+ pixelPositionVal = divStyle.top !== "1%";
+
+ // Support: Android 4.0 - 4.3 only, Firefox <=3 - 44
+ reliableMarginLeftVal = roundPixelMeasures( divStyle.marginLeft ) === 12;
+
+ // Support: Android 4.0 - 4.3 only, Safari <=9.1 - 10.1, iOS <=7.0 - 9.3
+ // Some styles come back with percentage values, even though they shouldn't
+ div.style.right = "60%";
+ pixelBoxStylesVal = roundPixelMeasures( divStyle.right ) === 36;
+
+ // Support: IE 9 - 11 only
+ // Detect misreporting of content dimensions for box-sizing:border-box elements
+ boxSizingReliableVal = roundPixelMeasures( divStyle.width ) === 36;
+
+ // Support: IE 9 only
+ // Detect overflow:scroll screwiness (gh-3699)
+ // Support: Chrome <=64
+ // Don't get tricked when zoom affects offsetWidth (gh-4029)
+ div.style.position = "absolute";
+ scrollboxSizeVal = roundPixelMeasures( div.offsetWidth / 3 ) === 12;
+
+ documentElement.removeChild( container );
+
+ // Nullify the div so it wouldn't be stored in the memory and
+ // it will also be a sign that checks already performed
+ div = null;
+ }
+
+ function roundPixelMeasures( measure ) {
+ return Math.round( parseFloat( measure ) );
+ }
+
+ var pixelPositionVal, boxSizingReliableVal, scrollboxSizeVal, pixelBoxStylesVal,
+ reliableTrDimensionsVal, reliableMarginLeftVal,
+ container = document.createElement( "div" ),
+ div = document.createElement( "div" );
+
+ // Finish early in limited (non-browser) environments
+ if ( !div.style ) {
+ return;
+ }
+
+ // Support: IE <=9 - 11 only
+ // Style of cloned element affects source element cloned (#8908)
+ div.style.backgroundClip = "content-box";
+ div.cloneNode( true ).style.backgroundClip = "";
+ support.clearCloneStyle = div.style.backgroundClip === "content-box";
+
+ jQuery.extend( support, {
+ boxSizingReliable: function() {
+ computeStyleTests();
+ return boxSizingReliableVal;
+ },
+ pixelBoxStyles: function() {
+ computeStyleTests();
+ return pixelBoxStylesVal;
+ },
+ pixelPosition: function() {
+ computeStyleTests();
+ return pixelPositionVal;
+ },
+ reliableMarginLeft: function() {
+ computeStyleTests();
+ return reliableMarginLeftVal;
+ },
+ scrollboxSize: function() {
+ computeStyleTests();
+ return scrollboxSizeVal;
+ },
+
+ // Support: IE 9 - 11+, Edge 15 - 18+
+ // IE/Edge misreport `getComputedStyle` of table rows with width/height
+ // set in CSS while `offset*` properties report correct values.
+ // Behavior in IE 9 is more subtle than in newer versions & it passes
+ // some versions of this test; make sure not to make it pass there!
+ reliableTrDimensions: function() {
+ var table, tr, trChild, trStyle;
+ if ( reliableTrDimensionsVal == null ) {
+ table = document.createElement( "table" );
+ tr = document.createElement( "tr" );
+ trChild = document.createElement( "div" );
+
+ table.style.cssText = "position:absolute;left:-11111px";
+ tr.style.height = "1px";
+ trChild.style.height = "9px";
+
+ documentElement
+ .appendChild( table )
+ .appendChild( tr )
+ .appendChild( trChild );
+
+ trStyle = window.getComputedStyle( tr );
+ reliableTrDimensionsVal = parseInt( trStyle.height ) > 3;
+
+ documentElement.removeChild( table );
+ }
+ return reliableTrDimensionsVal;
+ }
+ } );
+} )();
+
+
+function curCSS( elem, name, computed ) {
+ var width, minWidth, maxWidth, ret,
+
+ // Support: Firefox 51+
+ // Retrieving style before computed somehow
+ // fixes an issue with getting wrong values
+ // on detached elements
+ style = elem.style;
+
+ computed = computed || getStyles( elem );
+
+ // getPropertyValue is needed for:
+ // .css('filter') (IE 9 only, #12537)
+ // .css('--customProperty) (#3144)
+ if ( computed ) {
+ ret = computed.getPropertyValue( name ) || computed[ name ];
+
+ if ( ret === "" && !isAttached( elem ) ) {
+ ret = jQuery.style( elem, name );
+ }
+
+ // A tribute to the "awesome hack by Dean Edwards"
+ // Android Browser returns percentage for some values,
+ // but width seems to be reliably pixels.
+ // This is against the CSSOM draft spec:
+ // https://drafts.csswg.org/cssom/#resolved-values
+ if ( !support.pixelBoxStyles() && rnumnonpx.test( ret ) && rboxStyle.test( name ) ) {
+
+ // Remember the original values
+ width = style.width;
+ minWidth = style.minWidth;
+ maxWidth = style.maxWidth;
+
+ // Put in the new values to get a computed value out
+ style.minWidth = style.maxWidth = style.width = ret;
+ ret = computed.width;
+
+ // Revert the changed values
+ style.width = width;
+ style.minWidth = minWidth;
+ style.maxWidth = maxWidth;
+ }
+ }
+
+ return ret !== undefined ?
+
+ // Support: IE <=9 - 11 only
+ // IE returns zIndex value as an integer.
+ ret + "" :
+ ret;
+}
+
+
+function addGetHookIf( conditionFn, hookFn ) {
+
+ // Define the hook, we'll check on the first run if it's really needed.
+ return {
+ get: function() {
+ if ( conditionFn() ) {
+
+ // Hook not needed (or it's not possible to use it due
+ // to missing dependency), remove it.
+ delete this.get;
+ return;
+ }
+
+ // Hook needed; redefine it so that the support test is not executed again.
+ return ( this.get = hookFn ).apply( this, arguments );
+ }
+ };
+}
+
+
+var cssPrefixes = [ "Webkit", "Moz", "ms" ],
+ emptyStyle = document.createElement( "div" ).style,
+ vendorProps = {};
+
+// Return a vendor-prefixed property or undefined
+function vendorPropName( name ) {
+
+ // Check for vendor prefixed names
+ var capName = name[ 0 ].toUpperCase() + name.slice( 1 ),
+ i = cssPrefixes.length;
+
+ while ( i-- ) {
+ name = cssPrefixes[ i ] + capName;
+ if ( name in emptyStyle ) {
+ return name;
+ }
+ }
+}
+
+// Return a potentially-mapped jQuery.cssProps or vendor prefixed property
+function finalPropName( name ) {
+ var final = jQuery.cssProps[ name ] || vendorProps[ name ];
+
+ if ( final ) {
+ return final;
+ }
+ if ( name in emptyStyle ) {
+ return name;
+ }
+ return vendorProps[ name ] = vendorPropName( name ) || name;
+}
+
+
+var
+
+ // Swappable if display is none or starts with table
+ // except "table", "table-cell", or "table-caption"
+ // See here for display values: https://developer.mozilla.org/en-US/docs/CSS/display
+ rdisplayswap = /^(none|table(?!-c[ea]).+)/,
+ rcustomProp = /^--/,
+ cssShow = { position: "absolute", visibility: "hidden", display: "block" },
+ cssNormalTransform = {
+ letterSpacing: "0",
+ fontWeight: "400"
+ };
+
+function setPositiveNumber( _elem, value, subtract ) {
+
+ // Any relative (+/-) values have already been
+ // normalized at this point
+ var matches = rcssNum.exec( value );
+ return matches ?
+
+ // Guard against undefined "subtract", e.g., when used as in cssHooks
+ Math.max( 0, matches[ 2 ] - ( subtract || 0 ) ) + ( matches[ 3 ] || "px" ) :
+ value;
+}
+
+function boxModelAdjustment( elem, dimension, box, isBorderBox, styles, computedVal ) {
+ var i = dimension === "width" ? 1 : 0,
+ extra = 0,
+ delta = 0;
+
+ // Adjustment may not be necessary
+ if ( box === ( isBorderBox ? "border" : "content" ) ) {
+ return 0;
+ }
+
+ for ( ; i < 4; i += 2 ) {
+
+ // Both box models exclude margin
+ if ( box === "margin" ) {
+ delta += jQuery.css( elem, box + cssExpand[ i ], true, styles );
+ }
+
+ // If we get here with a content-box, we're seeking "padding" or "border" or "margin"
+ if ( !isBorderBox ) {
+
+ // Add padding
+ delta += jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+
+ // For "border" or "margin", add border
+ if ( box !== "padding" ) {
+ delta += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+
+ // But still keep track of it otherwise
+ } else {
+ extra += jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+ }
+
+ // If we get here with a border-box (content + padding + border), we're seeking "content" or
+ // "padding" or "margin"
+ } else {
+
+ // For "content", subtract padding
+ if ( box === "content" ) {
+ delta -= jQuery.css( elem, "padding" + cssExpand[ i ], true, styles );
+ }
+
+ // For "content" or "padding", subtract border
+ if ( box !== "margin" ) {
+ delta -= jQuery.css( elem, "border" + cssExpand[ i ] + "Width", true, styles );
+ }
+ }
+ }
+
+ // Account for positive content-box scroll gutter when requested by providing computedVal
+ if ( !isBorderBox && computedVal >= 0 ) {
+
+ // offsetWidth/offsetHeight is a rounded sum of content, padding, scroll gutter, and border
+ // Assuming integer scroll gutter, subtract the rest and round down
+ delta += Math.max( 0, Math.ceil(
+ elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+ computedVal -
+ delta -
+ extra -
+ 0.5
+
+ // If offsetWidth/offsetHeight is unknown, then we can't determine content-box scroll gutter
+ // Use an explicit zero to avoid NaN (gh-3964)
+ ) ) || 0;
+ }
+
+ return delta;
+}
+
+function getWidthOrHeight( elem, dimension, extra ) {
+
+ // Start with computed style
+ var styles = getStyles( elem ),
+
+ // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-4322).
+ // Fake content-box until we know it's needed to know the true value.
+ boxSizingNeeded = !support.boxSizingReliable() || extra,
+ isBorderBox = boxSizingNeeded &&
+ jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+ valueIsBorderBox = isBorderBox,
+
+ val = curCSS( elem, dimension, styles ),
+ offsetProp = "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 );
+
+ // Support: Firefox <=54
+ // Return a confounding non-pixel value or feign ignorance, as appropriate.
+ if ( rnumnonpx.test( val ) ) {
+ if ( !extra ) {
+ return val;
+ }
+ val = "auto";
+ }
+
+
+ // Support: IE 9 - 11 only
+ // Use offsetWidth/offsetHeight for when box sizing is unreliable.
+ // In those cases, the computed value can be trusted to be border-box.
+ if ( ( !support.boxSizingReliable() && isBorderBox ||
+
+ // Support: IE 10 - 11+, Edge 15 - 18+
+ // IE/Edge misreport `getComputedStyle` of table rows with width/height
+ // set in CSS while `offset*` properties report correct values.
+ // Interestingly, in some cases IE 9 doesn't suffer from this issue.
+ !support.reliableTrDimensions() && nodeName( elem, "tr" ) ||
+
+ // Fall back to offsetWidth/offsetHeight when value is "auto"
+ // This happens for inline elements with no explicit setting (gh-3571)
+ val === "auto" ||
+
+ // Support: Android <=4.1 - 4.3 only
+ // Also use offsetWidth/offsetHeight for misreported inline dimensions (gh-3602)
+ !parseFloat( val ) && jQuery.css( elem, "display", false, styles ) === "inline" ) &&
+
+ // Make sure the element is visible & connected
+ elem.getClientRects().length ) {
+
+ isBorderBox = jQuery.css( elem, "boxSizing", false, styles ) === "border-box";
+
+ // Where available, offsetWidth/offsetHeight approximate border box dimensions.
+ // Where not available (e.g., SVG), assume unreliable box-sizing and interpret the
+ // retrieved value as a content box dimension.
+ valueIsBorderBox = offsetProp in elem;
+ if ( valueIsBorderBox ) {
+ val = elem[ offsetProp ];
+ }
+ }
+
+ // Normalize "" and auto
+ val = parseFloat( val ) || 0;
+
+ // Adjust for the element's box model
+ return ( val +
+ boxModelAdjustment(
+ elem,
+ dimension,
+ extra || ( isBorderBox ? "border" : "content" ),
+ valueIsBorderBox,
+ styles,
+
+ // Provide the current computed size to request scroll gutter calculation (gh-3589)
+ val
+ )
+ ) + "px";
+}
+
+jQuery.extend( {
+
+ // Add in style property hooks for overriding the default
+ // behavior of getting and setting a style property
+ cssHooks: {
+ opacity: {
+ get: function( elem, computed ) {
+ if ( computed ) {
+
+ // We should always get a number back from opacity
+ var ret = curCSS( elem, "opacity" );
+ return ret === "" ? "1" : ret;
+ }
+ }
+ }
+ },
+
+ // Don't automatically add "px" to these possibly-unitless properties
+ cssNumber: {
+ "animationIterationCount": true,
+ "columnCount": true,
+ "fillOpacity": true,
+ "flexGrow": true,
+ "flexShrink": true,
+ "fontWeight": true,
+ "gridArea": true,
+ "gridColumn": true,
+ "gridColumnEnd": true,
+ "gridColumnStart": true,
+ "gridRow": true,
+ "gridRowEnd": true,
+ "gridRowStart": true,
+ "lineHeight": true,
+ "opacity": true,
+ "order": true,
+ "orphans": true,
+ "widows": true,
+ "zIndex": true,
+ "zoom": true
+ },
+
+ // Add in properties whose names you wish to fix before
+ // setting or getting the value
+ cssProps: {},
+
+ // Get and set the style property on a DOM Node
+ style: function( elem, name, value, extra ) {
+
+ // Don't set styles on text and comment nodes
+ if ( !elem || elem.nodeType === 3 || elem.nodeType === 8 || !elem.style ) {
+ return;
+ }
+
+ // Make sure that we're working with the right name
+ var ret, type, hooks,
+ origName = camelCase( name ),
+ isCustomProp = rcustomProp.test( name ),
+ style = elem.style;
+
+ // Make sure that we're working with the right name. We don't
+ // want to query the value if it is a CSS custom property
+ // since they are user-defined.
+ if ( !isCustomProp ) {
+ name = finalPropName( origName );
+ }
+
+ // Gets hook for the prefixed version, then unprefixed version
+ hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+ // Check if we're setting a value
+ if ( value !== undefined ) {
+ type = typeof value;
+
+ // Convert "+=" or "-=" to relative numbers (#7345)
+ if ( type === "string" && ( ret = rcssNum.exec( value ) ) && ret[ 1 ] ) {
+ value = adjustCSS( elem, name, ret );
+
+ // Fixes bug #9237
+ type = "number";
+ }
+
+ // Make sure that null and NaN values aren't set (#7116)
+ if ( value == null || value !== value ) {
+ return;
+ }
+
+ // If a number was passed in, add the unit (except for certain CSS properties)
+ // The isCustomProp check can be removed in jQuery 4.0 when we only auto-append
+ // "px" to a few hardcoded values.
+ if ( type === "number" && !isCustomProp ) {
+ value += ret && ret[ 3 ] || ( jQuery.cssNumber[ origName ] ? "" : "px" );
+ }
+
+ // background-* props affect original clone's values
+ if ( !support.clearCloneStyle && value === "" && name.indexOf( "background" ) === 0 ) {
+ style[ name ] = "inherit";
+ }
+
+ // If a hook was provided, use that value, otherwise just set the specified value
+ if ( !hooks || !( "set" in hooks ) ||
+ ( value = hooks.set( elem, value, extra ) ) !== undefined ) {
+
+ if ( isCustomProp ) {
+ style.setProperty( name, value );
+ } else {
+ style[ name ] = value;
+ }
+ }
+
+ } else {
+
+ // If a hook was provided get the non-computed value from there
+ if ( hooks && "get" in hooks &&
+ ( ret = hooks.get( elem, false, extra ) ) !== undefined ) {
+
+ return ret;
+ }
+
+ // Otherwise just get the value from the style object
+ return style[ name ];
+ }
+ },
+
+ css: function( elem, name, extra, styles ) {
+ var val, num, hooks,
+ origName = camelCase( name ),
+ isCustomProp = rcustomProp.test( name );
+
+ // Make sure that we're working with the right name. We don't
+ // want to modify the value if it is a CSS custom property
+ // since they are user-defined.
+ if ( !isCustomProp ) {
+ name = finalPropName( origName );
+ }
+
+ // Try prefixed name followed by the unprefixed name
+ hooks = jQuery.cssHooks[ name ] || jQuery.cssHooks[ origName ];
+
+ // If a hook was provided get the computed value from there
+ if ( hooks && "get" in hooks ) {
+ val = hooks.get( elem, true, extra );
+ }
+
+ // Otherwise, if a way to get the computed value exists, use that
+ if ( val === undefined ) {
+ val = curCSS( elem, name, styles );
+ }
+
+ // Convert "normal" to computed value
+ if ( val === "normal" && name in cssNormalTransform ) {
+ val = cssNormalTransform[ name ];
+ }
+
+ // Make numeric if forced or a qualifier was provided and val looks numeric
+ if ( extra === "" || extra ) {
+ num = parseFloat( val );
+ return extra === true || isFinite( num ) ? num || 0 : val;
+ }
+
+ return val;
+ }
+} );
+
+jQuery.each( [ "height", "width" ], function( _i, dimension ) {
+ jQuery.cssHooks[ dimension ] = {
+ get: function( elem, computed, extra ) {
+ if ( computed ) {
+
+ // Certain elements can have dimension info if we invisibly show them
+ // but it must have a current display style that would benefit
+ return rdisplayswap.test( jQuery.css( elem, "display" ) ) &&
+
+ // Support: Safari 8+
+ // Table columns in Safari have non-zero offsetWidth & zero
+ // getBoundingClientRect().width unless display is changed.
+ // Support: IE <=11 only
+ // Running getBoundingClientRect on a disconnected node
+ // in IE throws an error.
+ ( !elem.getClientRects().length || !elem.getBoundingClientRect().width ) ?
+ swap( elem, cssShow, function() {
+ return getWidthOrHeight( elem, dimension, extra );
+ } ) :
+ getWidthOrHeight( elem, dimension, extra );
+ }
+ },
+
+ set: function( elem, value, extra ) {
+ var matches,
+ styles = getStyles( elem ),
+
+ // Only read styles.position if the test has a chance to fail
+ // to avoid forcing a reflow.
+ scrollboxSizeBuggy = !support.scrollboxSize() &&
+ styles.position === "absolute",
+
+ // To avoid forcing a reflow, only fetch boxSizing if we need it (gh-3991)
+ boxSizingNeeded = scrollboxSizeBuggy || extra,
+ isBorderBox = boxSizingNeeded &&
+ jQuery.css( elem, "boxSizing", false, styles ) === "border-box",
+ subtract = extra ?
+ boxModelAdjustment(
+ elem,
+ dimension,
+ extra,
+ isBorderBox,
+ styles
+ ) :
+ 0;
+
+ // Account for unreliable border-box dimensions by comparing offset* to computed and
+ // faking a content-box to get border and padding (gh-3699)
+ if ( isBorderBox && scrollboxSizeBuggy ) {
+ subtract -= Math.ceil(
+ elem[ "offset" + dimension[ 0 ].toUpperCase() + dimension.slice( 1 ) ] -
+ parseFloat( styles[ dimension ] ) -
+ boxModelAdjustment( elem, dimension, "border", false, styles ) -
+ 0.5
+ );
+ }
+
+ // Convert to pixels if value adjustment is needed
+ if ( subtract && ( matches = rcssNum.exec( value ) ) &&
+ ( matches[ 3 ] || "px" ) !== "px" ) {
+
+ elem.style[ dimension ] = value;
+ value = jQuery.css( elem, dimension );
+ }
+
+ return setPositiveNumber( elem, value, subtract );
+ }
+ };
+} );
+
+jQuery.cssHooks.marginLeft = addGetHookIf( support.reliableMarginLeft,
+ function( elem, computed ) {
+ if ( computed ) {
+ return ( parseFloat( curCSS( elem, "marginLeft" ) ) ||
+ elem.getBoundingClientRect().left -
+ swap( elem, { marginLeft: 0 }, function() {
+ return elem.getBoundingClientRect().left;
+ } )
+ ) + "px";
+ }
+ }
+);
+
+// These hooks are used by animate to expand properties
+jQuery.each( {
+ margin: "",
+ padding: "",
+ border: "Width"
+}, function( prefix, suffix ) {
+ jQuery.cssHooks[ prefix + suffix ] = {
+ expand: function( value ) {
+ var i = 0,
+ expanded = {},
+
+ // Assumes a single number if not a string
+ parts = typeof value === "string" ? value.split( " " ) : [ value ];
+
+ for ( ; i < 4; i++ ) {
+ expanded[ prefix + cssExpand[ i ] + suffix ] =
+ parts[ i ] || parts[ i - 2 ] || parts[ 0 ];
+ }
+
+ return expanded;
+ }
+ };
+
+ if ( prefix !== "margin" ) {
+ jQuery.cssHooks[ prefix + suffix ].set = setPositiveNumber;
+ }
+} );
+
+jQuery.fn.extend( {
+ css: function( name, value ) {
+ return access( this, function( elem, name, value ) {
+ var styles, len,
+ map = {},
+ i = 0;
+
+ if ( Array.isArray( name ) ) {
+ styles = getStyles( elem );
+ len = name.length;
+
+ for ( ; i < len; i++ ) {
+ map[ name[ i ] ] = jQuery.css( elem, name[ i ], false, styles );
+ }
+
+ return map;
+ }
+
+ return value !== undefined ?
+ jQuery.style( elem, name, value ) :
+ jQuery.css( elem, name );
+ }, name, value, arguments.length > 1 );
+ }
+} );
+
+
+function Tween( elem, options, prop, end, easing ) {
+ return new Tween.prototype.init( elem, options, prop, end, easing );
+}
+jQuery.Tween = Tween;
+
+Tween.prototype = {
+ constructor: Tween,
+ init: function( elem, options, prop, end, easing, unit ) {
+ this.elem = elem;
+ this.prop = prop;
+ this.easing = easing || jQuery.easing._default;
+ this.options = options;
+ this.start = this.now = this.cur();
+ this.end = end;
+ this.unit = unit || ( jQuery.cssNumber[ prop ] ? "" : "px" );
+ },
+ cur: function() {
+ var hooks = Tween.propHooks[ this.prop ];
+
+ return hooks && hooks.get ?
+ hooks.get( this ) :
+ Tween.propHooks._default.get( this );
+ },
+ run: function( percent ) {
+ var eased,
+ hooks = Tween.propHooks[ this.prop ];
+
+ if ( this.options.duration ) {
+ this.pos = eased = jQuery.easing[ this.easing ](
+ percent, this.options.duration * percent, 0, 1, this.options.duration
+ );
+ } else {
+ this.pos = eased = percent;
+ }
+ this.now = ( this.end - this.start ) * eased + this.start;
+
+ if ( this.options.step ) {
+ this.options.step.call( this.elem, this.now, this );
+ }
+
+ if ( hooks && hooks.set ) {
+ hooks.set( this );
+ } else {
+ Tween.propHooks._default.set( this );
+ }
+ return this;
+ }
+};
+
+Tween.prototype.init.prototype = Tween.prototype;
+
+Tween.propHooks = {
+ _default: {
+ get: function( tween ) {
+ var result;
+
+ // Use a property on the element directly when it is not a DOM element,
+ // or when there is no matching style property that exists.
+ if ( tween.elem.nodeType !== 1 ||
+ tween.elem[ tween.prop ] != null && tween.elem.style[ tween.prop ] == null ) {
+ return tween.elem[ tween.prop ];
+ }
+
+ // Passing an empty string as a 3rd parameter to .css will automatically
+ // attempt a parseFloat and fallback to a string if the parse fails.
+ // Simple values such as "10px" are parsed to Float;
+ // complex values such as "rotate(1rad)" are returned as-is.
+ result = jQuery.css( tween.elem, tween.prop, "" );
+
+ // Empty strings, null, undefined and "auto" are converted to 0.
+ return !result || result === "auto" ? 0 : result;
+ },
+ set: function( tween ) {
+
+ // Use step hook for back compat.
+ // Use cssHook if its there.
+ // Use .style if available and use plain properties where available.
+ if ( jQuery.fx.step[ tween.prop ] ) {
+ jQuery.fx.step[ tween.prop ]( tween );
+ } else if ( tween.elem.nodeType === 1 && (
+ jQuery.cssHooks[ tween.prop ] ||
+ tween.elem.style[ finalPropName( tween.prop ) ] != null ) ) {
+ jQuery.style( tween.elem, tween.prop, tween.now + tween.unit );
+ } else {
+ tween.elem[ tween.prop ] = tween.now;
+ }
+ }
+ }
+};
+
+// Support: IE <=9 only
+// Panic based approach to setting things on disconnected nodes
+Tween.propHooks.scrollTop = Tween.propHooks.scrollLeft = {
+ set: function( tween ) {
+ if ( tween.elem.nodeType && tween.elem.parentNode ) {
+ tween.elem[ tween.prop ] = tween.now;
+ }
+ }
+};
+
+jQuery.easing = {
+ linear: function( p ) {
+ return p;
+ },
+ swing: function( p ) {
+ return 0.5 - Math.cos( p * Math.PI ) / 2;
+ },
+ _default: "swing"
+};
+
+jQuery.fx = Tween.prototype.init;
+
+// Back compat <1.8 extension point
+jQuery.fx.step = {};
+
+
+
+
+var
+ fxNow, inProgress,
+ rfxtypes = /^(?:toggle|show|hide)$/,
+ rrun = /queueHooks$/;
+
+function schedule() {
+ if ( inProgress ) {
+ if ( document.hidden === false && window.requestAnimationFrame ) {
+ window.requestAnimationFrame( schedule );
+ } else {
+ window.setTimeout( schedule, jQuery.fx.interval );
+ }
+
+ jQuery.fx.tick();
+ }
+}
+
+// Animations created synchronously will run synchronously
+function createFxNow() {
+ window.setTimeout( function() {
+ fxNow = undefined;
+ } );
+ return ( fxNow = Date.now() );
+}
+
+// Generate parameters to create a standard animation
+function genFx( type, includeWidth ) {
+ var which,
+ i = 0,
+ attrs = { height: type };
+
+ // If we include width, step value is 1 to do all cssExpand values,
+ // otherwise step value is 2 to skip over Left and Right
+ includeWidth = includeWidth ? 1 : 0;
+ for ( ; i < 4; i += 2 - includeWidth ) {
+ which = cssExpand[ i ];
+ attrs[ "margin" + which ] = attrs[ "padding" + which ] = type;
+ }
+
+ if ( includeWidth ) {
+ attrs.opacity = attrs.width = type;
+ }
+
+ return attrs;
+}
+
+function createTween( value, prop, animation ) {
+ var tween,
+ collection = ( Animation.tweeners[ prop ] || [] ).concat( Animation.tweeners[ "*" ] ),
+ index = 0,
+ length = collection.length;
+ for ( ; index < length; index++ ) {
+ if ( ( tween = collection[ index ].call( animation, prop, value ) ) ) {
+
+ // We're done with this property
+ return tween;
+ }
+ }
+}
+
+function defaultPrefilter( elem, props, opts ) {
+ var prop, value, toggle, hooks, oldfire, propTween, restoreDisplay, display,
+ isBox = "width" in props || "height" in props,
+ anim = this,
+ orig = {},
+ style = elem.style,
+ hidden = elem.nodeType && isHiddenWithinTree( elem ),
+ dataShow = dataPriv.get( elem, "fxshow" );
+
+ // Queue-skipping animations hijack the fx hooks
+ if ( !opts.queue ) {
+ hooks = jQuery._queueHooks( elem, "fx" );
+ if ( hooks.unqueued == null ) {
+ hooks.unqueued = 0;
+ oldfire = hooks.empty.fire;
+ hooks.empty.fire = function() {
+ if ( !hooks.unqueued ) {
+ oldfire();
+ }
+ };
+ }
+ hooks.unqueued++;
+
+ anim.always( function() {
+
+ // Ensure the complete handler is called before this completes
+ anim.always( function() {
+ hooks.unqueued--;
+ if ( !jQuery.queue( elem, "fx" ).length ) {
+ hooks.empty.fire();
+ }
+ } );
+ } );
+ }
+
+ // Detect show/hide animations
+ for ( prop in props ) {
+ value = props[ prop ];
+ if ( rfxtypes.test( value ) ) {
+ delete props[ prop ];
+ toggle = toggle || value === "toggle";
+ if ( value === ( hidden ? "hide" : "show" ) ) {
+
+ // Pretend to be hidden if this is a "show" and
+ // there is still data from a stopped show/hide
+ if ( value === "show" && dataShow && dataShow[ prop ] !== undefined ) {
+ hidden = true;
+
+ // Ignore all other no-op show/hide data
+ } else {
+ continue;
+ }
+ }
+ orig[ prop ] = dataShow && dataShow[ prop ] || jQuery.style( elem, prop );
+ }
+ }
+
+ // Bail out if this is a no-op like .hide().hide()
+ propTween = !jQuery.isEmptyObject( props );
+ if ( !propTween && jQuery.isEmptyObject( orig ) ) {
+ return;
+ }
+
+ // Restrict "overflow" and "display" styles during box animations
+ if ( isBox && elem.nodeType === 1 ) {
+
+ // Support: IE <=9 - 11, Edge 12 - 15
+ // Record all 3 overflow attributes because IE does not infer the shorthand
+ // from identically-valued overflowX and overflowY and Edge just mirrors
+ // the overflowX value there.
+ opts.overflow = [ style.overflow, style.overflowX, style.overflowY ];
+
+ // Identify a display type, preferring old show/hide data over the CSS cascade
+ restoreDisplay = dataShow && dataShow.display;
+ if ( restoreDisplay == null ) {
+ restoreDisplay = dataPriv.get( elem, "display" );
+ }
+ display = jQuery.css( elem, "display" );
+ if ( display === "none" ) {
+ if ( restoreDisplay ) {
+ display = restoreDisplay;
+ } else {
+
+ // Get nonempty value(s) by temporarily forcing visibility
+ showHide( [ elem ], true );
+ restoreDisplay = elem.style.display || restoreDisplay;
+ display = jQuery.css( elem, "display" );
+ showHide( [ elem ] );
+ }
+ }
+
+ // Animate inline elements as inline-block
+ if ( display === "inline" || display === "inline-block" && restoreDisplay != null ) {
+ if ( jQuery.css( elem, "float" ) === "none" ) {
+
+ // Restore the original display value at the end of pure show/hide animations
+ if ( !propTween ) {
+ anim.done( function() {
+ style.display = restoreDisplay;
+ } );
+ if ( restoreDisplay == null ) {
+ display = style.display;
+ restoreDisplay = display === "none" ? "" : display;
+ }
+ }
+ style.display = "inline-block";
+ }
+ }
+ }
+
+ if ( opts.overflow ) {
+ style.overflow = "hidden";
+ anim.always( function() {
+ style.overflow = opts.overflow[ 0 ];
+ style.overflowX = opts.overflow[ 1 ];
+ style.overflowY = opts.overflow[ 2 ];
+ } );
+ }
+
+ // Implement show/hide animations
+ propTween = false;
+ for ( prop in orig ) {
+
+ // General show/hide setup for this element animation
+ if ( !propTween ) {
+ if ( dataShow ) {
+ if ( "hidden" in dataShow ) {
+ hidden = dataShow.hidden;
+ }
+ } else {
+ dataShow = dataPriv.access( elem, "fxshow", { display: restoreDisplay } );
+ }
+
+ // Store hidden/visible for toggle so `.stop().toggle()` "reverses"
+ if ( toggle ) {
+ dataShow.hidden = !hidden;
+ }
+
+ // Show elements before animating them
+ if ( hidden ) {
+ showHide( [ elem ], true );
+ }
+
+ /* eslint-disable no-loop-func */
+
+ anim.done( function() {
+
+ /* eslint-enable no-loop-func */
+
+ // The final step of a "hide" animation is actually hiding the element
+ if ( !hidden ) {
+ showHide( [ elem ] );
+ }
+ dataPriv.remove( elem, "fxshow" );
+ for ( prop in orig ) {
+ jQuery.style( elem, prop, orig[ prop ] );
+ }
+ } );
+ }
+
+ // Per-property setup
+ propTween = createTween( hidden ? dataShow[ prop ] : 0, prop, anim );
+ if ( !( prop in dataShow ) ) {
+ dataShow[ prop ] = propTween.start;
+ if ( hidden ) {
+ propTween.end = propTween.start;
+ propTween.start = 0;
+ }
+ }
+ }
+}
+
+function propFilter( props, specialEasing ) {
+ var index, name, easing, value, hooks;
+
+ // camelCase, specialEasing and expand cssHook pass
+ for ( index in props ) {
+ name = camelCase( index );
+ easing = specialEasing[ name ];
+ value = props[ index ];
+ if ( Array.isArray( value ) ) {
+ easing = value[ 1 ];
+ value = props[ index ] = value[ 0 ];
+ }
+
+ if ( index !== name ) {
+ props[ name ] = value;
+ delete props[ index ];
+ }
+
+ hooks = jQuery.cssHooks[ name ];
+ if ( hooks && "expand" in hooks ) {
+ value = hooks.expand( value );
+ delete props[ name ];
+
+ // Not quite $.extend, this won't overwrite existing keys.
+ // Reusing 'index' because we have the correct "name"
+ for ( index in value ) {
+ if ( !( index in props ) ) {
+ props[ index ] = value[ index ];
+ specialEasing[ index ] = easing;
+ }
+ }
+ } else {
+ specialEasing[ name ] = easing;
+ }
+ }
+}
+
+function Animation( elem, properties, options ) {
+ var result,
+ stopped,
+ index = 0,
+ length = Animation.prefilters.length,
+ deferred = jQuery.Deferred().always( function() {
+
+ // Don't match elem in the :animated selector
+ delete tick.elem;
+ } ),
+ tick = function() {
+ if ( stopped ) {
+ return false;
+ }
+ var currentTime = fxNow || createFxNow(),
+ remaining = Math.max( 0, animation.startTime + animation.duration - currentTime ),
+
+ // Support: Android 2.3 only
+ // Archaic crash bug won't allow us to use `1 - ( 0.5 || 0 )` (#12497)
+ temp = remaining / animation.duration || 0,
+ percent = 1 - temp,
+ index = 0,
+ length = animation.tweens.length;
+
+ for ( ; index < length; index++ ) {
+ animation.tweens[ index ].run( percent );
+ }
+
+ deferred.notifyWith( elem, [ animation, percent, remaining ] );
+
+ // If there's more to do, yield
+ if ( percent < 1 && length ) {
+ return remaining;
+ }
+
+ // If this was an empty animation, synthesize a final progress notification
+ if ( !length ) {
+ deferred.notifyWith( elem, [ animation, 1, 0 ] );
+ }
+
+ // Resolve the animation and report its conclusion
+ deferred.resolveWith( elem, [ animation ] );
+ return false;
+ },
+ animation = deferred.promise( {
+ elem: elem,
+ props: jQuery.extend( {}, properties ),
+ opts: jQuery.extend( true, {
+ specialEasing: {},
+ easing: jQuery.easing._default
+ }, options ),
+ originalProperties: properties,
+ originalOptions: options,
+ startTime: fxNow || createFxNow(),
+ duration: options.duration,
+ tweens: [],
+ createTween: function( prop, end ) {
+ var tween = jQuery.Tween( elem, animation.opts, prop, end,
+ animation.opts.specialEasing[ prop ] || animation.opts.easing );
+ animation.tweens.push( tween );
+ return tween;
+ },
+ stop: function( gotoEnd ) {
+ var index = 0,
+
+ // If we are going to the end, we want to run all the tweens
+ // otherwise we skip this part
+ length = gotoEnd ? animation.tweens.length : 0;
+ if ( stopped ) {
+ return this;
+ }
+ stopped = true;
+ for ( ; index < length; index++ ) {
+ animation.tweens[ index ].run( 1 );
+ }
+
+ // Resolve when we played the last frame; otherwise, reject
+ if ( gotoEnd ) {
+ deferred.notifyWith( elem, [ animation, 1, 0 ] );
+ deferred.resolveWith( elem, [ animation, gotoEnd ] );
+ } else {
+ deferred.rejectWith( elem, [ animation, gotoEnd ] );
+ }
+ return this;
+ }
+ } ),
+ props = animation.props;
+
+ propFilter( props, animation.opts.specialEasing );
+
+ for ( ; index < length; index++ ) {
+ result = Animation.prefilters[ index ].call( animation, elem, props, animation.opts );
+ if ( result ) {
+ if ( isFunction( result.stop ) ) {
+ jQuery._queueHooks( animation.elem, animation.opts.queue ).stop =
+ result.stop.bind( result );
+ }
+ return result;
+ }
+ }
+
+ jQuery.map( props, createTween, animation );
+
+ if ( isFunction( animation.opts.start ) ) {
+ animation.opts.start.call( elem, animation );
+ }
+
+ // Attach callbacks from options
+ animation
+ .progress( animation.opts.progress )
+ .done( animation.opts.done, animation.opts.complete )
+ .fail( animation.opts.fail )
+ .always( animation.opts.always );
+
+ jQuery.fx.timer(
+ jQuery.extend( tick, {
+ elem: elem,
+ anim: animation,
+ queue: animation.opts.queue
+ } )
+ );
+
+ return animation;
+}
+
+jQuery.Animation = jQuery.extend( Animation, {
+
+ tweeners: {
+ "*": [ function( prop, value ) {
+ var tween = this.createTween( prop, value );
+ adjustCSS( tween.elem, prop, rcssNum.exec( value ), tween );
+ return tween;
+ } ]
+ },
+
+ tweener: function( props, callback ) {
+ if ( isFunction( props ) ) {
+ callback = props;
+ props = [ "*" ];
+ } else {
+ props = props.match( rnothtmlwhite );
+ }
+
+ var prop,
+ index = 0,
+ length = props.length;
+
+ for ( ; index < length; index++ ) {
+ prop = props[ index ];
+ Animation.tweeners[ prop ] = Animation.tweeners[ prop ] || [];
+ Animation.tweeners[ prop ].unshift( callback );
+ }
+ },
+
+ prefilters: [ defaultPrefilter ],
+
+ prefilter: function( callback, prepend ) {
+ if ( prepend ) {
+ Animation.prefilters.unshift( callback );
+ } else {
+ Animation.prefilters.push( callback );
+ }
+ }
+} );
+
+jQuery.speed = function( speed, easing, fn ) {
+ var opt = speed && typeof speed === "object" ? jQuery.extend( {}, speed ) : {
+ complete: fn || !fn && easing ||
+ isFunction( speed ) && speed,
+ duration: speed,
+ easing: fn && easing || easing && !isFunction( easing ) && easing
+ };
+
+ // Go to the end state if fx are off
+ if ( jQuery.fx.off ) {
+ opt.duration = 0;
+
+ } else {
+ if ( typeof opt.duration !== "number" ) {
+ if ( opt.duration in jQuery.fx.speeds ) {
+ opt.duration = jQuery.fx.speeds[ opt.duration ];
+
+ } else {
+ opt.duration = jQuery.fx.speeds._default;
+ }
+ }
+ }
+
+ // Normalize opt.queue - true/undefined/null -> "fx"
+ if ( opt.queue == null || opt.queue === true ) {
+ opt.queue = "fx";
+ }
+
+ // Queueing
+ opt.old = opt.complete;
+
+ opt.complete = function() {
+ if ( isFunction( opt.old ) ) {
+ opt.old.call( this );
+ }
+
+ if ( opt.queue ) {
+ jQuery.dequeue( this, opt.queue );
+ }
+ };
+
+ return opt;
+};
+
+jQuery.fn.extend( {
+ fadeTo: function( speed, to, easing, callback ) {
+
+ // Show any hidden elements after setting opacity to 0
+ return this.filter( isHiddenWithinTree ).css( "opacity", 0 ).show()
+
+ // Animate to the value specified
+ .end().animate( { opacity: to }, speed, easing, callback );
+ },
+ animate: function( prop, speed, easing, callback ) {
+ var empty = jQuery.isEmptyObject( prop ),
+ optall = jQuery.speed( speed, easing, callback ),
+ doAnimation = function() {
+
+ // Operate on a copy of prop so per-property easing won't be lost
+ var anim = Animation( this, jQuery.extend( {}, prop ), optall );
+
+ // Empty animations, or finishing resolves immediately
+ if ( empty || dataPriv.get( this, "finish" ) ) {
+ anim.stop( true );
+ }
+ };
+ doAnimation.finish = doAnimation;
+
+ return empty || optall.queue === false ?
+ this.each( doAnimation ) :
+ this.queue( optall.queue, doAnimation );
+ },
+ stop: function( type, clearQueue, gotoEnd ) {
+ var stopQueue = function( hooks ) {
+ var stop = hooks.stop;
+ delete hooks.stop;
+ stop( gotoEnd );
+ };
+
+ if ( typeof type !== "string" ) {
+ gotoEnd = clearQueue;
+ clearQueue = type;
+ type = undefined;
+ }
+ if ( clearQueue ) {
+ this.queue( type || "fx", [] );
+ }
+
+ return this.each( function() {
+ var dequeue = true,
+ index = type != null && type + "queueHooks",
+ timers = jQuery.timers,
+ data = dataPriv.get( this );
+
+ if ( index ) {
+ if ( data[ index ] && data[ index ].stop ) {
+ stopQueue( data[ index ] );
+ }
+ } else {
+ for ( index in data ) {
+ if ( data[ index ] && data[ index ].stop && rrun.test( index ) ) {
+ stopQueue( data[ index ] );
+ }
+ }
+ }
+
+ for ( index = timers.length; index--; ) {
+ if ( timers[ index ].elem === this &&
+ ( type == null || timers[ index ].queue === type ) ) {
+
+ timers[ index ].anim.stop( gotoEnd );
+ dequeue = false;
+ timers.splice( index, 1 );
+ }
+ }
+
+ // Start the next in the queue if the last step wasn't forced.
+ // Timers currently will call their complete callbacks, which
+ // will dequeue but only if they were gotoEnd.
+ if ( dequeue || !gotoEnd ) {
+ jQuery.dequeue( this, type );
+ }
+ } );
+ },
+ finish: function( type ) {
+ if ( type !== false ) {
+ type = type || "fx";
+ }
+ return this.each( function() {
+ var index,
+ data = dataPriv.get( this ),
+ queue = data[ type + "queue" ],
+ hooks = data[ type + "queueHooks" ],
+ timers = jQuery.timers,
+ length = queue ? queue.length : 0;
+
+ // Enable finishing flag on private data
+ data.finish = true;
+
+ // Empty the queue first
+ jQuery.queue( this, type, [] );
+
+ if ( hooks && hooks.stop ) {
+ hooks.stop.call( this, true );
+ }
+
+ // Look for any active animations, and finish them
+ for ( index = timers.length; index--; ) {
+ if ( timers[ index ].elem === this && timers[ index ].queue === type ) {
+ timers[ index ].anim.stop( true );
+ timers.splice( index, 1 );
+ }
+ }
+
+ // Look for any animations in the old queue and finish them
+ for ( index = 0; index < length; index++ ) {
+ if ( queue[ index ] && queue[ index ].finish ) {
+ queue[ index ].finish.call( this );
+ }
+ }
+
+ // Turn off finishing flag
+ delete data.finish;
+ } );
+ }
+} );
+
+jQuery.each( [ "toggle", "show", "hide" ], function( _i, name ) {
+ var cssFn = jQuery.fn[ name ];
+ jQuery.fn[ name ] = function( speed, easing, callback ) {
+ return speed == null || typeof speed === "boolean" ?
+ cssFn.apply( this, arguments ) :
+ this.animate( genFx( name, true ), speed, easing, callback );
+ };
+} );
+
+// Generate shortcuts for custom animations
+jQuery.each( {
+ slideDown: genFx( "show" ),
+ slideUp: genFx( "hide" ),
+ slideToggle: genFx( "toggle" ),
+ fadeIn: { opacity: "show" },
+ fadeOut: { opacity: "hide" },
+ fadeToggle: { opacity: "toggle" }
+}, function( name, props ) {
+ jQuery.fn[ name ] = function( speed, easing, callback ) {
+ return this.animate( props, speed, easing, callback );
+ };
+} );
+
+jQuery.timers = [];
+jQuery.fx.tick = function() {
+ var timer,
+ i = 0,
+ timers = jQuery.timers;
+
+ fxNow = Date.now();
+
+ for ( ; i < timers.length; i++ ) {
+ timer = timers[ i ];
+
+ // Run the timer and safely remove it when done (allowing for external removal)
+ if ( !timer() && timers[ i ] === timer ) {
+ timers.splice( i--, 1 );
+ }
+ }
+
+ if ( !timers.length ) {
+ jQuery.fx.stop();
+ }
+ fxNow = undefined;
+};
+
+jQuery.fx.timer = function( timer ) {
+ jQuery.timers.push( timer );
+ jQuery.fx.start();
+};
+
+jQuery.fx.interval = 13;
+jQuery.fx.start = function() {
+ if ( inProgress ) {
+ return;
+ }
+
+ inProgress = true;
+ schedule();
+};
+
+jQuery.fx.stop = function() {
+ inProgress = null;
+};
+
+jQuery.fx.speeds = {
+ slow: 600,
+ fast: 200,
+
+ // Default speed
+ _default: 400
+};
+
+
+// Based off of the plugin by Clint Helfers, with permission.
+// https://web.archive.org/web/20100324014747/http://blindsignals.com/index.php/2009/07/jquery-delay/
+jQuery.fn.delay = function( time, type ) {
+ time = jQuery.fx ? jQuery.fx.speeds[ time ] || time : time;
+ type = type || "fx";
+
+ return this.queue( type, function( next, hooks ) {
+ var timeout = window.setTimeout( next, time );
+ hooks.stop = function() {
+ window.clearTimeout( timeout );
+ };
+ } );
+};
+
+
+( function() {
+ var input = document.createElement( "input" ),
+ select = document.createElement( "select" ),
+ opt = select.appendChild( document.createElement( "option" ) );
+
+ input.type = "checkbox";
+
+ // Support: Android <=4.3 only
+ // Default value for a checkbox should be "on"
+ support.checkOn = input.value !== "";
+
+ // Support: IE <=11 only
+ // Must access selectedIndex to make default options select
+ support.optSelected = opt.selected;
+
+ // Support: IE <=11 only
+ // An input loses its value after becoming a radio
+ input = document.createElement( "input" );
+ input.value = "t";
+ input.type = "radio";
+ support.radioValue = input.value === "t";
+} )();
+
+
+var boolHook,
+ attrHandle = jQuery.expr.attrHandle;
+
+jQuery.fn.extend( {
+ attr: function( name, value ) {
+ return access( this, jQuery.attr, name, value, arguments.length > 1 );
+ },
+
+ removeAttr: function( name ) {
+ return this.each( function() {
+ jQuery.removeAttr( this, name );
+ } );
+ }
+} );
+
+jQuery.extend( {
+ attr: function( elem, name, value ) {
+ var ret, hooks,
+ nType = elem.nodeType;
+
+ // Don't get/set attributes on text, comment and attribute nodes
+ if ( nType === 3 || nType === 8 || nType === 2 ) {
+ return;
+ }
+
+ // Fallback to prop when attributes are not supported
+ if ( typeof elem.getAttribute === "undefined" ) {
+ return jQuery.prop( elem, name, value );
+ }
+
+ // Attribute hooks are determined by the lowercase version
+ // Grab necessary hook if one is defined
+ if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+ hooks = jQuery.attrHooks[ name.toLowerCase() ] ||
+ ( jQuery.expr.match.bool.test( name ) ? boolHook : undefined );
+ }
+
+ if ( value !== undefined ) {
+ if ( value === null ) {
+ jQuery.removeAttr( elem, name );
+ return;
+ }
+
+ if ( hooks && "set" in hooks &&
+ ( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+ return ret;
+ }
+
+ elem.setAttribute( name, value + "" );
+ return value;
+ }
+
+ if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+ return ret;
+ }
+
+ ret = jQuery.find.attr( elem, name );
+
+ // Non-existent attributes return null, we normalize to undefined
+ return ret == null ? undefined : ret;
+ },
+
+ attrHooks: {
+ type: {
+ set: function( elem, value ) {
+ if ( !support.radioValue && value === "radio" &&
+ nodeName( elem, "input" ) ) {
+ var val = elem.value;
+ elem.setAttribute( "type", value );
+ if ( val ) {
+ elem.value = val;
+ }
+ return value;
+ }
+ }
+ }
+ },
+
+ removeAttr: function( elem, value ) {
+ var name,
+ i = 0,
+
+ // Attribute names can contain non-HTML whitespace characters
+ // https://html.spec.whatwg.org/multipage/syntax.html#attributes-2
+ attrNames = value && value.match( rnothtmlwhite );
+
+ if ( attrNames && elem.nodeType === 1 ) {
+ while ( ( name = attrNames[ i++ ] ) ) {
+ elem.removeAttribute( name );
+ }
+ }
+ }
+} );
+
+// Hooks for boolean attributes
+boolHook = {
+ set: function( elem, value, name ) {
+ if ( value === false ) {
+
+ // Remove boolean attributes when set to false
+ jQuery.removeAttr( elem, name );
+ } else {
+ elem.setAttribute( name, name );
+ }
+ return name;
+ }
+};
+
+jQuery.each( jQuery.expr.match.bool.source.match( /\w+/g ), function( _i, name ) {
+ var getter = attrHandle[ name ] || jQuery.find.attr;
+
+ attrHandle[ name ] = function( elem, name, isXML ) {
+ var ret, handle,
+ lowercaseName = name.toLowerCase();
+
+ if ( !isXML ) {
+
+ // Avoid an infinite loop by temporarily removing this function from the getter
+ handle = attrHandle[ lowercaseName ];
+ attrHandle[ lowercaseName ] = ret;
+ ret = getter( elem, name, isXML ) != null ?
+ lowercaseName :
+ null;
+ attrHandle[ lowercaseName ] = handle;
+ }
+ return ret;
+ };
+} );
+
+
+
+
+var rfocusable = /^(?:input|select|textarea|button)$/i,
+ rclickable = /^(?:a|area)$/i;
+
+jQuery.fn.extend( {
+ prop: function( name, value ) {
+ return access( this, jQuery.prop, name, value, arguments.length > 1 );
+ },
+
+ removeProp: function( name ) {
+ return this.each( function() {
+ delete this[ jQuery.propFix[ name ] || name ];
+ } );
+ }
+} );
+
+jQuery.extend( {
+ prop: function( elem, name, value ) {
+ var ret, hooks,
+ nType = elem.nodeType;
+
+ // Don't get/set properties on text, comment and attribute nodes
+ if ( nType === 3 || nType === 8 || nType === 2 ) {
+ return;
+ }
+
+ if ( nType !== 1 || !jQuery.isXMLDoc( elem ) ) {
+
+ // Fix name and attach hooks
+ name = jQuery.propFix[ name ] || name;
+ hooks = jQuery.propHooks[ name ];
+ }
+
+ if ( value !== undefined ) {
+ if ( hooks && "set" in hooks &&
+ ( ret = hooks.set( elem, value, name ) ) !== undefined ) {
+ return ret;
+ }
+
+ return ( elem[ name ] = value );
+ }
+
+ if ( hooks && "get" in hooks && ( ret = hooks.get( elem, name ) ) !== null ) {
+ return ret;
+ }
+
+ return elem[ name ];
+ },
+
+ propHooks: {
+ tabIndex: {
+ get: function( elem ) {
+
+ // Support: IE <=9 - 11 only
+ // elem.tabIndex doesn't always return the
+ // correct value when it hasn't been explicitly set
+ // https://web.archive.org/web/20141116233347/http://fluidproject.org/blog/2008/01/09/getting-setting-and-removing-tabindex-values-with-javascript/
+ // Use proper attribute retrieval(#12072)
+ var tabindex = jQuery.find.attr( elem, "tabindex" );
+
+ if ( tabindex ) {
+ return parseInt( tabindex, 10 );
+ }
+
+ if (
+ rfocusable.test( elem.nodeName ) ||
+ rclickable.test( elem.nodeName ) &&
+ elem.href
+ ) {
+ return 0;
+ }
+
+ return -1;
+ }
+ }
+ },
+
+ propFix: {
+ "for": "htmlFor",
+ "class": "className"
+ }
+} );
+
+// Support: IE <=11 only
+// Accessing the selectedIndex property
+// forces the browser to respect setting selected
+// on the option
+// The getter ensures a default option is selected
+// when in an optgroup
+// eslint rule "no-unused-expressions" is disabled for this code
+// since it considers such accessions noop
+if ( !support.optSelected ) {
+ jQuery.propHooks.selected = {
+ get: function( elem ) {
+
+ /* eslint no-unused-expressions: "off" */
+
+ var parent = elem.parentNode;
+ if ( parent && parent.parentNode ) {
+ parent.parentNode.selectedIndex;
+ }
+ return null;
+ },
+ set: function( elem ) {
+
+ /* eslint no-unused-expressions: "off" */
+
+ var parent = elem.parentNode;
+ if ( parent ) {
+ parent.selectedIndex;
+
+ if ( parent.parentNode ) {
+ parent.parentNode.selectedIndex;
+ }
+ }
+ }
+ };
+}
+
+jQuery.each( [
+ "tabIndex",
+ "readOnly",
+ "maxLength",
+ "cellSpacing",
+ "cellPadding",
+ "rowSpan",
+ "colSpan",
+ "useMap",
+ "frameBorder",
+ "contentEditable"
+], function() {
+ jQuery.propFix[ this.toLowerCase() ] = this;
+} );
+
+
+
+
+ // Strip and collapse whitespace according to HTML spec
+ // https://infra.spec.whatwg.org/#strip-and-collapse-ascii-whitespace
+ function stripAndCollapse( value ) {
+ var tokens = value.match( rnothtmlwhite ) || [];
+ return tokens.join( " " );
+ }
+
+
+function getClass( elem ) {
+ return elem.getAttribute && elem.getAttribute( "class" ) || "";
+}
+
+function classesToArray( value ) {
+ if ( Array.isArray( value ) ) {
+ return value;
+ }
+ if ( typeof value === "string" ) {
+ return value.match( rnothtmlwhite ) || [];
+ }
+ return [];
+}
+
+jQuery.fn.extend( {
+ addClass: function( value ) {
+ var classes, elem, cur, curValue, clazz, j, finalValue,
+ i = 0;
+
+ if ( isFunction( value ) ) {
+ return this.each( function( j ) {
+ jQuery( this ).addClass( value.call( this, j, getClass( this ) ) );
+ } );
+ }
+
+ classes = classesToArray( value );
+
+ if ( classes.length ) {
+ while ( ( elem = this[ i++ ] ) ) {
+ curValue = getClass( elem );
+ cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+ if ( cur ) {
+ j = 0;
+ while ( ( clazz = classes[ j++ ] ) ) {
+ if ( cur.indexOf( " " + clazz + " " ) < 0 ) {
+ cur += clazz + " ";
+ }
+ }
+
+ // Only assign if different to avoid unneeded rendering.
+ finalValue = stripAndCollapse( cur );
+ if ( curValue !== finalValue ) {
+ elem.setAttribute( "class", finalValue );
+ }
+ }
+ }
+ }
+
+ return this;
+ },
+
+ removeClass: function( value ) {
+ var classes, elem, cur, curValue, clazz, j, finalValue,
+ i = 0;
+
+ if ( isFunction( value ) ) {
+ return this.each( function( j ) {
+ jQuery( this ).removeClass( value.call( this, j, getClass( this ) ) );
+ } );
+ }
+
+ if ( !arguments.length ) {
+ return this.attr( "class", "" );
+ }
+
+ classes = classesToArray( value );
+
+ if ( classes.length ) {
+ while ( ( elem = this[ i++ ] ) ) {
+ curValue = getClass( elem );
+
+ // This expression is here for better compressibility (see addClass)
+ cur = elem.nodeType === 1 && ( " " + stripAndCollapse( curValue ) + " " );
+
+ if ( cur ) {
+ j = 0;
+ while ( ( clazz = classes[ j++ ] ) ) {
+
+ // Remove *all* instances
+ while ( cur.indexOf( " " + clazz + " " ) > -1 ) {
+ cur = cur.replace( " " + clazz + " ", " " );
+ }
+ }
+
+ // Only assign if different to avoid unneeded rendering.
+ finalValue = stripAndCollapse( cur );
+ if ( curValue !== finalValue ) {
+ elem.setAttribute( "class", finalValue );
+ }
+ }
+ }
+ }
+
+ return this;
+ },
+
+ toggleClass: function( value, stateVal ) {
+ var type = typeof value,
+ isValidValue = type === "string" || Array.isArray( value );
+
+ if ( typeof stateVal === "boolean" && isValidValue ) {
+ return stateVal ? this.addClass( value ) : this.removeClass( value );
+ }
+
+ if ( isFunction( value ) ) {
+ return this.each( function( i ) {
+ jQuery( this ).toggleClass(
+ value.call( this, i, getClass( this ), stateVal ),
+ stateVal
+ );
+ } );
+ }
+
+ return this.each( function() {
+ var className, i, self, classNames;
+
+ if ( isValidValue ) {
+
+ // Toggle individual class names
+ i = 0;
+ self = jQuery( this );
+ classNames = classesToArray( value );
+
+ while ( ( className = classNames[ i++ ] ) ) {
+
+ // Check each className given, space separated list
+ if ( self.hasClass( className ) ) {
+ self.removeClass( className );
+ } else {
+ self.addClass( className );
+ }
+ }
+
+ // Toggle whole class name
+ } else if ( value === undefined || type === "boolean" ) {
+ className = getClass( this );
+ if ( className ) {
+
+ // Store className if set
+ dataPriv.set( this, "__className__", className );
+ }
+
+ // If the element has a class name or if we're passed `false`,
+ // then remove the whole classname (if there was one, the above saved it).
+ // Otherwise bring back whatever was previously saved (if anything),
+ // falling back to the empty string if nothing was stored.
+ if ( this.setAttribute ) {
+ this.setAttribute( "class",
+ className || value === false ?
+ "" :
+ dataPriv.get( this, "__className__" ) || ""
+ );
+ }
+ }
+ } );
+ },
+
+ hasClass: function( selector ) {
+ var className, elem,
+ i = 0;
+
+ className = " " + selector + " ";
+ while ( ( elem = this[ i++ ] ) ) {
+ if ( elem.nodeType === 1 &&
+ ( " " + stripAndCollapse( getClass( elem ) ) + " " ).indexOf( className ) > -1 ) {
+ return true;
+ }
+ }
+
+ return false;
+ }
+} );
+
+
+
+
+var rreturn = /\r/g;
+
+jQuery.fn.extend( {
+ val: function( value ) {
+ var hooks, ret, valueIsFunction,
+ elem = this[ 0 ];
+
+ if ( !arguments.length ) {
+ if ( elem ) {
+ hooks = jQuery.valHooks[ elem.type ] ||
+ jQuery.valHooks[ elem.nodeName.toLowerCase() ];
+
+ if ( hooks &&
+ "get" in hooks &&
+ ( ret = hooks.get( elem, "value" ) ) !== undefined
+ ) {
+ return ret;
+ }
+
+ ret = elem.value;
+
+ // Handle most common string cases
+ if ( typeof ret === "string" ) {
+ return ret.replace( rreturn, "" );
+ }
+
+ // Handle cases where value is null/undef or number
+ return ret == null ? "" : ret;
+ }
+
+ return;
+ }
+
+ valueIsFunction = isFunction( value );
+
+ return this.each( function( i ) {
+ var val;
+
+ if ( this.nodeType !== 1 ) {
+ return;
+ }
+
+ if ( valueIsFunction ) {
+ val = value.call( this, i, jQuery( this ).val() );
+ } else {
+ val = value;
+ }
+
+ // Treat null/undefined as ""; convert numbers to string
+ if ( val == null ) {
+ val = "";
+
+ } else if ( typeof val === "number" ) {
+ val += "";
+
+ } else if ( Array.isArray( val ) ) {
+ val = jQuery.map( val, function( value ) {
+ return value == null ? "" : value + "";
+ } );
+ }
+
+ hooks = jQuery.valHooks[ this.type ] || jQuery.valHooks[ this.nodeName.toLowerCase() ];
+
+ // If set returns undefined, fall back to normal setting
+ if ( !hooks || !( "set" in hooks ) || hooks.set( this, val, "value" ) === undefined ) {
+ this.value = val;
+ }
+ } );
+ }
+} );
+
+jQuery.extend( {
+ valHooks: {
+ option: {
+ get: function( elem ) {
+
+ var val = jQuery.find.attr( elem, "value" );
+ return val != null ?
+ val :
+
+ // Support: IE <=10 - 11 only
+ // option.text throws exceptions (#14686, #14858)
+ // Strip and collapse whitespace
+ // https://html.spec.whatwg.org/#strip-and-collapse-whitespace
+ stripAndCollapse( jQuery.text( elem ) );
+ }
+ },
+ select: {
+ get: function( elem ) {
+ var value, option, i,
+ options = elem.options,
+ index = elem.selectedIndex,
+ one = elem.type === "select-one",
+ values = one ? null : [],
+ max = one ? index + 1 : options.length;
+
+ if ( index < 0 ) {
+ i = max;
+
+ } else {
+ i = one ? index : 0;
+ }
+
+ // Loop through all the selected options
+ for ( ; i < max; i++ ) {
+ option = options[ i ];
+
+ // Support: IE <=9 only
+ // IE8-9 doesn't update selected after form reset (#2551)
+ if ( ( option.selected || i === index ) &&
+
+ // Don't return options that are disabled or in a disabled optgroup
+ !option.disabled &&
+ ( !option.parentNode.disabled ||
+ !nodeName( option.parentNode, "optgroup" ) ) ) {
+
+ // Get the specific value for the option
+ value = jQuery( option ).val();
+
+ // We don't need an array for one selects
+ if ( one ) {
+ return value;
+ }
+
+ // Multi-Selects return an array
+ values.push( value );
+ }
+ }
+
+ return values;
+ },
+
+ set: function( elem, value ) {
+ var optionSet, option,
+ options = elem.options,
+ values = jQuery.makeArray( value ),
+ i = options.length;
+
+ while ( i-- ) {
+ option = options[ i ];
+
+ /* eslint-disable no-cond-assign */
+
+ if ( option.selected =
+ jQuery.inArray( jQuery.valHooks.option.get( option ), values ) > -1
+ ) {
+ optionSet = true;
+ }
+
+ /* eslint-enable no-cond-assign */
+ }
+
+ // Force browsers to behave consistently when non-matching value is set
+ if ( !optionSet ) {
+ elem.selectedIndex = -1;
+ }
+ return values;
+ }
+ }
+ }
+} );
+
+// Radios and checkboxes getter/setter
+jQuery.each( [ "radio", "checkbox" ], function() {
+ jQuery.valHooks[ this ] = {
+ set: function( elem, value ) {
+ if ( Array.isArray( value ) ) {
+ return ( elem.checked = jQuery.inArray( jQuery( elem ).val(), value ) > -1 );
+ }
+ }
+ };
+ if ( !support.checkOn ) {
+ jQuery.valHooks[ this ].get = function( elem ) {
+ return elem.getAttribute( "value" ) === null ? "on" : elem.value;
+ };
+ }
+} );
+
+
+
+
+// Return jQuery for attributes-only inclusion
+
+
+support.focusin = "onfocusin" in window;
+
+
+var rfocusMorph = /^(?:focusinfocus|focusoutblur)$/,
+ stopPropagationCallback = function( e ) {
+ e.stopPropagation();
+ };
+
+jQuery.extend( jQuery.event, {
+
+ trigger: function( event, data, elem, onlyHandlers ) {
+
+ var i, cur, tmp, bubbleType, ontype, handle, special, lastElement,
+ eventPath = [ elem || document ],
+ type = hasOwn.call( event, "type" ) ? event.type : event,
+ namespaces = hasOwn.call( event, "namespace" ) ? event.namespace.split( "." ) : [];
+
+ cur = lastElement = tmp = elem = elem || document;
+
+ // Don't do events on text and comment nodes
+ if ( elem.nodeType === 3 || elem.nodeType === 8 ) {
+ return;
+ }
+
+ // focus/blur morphs to focusin/out; ensure we're not firing them right now
+ if ( rfocusMorph.test( type + jQuery.event.triggered ) ) {
+ return;
+ }
+
+ if ( type.indexOf( "." ) > -1 ) {
+
+ // Namespaced trigger; create a regexp to match event type in handle()
+ namespaces = type.split( "." );
+ type = namespaces.shift();
+ namespaces.sort();
+ }
+ ontype = type.indexOf( ":" ) < 0 && "on" + type;
+
+ // Caller can pass in a jQuery.Event object, Object, or just an event type string
+ event = event[ jQuery.expando ] ?
+ event :
+ new jQuery.Event( type, typeof event === "object" && event );
+
+ // Trigger bitmask: & 1 for native handlers; & 2 for jQuery (always true)
+ event.isTrigger = onlyHandlers ? 2 : 3;
+ event.namespace = namespaces.join( "." );
+ event.rnamespace = event.namespace ?
+ new RegExp( "(^|\\.)" + namespaces.join( "\\.(?:.*\\.|)" ) + "(\\.|$)" ) :
+ null;
+
+ // Clean up the event in case it is being reused
+ event.result = undefined;
+ if ( !event.target ) {
+ event.target = elem;
+ }
+
+ // Clone any incoming data and prepend the event, creating the handler arg list
+ data = data == null ?
+ [ event ] :
+ jQuery.makeArray( data, [ event ] );
+
+ // Allow special events to draw outside the lines
+ special = jQuery.event.special[ type ] || {};
+ if ( !onlyHandlers && special.trigger && special.trigger.apply( elem, data ) === false ) {
+ return;
+ }
+
+ // Determine event propagation path in advance, per W3C events spec (#9951)
+ // Bubble up to document, then to window; watch for a global ownerDocument var (#9724)
+ if ( !onlyHandlers && !special.noBubble && !isWindow( elem ) ) {
+
+ bubbleType = special.delegateType || type;
+ if ( !rfocusMorph.test( bubbleType + type ) ) {
+ cur = cur.parentNode;
+ }
+ for ( ; cur; cur = cur.parentNode ) {
+ eventPath.push( cur );
+ tmp = cur;
+ }
+
+ // Only add window if we got to document (e.g., not plain obj or detached DOM)
+ if ( tmp === ( elem.ownerDocument || document ) ) {
+ eventPath.push( tmp.defaultView || tmp.parentWindow || window );
+ }
+ }
+
+ // Fire handlers on the event path
+ i = 0;
+ while ( ( cur = eventPath[ i++ ] ) && !event.isPropagationStopped() ) {
+ lastElement = cur;
+ event.type = i > 1 ?
+ bubbleType :
+ special.bindType || type;
+
+ // jQuery handler
+ handle = (
+ dataPriv.get( cur, "events" ) || Object.create( null )
+ )[ event.type ] &&
+ dataPriv.get( cur, "handle" );
+ if ( handle ) {
+ handle.apply( cur, data );
+ }
+
+ // Native handler
+ handle = ontype && cur[ ontype ];
+ if ( handle && handle.apply && acceptData( cur ) ) {
+ event.result = handle.apply( cur, data );
+ if ( event.result === false ) {
+ event.preventDefault();
+ }
+ }
+ }
+ event.type = type;
+
+ // If nobody prevented the default action, do it now
+ if ( !onlyHandlers && !event.isDefaultPrevented() ) {
+
+ if ( ( !special._default ||
+ special._default.apply( eventPath.pop(), data ) === false ) &&
+ acceptData( elem ) ) {
+
+ // Call a native DOM method on the target with the same name as the event.
+ // Don't do default actions on window, that's where global variables be (#6170)
+ if ( ontype && isFunction( elem[ type ] ) && !isWindow( elem ) ) {
+
+ // Don't re-trigger an onFOO event when we call its FOO() method
+ tmp = elem[ ontype ];
+
+ if ( tmp ) {
+ elem[ ontype ] = null;
+ }
+
+ // Prevent re-triggering of the same event, since we already bubbled it above
+ jQuery.event.triggered = type;
+
+ if ( event.isPropagationStopped() ) {
+ lastElement.addEventListener( type, stopPropagationCallback );
+ }
+
+ elem[ type ]();
+
+ if ( event.isPropagationStopped() ) {
+ lastElement.removeEventListener( type, stopPropagationCallback );
+ }
+
+ jQuery.event.triggered = undefined;
+
+ if ( tmp ) {
+ elem[ ontype ] = tmp;
+ }
+ }
+ }
+ }
+
+ return event.result;
+ },
+
+ // Piggyback on a donor event to simulate a different one
+ // Used only for `focus(in | out)` events
+ simulate: function( type, elem, event ) {
+ var e = jQuery.extend(
+ new jQuery.Event(),
+ event,
+ {
+ type: type,
+ isSimulated: true
+ }
+ );
+
+ jQuery.event.trigger( e, null, elem );
+ }
+
+} );
+
+jQuery.fn.extend( {
+
+ trigger: function( type, data ) {
+ return this.each( function() {
+ jQuery.event.trigger( type, data, this );
+ } );
+ },
+ triggerHandler: function( type, data ) {
+ var elem = this[ 0 ];
+ if ( elem ) {
+ return jQuery.event.trigger( type, data, elem, true );
+ }
+ }
+} );
+
+
+// Support: Firefox <=44
+// Firefox doesn't have focus(in | out) events
+// Related ticket - https://bugzilla.mozilla.org/show_bug.cgi?id=687787
+//
+// Support: Chrome <=48 - 49, Safari <=9.0 - 9.1
+// focus(in | out) events fire after focus & blur events,
+// which is spec violation - http://www.w3.org/TR/DOM-Level-3-Events/#events-focusevent-event-order
+// Related ticket - https://bugs.chromium.org/p/chromium/issues/detail?id=449857
+if ( !support.focusin ) {
+ jQuery.each( { focus: "focusin", blur: "focusout" }, function( orig, fix ) {
+
+ // Attach a single capturing handler on the document while someone wants focusin/focusout
+ var handler = function( event ) {
+ jQuery.event.simulate( fix, event.target, jQuery.event.fix( event ) );
+ };
+
+ jQuery.event.special[ fix ] = {
+ setup: function() {
+
+ // Handle: regular nodes (via `this.ownerDocument`), window
+ // (via `this.document`) & document (via `this`).
+ var doc = this.ownerDocument || this.document || this,
+ attaches = dataPriv.access( doc, fix );
+
+ if ( !attaches ) {
+ doc.addEventListener( orig, handler, true );
+ }
+ dataPriv.access( doc, fix, ( attaches || 0 ) + 1 );
+ },
+ teardown: function() {
+ var doc = this.ownerDocument || this.document || this,
+ attaches = dataPriv.access( doc, fix ) - 1;
+
+ if ( !attaches ) {
+ doc.removeEventListener( orig, handler, true );
+ dataPriv.remove( doc, fix );
+
+ } else {
+ dataPriv.access( doc, fix, attaches );
+ }
+ }
+ };
+ } );
+}
+var location = window.location;
+
+var nonce = { guid: Date.now() };
+
+var rquery = ( /\?/ );
+
+
+
+// Cross-browser xml parsing
+jQuery.parseXML = function( data ) {
+ var xml;
+ if ( !data || typeof data !== "string" ) {
+ return null;
+ }
+
+ // Support: IE 9 - 11 only
+ // IE throws on parseFromString with invalid input.
+ try {
+ xml = ( new window.DOMParser() ).parseFromString( data, "text/xml" );
+ } catch ( e ) {
+ xml = undefined;
+ }
+
+ if ( !xml || xml.getElementsByTagName( "parsererror" ).length ) {
+ jQuery.error( "Invalid XML: " + data );
+ }
+ return xml;
+};
+
+
+var
+ rbracket = /\[\]$/,
+ rCRLF = /\r?\n/g,
+ rsubmitterTypes = /^(?:submit|button|image|reset|file)$/i,
+ rsubmittable = /^(?:input|select|textarea|keygen)/i;
+
+function buildParams( prefix, obj, traditional, add ) {
+ var name;
+
+ if ( Array.isArray( obj ) ) {
+
+ // Serialize array item.
+ jQuery.each( obj, function( i, v ) {
+ if ( traditional || rbracket.test( prefix ) ) {
+
+ // Treat each array item as a scalar.
+ add( prefix, v );
+
+ } else {
+
+ // Item is non-scalar (array or object), encode its numeric index.
+ buildParams(
+ prefix + "[" + ( typeof v === "object" && v != null ? i : "" ) + "]",
+ v,
+ traditional,
+ add
+ );
+ }
+ } );
+
+ } else if ( !traditional && toType( obj ) === "object" ) {
+
+ // Serialize object item.
+ for ( name in obj ) {
+ buildParams( prefix + "[" + name + "]", obj[ name ], traditional, add );
+ }
+
+ } else {
+
+ // Serialize scalar item.
+ add( prefix, obj );
+ }
+}
+
+// Serialize an array of form elements or a set of
+// key/values into a query string
+jQuery.param = function( a, traditional ) {
+ var prefix,
+ s = [],
+ add = function( key, valueOrFunction ) {
+
+ // If value is a function, invoke it and use its return value
+ var value = isFunction( valueOrFunction ) ?
+ valueOrFunction() :
+ valueOrFunction;
+
+ s[ s.length ] = encodeURIComponent( key ) + "=" +
+ encodeURIComponent( value == null ? "" : value );
+ };
+
+ if ( a == null ) {
+ return "";
+ }
+
+ // If an array was passed in, assume that it is an array of form elements.
+ if ( Array.isArray( a ) || ( a.jquery && !jQuery.isPlainObject( a ) ) ) {
+
+ // Serialize the form elements
+ jQuery.each( a, function() {
+ add( this.name, this.value );
+ } );
+
+ } else {
+
+ // If traditional, encode the "old" way (the way 1.3.2 or older
+ // did it), otherwise encode params recursively.
+ for ( prefix in a ) {
+ buildParams( prefix, a[ prefix ], traditional, add );
+ }
+ }
+
+ // Return the resulting serialization
+ return s.join( "&" );
+};
+
+jQuery.fn.extend( {
+ serialize: function() {
+ return jQuery.param( this.serializeArray() );
+ },
+ serializeArray: function() {
+ return this.map( function() {
+
+ // Can add propHook for "elements" to filter or add form elements
+ var elements = jQuery.prop( this, "elements" );
+ return elements ? jQuery.makeArray( elements ) : this;
+ } )
+ .filter( function() {
+ var type = this.type;
+
+ // Use .is( ":disabled" ) so that fieldset[disabled] works
+ return this.name && !jQuery( this ).is( ":disabled" ) &&
+ rsubmittable.test( this.nodeName ) && !rsubmitterTypes.test( type ) &&
+ ( this.checked || !rcheckableType.test( type ) );
+ } )
+ .map( function( _i, elem ) {
+ var val = jQuery( this ).val();
+
+ if ( val == null ) {
+ return null;
+ }
+
+ if ( Array.isArray( val ) ) {
+ return jQuery.map( val, function( val ) {
+ return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+ } );
+ }
+
+ return { name: elem.name, value: val.replace( rCRLF, "\r\n" ) };
+ } ).get();
+ }
+} );
+
+
+var
+ r20 = /%20/g,
+ rhash = /#.*$/,
+ rantiCache = /([?&])_=[^&]*/,
+ rheaders = /^(.*?):[ \t]*([^\r\n]*)$/mg,
+
+ // #7653, #8125, #8152: local protocol detection
+ rlocalProtocol = /^(?:about|app|app-storage|.+-extension|file|res|widget):$/,
+ rnoContent = /^(?:GET|HEAD)$/,
+ rprotocol = /^\/\//,
+
+ /* Prefilters
+ * 1) They are useful to introduce custom dataTypes (see ajax/jsonp.js for an example)
+ * 2) These are called:
+ * - BEFORE asking for a transport
+ * - AFTER param serialization (s.data is a string if s.processData is true)
+ * 3) key is the dataType
+ * 4) the catchall symbol "*" can be used
+ * 5) execution will start with transport dataType and THEN continue down to "*" if needed
+ */
+ prefilters = {},
+
+ /* Transports bindings
+ * 1) key is the dataType
+ * 2) the catchall symbol "*" can be used
+ * 3) selection will start with transport dataType and THEN go to "*" if needed
+ */
+ transports = {},
+
+ // Avoid comment-prolog char sequence (#10098); must appease lint and evade compression
+ allTypes = "*/".concat( "*" ),
+
+ // Anchor tag for parsing the document origin
+ originAnchor = document.createElement( "a" );
+ originAnchor.href = location.href;
+
+// Base "constructor" for jQuery.ajaxPrefilter and jQuery.ajaxTransport
+function addToPrefiltersOrTransports( structure ) {
+
+ // dataTypeExpression is optional and defaults to "*"
+ return function( dataTypeExpression, func ) {
+
+ if ( typeof dataTypeExpression !== "string" ) {
+ func = dataTypeExpression;
+ dataTypeExpression = "*";
+ }
+
+ var dataType,
+ i = 0,
+ dataTypes = dataTypeExpression.toLowerCase().match( rnothtmlwhite ) || [];
+
+ if ( isFunction( func ) ) {
+
+ // For each dataType in the dataTypeExpression
+ while ( ( dataType = dataTypes[ i++ ] ) ) {
+
+ // Prepend if requested
+ if ( dataType[ 0 ] === "+" ) {
+ dataType = dataType.slice( 1 ) || "*";
+ ( structure[ dataType ] = structure[ dataType ] || [] ).unshift( func );
+
+ // Otherwise append
+ } else {
+ ( structure[ dataType ] = structure[ dataType ] || [] ).push( func );
+ }
+ }
+ }
+ };
+}
+
+// Base inspection function for prefilters and transports
+function inspectPrefiltersOrTransports( structure, options, originalOptions, jqXHR ) {
+
+ var inspected = {},
+ seekingTransport = ( structure === transports );
+
+ function inspect( dataType ) {
+ var selected;
+ inspected[ dataType ] = true;
+ jQuery.each( structure[ dataType ] || [], function( _, prefilterOrFactory ) {
+ var dataTypeOrTransport = prefilterOrFactory( options, originalOptions, jqXHR );
+ if ( typeof dataTypeOrTransport === "string" &&
+ !seekingTransport && !inspected[ dataTypeOrTransport ] ) {
+
+ options.dataTypes.unshift( dataTypeOrTransport );
+ inspect( dataTypeOrTransport );
+ return false;
+ } else if ( seekingTransport ) {
+ return !( selected = dataTypeOrTransport );
+ }
+ } );
+ return selected;
+ }
+
+ return inspect( options.dataTypes[ 0 ] ) || !inspected[ "*" ] && inspect( "*" );
+}
+
+// A special extend for ajax options
+// that takes "flat" options (not to be deep extended)
+// Fixes #9887
+function ajaxExtend( target, src ) {
+ var key, deep,
+ flatOptions = jQuery.ajaxSettings.flatOptions || {};
+
+ for ( key in src ) {
+ if ( src[ key ] !== undefined ) {
+ ( flatOptions[ key ] ? target : ( deep || ( deep = {} ) ) )[ key ] = src[ key ];
+ }
+ }
+ if ( deep ) {
+ jQuery.extend( true, target, deep );
+ }
+
+ return target;
+}
+
+/* Handles responses to an ajax request:
+ * - finds the right dataType (mediates between content-type and expected dataType)
+ * - returns the corresponding response
+ */
+function ajaxHandleResponses( s, jqXHR, responses ) {
+
+ var ct, type, finalDataType, firstDataType,
+ contents = s.contents,
+ dataTypes = s.dataTypes;
+
+ // Remove auto dataType and get content-type in the process
+ while ( dataTypes[ 0 ] === "*" ) {
+ dataTypes.shift();
+ if ( ct === undefined ) {
+ ct = s.mimeType || jqXHR.getResponseHeader( "Content-Type" );
+ }
+ }
+
+ // Check if we're dealing with a known content-type
+ if ( ct ) {
+ for ( type in contents ) {
+ if ( contents[ type ] && contents[ type ].test( ct ) ) {
+ dataTypes.unshift( type );
+ break;
+ }
+ }
+ }
+
+ // Check to see if we have a response for the expected dataType
+ if ( dataTypes[ 0 ] in responses ) {
+ finalDataType = dataTypes[ 0 ];
+ } else {
+
+ // Try convertible dataTypes
+ for ( type in responses ) {
+ if ( !dataTypes[ 0 ] || s.converters[ type + " " + dataTypes[ 0 ] ] ) {
+ finalDataType = type;
+ break;
+ }
+ if ( !firstDataType ) {
+ firstDataType = type;
+ }
+ }
+
+ // Or just use first one
+ finalDataType = finalDataType || firstDataType;
+ }
+
+ // If we found a dataType
+ // We add the dataType to the list if needed
+ // and return the corresponding response
+ if ( finalDataType ) {
+ if ( finalDataType !== dataTypes[ 0 ] ) {
+ dataTypes.unshift( finalDataType );
+ }
+ return responses[ finalDataType ];
+ }
+}
+
+/* Chain conversions given the request and the original response
+ * Also sets the responseXXX fields on the jqXHR instance
+ */
+function ajaxConvert( s, response, jqXHR, isSuccess ) {
+ var conv2, current, conv, tmp, prev,
+ converters = {},
+
+ // Work with a copy of dataTypes in case we need to modify it for conversion
+ dataTypes = s.dataTypes.slice();
+
+ // Create converters map with lowercased keys
+ if ( dataTypes[ 1 ] ) {
+ for ( conv in s.converters ) {
+ converters[ conv.toLowerCase() ] = s.converters[ conv ];
+ }
+ }
+
+ current = dataTypes.shift();
+
+ // Convert to each sequential dataType
+ while ( current ) {
+
+ if ( s.responseFields[ current ] ) {
+ jqXHR[ s.responseFields[ current ] ] = response;
+ }
+
+ // Apply the dataFilter if provided
+ if ( !prev && isSuccess && s.dataFilter ) {
+ response = s.dataFilter( response, s.dataType );
+ }
+
+ prev = current;
+ current = dataTypes.shift();
+
+ if ( current ) {
+
+ // There's only work to do if current dataType is non-auto
+ if ( current === "*" ) {
+
+ current = prev;
+
+ // Convert response if prev dataType is non-auto and differs from current
+ } else if ( prev !== "*" && prev !== current ) {
+
+ // Seek a direct converter
+ conv = converters[ prev + " " + current ] || converters[ "* " + current ];
+
+ // If none found, seek a pair
+ if ( !conv ) {
+ for ( conv2 in converters ) {
+
+ // If conv2 outputs current
+ tmp = conv2.split( " " );
+ if ( tmp[ 1 ] === current ) {
+
+ // If prev can be converted to accepted input
+ conv = converters[ prev + " " + tmp[ 0 ] ] ||
+ converters[ "* " + tmp[ 0 ] ];
+ if ( conv ) {
+
+ // Condense equivalence converters
+ if ( conv === true ) {
+ conv = converters[ conv2 ];
+
+ // Otherwise, insert the intermediate dataType
+ } else if ( converters[ conv2 ] !== true ) {
+ current = tmp[ 0 ];
+ dataTypes.unshift( tmp[ 1 ] );
+ }
+ break;
+ }
+ }
+ }
+ }
+
+ // Apply converter (if not an equivalence)
+ if ( conv !== true ) {
+
+ // Unless errors are allowed to bubble, catch and return them
+ if ( conv && s.throws ) {
+ response = conv( response );
+ } else {
+ try {
+ response = conv( response );
+ } catch ( e ) {
+ return {
+ state: "parsererror",
+ error: conv ? e : "No conversion from " + prev + " to " + current
+ };
+ }
+ }
+ }
+ }
+ }
+ }
+
+ return { state: "success", data: response };
+}
+
+jQuery.extend( {
+
+ // Counter for holding the number of active queries
+ active: 0,
+
+ // Last-Modified header cache for next request
+ lastModified: {},
+ etag: {},
+
+ ajaxSettings: {
+ url: location.href,
+ type: "GET",
+ isLocal: rlocalProtocol.test( location.protocol ),
+ global: true,
+ processData: true,
+ async: true,
+ contentType: "application/x-www-form-urlencoded; charset=UTF-8",
+
+ /*
+ timeout: 0,
+ data: null,
+ dataType: null,
+ username: null,
+ password: null,
+ cache: null,
+ throws: false,
+ traditional: false,
+ headers: {},
+ */
+
+ accepts: {
+ "*": allTypes,
+ text: "text/plain",
+ html: "text/html",
+ xml: "application/xml, text/xml",
+ json: "application/json, text/javascript"
+ },
+
+ contents: {
+ xml: /\bxml\b/,
+ html: /\bhtml/,
+ json: /\bjson\b/
+ },
+
+ responseFields: {
+ xml: "responseXML",
+ text: "responseText",
+ json: "responseJSON"
+ },
+
+ // Data converters
+ // Keys separate source (or catchall "*") and destination types with a single space
+ converters: {
+
+ // Convert anything to text
+ "* text": String,
+
+ // Text to html (true = no transformation)
+ "text html": true,
+
+ // Evaluate text as a json expression
+ "text json": JSON.parse,
+
+ // Parse text as xml
+ "text xml": jQuery.parseXML
+ },
+
+ // For options that shouldn't be deep extended:
+ // you can add your own custom options here if
+ // and when you create one that shouldn't be
+ // deep extended (see ajaxExtend)
+ flatOptions: {
+ url: true,
+ context: true
+ }
+ },
+
+ // Creates a full fledged settings object into target
+ // with both ajaxSettings and settings fields.
+ // If target is omitted, writes into ajaxSettings.
+ ajaxSetup: function( target, settings ) {
+ return settings ?
+
+ // Building a settings object
+ ajaxExtend( ajaxExtend( target, jQuery.ajaxSettings ), settings ) :
+
+ // Extending ajaxSettings
+ ajaxExtend( jQuery.ajaxSettings, target );
+ },
+
+ ajaxPrefilter: addToPrefiltersOrTransports( prefilters ),
+ ajaxTransport: addToPrefiltersOrTransports( transports ),
+
+ // Main method
+ ajax: function( url, options ) {
+
+ // If url is an object, simulate pre-1.5 signature
+ if ( typeof url === "object" ) {
+ options = url;
+ url = undefined;
+ }
+
+ // Force options to be an object
+ options = options || {};
+
+ var transport,
+
+ // URL without anti-cache param
+ cacheURL,
+
+ // Response headers
+ responseHeadersString,
+ responseHeaders,
+
+ // timeout handle
+ timeoutTimer,
+
+ // Url cleanup var
+ urlAnchor,
+
+ // Request state (becomes false upon send and true upon completion)
+ completed,
+
+ // To know if global events are to be dispatched
+ fireGlobals,
+
+ // Loop variable
+ i,
+
+ // uncached part of the url
+ uncached,
+
+ // Create the final options object
+ s = jQuery.ajaxSetup( {}, options ),
+
+ // Callbacks context
+ callbackContext = s.context || s,
+
+ // Context for global events is callbackContext if it is a DOM node or jQuery collection
+ globalEventContext = s.context &&
+ ( callbackContext.nodeType || callbackContext.jquery ) ?
+ jQuery( callbackContext ) :
+ jQuery.event,
+
+ // Deferreds
+ deferred = jQuery.Deferred(),
+ completeDeferred = jQuery.Callbacks( "once memory" ),
+
+ // Status-dependent callbacks
+ statusCode = s.statusCode || {},
+
+ // Headers (they are sent all at once)
+ requestHeaders = {},
+ requestHeadersNames = {},
+
+ // Default abort message
+ strAbort = "canceled",
+
+ // Fake xhr
+ jqXHR = {
+ readyState: 0,
+
+ // Builds headers hashtable if needed
+ getResponseHeader: function( key ) {
+ var match;
+ if ( completed ) {
+ if ( !responseHeaders ) {
+ responseHeaders = {};
+ while ( ( match = rheaders.exec( responseHeadersString ) ) ) {
+ responseHeaders[ match[ 1 ].toLowerCase() + " " ] =
+ ( responseHeaders[ match[ 1 ].toLowerCase() + " " ] || [] )
+ .concat( match[ 2 ] );
+ }
+ }
+ match = responseHeaders[ key.toLowerCase() + " " ];
+ }
+ return match == null ? null : match.join( ", " );
+ },
+
+ // Raw string
+ getAllResponseHeaders: function() {
+ return completed ? responseHeadersString : null;
+ },
+
+ // Caches the header
+ setRequestHeader: function( name, value ) {
+ if ( completed == null ) {
+ name = requestHeadersNames[ name.toLowerCase() ] =
+ requestHeadersNames[ name.toLowerCase() ] || name;
+ requestHeaders[ name ] = value;
+ }
+ return this;
+ },
+
+ // Overrides response content-type header
+ overrideMimeType: function( type ) {
+ if ( completed == null ) {
+ s.mimeType = type;
+ }
+ return this;
+ },
+
+ // Status-dependent callbacks
+ statusCode: function( map ) {
+ var code;
+ if ( map ) {
+ if ( completed ) {
+
+ // Execute the appropriate callbacks
+ jqXHR.always( map[ jqXHR.status ] );
+ } else {
+
+ // Lazy-add the new callbacks in a way that preserves old ones
+ for ( code in map ) {
+ statusCode[ code ] = [ statusCode[ code ], map[ code ] ];
+ }
+ }
+ }
+ return this;
+ },
+
+ // Cancel the request
+ abort: function( statusText ) {
+ var finalText = statusText || strAbort;
+ if ( transport ) {
+ transport.abort( finalText );
+ }
+ done( 0, finalText );
+ return this;
+ }
+ };
+
+ // Attach deferreds
+ deferred.promise( jqXHR );
+
+ // Add protocol if not provided (prefilters might expect it)
+ // Handle falsy url in the settings object (#10093: consistency with old signature)
+ // We also use the url parameter if available
+ s.url = ( ( url || s.url || location.href ) + "" )
+ .replace( rprotocol, location.protocol + "//" );
+
+ // Alias method option to type as per ticket #12004
+ s.type = options.method || options.type || s.method || s.type;
+
+ // Extract dataTypes list
+ s.dataTypes = ( s.dataType || "*" ).toLowerCase().match( rnothtmlwhite ) || [ "" ];
+
+ // A cross-domain request is in order when the origin doesn't match the current origin.
+ if ( s.crossDomain == null ) {
+ urlAnchor = document.createElement( "a" );
+
+ // Support: IE <=8 - 11, Edge 12 - 15
+ // IE throws exception on accessing the href property if url is malformed,
+ // e.g. http://example.com:80x/
+ try {
+ urlAnchor.href = s.url;
+
+ // Support: IE <=8 - 11 only
+ // Anchor's host property isn't correctly set when s.url is relative
+ urlAnchor.href = urlAnchor.href;
+ s.crossDomain = originAnchor.protocol + "//" + originAnchor.host !==
+ urlAnchor.protocol + "//" + urlAnchor.host;
+ } catch ( e ) {
+
+ // If there is an error parsing the URL, assume it is crossDomain,
+ // it can be rejected by the transport if it is invalid
+ s.crossDomain = true;
+ }
+ }
+
+ // Convert data if not already a string
+ if ( s.data && s.processData && typeof s.data !== "string" ) {
+ s.data = jQuery.param( s.data, s.traditional );
+ }
+
+ // Apply prefilters
+ inspectPrefiltersOrTransports( prefilters, s, options, jqXHR );
+
+ // If request was aborted inside a prefilter, stop there
+ if ( completed ) {
+ return jqXHR;
+ }
+
+ // We can fire global events as of now if asked to
+ // Don't fire events if jQuery.event is undefined in an AMD-usage scenario (#15118)
+ fireGlobals = jQuery.event && s.global;
+
+ // Watch for a new set of requests
+ if ( fireGlobals && jQuery.active++ === 0 ) {
+ jQuery.event.trigger( "ajaxStart" );
+ }
+
+ // Uppercase the type
+ s.type = s.type.toUpperCase();
+
+ // Determine if request has content
+ s.hasContent = !rnoContent.test( s.type );
+
+ // Save the URL in case we're toying with the If-Modified-Since
+ // and/or If-None-Match header later on
+ // Remove hash to simplify url manipulation
+ cacheURL = s.url.replace( rhash, "" );
+
+ // More options handling for requests with no content
+ if ( !s.hasContent ) {
+
+ // Remember the hash so we can put it back
+ uncached = s.url.slice( cacheURL.length );
+
+ // If data is available and should be processed, append data to url
+ if ( s.data && ( s.processData || typeof s.data === "string" ) ) {
+ cacheURL += ( rquery.test( cacheURL ) ? "&" : "?" ) + s.data;
+
+ // #9682: remove data so that it's not used in an eventual retry
+ delete s.data;
+ }
+
+ // Add or update anti-cache param if needed
+ if ( s.cache === false ) {
+ cacheURL = cacheURL.replace( rantiCache, "$1" );
+ uncached = ( rquery.test( cacheURL ) ? "&" : "?" ) + "_=" + ( nonce.guid++ ) +
+ uncached;
+ }
+
+ // Put hash and anti-cache on the URL that will be requested (gh-1732)
+ s.url = cacheURL + uncached;
+
+ // Change '%20' to '+' if this is encoded form body content (gh-2658)
+ } else if ( s.data && s.processData &&
+ ( s.contentType || "" ).indexOf( "application/x-www-form-urlencoded" ) === 0 ) {
+ s.data = s.data.replace( r20, "+" );
+ }
+
+ // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+ if ( s.ifModified ) {
+ if ( jQuery.lastModified[ cacheURL ] ) {
+ jqXHR.setRequestHeader( "If-Modified-Since", jQuery.lastModified[ cacheURL ] );
+ }
+ if ( jQuery.etag[ cacheURL ] ) {
+ jqXHR.setRequestHeader( "If-None-Match", jQuery.etag[ cacheURL ] );
+ }
+ }
+
+ // Set the correct header, if data is being sent
+ if ( s.data && s.hasContent && s.contentType !== false || options.contentType ) {
+ jqXHR.setRequestHeader( "Content-Type", s.contentType );
+ }
+
+ // Set the Accepts header for the server, depending on the dataType
+ jqXHR.setRequestHeader(
+ "Accept",
+ s.dataTypes[ 0 ] && s.accepts[ s.dataTypes[ 0 ] ] ?
+ s.accepts[ s.dataTypes[ 0 ] ] +
+ ( s.dataTypes[ 0 ] !== "*" ? ", " + allTypes + "; q=0.01" : "" ) :
+ s.accepts[ "*" ]
+ );
+
+ // Check for headers option
+ for ( i in s.headers ) {
+ jqXHR.setRequestHeader( i, s.headers[ i ] );
+ }
+
+ // Allow custom headers/mimetypes and early abort
+ if ( s.beforeSend &&
+ ( s.beforeSend.call( callbackContext, jqXHR, s ) === false || completed ) ) {
+
+ // Abort if not done already and return
+ return jqXHR.abort();
+ }
+
+ // Aborting is no longer a cancellation
+ strAbort = "abort";
+
+ // Install callbacks on deferreds
+ completeDeferred.add( s.complete );
+ jqXHR.done( s.success );
+ jqXHR.fail( s.error );
+
+ // Get transport
+ transport = inspectPrefiltersOrTransports( transports, s, options, jqXHR );
+
+ // If no transport, we auto-abort
+ if ( !transport ) {
+ done( -1, "No Transport" );
+ } else {
+ jqXHR.readyState = 1;
+
+ // Send global event
+ if ( fireGlobals ) {
+ globalEventContext.trigger( "ajaxSend", [ jqXHR, s ] );
+ }
+
+ // If request was aborted inside ajaxSend, stop there
+ if ( completed ) {
+ return jqXHR;
+ }
+
+ // Timeout
+ if ( s.async && s.timeout > 0 ) {
+ timeoutTimer = window.setTimeout( function() {
+ jqXHR.abort( "timeout" );
+ }, s.timeout );
+ }
+
+ try {
+ completed = false;
+ transport.send( requestHeaders, done );
+ } catch ( e ) {
+
+ // Rethrow post-completion exceptions
+ if ( completed ) {
+ throw e;
+ }
+
+ // Propagate others as results
+ done( -1, e );
+ }
+ }
+
+ // Callback for when everything is done
+ function done( status, nativeStatusText, responses, headers ) {
+ var isSuccess, success, error, response, modified,
+ statusText = nativeStatusText;
+
+ // Ignore repeat invocations
+ if ( completed ) {
+ return;
+ }
+
+ completed = true;
+
+ // Clear timeout if it exists
+ if ( timeoutTimer ) {
+ window.clearTimeout( timeoutTimer );
+ }
+
+ // Dereference transport for early garbage collection
+ // (no matter how long the jqXHR object will be used)
+ transport = undefined;
+
+ // Cache response headers
+ responseHeadersString = headers || "";
+
+ // Set readyState
+ jqXHR.readyState = status > 0 ? 4 : 0;
+
+ // Determine if successful
+ isSuccess = status >= 200 && status < 300 || status === 304;
+
+ // Get response data
+ if ( responses ) {
+ response = ajaxHandleResponses( s, jqXHR, responses );
+ }
+
+ // Use a noop converter for missing script
+ if ( !isSuccess && jQuery.inArray( "script", s.dataTypes ) > -1 ) {
+ s.converters[ "text script" ] = function() {};
+ }
+
+ // Convert no matter what (that way responseXXX fields are always set)
+ response = ajaxConvert( s, response, jqXHR, isSuccess );
+
+ // If successful, handle type chaining
+ if ( isSuccess ) {
+
+ // Set the If-Modified-Since and/or If-None-Match header, if in ifModified mode.
+ if ( s.ifModified ) {
+ modified = jqXHR.getResponseHeader( "Last-Modified" );
+ if ( modified ) {
+ jQuery.lastModified[ cacheURL ] = modified;
+ }
+ modified = jqXHR.getResponseHeader( "etag" );
+ if ( modified ) {
+ jQuery.etag[ cacheURL ] = modified;
+ }
+ }
+
+ // if no content
+ if ( status === 204 || s.type === "HEAD" ) {
+ statusText = "nocontent";
+
+ // if not modified
+ } else if ( status === 304 ) {
+ statusText = "notmodified";
+
+ // If we have data, let's convert it
+ } else {
+ statusText = response.state;
+ success = response.data;
+ error = response.error;
+ isSuccess = !error;
+ }
+ } else {
+
+ // Extract error from statusText and normalize for non-aborts
+ error = statusText;
+ if ( status || !statusText ) {
+ statusText = "error";
+ if ( status < 0 ) {
+ status = 0;
+ }
+ }
+ }
+
+ // Set data for the fake xhr object
+ jqXHR.status = status;
+ jqXHR.statusText = ( nativeStatusText || statusText ) + "";
+
+ // Success/Error
+ if ( isSuccess ) {
+ deferred.resolveWith( callbackContext, [ success, statusText, jqXHR ] );
+ } else {
+ deferred.rejectWith( callbackContext, [ jqXHR, statusText, error ] );
+ }
+
+ // Status-dependent callbacks
+ jqXHR.statusCode( statusCode );
+ statusCode = undefined;
+
+ if ( fireGlobals ) {
+ globalEventContext.trigger( isSuccess ? "ajaxSuccess" : "ajaxError",
+ [ jqXHR, s, isSuccess ? success : error ] );
+ }
+
+ // Complete
+ completeDeferred.fireWith( callbackContext, [ jqXHR, statusText ] );
+
+ if ( fireGlobals ) {
+ globalEventContext.trigger( "ajaxComplete", [ jqXHR, s ] );
+
+ // Handle the global AJAX counter
+ if ( !( --jQuery.active ) ) {
+ jQuery.event.trigger( "ajaxStop" );
+ }
+ }
+ }
+
+ return jqXHR;
+ },
+
+ getJSON: function( url, data, callback ) {
+ return jQuery.get( url, data, callback, "json" );
+ },
+
+ getScript: function( url, callback ) {
+ return jQuery.get( url, undefined, callback, "script" );
+ }
+} );
+
+jQuery.each( [ "get", "post" ], function( _i, method ) {
+ jQuery[ method ] = function( url, data, callback, type ) {
+
+ // Shift arguments if data argument was omitted
+ if ( isFunction( data ) ) {
+ type = type || callback;
+ callback = data;
+ data = undefined;
+ }
+
+ // The url can be an options object (which then must have .url)
+ return jQuery.ajax( jQuery.extend( {
+ url: url,
+ type: method,
+ dataType: type,
+ data: data,
+ success: callback
+ }, jQuery.isPlainObject( url ) && url ) );
+ };
+} );
+
+jQuery.ajaxPrefilter( function( s ) {
+ var i;
+ for ( i in s.headers ) {
+ if ( i.toLowerCase() === "content-type" ) {
+ s.contentType = s.headers[ i ] || "";
+ }
+ }
+} );
+
+
+jQuery._evalUrl = function( url, options, doc ) {
+ return jQuery.ajax( {
+ url: url,
+
+ // Make this explicit, since user can override this through ajaxSetup (#11264)
+ type: "GET",
+ dataType: "script",
+ cache: true,
+ async: false,
+ global: false,
+
+ // Only evaluate the response if it is successful (gh-4126)
+ // dataFilter is not invoked for failure responses, so using it instead
+ // of the default converter is kludgy but it works.
+ converters: {
+ "text script": function() {}
+ },
+ dataFilter: function( response ) {
+ jQuery.globalEval( response, options, doc );
+ }
+ } );
+};
+
+
+jQuery.fn.extend( {
+ wrapAll: function( html ) {
+ var wrap;
+
+ if ( this[ 0 ] ) {
+ if ( isFunction( html ) ) {
+ html = html.call( this[ 0 ] );
+ }
+
+ // The elements to wrap the target around
+ wrap = jQuery( html, this[ 0 ].ownerDocument ).eq( 0 ).clone( true );
+
+ if ( this[ 0 ].parentNode ) {
+ wrap.insertBefore( this[ 0 ] );
+ }
+
+ wrap.map( function() {
+ var elem = this;
+
+ while ( elem.firstElementChild ) {
+ elem = elem.firstElementChild;
+ }
+
+ return elem;
+ } ).append( this );
+ }
+
+ return this;
+ },
+
+ wrapInner: function( html ) {
+ if ( isFunction( html ) ) {
+ return this.each( function( i ) {
+ jQuery( this ).wrapInner( html.call( this, i ) );
+ } );
+ }
+
+ return this.each( function() {
+ var self = jQuery( this ),
+ contents = self.contents();
+
+ if ( contents.length ) {
+ contents.wrapAll( html );
+
+ } else {
+ self.append( html );
+ }
+ } );
+ },
+
+ wrap: function( html ) {
+ var htmlIsFunction = isFunction( html );
+
+ return this.each( function( i ) {
+ jQuery( this ).wrapAll( htmlIsFunction ? html.call( this, i ) : html );
+ } );
+ },
+
+ unwrap: function( selector ) {
+ this.parent( selector ).not( "body" ).each( function() {
+ jQuery( this ).replaceWith( this.childNodes );
+ } );
+ return this;
+ }
+} );
+
+
+jQuery.expr.pseudos.hidden = function( elem ) {
+ return !jQuery.expr.pseudos.visible( elem );
+};
+jQuery.expr.pseudos.visible = function( elem ) {
+ return !!( elem.offsetWidth || elem.offsetHeight || elem.getClientRects().length );
+};
+
+
+
+
+jQuery.ajaxSettings.xhr = function() {
+ try {
+ return new window.XMLHttpRequest();
+ } catch ( e ) {}
+};
+
+var xhrSuccessStatus = {
+
+ // File protocol always yields status code 0, assume 200
+ 0: 200,
+
+ // Support: IE <=9 only
+ // #1450: sometimes IE returns 1223 when it should be 204
+ 1223: 204
+ },
+ xhrSupported = jQuery.ajaxSettings.xhr();
+
+support.cors = !!xhrSupported && ( "withCredentials" in xhrSupported );
+support.ajax = xhrSupported = !!xhrSupported;
+
+jQuery.ajaxTransport( function( options ) {
+ var callback, errorCallback;
+
+ // Cross domain only allowed if supported through XMLHttpRequest
+ if ( support.cors || xhrSupported && !options.crossDomain ) {
+ return {
+ send: function( headers, complete ) {
+ var i,
+ xhr = options.xhr();
+
+ xhr.open(
+ options.type,
+ options.url,
+ options.async,
+ options.username,
+ options.password
+ );
+
+ // Apply custom fields if provided
+ if ( options.xhrFields ) {
+ for ( i in options.xhrFields ) {
+ xhr[ i ] = options.xhrFields[ i ];
+ }
+ }
+
+ // Override mime type if needed
+ if ( options.mimeType && xhr.overrideMimeType ) {
+ xhr.overrideMimeType( options.mimeType );
+ }
+
+ // X-Requested-With header
+ // For cross-domain requests, seeing as conditions for a preflight are
+ // akin to a jigsaw puzzle, we simply never set it to be sure.
+ // (it can always be set on a per-request basis or even using ajaxSetup)
+ // For same-domain requests, won't change header if already provided.
+ if ( !options.crossDomain && !headers[ "X-Requested-With" ] ) {
+ headers[ "X-Requested-With" ] = "XMLHttpRequest";
+ }
+
+ // Set headers
+ for ( i in headers ) {
+ xhr.setRequestHeader( i, headers[ i ] );
+ }
+
+ // Callback
+ callback = function( type ) {
+ return function() {
+ if ( callback ) {
+ callback = errorCallback = xhr.onload =
+ xhr.onerror = xhr.onabort = xhr.ontimeout =
+ xhr.onreadystatechange = null;
+
+ if ( type === "abort" ) {
+ xhr.abort();
+ } else if ( type === "error" ) {
+
+ // Support: IE <=9 only
+ // On a manual native abort, IE9 throws
+ // errors on any property access that is not readyState
+ if ( typeof xhr.status !== "number" ) {
+ complete( 0, "error" );
+ } else {
+ complete(
+
+ // File: protocol always yields status 0; see #8605, #14207
+ xhr.status,
+ xhr.statusText
+ );
+ }
+ } else {
+ complete(
+ xhrSuccessStatus[ xhr.status ] || xhr.status,
+ xhr.statusText,
+
+ // Support: IE <=9 only
+ // IE9 has no XHR2 but throws on binary (trac-11426)
+ // For XHR2 non-text, let the caller handle it (gh-2498)
+ ( xhr.responseType || "text" ) !== "text" ||
+ typeof xhr.responseText !== "string" ?
+ { binary: xhr.response } :
+ { text: xhr.responseText },
+ xhr.getAllResponseHeaders()
+ );
+ }
+ }
+ };
+ };
+
+ // Listen to events
+ xhr.onload = callback();
+ errorCallback = xhr.onerror = xhr.ontimeout = callback( "error" );
+
+ // Support: IE 9 only
+ // Use onreadystatechange to replace onabort
+ // to handle uncaught aborts
+ if ( xhr.onabort !== undefined ) {
+ xhr.onabort = errorCallback;
+ } else {
+ xhr.onreadystatechange = function() {
+
+ // Check readyState before timeout as it changes
+ if ( xhr.readyState === 4 ) {
+
+ // Allow onerror to be called first,
+ // but that will not handle a native abort
+ // Also, save errorCallback to a variable
+ // as xhr.onerror cannot be accessed
+ window.setTimeout( function() {
+ if ( callback ) {
+ errorCallback();
+ }
+ } );
+ }
+ };
+ }
+
+ // Create the abort callback
+ callback = callback( "abort" );
+
+ try {
+
+ // Do send the request (this may raise an exception)
+ xhr.send( options.hasContent && options.data || null );
+ } catch ( e ) {
+
+ // #14683: Only rethrow if this hasn't been notified as an error yet
+ if ( callback ) {
+ throw e;
+ }
+ }
+ },
+
+ abort: function() {
+ if ( callback ) {
+ callback();
+ }
+ }
+ };
+ }
+} );
+
+
+
+
+// Prevent auto-execution of scripts when no explicit dataType was provided (See gh-2432)
+jQuery.ajaxPrefilter( function( s ) {
+ if ( s.crossDomain ) {
+ s.contents.script = false;
+ }
+} );
+
+// Install script dataType
+jQuery.ajaxSetup( {
+ accepts: {
+ script: "text/javascript, application/javascript, " +
+ "application/ecmascript, application/x-ecmascript"
+ },
+ contents: {
+ script: /\b(?:java|ecma)script\b/
+ },
+ converters: {
+ "text script": function( text ) {
+ jQuery.globalEval( text );
+ return text;
+ }
+ }
+} );
+
+// Handle cache's special case and crossDomain
+jQuery.ajaxPrefilter( "script", function( s ) {
+ if ( s.cache === undefined ) {
+ s.cache = false;
+ }
+ if ( s.crossDomain ) {
+ s.type = "GET";
+ }
+} );
+
+// Bind script tag hack transport
+jQuery.ajaxTransport( "script", function( s ) {
+
+ // This transport only deals with cross domain or forced-by-attrs requests
+ if ( s.crossDomain || s.scriptAttrs ) {
+ var script, callback;
+ return {
+ send: function( _, complete ) {
+ script = jQuery( "<script>" )
+ .attr( s.scriptAttrs || {} )
+ .prop( { charset: s.scriptCharset, src: s.url } )
+ .on( "load error", callback = function( evt ) {
+ script.remove();
+ callback = null;
+ if ( evt ) {
+ complete( evt.type === "error" ? 404 : 200, evt.type );
+ }
+ } );
+
+ // Use native DOM manipulation to avoid our domManip AJAX trickery
+ document.head.appendChild( script[ 0 ] );
+ },
+ abort: function() {
+ if ( callback ) {
+ callback();
+ }
+ }
+ };
+ }
+} );
+
+
+
+
+var oldCallbacks = [],
+ rjsonp = /(=)\?(?=&|$)|\?\?/;
+
+// Default jsonp settings
+jQuery.ajaxSetup( {
+ jsonp: "callback",
+ jsonpCallback: function() {
+ var callback = oldCallbacks.pop() || ( jQuery.expando + "_" + ( nonce.guid++ ) );
+ this[ callback ] = true;
+ return callback;
+ }
+} );
+
+// Detect, normalize options and install callbacks for jsonp requests
+jQuery.ajaxPrefilter( "json jsonp", function( s, originalSettings, jqXHR ) {
+
+ var callbackName, overwritten, responseContainer,
+ jsonProp = s.jsonp !== false && ( rjsonp.test( s.url ) ?
+ "url" :
+ typeof s.data === "string" &&
+ ( s.contentType || "" )
+ .indexOf( "application/x-www-form-urlencoded" ) === 0 &&
+ rjsonp.test( s.data ) && "data"
+ );
+
+ // Handle iff the expected data type is "jsonp" or we have a parameter to set
+ if ( jsonProp || s.dataTypes[ 0 ] === "jsonp" ) {
+
+ // Get callback name, remembering preexisting value associated with it
+ callbackName = s.jsonpCallback = isFunction( s.jsonpCallback ) ?
+ s.jsonpCallback() :
+ s.jsonpCallback;
+
+ // Insert callback into url or form data
+ if ( jsonProp ) {
+ s[ jsonProp ] = s[ jsonProp ].replace( rjsonp, "$1" + callbackName );
+ } else if ( s.jsonp !== false ) {
+ s.url += ( rquery.test( s.url ) ? "&" : "?" ) + s.jsonp + "=" + callbackName;
+ }
+
+ // Use data converter to retrieve json after script execution
+ s.converters[ "script json" ] = function() {
+ if ( !responseContainer ) {
+ jQuery.error( callbackName + " was not called" );
+ }
+ return responseContainer[ 0 ];
+ };
+
+ // Force json dataType
+ s.dataTypes[ 0 ] = "json";
+
+ // Install callback
+ overwritten = window[ callbackName ];
+ window[ callbackName ] = function() {
+ responseContainer = arguments;
+ };
+
+ // Clean-up function (fires after converters)
+ jqXHR.always( function() {
+
+ // If previous value didn't exist - remove it
+ if ( overwritten === undefined ) {
+ jQuery( window ).removeProp( callbackName );
+
+ // Otherwise restore preexisting value
+ } else {
+ window[ callbackName ] = overwritten;
+ }
+
+ // Save back as free
+ if ( s[ callbackName ] ) {
+
+ // Make sure that re-using the options doesn't screw things around
+ s.jsonpCallback = originalSettings.jsonpCallback;
+
+ // Save the callback name for future use
+ oldCallbacks.push( callbackName );
+ }
+
+ // Call if it was a function and we have a response
+ if ( responseContainer && isFunction( overwritten ) ) {
+ overwritten( responseContainer[ 0 ] );
+ }
+
+ responseContainer = overwritten = undefined;
+ } );
+
+ // Delegate to script
+ return "script";
+ }
+} );
+
+
+
+
+// Support: Safari 8 only
+// In Safari 8 documents created via document.implementation.createHTMLDocument
+// collapse sibling forms: the second one becomes a child of the first one.
+// Because of that, this security measure has to be disabled in Safari 8.
+// https://bugs.webkit.org/show_bug.cgi?id=137337
+support.createHTMLDocument = ( function() {
+ var body = document.implementation.createHTMLDocument( "" ).body;
+ body.innerHTML = "<form></form><form></form>";
+ return body.childNodes.length === 2;
+} )();
+
+
+// Argument "data" should be string of html
+// context (optional): If specified, the fragment will be created in this context,
+// defaults to document
+// keepScripts (optional): If true, will include scripts passed in the html string
+jQuery.parseHTML = function( data, context, keepScripts ) {
+ if ( typeof data !== "string" ) {
+ return [];
+ }
+ if ( typeof context === "boolean" ) {
+ keepScripts = context;
+ context = false;
+ }
+
+ var base, parsed, scripts;
+
+ if ( !context ) {
+
+ // Stop scripts or inline event handlers from being executed immediately
+ // by using document.implementation
+ if ( support.createHTMLDocument ) {
+ context = document.implementation.createHTMLDocument( "" );
+
+ // Set the base href for the created document
+ // so any parsed elements with URLs
+ // are based on the document's URL (gh-2965)
+ base = context.createElement( "base" );
+ base.href = document.location.href;
+ context.head.appendChild( base );
+ } else {
+ context = document;
+ }
+ }
+
+ parsed = rsingleTag.exec( data );
+ scripts = !keepScripts && [];
+
+ // Single tag
+ if ( parsed ) {
+ return [ context.createElement( parsed[ 1 ] ) ];
+ }
+
+ parsed = buildFragment( [ data ], context, scripts );
+
+ if ( scripts && scripts.length ) {
+ jQuery( scripts ).remove();
+ }
+
+ return jQuery.merge( [], parsed.childNodes );
+};
+
+
+/**
+ * Load a url into a page
+ */
+jQuery.fn.load = function( url, params, callback ) {
+ var selector, type, response,
+ self = this,
+ off = url.indexOf( " " );
+
+ if ( off > -1 ) {
+ selector = stripAndCollapse( url.slice( off ) );
+ url = url.slice( 0, off );
+ }
+
+ // If it's a function
+ if ( isFunction( params ) ) {
+
+ // We assume that it's the callback
+ callback = params;
+ params = undefined;
+
+ // Otherwise, build a param string
+ } else if ( params && typeof params === "object" ) {
+ type = "POST";
+ }
+
+ // If we have elements to modify, make the request
+ if ( self.length > 0 ) {
+ jQuery.ajax( {
+ url: url,
+
+ // If "type" variable is undefined, then "GET" method will be used.
+ // Make value of this field explicit since
+ // user can override it through ajaxSetup method
+ type: type || "GET",
+ dataType: "html",
+ data: params
+ } ).done( function( responseText ) {
+
+ // Save response for use in complete callback
+ response = arguments;
+
+ self.html( selector ?
+
+ // If a selector was specified, locate the right elements in a dummy div
+ // Exclude scripts to avoid IE 'Permission Denied' errors
+ jQuery( "<div>" ).append( jQuery.parseHTML( responseText ) ).find( selector ) :
+
+ // Otherwise use the full result
+ responseText );
+
+ // If the request succeeds, this function gets "data", "status", "jqXHR"
+ // but they are ignored because response was set above.
+ // If it fails, this function gets "jqXHR", "status", "error"
+ } ).always( callback && function( jqXHR, status ) {
+ self.each( function() {
+ callback.apply( this, response || [ jqXHR.responseText, status, jqXHR ] );
+ } );
+ } );
+ }
+
+ return this;
+};
+
+
+
+
+jQuery.expr.pseudos.animated = function( elem ) {
+ return jQuery.grep( jQuery.timers, function( fn ) {
+ return elem === fn.elem;
+ } ).length;
+};
+
+
+
+
+jQuery.offset = {
+ setOffset: function( elem, options, i ) {
+ var curPosition, curLeft, curCSSTop, curTop, curOffset, curCSSLeft, calculatePosition,
+ position = jQuery.css( elem, "position" ),
+ curElem = jQuery( elem ),
+ props = {};
+
+ // Set position first, in-case top/left are set even on static elem
+ if ( position === "static" ) {
+ elem.style.position = "relative";
+ }
+
+ curOffset = curElem.offset();
+ curCSSTop = jQuery.css( elem, "top" );
+ curCSSLeft = jQuery.css( elem, "left" );
+ calculatePosition = ( position === "absolute" || position === "fixed" ) &&
+ ( curCSSTop + curCSSLeft ).indexOf( "auto" ) > -1;
+
+ // Need to be able to calculate position if either
+ // top or left is auto and position is either absolute or fixed
+ if ( calculatePosition ) {
+ curPosition = curElem.position();
+ curTop = curPosition.top;
+ curLeft = curPosition.left;
+
+ } else {
+ curTop = parseFloat( curCSSTop ) || 0;
+ curLeft = parseFloat( curCSSLeft ) || 0;
+ }
+
+ if ( isFunction( options ) ) {
+
+ // Use jQuery.extend here to allow modification of coordinates argument (gh-1848)
+ options = options.call( elem, i, jQuery.extend( {}, curOffset ) );
+ }
+
+ if ( options.top != null ) {
+ props.top = ( options.top - curOffset.top ) + curTop;
+ }
+ if ( options.left != null ) {
+ props.left = ( options.left - curOffset.left ) + curLeft;
+ }
+
+ if ( "using" in options ) {
+ options.using.call( elem, props );
+
+ } else {
+ if ( typeof props.top === "number" ) {
+ props.top += "px";
+ }
+ if ( typeof props.left === "number" ) {
+ props.left += "px";
+ }
+ curElem.css( props );
+ }
+ }
+};
+
+jQuery.fn.extend( {
+
+ // offset() relates an element's border box to the document origin
+ offset: function( options ) {
+
+ // Preserve chaining for setter
+ if ( arguments.length ) {
+ return options === undefined ?
+ this :
+ this.each( function( i ) {
+ jQuery.offset.setOffset( this, options, i );
+ } );
+ }
+
+ var rect, win,
+ elem = this[ 0 ];
+
+ if ( !elem ) {
+ return;
+ }
+
+ // Return zeros for disconnected and hidden (display: none) elements (gh-2310)
+ // Support: IE <=11 only
+ // Running getBoundingClientRect on a
+ // disconnected node in IE throws an error
+ if ( !elem.getClientRects().length ) {
+ return { top: 0, left: 0 };
+ }
+
+ // Get document-relative position by adding viewport scroll to viewport-relative gBCR
+ rect = elem.getBoundingClientRect();
+ win = elem.ownerDocument.defaultView;
+ return {
+ top: rect.top + win.pageYOffset,
+ left: rect.left + win.pageXOffset
+ };
+ },
+
+ // position() relates an element's margin box to its offset parent's padding box
+ // This corresponds to the behavior of CSS absolute positioning
+ position: function() {
+ if ( !this[ 0 ] ) {
+ return;
+ }
+
+ var offsetParent, offset, doc,
+ elem = this[ 0 ],
+ parentOffset = { top: 0, left: 0 };
+
+ // position:fixed elements are offset from the viewport, which itself always has zero offset
+ if ( jQuery.css( elem, "position" ) === "fixed" ) {
+
+ // Assume position:fixed implies availability of getBoundingClientRect
+ offset = elem.getBoundingClientRect();
+
+ } else {
+ offset = this.offset();
+
+ // Account for the *real* offset parent, which can be the document or its root element
+ // when a statically positioned element is identified
+ doc = elem.ownerDocument;
+ offsetParent = elem.offsetParent || doc.documentElement;
+ while ( offsetParent &&
+ ( offsetParent === doc.body || offsetParent === doc.documentElement ) &&
+ jQuery.css( offsetParent, "position" ) === "static" ) {
+
+ offsetParent = offsetParent.parentNode;
+ }
+ if ( offsetParent && offsetParent !== elem && offsetParent.nodeType === 1 ) {
+
+ // Incorporate borders into its offset, since they are outside its content origin
+ parentOffset = jQuery( offsetParent ).offset();
+ parentOffset.top += jQuery.css( offsetParent, "borderTopWidth", true );
+ parentOffset.left += jQuery.css( offsetParent, "borderLeftWidth", true );
+ }
+ }
+
+ // Subtract parent offsets and element margins
+ return {
+ top: offset.top - parentOffset.top - jQuery.css( elem, "marginTop", true ),
+ left: offset.left - parentOffset.left - jQuery.css( elem, "marginLeft", true )
+ };
+ },
+
+ // This method will return documentElement in the following cases:
+ // 1) For the element inside the iframe without offsetParent, this method will return
+ // documentElement of the parent window
+ // 2) For the hidden or detached element
+ // 3) For body or html element, i.e. in case of the html node - it will return itself
+ //
+ // but those exceptions were never presented as a real life use-cases
+ // and might be considered as more preferable results.
+ //
+ // This logic, however, is not guaranteed and can change at any point in the future
+ offsetParent: function() {
+ return this.map( function() {
+ var offsetParent = this.offsetParent;
+
+ while ( offsetParent && jQuery.css( offsetParent, "position" ) === "static" ) {
+ offsetParent = offsetParent.offsetParent;
+ }
+
+ return offsetParent || documentElement;
+ } );
+ }
+} );
+
+// Create scrollLeft and scrollTop methods
+jQuery.each( { scrollLeft: "pageXOffset", scrollTop: "pageYOffset" }, function( method, prop ) {
+ var top = "pageYOffset" === prop;
+
+ jQuery.fn[ method ] = function( val ) {
+ return access( this, function( elem, method, val ) {
+
+ // Coalesce documents and windows
+ var win;
+ if ( isWindow( elem ) ) {
+ win = elem;
+ } else if ( elem.nodeType === 9 ) {
+ win = elem.defaultView;
+ }
+
+ if ( val === undefined ) {
+ return win ? win[ prop ] : elem[ method ];
+ }
+
+ if ( win ) {
+ win.scrollTo(
+ !top ? val : win.pageXOffset,
+ top ? val : win.pageYOffset
+ );
+
+ } else {
+ elem[ method ] = val;
+ }
+ }, method, val, arguments.length );
+ };
+} );
+
+// Support: Safari <=7 - 9.1, Chrome <=37 - 49
+// Add the top/left cssHooks using jQuery.fn.position
+// Webkit bug: https://bugs.webkit.org/show_bug.cgi?id=29084
+// Blink bug: https://bugs.chromium.org/p/chromium/issues/detail?id=589347
+// getComputedStyle returns percent when specified for top/left/bottom/right;
+// rather than make the css module depend on the offset module, just check for it here
+jQuery.each( [ "top", "left" ], function( _i, prop ) {
+ jQuery.cssHooks[ prop ] = addGetHookIf( support.pixelPosition,
+ function( elem, computed ) {
+ if ( computed ) {
+ computed = curCSS( elem, prop );
+
+ // If curCSS returns percentage, fallback to offset
+ return rnumnonpx.test( computed ) ?
+ jQuery( elem ).position()[ prop ] + "px" :
+ computed;
+ }
+ }
+ );
+} );
+
+
+// Create innerHeight, innerWidth, height, width, outerHeight and outerWidth methods
+jQuery.each( { Height: "height", Width: "width" }, function( name, type ) {
+ jQuery.each( { padding: "inner" + name, content: type, "": "outer" + name },
+ function( defaultExtra, funcName ) {
+
+ // Margin is only for outerHeight, outerWidth
+ jQuery.fn[ funcName ] = function( margin, value ) {
+ var chainable = arguments.length && ( defaultExtra || typeof margin !== "boolean" ),
+ extra = defaultExtra || ( margin === true || value === true ? "margin" : "border" );
+
+ return access( this, function( elem, type, value ) {
+ var doc;
+
+ if ( isWindow( elem ) ) {
+
+ // $( window ).outerWidth/Height return w/h including scrollbars (gh-1729)
+ return funcName.indexOf( "outer" ) === 0 ?
+ elem[ "inner" + name ] :
+ elem.document.documentElement[ "client" + name ];
+ }
+
+ // Get document width or height
+ if ( elem.nodeType === 9 ) {
+ doc = elem.documentElement;
+
+ // Either scroll[Width/Height] or offset[Width/Height] or client[Width/Height],
+ // whichever is greatest
+ return Math.max(
+ elem.body[ "scroll" + name ], doc[ "scroll" + name ],
+ elem.body[ "offset" + name ], doc[ "offset" + name ],
+ doc[ "client" + name ]
+ );
+ }
+
+ return value === undefined ?
+
+ // Get width or height on the element, requesting but not forcing parseFloat
+ jQuery.css( elem, type, extra ) :
+
+ // Set width or height on the element
+ jQuery.style( elem, type, value, extra );
+ }, type, chainable ? margin : undefined, chainable );
+ };
+ } );
+} );
+
+
+jQuery.each( [
+ "ajaxStart",
+ "ajaxStop",
+ "ajaxComplete",
+ "ajaxError",
+ "ajaxSuccess",
+ "ajaxSend"
+], function( _i, type ) {
+ jQuery.fn[ type ] = function( fn ) {
+ return this.on( type, fn );
+ };
+} );
+
+
+
+
+jQuery.fn.extend( {
+
+ bind: function( types, data, fn ) {
+ return this.on( types, null, data, fn );
+ },
+ unbind: function( types, fn ) {
+ return this.off( types, null, fn );
+ },
+
+ delegate: function( selector, types, data, fn ) {
+ return this.on( types, selector, data, fn );
+ },
+ undelegate: function( selector, types, fn ) {
+
+ // ( namespace ) or ( selector, types [, fn] )
+ return arguments.length === 1 ?
+ this.off( selector, "**" ) :
+ this.off( types, selector || "**", fn );
+ },
+
+ hover: function( fnOver, fnOut ) {
+ return this.mouseenter( fnOver ).mouseleave( fnOut || fnOver );
+ }
+} );
+
+jQuery.each( ( "blur focus focusin focusout resize scroll click dblclick " +
+ "mousedown mouseup mousemove mouseover mouseout mouseenter mouseleave " +
+ "change select submit keydown keypress keyup contextmenu" ).split( " " ),
+ function( _i, name ) {
+
+ // Handle event binding
+ jQuery.fn[ name ] = function( data, fn ) {
+ return arguments.length > 0 ?
+ this.on( name, null, data, fn ) :
+ this.trigger( name );
+ };
+ } );
+
+
+
+
+// Support: Android <=4.0 only
+// Make sure we trim BOM and NBSP
+var rtrim = /^[\s\uFEFF\xA0]+|[\s\uFEFF\xA0]+$/g;
+
+// Bind a function to a context, optionally partially applying any
+// arguments.
+// jQuery.proxy is deprecated to promote standards (specifically Function#bind)
+// However, it is not slated for removal any time soon
+jQuery.proxy = function( fn, context ) {
+ var tmp, args, proxy;
+
+ if ( typeof context === "string" ) {
+ tmp = fn[ context ];
+ context = fn;
+ fn = tmp;
+ }
+
+ // Quick check to determine if target is callable, in the spec
+ // this throws a TypeError, but we will just return undefined.
+ if ( !isFunction( fn ) ) {
+ return undefined;
+ }
+
+ // Simulated bind
+ args = slice.call( arguments, 2 );
+ proxy = function() {
+ return fn.apply( context || this, args.concat( slice.call( arguments ) ) );
+ };
+
+ // Set the guid of unique handler to the same of original handler, so it can be removed
+ proxy.guid = fn.guid = fn.guid || jQuery.guid++;
+
+ return proxy;
+};
+
+jQuery.holdReady = function( hold ) {
+ if ( hold ) {
+ jQuery.readyWait++;
+ } else {
+ jQuery.ready( true );
+ }
+};
+jQuery.isArray = Array.isArray;
+jQuery.parseJSON = JSON.parse;
+jQuery.nodeName = nodeName;
+jQuery.isFunction = isFunction;
+jQuery.isWindow = isWindow;
+jQuery.camelCase = camelCase;
+jQuery.type = toType;
+
+jQuery.now = Date.now;
+
+jQuery.isNumeric = function( obj ) {
+
+ // As of jQuery 3.0, isNumeric is limited to
+ // strings and numbers (primitives or objects)
+ // that can be coerced to finite numbers (gh-2662)
+ var type = jQuery.type( obj );
+ return ( type === "number" || type === "string" ) &&
+
+ // parseFloat NaNs numeric-cast false positives ("")
+ // ...but misinterprets leading-number strings, particularly hex literals ("0x...")
+ // subtraction forces infinities to NaN
+ !isNaN( obj - parseFloat( obj ) );
+};
+
+jQuery.trim = function( text ) {
+ return text == null ?
+ "" :
+ ( text + "" ).replace( rtrim, "" );
+};
+
+
+
+// Register as a named AMD module, since jQuery can be concatenated with other
+// files that may use define, but not via a proper concatenation script that
+// understands anonymous AMD modules. A named AMD is safest and most robust
+// way to register. Lowercase jquery is used because AMD module names are
+// derived from file names, and jQuery is normally delivered in a lowercase
+// file name. Do this after creating the global so that if an AMD module wants
+// to call noConflict to hide this version of jQuery, it will work.
+
+// Note that for maximum portability, libraries that are not jQuery should
+// declare themselves as anonymous modules, and avoid setting a global if an
+// AMD loader is present. jQuery is a special case. For more information, see
+// https://github.com/jrburke/requirejs/wiki/Updating-existing-libraries#wiki-anon
+
+if ( typeof define === "function" && define.amd ) {
+ define( "jquery", [], function() {
+ return jQuery;
+ } );
+}
+
+
+
+
+var
+
+ // Map over jQuery in case of overwrite
+ _jQuery = window.jQuery,
+
+ // Map over the $ in case of overwrite
+ _$ = window.$;
+
+jQuery.noConflict = function( deep ) {
+ if ( window.$ === jQuery ) {
+ window.$ = _$;
+ }
+
+ if ( deep && window.jQuery === jQuery ) {
+ window.jQuery = _jQuery;
+ }
+
+ return jQuery;
+};
+
+// Expose jQuery and $ identifiers, even in AMD
+// (#7102#comment:10, https://github.com/jquery/jquery/pull/557)
+// and CommonJS for browser emulators (#13566)
+if ( typeof noGlobal === "undefined" ) {
+ window.jQuery = window.$ = jQuery;
+}
+
+
+
+
+return jQuery;
+} );
diff --git a/_static/jquery.js b/_static/jquery.js
new file mode 100644
index 00000000000..b0614034ad3
--- /dev/null
+++ b/_static/jquery.js
@@ -0,0 +1,2 @@
+/*! jQuery v3.5.1 | (c) JS Foundation and other contributors | jquery.org/license */
+!function(e,t){"use strict";"object"==typeof module&&"object"==typeof module.exports?module.exports=e.document?t(e,!0):function(e){if(!e.document)throw new Error("jQuery requires a window with a document");return t(e)}:t(e)}("undefined"!=typeof window?window:this,function(C,e){"use strict";var t=[],r=Object.getPrototypeOf,s=t.slice,g=t.flat?function(e){return t.flat.call(e)}:function(e){return t.concat.apply([],e)},u=t.push,i=t.indexOf,n={},o=n.toString,v=n.hasOwnProperty,a=v.toString,l=a.call(Object),y={},m=function(e){return"function"==typeof e&&"number"!=typeof e.nodeType},x=function(e){return null!=e&&e===e.window},E=C.document,c={type:!0,src:!0,nonce:!0,noModule:!0};function b(e,t,n){var r,i,o=(n=n||E).createElement("script");if(o.text=e,t)for(r in c)(i=t[r]||t.getAttribute&&t.getAttribute(r))&&o.setAttribute(r,i);n.head.appendChild(o).parentNode.removeChild(o)}function w(e){return null==e?e+"":"object"==typeof e||"function"==typeof e?n[o.call(e)]||"object":typeof e}var 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[id="'+n.substring(1)+'"]').closest("div.section");0===(t=e.find('[href="#'+i.attr("id")+'"]')).length&&(t=e.find('[href="#"]'))}if(t.length>0){$(".wy-menu-vertical .current").removeClass("current").attr("aria-expanded","false"),t.addClass("current").attr("aria-expanded","true"),t.closest("li.toctree-l1").parent().addClass("current").attr("aria-expanded","true");for(let n=1;n<=10;n++)t.closest("li.toctree-l"+n).addClass("current").attr("aria-expanded","true");t[0].scrollIntoView()}}catch(n){console.log("Error expanding nav for anchor",n)}},onScroll:function(){this.winScroll=!1;var n=this.win.scrollTop(),e=n+this.winHeight,t=this.navBar.scrollTop()+(n-this.winPosition);n<0||e>this.docHeight||(this.navBar.scrollTop(t),this.winPosition=n)},onResize:function(){this.winResize=!1,this.winHeight=this.win.height(),this.docHeight=$(document).height()},hashChange:function(){this.linkScroll=!0,this.win.one("hashchange",(function(){this.linkScroll=!1}))},toggleCurrent:function(n){var e=n.closest("li");e.siblings("li.current").removeClass("current").attr("aria-expanded","false"),e.siblings().find("li.current").removeClass("current").attr("aria-expanded","false");var t=e.find("> ul li");t.length&&(t.removeClass("current").attr("aria-expanded","false"),e.toggleClass("current").attr("aria-expanded",(function(n,e){return"true"==e?"false":"true"})))}},"undefined"!=typeof window&&(window.SphinxRtdTheme={Navigation:n.exports.ThemeNav,StickyNav:n.exports.ThemeNav}),function(){for(var n=0,e=["ms","moz","webkit","o"],t=0;t<e.length&&!window.requestAnimationFrame;++t)window.requestAnimationFrame=window[e[t]+"RequestAnimationFrame"],window.cancelAnimationFrame=window[e[t]+"CancelAnimationFrame"]||window[e[t]+"CancelRequestAnimationFrame"];window.requestAnimationFrame||(window.requestAnimationFrame=function(e,t){var i=(new Date).getTime(),o=Math.max(0,16-(i-n)),r=window.setTimeout((function(){e(i+o)}),o);return 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\ No newline at end of file
diff --git a/_static/language_data.js b/_static/language_data.js
new file mode 100644
index 00000000000..863704b310d
--- /dev/null
+++ b/_static/language_data.js
@@ -0,0 +1,297 @@
+/*
+ * language_data.js
+ * ~~~~~~~~~~~~~~~~
+ *
+ * This script contains the language-specific data used by searchtools.js,
+ * namely the list of stopwords, stemmer, scorer and splitter.
+ *
+ * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+var stopwords = ["a","and","are","as","at","be","but","by","for","if","in","into","is","it","near","no","not","of","on","or","such","that","the","their","then","there","these","they","this","to","was","will","with"];
+
+
+/* Non-minified version is copied as a separate JS file, is available */
+
+/**
+ * Porter Stemmer
+ */
+var Stemmer = function() {
+
+ var step2list = {
+ ational: 'ate',
+ tional: 'tion',
+ enci: 'ence',
+ anci: 'ance',
+ izer: 'ize',
+ bli: 'ble',
+ alli: 'al',
+ entli: 'ent',
+ eli: 'e',
+ ousli: 'ous',
+ ization: 'ize',
+ ation: 'ate',
+ ator: 'ate',
+ alism: 'al',
+ iveness: 'ive',
+ fulness: 'ful',
+ ousness: 'ous',
+ aliti: 'al',
+ iviti: 'ive',
+ biliti: 'ble',
+ logi: 'log'
+ };
+
+ var step3list = {
+ icate: 'ic',
+ ative: '',
+ alize: 'al',
+ iciti: 'ic',
+ ical: 'ic',
+ ful: '',
+ ness: ''
+ };
+
+ var c = "[^aeiou]"; // consonant
+ var v = "[aeiouy]"; // vowel
+ var C = c + "[^aeiouy]*"; // consonant sequence
+ var V = v + "[aeiou]*"; // vowel sequence
+
+ var mgr0 = "^(" + C + ")?" + V + C; // [C]VC... is m>0
+ var meq1 = "^(" + C + ")?" + V + C + "(" + V + ")?$"; // [C]VC[V] is m=1
+ var mgr1 = "^(" + C + ")?" + V + C + V + C; // [C]VCVC... is m>1
+ var s_v = "^(" + C + ")?" + v; // vowel in stem
+
+ this.stemWord = function (w) {
+ var stem;
+ var suffix;
+ var firstch;
+ var origword = w;
+
+ if (w.length < 3)
+ return w;
+
+ var re;
+ var re2;
+ var re3;
+ var re4;
+
+ firstch = w.substr(0,1);
+ if (firstch == "y")
+ w = firstch.toUpperCase() + w.substr(1);
+
+ // Step 1a
+ re = /^(.+?)(ss|i)es$/;
+ re2 = /^(.+?)([^s])s$/;
+
+ if (re.test(w))
+ w = w.replace(re,"$1$2");
+ else if (re2.test(w))
+ w = w.replace(re2,"$1$2");
+
+ // Step 1b
+ re = /^(.+?)eed$/;
+ re2 = /^(.+?)(ed|ing)$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ re = new RegExp(mgr0);
+ if (re.test(fp[1])) {
+ re = /.$/;
+ w = w.replace(re,"");
+ }
+ }
+ else if (re2.test(w)) {
+ var fp = re2.exec(w);
+ stem = fp[1];
+ re2 = new RegExp(s_v);
+ if (re2.test(stem)) {
+ w = stem;
+ re2 = /(at|bl|iz)$/;
+ re3 = new RegExp("([^aeiouylsz])\\1$");
+ re4 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+ if (re2.test(w))
+ w = w + "e";
+ else if (re3.test(w)) {
+ re = /.$/;
+ w = w.replace(re,"");
+ }
+ else if (re4.test(w))
+ w = w + "e";
+ }
+ }
+
+ // Step 1c
+ re = /^(.+?)y$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ stem = fp[1];
+ re = new RegExp(s_v);
+ if (re.test(stem))
+ w = stem + "i";
+ }
+
+ // Step 2
+ re = /^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ stem = fp[1];
+ suffix = fp[2];
+ re = new RegExp(mgr0);
+ if (re.test(stem))
+ w = stem + step2list[suffix];
+ }
+
+ // Step 3
+ re = /^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ stem = fp[1];
+ suffix = fp[2];
+ re = new RegExp(mgr0);
+ if (re.test(stem))
+ w = stem + step3list[suffix];
+ }
+
+ // Step 4
+ re = /^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/;
+ re2 = /^(.+?)(s|t)(ion)$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ stem = fp[1];
+ re = new RegExp(mgr1);
+ if (re.test(stem))
+ w = stem;
+ }
+ else if (re2.test(w)) {
+ var fp = re2.exec(w);
+ stem = fp[1] + fp[2];
+ re2 = new RegExp(mgr1);
+ if (re2.test(stem))
+ w = stem;
+ }
+
+ // Step 5
+ re = /^(.+?)e$/;
+ if (re.test(w)) {
+ var fp = re.exec(w);
+ stem = fp[1];
+ re = new RegExp(mgr1);
+ re2 = new RegExp(meq1);
+ re3 = new RegExp("^" + C + v + "[^aeiouwxy]$");
+ if (re.test(stem) || (re2.test(stem) && !(re3.test(stem))))
+ w = stem;
+ }
+ re = /ll$/;
+ re2 = new RegExp(mgr1);
+ if (re.test(w) && re2.test(w)) {
+ re = /.$/;
+ w = w.replace(re,"");
+ }
+
+ // and turn initial Y back to y
+ if (firstch == "y")
+ w = firstch.toLowerCase() + w.substr(1);
+ return w;
+ }
+}
+
+
+
+
+var splitChars = (function() {
+ var result = {};
+ var singles = [96, 180, 187, 191, 215, 247, 749, 885, 903, 907, 909, 930, 1014, 1648,
+ 1748, 1809, 2416, 2473, 2481, 2526, 2601, 2609, 2612, 2615, 2653, 2702,
+ 2706, 2729, 2737, 2740, 2857, 2865, 2868, 2910, 2928, 2948, 2961, 2971,
+ 2973, 3085, 3089, 3113, 3124, 3213, 3217, 3241, 3252, 3295, 3341, 3345,
+ 3369, 3506, 3516, 3633, 3715, 3721, 3736, 3744, 3748, 3750, 3756, 3761,
+ 3781, 3912, 4239, 4347, 4681, 4695, 4697, 4745, 4785, 4799, 4801, 4823,
+ 4881, 5760, 5901, 5997, 6313, 7405, 8024, 8026, 8028, 8030, 8117, 8125,
+ 8133, 8181, 8468, 8485, 8487, 8489, 8494, 8527, 11311, 11359, 11687, 11695,
+ 11703, 11711, 11719, 11727, 11735, 12448, 12539, 43010, 43014, 43019, 43587,
+ 43696, 43713, 64286, 64297, 64311, 64317, 64319, 64322, 64325, 65141];
+ var i, j, start, end;
+ for (i = 0; i < singles.length; i++) {
+ result[singles[i]] = true;
+ }
+ var ranges = [[0, 47], [58, 64], [91, 94], [123, 169], [171, 177], [182, 184], [706, 709],
+ [722, 735], [741, 747], [751, 879], [888, 889], [894, 901], [1154, 1161],
+ [1318, 1328], [1367, 1368], [1370, 1376], [1416, 1487], [1515, 1519], [1523, 1568],
+ [1611, 1631], [1642, 1645], [1750, 1764], [1767, 1773], [1789, 1790], [1792, 1807],
+ [1840, 1868], [1958, 1968], [1970, 1983], [2027, 2035], [2038, 2041], [2043, 2047],
+ [2070, 2073], [2075, 2083], [2085, 2087], [2089, 2307], [2362, 2364], [2366, 2383],
+ [2385, 2391], [2402, 2405], [2419, 2424], [2432, 2436], [2445, 2446], [2449, 2450],
+ [2483, 2485], [2490, 2492], [2494, 2509], [2511, 2523], [2530, 2533], [2546, 2547],
+ [2554, 2564], [2571, 2574], [2577, 2578], [2618, 2648], [2655, 2661], [2672, 2673],
+ [2677, 2692], [2746, 2748], [2750, 2767], [2769, 2783], [2786, 2789], [2800, 2820],
+ [2829, 2830], [2833, 2834], [2874, 2876], [2878, 2907], [2914, 2917], [2930, 2946],
+ [2955, 2957], [2966, 2968], [2976, 2978], [2981, 2983], [2987, 2989], [3002, 3023],
+ [3025, 3045], [3059, 3076], [3130, 3132], [3134, 3159], [3162, 3167], [3170, 3173],
+ [3184, 3191], [3199, 3204], [3258, 3260], [3262, 3293], [3298, 3301], [3312, 3332],
+ [3386, 3388], [3390, 3423], [3426, 3429], [3446, 3449], [3456, 3460], [3479, 3481],
+ [3518, 3519], [3527, 3584], [3636, 3647], [3655, 3663], [3674, 3712], [3717, 3718],
+ [3723, 3724], [3726, 3731], [3752, 3753], [3764, 3772], [3774, 3775], [3783, 3791],
+ [3802, 3803], [3806, 3839], [3841, 3871], [3892, 3903], [3949, 3975], [3980, 4095],
+ [4139, 4158], [4170, 4175], [4182, 4185], [4190, 4192], [4194, 4196], [4199, 4205],
+ [4209, 4212], [4226, 4237], [4250, 4255], [4294, 4303], [4349, 4351], [4686, 4687],
+ [4702, 4703], [4750, 4751], [4790, 4791], [4806, 4807], [4886, 4887], [4955, 4968],
+ [4989, 4991], [5008, 5023], [5109, 5120], [5741, 5742], [5787, 5791], [5867, 5869],
+ [5873, 5887], [5906, 5919], [5938, 5951], [5970, 5983], [6001, 6015], [6068, 6102],
+ [6104, 6107], [6109, 6111], [6122, 6127], [6138, 6159], [6170, 6175], [6264, 6271],
+ [6315, 6319], [6390, 6399], [6429, 6469], [6510, 6511], [6517, 6527], [6572, 6592],
+ [6600, 6607], [6619, 6655], [6679, 6687], [6741, 6783], [6794, 6799], [6810, 6822],
+ [6824, 6916], [6964, 6980], [6988, 6991], [7002, 7042], [7073, 7085], [7098, 7167],
+ [7204, 7231], [7242, 7244], [7294, 7400], [7410, 7423], [7616, 7679], [7958, 7959],
+ [7966, 7967], [8006, 8007], [8014, 8015], [8062, 8063], [8127, 8129], [8141, 8143],
+ [8148, 8149], [8156, 8159], [8173, 8177], [8189, 8303], [8306, 8307], [8314, 8318],
+ [8330, 8335], [8341, 8449], [8451, 8454], [8456, 8457], [8470, 8472], [8478, 8483],
+ [8506, 8507], [8512, 8516], [8522, 8525], [8586, 9311], [9372, 9449], [9472, 10101],
+ [10132, 11263], [11493, 11498], [11503, 11516], [11518, 11519], [11558, 11567],
+ [11622, 11630], [11632, 11647], [11671, 11679], [11743, 11822], [11824, 12292],
+ [12296, 12320], [12330, 12336], [12342, 12343], [12349, 12352], [12439, 12444],
+ [12544, 12548], [12590, 12592], [12687, 12689], [12694, 12703], [12728, 12783],
+ [12800, 12831], [12842, 12880], [12896, 12927], [12938, 12976], [12992, 13311],
+ [19894, 19967], [40908, 40959], [42125, 42191], [42238, 42239], [42509, 42511],
+ [42540, 42559], [42592, 42593], [42607, 42622], [42648, 42655], [42736, 42774],
+ [42784, 42785], [42889, 42890], [42893, 43002], [43043, 43055], [43062, 43071],
+ [43124, 43137], [43188, 43215], [43226, 43249], [43256, 43258], [43260, 43263],
+ [43302, 43311], [43335, 43359], [43389, 43395], [43443, 43470], [43482, 43519],
+ [43561, 43583], [43596, 43599], [43610, 43615], [43639, 43641], [43643, 43647],
+ [43698, 43700], [43703, 43704], [43710, 43711], [43715, 43738], [43742, 43967],
+ [44003, 44015], [44026, 44031], [55204, 55215], [55239, 55242], [55292, 55295],
+ [57344, 63743], [64046, 64047], [64110, 64111], [64218, 64255], [64263, 64274],
+ [64280, 64284], [64434, 64466], [64830, 64847], [64912, 64913], [64968, 65007],
+ [65020, 65135], [65277, 65295], [65306, 65312], [65339, 65344], [65371, 65381],
+ [65471, 65473], [65480, 65481], [65488, 65489], [65496, 65497]];
+ for (i = 0; i < ranges.length; i++) {
+ start = ranges[i][0];
+ end = ranges[i][1];
+ for (j = start; j <= end; j++) {
+ result[j] = true;
+ }
+ }
+ return result;
+})();
+
+function splitQuery(query) {
+ var result = [];
+ var start = -1;
+ for (var i = 0; i < query.length; i++) {
+ if (splitChars[query.charCodeAt(i)]) {
+ if (start !== -1) {
+ result.push(query.slice(start, i));
+ start = -1;
+ }
+ } else if (start === -1) {
+ start = i;
+ }
+ }
+ if (start !== -1) {
+ result.push(query.slice(start));
+ }
+ return result;
+}
+
+
diff --git a/_static/minus.png b/_static/minus.png
new file mode 100644
index 00000000000..d96755fdaf8
Binary files /dev/null and b/_static/minus.png differ
diff --git a/_static/plot_directive.css b/_static/plot_directive.css
new file mode 100644
index 00000000000..d45593c93c9
--- /dev/null
+++ b/_static/plot_directive.css
@@ -0,0 +1,16 @@
+/*
+ * plot_directive.css
+ * ~~~~~~~~~~~~
+ *
+ * Stylesheet controlling images created using the `plot` directive within
+ * Sphinx.
+ *
+ * :copyright: Copyright 2020-* by the Matplotlib development team.
+ * :license: Matplotlib, see LICENSE for details.
+ *
+ */
+
+img.plot-directive {
+ border: 0;
+ max-width: 100%;
+}
diff --git a/_static/plus.png b/_static/plus.png
new file mode 100644
index 00000000000..7107cec93a9
Binary files /dev/null and b/_static/plus.png differ
diff --git a/_static/pygments.css b/_static/pygments.css
new file mode 100644
index 00000000000..691aeb82d00
--- /dev/null
+++ b/_static/pygments.css
@@ -0,0 +1,74 @@
+pre { line-height: 125%; }
+td.linenos .normal { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+span.linenos { color: inherit; background-color: transparent; padding-left: 5px; padding-right: 5px; }
+td.linenos .special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
+span.linenos.special { color: #000000; background-color: #ffffc0; padding-left: 5px; padding-right: 5px; }
+.highlight .hll { background-color: #ffffcc }
+.highlight { background: #eeffcc; }
+.highlight .c { color: #408090; font-style: italic } /* Comment */
+.highlight .err { border: 1px solid #FF0000 } /* Error */
+.highlight .k { color: #007020; font-weight: bold } /* Keyword */
+.highlight .o { color: #666666 } /* Operator */
+.highlight .ch { color: #408090; font-style: italic } /* Comment.Hashbang */
+.highlight .cm { color: #408090; font-style: italic } /* Comment.Multiline */
+.highlight .cp { color: #007020 } /* Comment.Preproc */
+.highlight .cpf { color: #408090; font-style: italic } /* Comment.PreprocFile */
+.highlight .c1 { color: #408090; font-style: italic } /* Comment.Single */
+.highlight .cs { color: #408090; background-color: #fff0f0 } /* Comment.Special */
+.highlight .gd { color: #A00000 } /* Generic.Deleted */
+.highlight .ge { font-style: italic } /* Generic.Emph */
+.highlight .gr { color: #FF0000 } /* Generic.Error */
+.highlight .gh { color: #000080; font-weight: bold } /* Generic.Heading */
+.highlight .gi { color: #00A000 } /* Generic.Inserted */
+.highlight .go { color: #333333 } /* Generic.Output */
+.highlight .gp { color: #c65d09; font-weight: bold } /* Generic.Prompt */
+.highlight .gs { font-weight: bold } /* Generic.Strong */
+.highlight .gu { color: #800080; font-weight: bold } /* Generic.Subheading */
+.highlight .gt { color: #0044DD } /* Generic.Traceback */
+.highlight .kc { color: #007020; font-weight: bold } /* Keyword.Constant */
+.highlight .kd { color: #007020; font-weight: bold } /* Keyword.Declaration */
+.highlight .kn { color: #007020; font-weight: bold } /* Keyword.Namespace */
+.highlight .kp { color: #007020 } /* Keyword.Pseudo */
+.highlight .kr { color: #007020; font-weight: bold } /* Keyword.Reserved */
+.highlight .kt { color: #902000 } /* Keyword.Type */
+.highlight .m { color: #208050 } /* Literal.Number */
+.highlight .s { color: #4070a0 } /* Literal.String */
+.highlight .na { color: #4070a0 } /* Name.Attribute */
+.highlight .nb { color: #007020 } /* Name.Builtin */
+.highlight .nc { color: #0e84b5; font-weight: bold } /* Name.Class */
+.highlight .no { color: #60add5 } /* Name.Constant */
+.highlight .nd { color: #555555; font-weight: bold } /* Name.Decorator */
+.highlight .ni { color: #d55537; font-weight: bold } /* Name.Entity */
+.highlight .ne { color: #007020 } /* Name.Exception */
+.highlight .nf { color: #06287e } /* Name.Function */
+.highlight .nl { color: #002070; font-weight: bold } /* Name.Label */
+.highlight .nn { color: #0e84b5; font-weight: bold } /* Name.Namespace */
+.highlight .nt { color: #062873; font-weight: bold } /* Name.Tag */
+.highlight .nv { color: #bb60d5 } /* Name.Variable */
+.highlight .ow { color: #007020; font-weight: bold } /* Operator.Word */
+.highlight .w { color: #bbbbbb } /* Text.Whitespace */
+.highlight .mb { color: #208050 } /* Literal.Number.Bin */
+.highlight .mf { color: #208050 } /* Literal.Number.Float */
+.highlight .mh { color: #208050 } /* Literal.Number.Hex */
+.highlight .mi { color: #208050 } /* Literal.Number.Integer */
+.highlight .mo { color: #208050 } /* Literal.Number.Oct */
+.highlight .sa { color: #4070a0 } /* Literal.String.Affix */
+.highlight .sb { color: #4070a0 } /* Literal.String.Backtick */
+.highlight .sc { color: #4070a0 } /* Literal.String.Char */
+.highlight .dl { color: #4070a0 } /* Literal.String.Delimiter */
+.highlight .sd { color: #4070a0; font-style: italic } /* Literal.String.Doc */
+.highlight .s2 { color: #4070a0 } /* Literal.String.Double */
+.highlight .se { color: #4070a0; font-weight: bold } /* Literal.String.Escape */
+.highlight .sh { color: #4070a0 } /* Literal.String.Heredoc */
+.highlight .si { color: #70a0d0; font-style: italic } /* Literal.String.Interpol */
+.highlight .sx { color: #c65d09 } /* Literal.String.Other */
+.highlight .sr { color: #235388 } /* Literal.String.Regex */
+.highlight .s1 { color: #4070a0 } /* Literal.String.Single */
+.highlight .ss { color: #517918 } /* Literal.String.Symbol */
+.highlight .bp { color: #007020 } /* Name.Builtin.Pseudo */
+.highlight .fm { color: #06287e } /* Name.Function.Magic */
+.highlight .vc { color: #bb60d5 } /* Name.Variable.Class */
+.highlight .vg { color: #bb60d5 } /* Name.Variable.Global */
+.highlight .vi { color: #bb60d5 } /* Name.Variable.Instance */
+.highlight .vm { color: #bb60d5 } /* Name.Variable.Magic */
+.highlight .il { color: #208050 } /* Literal.Number.Integer.Long */
\ No newline at end of file
diff --git a/_static/searchtools.js b/_static/searchtools.js
new file mode 100644
index 00000000000..002e9c4a20f
--- /dev/null
+++ b/_static/searchtools.js
@@ -0,0 +1,529 @@
+/*
+ * searchtools.js
+ * ~~~~~~~~~~~~~~~~
+ *
+ * Sphinx JavaScript utilities for the full-text search.
+ *
+ * :copyright: Copyright 2007-2021 by the Sphinx team, see AUTHORS.
+ * :license: BSD, see LICENSE for details.
+ *
+ */
+
+if (!Scorer) {
+ /**
+ * Simple result scoring code.
+ */
+ var Scorer = {
+ // Implement the following function to further tweak the score for each result
+ // The function takes a result array [filename, title, anchor, descr, score]
+ // and returns the new score.
+ /*
+ score: function(result) {
+ return result[4];
+ },
+ */
+
+ // query matches the full name of an object
+ objNameMatch: 11,
+ // or matches in the last dotted part of the object name
+ objPartialMatch: 6,
+ // Additive scores depending on the priority of the object
+ objPrio: {0: 15, // used to be importantResults
+ 1: 5, // used to be objectResults
+ 2: -5}, // used to be unimportantResults
+ // Used when the priority is not in the mapping.
+ objPrioDefault: 0,
+
+ // query found in title
+ title: 15,
+ partialTitle: 7,
+ // query found in terms
+ term: 5,
+ partialTerm: 2
+ };
+}
+
+if (!splitQuery) {
+ function splitQuery(query) {
+ return query.split(/\s+/);
+ }
+}
+
+/**
+ * Search Module
+ */
+var Search = {
+
+ _index : null,
+ _queued_query : null,
+ _pulse_status : -1,
+
+ htmlToText : function(htmlString) {
+ var virtualDocument = document.implementation.createHTMLDocument('virtual');
+ var htmlElement = $(htmlString, virtualDocument);
+ htmlElement.find('.headerlink').remove();
+ docContent = htmlElement.find('[role=main]')[0];
+ if(docContent === undefined) {
+ console.warn("Content block not found. Sphinx search tries to obtain it " +
+ "via '[role=main]'. Could you check your theme or template.");
+ return "";
+ }
+ return docContent.textContent || docContent.innerText;
+ },
+
+ init : function() {
+ var params = $.getQueryParameters();
+ if (params.q) {
+ var query = params.q[0];
+ $('input[name="q"]')[0].value = query;
+ this.performSearch(query);
+ }
+ },
+
+ loadIndex : function(url) {
+ $.ajax({type: "GET", url: url, data: null,
+ dataType: "script", cache: true,
+ complete: function(jqxhr, textstatus) {
+ if (textstatus != "success") {
+ document.getElementById("searchindexloader").src = url;
+ }
+ }});
+ },
+
+ setIndex : function(index) {
+ var q;
+ this._index = index;
+ if ((q = this._queued_query) !== null) {
+ this._queued_query = null;
+ Search.query(q);
+ }
+ },
+
+ hasIndex : function() {
+ return this._index !== null;
+ },
+
+ deferQuery : function(query) {
+ this._queued_query = query;
+ },
+
+ stopPulse : function() {
+ this._pulse_status = 0;
+ },
+
+ startPulse : function() {
+ if (this._pulse_status >= 0)
+ return;
+ function pulse() {
+ var i;
+ Search._pulse_status = (Search._pulse_status + 1) % 4;
+ var dotString = '';
+ for (i = 0; i < Search._pulse_status; i++)
+ dotString += '.';
+ Search.dots.text(dotString);
+ if (Search._pulse_status > -1)
+ window.setTimeout(pulse, 500);
+ }
+ pulse();
+ },
+
+ /**
+ * perform a search for something (or wait until index is loaded)
+ */
+ performSearch : function(query) {
+ // create the required interface elements
+ this.out = $('#search-results');
+ this.title = $('<h2>' + _('Searching') + '</h2>').appendTo(this.out);
+ this.dots = $('<span></span>').appendTo(this.title);
+ this.status = $('<p class="search-summary"> </p>').appendTo(this.out);
+ this.output = $('<ul class="search"/>').appendTo(this.out);
+
+ $('#search-progress').text(_('Preparing search...'));
+ this.startPulse();
+
+ // index already loaded, the browser was quick!
+ if (this.hasIndex())
+ this.query(query);
+ else
+ this.deferQuery(query);
+ },
+
+ /**
+ * execute search (requires search index to be loaded)
+ */
+ query : function(query) {
+ var i;
+
+ // stem the searchterms and add them to the correct list
+ var stemmer = new Stemmer();
+ var searchterms = [];
+ var excluded = [];
+ var hlterms = [];
+ var tmp = splitQuery(query);
+ var objectterms = [];
+ for (i = 0; i < tmp.length; i++) {
+ if (tmp[i] !== "") {
+ objectterms.push(tmp[i].toLowerCase());
+ }
+
+ if ($u.indexOf(stopwords, tmp[i].toLowerCase()) != -1 || tmp[i] === "") {
+ // skip this "word"
+ continue;
+ }
+ // stem the word
+ var word = stemmer.stemWord(tmp[i].toLowerCase());
+ // prevent stemmer from cutting word smaller than two chars
+ if(word.length < 3 && tmp[i].length >= 3) {
+ word = tmp[i];
+ }
+ var toAppend;
+ // select the correct list
+ if (word[0] == '-') {
+ toAppend = excluded;
+ word = word.substr(1);
+ }
+ else {
+ toAppend = searchterms;
+ hlterms.push(tmp[i].toLowerCase());
+ }
+ // only add if not already in the list
+ if (!$u.contains(toAppend, word))
+ toAppend.push(word);
+ }
+ var highlightstring = '?highlight=' + $.urlencode(hlterms.join(" "));
+
+ // console.debug('SEARCH: searching for:');
+ // console.info('required: ', searchterms);
+ // console.info('excluded: ', excluded);
+
+ // prepare search
+ var terms = this._index.terms;
+ var titleterms = this._index.titleterms;
+
+ // array of [filename, title, anchor, descr, score]
+ var results = [];
+ $('#search-progress').empty();
+
+ // lookup as object
+ for (i = 0; i < objectterms.length; i++) {
+ var others = [].concat(objectterms.slice(0, i),
+ objectterms.slice(i+1, objectterms.length));
+ results = results.concat(this.performObjectSearch(objectterms[i], others));
+ }
+
+ // lookup as search terms in fulltext
+ results = results.concat(this.performTermsSearch(searchterms, excluded, terms, titleterms));
+
+ // let the scorer override scores with a custom scoring function
+ if (Scorer.score) {
+ for (i = 0; i < results.length; i++)
+ results[i][4] = Scorer.score(results[i]);
+ }
+
+ // now sort the results by score (in opposite order of appearance, since the
+ // display function below uses pop() to retrieve items) and then
+ // alphabetically
+ results.sort(function(a, b) {
+ var left = a[4];
+ var right = b[4];
+ if (left > right) {
+ return 1;
+ } else if (left < right) {
+ return -1;
+ } else {
+ // same score: sort alphabetically
+ left = a[1].toLowerCase();
+ right = b[1].toLowerCase();
+ return (left > right) ? -1 : ((left < right) ? 1 : 0);
+ }
+ });
+
+ // for debugging
+ //Search.lastresults = results.slice(); // a copy
+ //console.info('search results:', Search.lastresults);
+
+ // print the results
+ var resultCount = results.length;
+ function displayNextItem() {
+ // results left, load the summary and display it
+ if (results.length) {
+ var item = results.pop();
+ var listItem = $('<li></li>');
+ var requestUrl = "";
+ var linkUrl = "";
+ if (DOCUMENTATION_OPTIONS.BUILDER === 'dirhtml') {
+ // dirhtml builder
+ var dirname = item[0] + '/';
+ if (dirname.match(/\/index\/$/)) {
+ dirname = dirname.substring(0, dirname.length-6);
+ } else if (dirname == 'index/') {
+ dirname = '';
+ }
+ requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + dirname;
+ linkUrl = requestUrl;
+
+ } else {
+ // normal html builders
+ requestUrl = DOCUMENTATION_OPTIONS.URL_ROOT + item[0] + DOCUMENTATION_OPTIONS.FILE_SUFFIX;
+ linkUrl = item[0] + DOCUMENTATION_OPTIONS.LINK_SUFFIX;
+ }
+ listItem.append($('<a/>').attr('href',
+ linkUrl +
+ highlightstring + item[2]).html(item[1]));
+ if (item[3]) {
+ listItem.append($('<span> (' + item[3] + ')</span>'));
+ Search.output.append(listItem);
+ setTimeout(function() {
+ displayNextItem();
+ }, 5);
+ } else if (DOCUMENTATION_OPTIONS.HAS_SOURCE) {
+ $.ajax({url: requestUrl,
+ dataType: "text",
+ complete: function(jqxhr, textstatus) {
+ var data = jqxhr.responseText;
+ if (data !== '' && data !== undefined) {
+ var summary = Search.makeSearchSummary(data, searchterms, hlterms);
+ if (summary) {
+ listItem.append(summary);
+ }
+ }
+ Search.output.append(listItem);
+ setTimeout(function() {
+ displayNextItem();
+ }, 5);
+ }});
+ } else {
+ // no source available, just display title
+ Search.output.append(listItem);
+ setTimeout(function() {
+ displayNextItem();
+ }, 5);
+ }
+ }
+ // search finished, update title and status message
+ else {
+ Search.stopPulse();
+ Search.title.text(_('Search Results'));
+ if (!resultCount)
+ Search.status.text(_('Your search did not match any documents. Please make sure that all words are spelled correctly and that you\'ve selected enough categories.'));
+ else
+ Search.status.text(_('Search finished, found %s page(s) matching the search query.').replace('%s', resultCount));
+ Search.status.fadeIn(500);
+ }
+ }
+ displayNextItem();
+ },
+
+ /**
+ * search for object names
+ */
+ performObjectSearch : function(object, otherterms) {
+ var filenames = this._index.filenames;
+ var docnames = this._index.docnames;
+ var objects = this._index.objects;
+ var objnames = this._index.objnames;
+ var titles = this._index.titles;
+
+ var i;
+ var results = [];
+
+ for (var prefix in objects) {
+ for (var iMatch = 0; iMatch != objects[prefix].length; ++iMatch) {
+ var match = objects[prefix][iMatch];
+ var name = match[4];
+ var fullname = (prefix ? prefix + '.' : '') + name;
+ var fullnameLower = fullname.toLowerCase()
+ if (fullnameLower.indexOf(object) > -1) {
+ var score = 0;
+ var parts = fullnameLower.split('.');
+ // check for different match types: exact matches of full name or
+ // "last name" (i.e. last dotted part)
+ if (fullnameLower == object || parts[parts.length - 1] == object) {
+ score += Scorer.objNameMatch;
+ // matches in last name
+ } else if (parts[parts.length - 1].indexOf(object) > -1) {
+ score += Scorer.objPartialMatch;
+ }
+ var objname = objnames[match[1]][2];
+ var title = titles[match[0]];
+ // If more than one term searched for, we require other words to be
+ // found in the name/title/description
+ if (otherterms.length > 0) {
+ var haystack = (prefix + ' ' + name + ' ' +
+ objname + ' ' + title).toLowerCase();
+ var allfound = true;
+ for (i = 0; i < otherterms.length; i++) {
+ if (haystack.indexOf(otherterms[i]) == -1) {
+ allfound = false;
+ break;
+ }
+ }
+ if (!allfound) {
+ continue;
+ }
+ }
+ var descr = objname + _(', in ') + title;
+
+ var anchor = match[3];
+ if (anchor === '')
+ anchor = fullname;
+ else if (anchor == '-')
+ anchor = objnames[match[1]][1] + '-' + fullname;
+ // add custom score for some objects according to scorer
+ if (Scorer.objPrio.hasOwnProperty(match[2])) {
+ score += Scorer.objPrio[match[2]];
+ } else {
+ score += Scorer.objPrioDefault;
+ }
+ results.push([docnames[match[0]], fullname, '#'+anchor, descr, score, filenames[match[0]]]);
+ }
+ }
+ }
+
+ return results;
+ },
+
+ /**
+ * See https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Regular_Expressions
+ */
+ escapeRegExp : function(string) {
+ return string.replace(/[.*+\-?^${}()|[\]\\]/g, '\\$&'); // $& means the whole matched string
+ },
+
+ /**
+ * search for full-text terms in the index
+ */
+ performTermsSearch : function(searchterms, excluded, terms, titleterms) {
+ var docnames = this._index.docnames;
+ var filenames = this._index.filenames;
+ var titles = this._index.titles;
+
+ var i, j, file;
+ var fileMap = {};
+ var scoreMap = {};
+ var results = [];
+
+ // perform the search on the required terms
+ for (i = 0; i < searchterms.length; i++) {
+ var word = searchterms[i];
+ var files = [];
+ var _o = [
+ {files: terms[word], score: Scorer.term},
+ {files: titleterms[word], score: Scorer.title}
+ ];
+ // add support for partial matches
+ if (word.length > 2) {
+ var word_regex = this.escapeRegExp(word);
+ for (var w in terms) {
+ if (w.match(word_regex) && !terms[word]) {
+ _o.push({files: terms[w], score: Scorer.partialTerm})
+ }
+ }
+ for (var w in titleterms) {
+ if (w.match(word_regex) && !titleterms[word]) {
+ _o.push({files: titleterms[w], score: Scorer.partialTitle})
+ }
+ }
+ }
+
+ // no match but word was a required one
+ if ($u.every(_o, function(o){return o.files === undefined;})) {
+ break;
+ }
+ // found search word in contents
+ $u.each(_o, function(o) {
+ var _files = o.files;
+ if (_files === undefined)
+ return
+
+ if (_files.length === undefined)
+ _files = [_files];
+ files = files.concat(_files);
+
+ // set score for the word in each file to Scorer.term
+ for (j = 0; j < _files.length; j++) {
+ file = _files[j];
+ if (!(file in scoreMap))
+ scoreMap[file] = {};
+ scoreMap[file][word] = o.score;
+ }
+ });
+
+ // create the mapping
+ for (j = 0; j < files.length; j++) {
+ file = files[j];
+ if (file in fileMap && fileMap[file].indexOf(word) === -1)
+ fileMap[file].push(word);
+ else
+ fileMap[file] = [word];
+ }
+ }
+
+ // now check if the files don't contain excluded terms
+ for (file in fileMap) {
+ var valid = true;
+
+ // check if all requirements are matched
+ var filteredTermCount = // as search terms with length < 3 are discarded: ignore
+ searchterms.filter(function(term){return term.length > 2}).length
+ if (
+ fileMap[file].length != searchterms.length &&
+ fileMap[file].length != filteredTermCount
+ ) continue;
+
+ // ensure that none of the excluded terms is in the search result
+ for (i = 0; i < excluded.length; i++) {
+ if (terms[excluded[i]] == file ||
+ titleterms[excluded[i]] == file ||
+ $u.contains(terms[excluded[i]] || [], file) ||
+ $u.contains(titleterms[excluded[i]] || [], file)) {
+ valid = false;
+ break;
+ }
+ }
+
+ // if we have still a valid result we can add it to the result list
+ if (valid) {
+ // select one (max) score for the file.
+ // for better ranking, we should calculate ranking by using words statistics like basic tf-idf...
+ var score = $u.max($u.map(fileMap[file], function(w){return scoreMap[file][w]}));
+ results.push([docnames[file], titles[file], '', null, score, filenames[file]]);
+ }
+ }
+ return results;
+ },
+
+ /**
+ * helper function to return a node containing the
+ * search summary for a given text. keywords is a list
+ * of stemmed words, hlwords is the list of normal, unstemmed
+ * words. the first one is used to find the occurrence, the
+ * latter for highlighting it.
+ */
+ makeSearchSummary : function(htmlText, keywords, hlwords) {
+ var text = Search.htmlToText(htmlText);
+ if (text == "") {
+ return null;
+ }
+ var textLower = text.toLowerCase();
+ var start = 0;
+ $.each(keywords, function() {
+ var i = textLower.indexOf(this.toLowerCase());
+ if (i > -1)
+ start = i;
+ });
+ start = Math.max(start - 120, 0);
+ var excerpt = ((start > 0) ? '...' : '') +
+ $.trim(text.substr(start, 240)) +
+ ((start + 240 - text.length) ? '...' : '');
+ var rv = $('<p class="context"></p>').text(excerpt);
+ $.each(hlwords, function() {
+ rv = rv.highlightText(this, 'highlighted');
+ });
+ return rv;
+ }
+};
+
+$(document).ready(function() {
+ Search.init();
+});
diff --git a/_static/underscore-1.13.1.js b/_static/underscore-1.13.1.js
new file mode 100644
index 00000000000..ffd77af9648
--- /dev/null
+++ b/_static/underscore-1.13.1.js
@@ -0,0 +1,2042 @@
+(function (global, factory) {
+ typeof exports === 'object' && typeof module !== 'undefined' ? module.exports = factory() :
+ typeof define === 'function' && define.amd ? define('underscore', factory) :
+ (global = typeof globalThis !== 'undefined' ? globalThis : global || self, (function () {
+ var current = global._;
+ var exports = global._ = factory();
+ exports.noConflict = function () { global._ = current; return exports; };
+ }()));
+}(this, (function () {
+ // Underscore.js 1.13.1
+ // https://underscorejs.org
+ // (c) 2009-2021 Jeremy Ashkenas, Julian Gonggrijp, and DocumentCloud and Investigative Reporters & Editors
+ // Underscore may be freely distributed under the MIT license.
+
+ // Current version.
+ var VERSION = '1.13.1';
+
+ // Establish the root object, `window` (`self`) in the browser, `global`
+ // on the server, or `this` in some virtual machines. We use `self`
+ // instead of `window` for `WebWorker` support.
+ var root = typeof self == 'object' && self.self === self && self ||
+ typeof global == 'object' && global.global === global && global ||
+ Function('return this')() ||
+ {};
+
+ // Save bytes in the minified (but not gzipped) version:
+ var ArrayProto = Array.prototype, ObjProto = Object.prototype;
+ var SymbolProto = typeof Symbol !== 'undefined' ? Symbol.prototype : null;
+
+ // Create quick reference variables for speed access to core prototypes.
+ var push = ArrayProto.push,
+ slice = ArrayProto.slice,
+ toString = ObjProto.toString,
+ hasOwnProperty = ObjProto.hasOwnProperty;
+
+ // Modern feature detection.
+ var supportsArrayBuffer = typeof ArrayBuffer !== 'undefined',
+ supportsDataView = typeof DataView !== 'undefined';
+
+ // All **ECMAScript 5+** native function implementations that we hope to use
+ // are declared here.
+ var nativeIsArray = Array.isArray,
+ nativeKeys = Object.keys,
+ nativeCreate = Object.create,
+ nativeIsView = supportsArrayBuffer && ArrayBuffer.isView;
+
+ // Create references to these builtin functions because we override them.
+ var _isNaN = isNaN,
+ _isFinite = isFinite;
+
+ // Keys in IE < 9 that won't be iterated by `for key in ...` and thus missed.
+ var hasEnumBug = !{toString: null}.propertyIsEnumerable('toString');
+ var nonEnumerableProps = ['valueOf', 'isPrototypeOf', 'toString',
+ 'propertyIsEnumerable', 'hasOwnProperty', 'toLocaleString'];
+
+ // The largest integer that can be represented exactly.
+ var MAX_ARRAY_INDEX = Math.pow(2, 53) - 1;
+
+ // Some functions take a variable number of arguments, or a few expected
+ // arguments at the beginning and then a variable number of values to operate
+ // on. This helper accumulates all remaining arguments past the function’s
+ // argument length (or an explicit `startIndex`), into an array that becomes
+ // the last argument. Similar to ES6’s "rest parameter".
+ function restArguments(func, startIndex) {
+ startIndex = startIndex == null ? func.length - 1 : +startIndex;
+ return function() {
+ var length = Math.max(arguments.length - startIndex, 0),
+ rest = Array(length),
+ index = 0;
+ for (; index < length; index++) {
+ rest[index] = arguments[index + startIndex];
+ }
+ switch (startIndex) {
+ case 0: return func.call(this, rest);
+ case 1: return func.call(this, arguments[0], rest);
+ case 2: return func.call(this, arguments[0], arguments[1], rest);
+ }
+ var args = Array(startIndex + 1);
+ for (index = 0; index < startIndex; index++) {
+ args[index] = arguments[index];
+ }
+ args[startIndex] = rest;
+ return func.apply(this, args);
+ };
+ }
+
+ // Is a given variable an object?
+ function isObject(obj) {
+ var type = typeof obj;
+ return type === 'function' || type === 'object' && !!obj;
+ }
+
+ // Is a given value equal to null?
+ function isNull(obj) {
+ return obj === null;
+ }
+
+ // Is a given variable undefined?
+ function isUndefined(obj) {
+ return obj === void 0;
+ }
+
+ // Is a given value a boolean?
+ function isBoolean(obj) {
+ return obj === true || obj === false || toString.call(obj) === '[object Boolean]';
+ }
+
+ // Is a given value a DOM element?
+ function isElement(obj) {
+ return !!(obj && obj.nodeType === 1);
+ }
+
+ // Internal function for creating a `toString`-based type tester.
+ function tagTester(name) {
+ var tag = '[object ' + name + ']';
+ return function(obj) {
+ return toString.call(obj) === tag;
+ };
+ }
+
+ var isString = tagTester('String');
+
+ var isNumber = tagTester('Number');
+
+ var isDate = tagTester('Date');
+
+ var isRegExp = tagTester('RegExp');
+
+ var isError = tagTester('Error');
+
+ var isSymbol = tagTester('Symbol');
+
+ var isArrayBuffer = tagTester('ArrayBuffer');
+
+ var isFunction = tagTester('Function');
+
+ // Optimize `isFunction` if appropriate. Work around some `typeof` bugs in old
+ // v8, IE 11 (#1621), Safari 8 (#1929), and PhantomJS (#2236).
+ var nodelist = root.document && root.document.childNodes;
+ if (typeof /./ != 'function' && typeof Int8Array != 'object' && typeof nodelist != 'function') {
+ isFunction = function(obj) {
+ return typeof obj == 'function' || false;
+ };
+ }
+
+ var isFunction$1 = isFunction;
+
+ var hasObjectTag = tagTester('Object');
+
+ // In IE 10 - Edge 13, `DataView` has string tag `'[object Object]'`.
+ // In IE 11, the most common among them, this problem also applies to
+ // `Map`, `WeakMap` and `Set`.
+ var hasStringTagBug = (
+ supportsDataView && hasObjectTag(new DataView(new ArrayBuffer(8)))
+ ),
+ isIE11 = (typeof Map !== 'undefined' && hasObjectTag(new Map));
+
+ var isDataView = tagTester('DataView');
+
+ // In IE 10 - Edge 13, we need a different heuristic
+ // to determine whether an object is a `DataView`.
+ function ie10IsDataView(obj) {
+ return obj != null && isFunction$1(obj.getInt8) && isArrayBuffer(obj.buffer);
+ }
+
+ var isDataView$1 = (hasStringTagBug ? ie10IsDataView : isDataView);
+
+ // Is a given value an array?
+ // Delegates to ECMA5's native `Array.isArray`.
+ var isArray = nativeIsArray || tagTester('Array');
+
+ // Internal function to check whether `key` is an own property name of `obj`.
+ function has$1(obj, key) {
+ return obj != null && hasOwnProperty.call(obj, key);
+ }
+
+ var isArguments = tagTester('Arguments');
+
+ // Define a fallback version of the method in browsers (ahem, IE < 9), where
+ // there isn't any inspectable "Arguments" type.
+ (function() {
+ if (!isArguments(arguments)) {
+ isArguments = function(obj) {
+ return has$1(obj, 'callee');
+ };
+ }
+ }());
+
+ var isArguments$1 = isArguments;
+
+ // Is a given object a finite number?
+ function isFinite$1(obj) {
+ return !isSymbol(obj) && _isFinite(obj) && !isNaN(parseFloat(obj));
+ }
+
+ // Is the given value `NaN`?
+ function isNaN$1(obj) {
+ return isNumber(obj) && _isNaN(obj);
+ }
+
+ // Predicate-generating function. Often useful outside of Underscore.
+ function constant(value) {
+ return function() {
+ return value;
+ };
+ }
+
+ // Common internal logic for `isArrayLike` and `isBufferLike`.
+ function createSizePropertyCheck(getSizeProperty) {
+ return function(collection) {
+ var sizeProperty = getSizeProperty(collection);
+ return typeof sizeProperty == 'number' && sizeProperty >= 0 && sizeProperty <= MAX_ARRAY_INDEX;
+ }
+ }
+
+ // Internal helper to generate a function to obtain property `key` from `obj`.
+ function shallowProperty(key) {
+ return function(obj) {
+ return obj == null ? void 0 : obj[key];
+ };
+ }
+
+ // Internal helper to obtain the `byteLength` property of an object.
+ var getByteLength = shallowProperty('byteLength');
+
+ // Internal helper to determine whether we should spend extensive checks against
+ // `ArrayBuffer` et al.
+ var isBufferLike = createSizePropertyCheck(getByteLength);
+
+ // Is a given value a typed array?
+ var typedArrayPattern = /\[object ((I|Ui)nt(8|16|32)|Float(32|64)|Uint8Clamped|Big(I|Ui)nt64)Array\]/;
+ function isTypedArray(obj) {
+ // `ArrayBuffer.isView` is the most future-proof, so use it when available.
+ // Otherwise, fall back on the above regular expression.
+ return nativeIsView ? (nativeIsView(obj) && !isDataView$1(obj)) :
+ isBufferLike(obj) && typedArrayPattern.test(toString.call(obj));
+ }
+
+ var isTypedArray$1 = supportsArrayBuffer ? isTypedArray : constant(false);
+
+ // Internal helper to obtain the `length` property of an object.
+ var getLength = shallowProperty('length');
+
+ // Internal helper to create a simple lookup structure.
+ // `collectNonEnumProps` used to depend on `_.contains`, but this led to
+ // circular imports. `emulatedSet` is a one-off solution that only works for
+ // arrays of strings.
+ function emulatedSet(keys) {
+ var hash = {};
+ for (var l = keys.length, i = 0; i < l; ++i) hash[keys[i]] = true;
+ return {
+ contains: function(key) { return hash[key]; },
+ push: function(key) {
+ hash[key] = true;
+ return keys.push(key);
+ }
+ };
+ }
+
+ // Internal helper. Checks `keys` for the presence of keys in IE < 9 that won't
+ // be iterated by `for key in ...` and thus missed. Extends `keys` in place if
+ // needed.
+ function collectNonEnumProps(obj, keys) {
+ keys = emulatedSet(keys);
+ var nonEnumIdx = nonEnumerableProps.length;
+ var constructor = obj.constructor;
+ var proto = isFunction$1(constructor) && constructor.prototype || ObjProto;
+
+ // Constructor is a special case.
+ var prop = 'constructor';
+ if (has$1(obj, prop) && !keys.contains(prop)) keys.push(prop);
+
+ while (nonEnumIdx--) {
+ prop = nonEnumerableProps[nonEnumIdx];
+ if (prop in obj && obj[prop] !== proto[prop] && !keys.contains(prop)) {
+ keys.push(prop);
+ }
+ }
+ }
+
+ // Retrieve the names of an object's own properties.
+ // Delegates to **ECMAScript 5**'s native `Object.keys`.
+ function keys(obj) {
+ if (!isObject(obj)) return [];
+ if (nativeKeys) return nativeKeys(obj);
+ var keys = [];
+ for (var key in obj) if (has$1(obj, key)) keys.push(key);
+ // Ahem, IE < 9.
+ if (hasEnumBug) collectNonEnumProps(obj, keys);
+ return keys;
+ }
+
+ // Is a given array, string, or object empty?
+ // An "empty" object has no enumerable own-properties.
+ function isEmpty(obj) {
+ if (obj == null) return true;
+ // Skip the more expensive `toString`-based type checks if `obj` has no
+ // `.length`.
+ var length = getLength(obj);
+ if (typeof length == 'number' && (
+ isArray(obj) || isString(obj) || isArguments$1(obj)
+ )) return length === 0;
+ return getLength(keys(obj)) === 0;
+ }
+
+ // Returns whether an object has a given set of `key:value` pairs.
+ function isMatch(object, attrs) {
+ var _keys = keys(attrs), length = _keys.length;
+ if (object == null) return !length;
+ var obj = Object(object);
+ for (var i = 0; i < length; i++) {
+ var key = _keys[i];
+ if (attrs[key] !== obj[key] || !(key in obj)) return false;
+ }
+ return true;
+ }
+
+ // If Underscore is called as a function, it returns a wrapped object that can
+ // be used OO-style. This wrapper holds altered versions of all functions added
+ // through `_.mixin`. Wrapped objects may be chained.
+ function _$1(obj) {
+ if (obj instanceof _$1) return obj;
+ if (!(this instanceof _$1)) return new _$1(obj);
+ this._wrapped = obj;
+ }
+
+ _$1.VERSION = VERSION;
+
+ // Extracts the result from a wrapped and chained object.
+ _$1.prototype.value = function() {
+ return this._wrapped;
+ };
+
+ // Provide unwrapping proxies for some methods used in engine operations
+ // such as arithmetic and JSON stringification.
+ _$1.prototype.valueOf = _$1.prototype.toJSON = _$1.prototype.value;
+
+ _$1.prototype.toString = function() {
+ return String(this._wrapped);
+ };
+
+ // Internal function to wrap or shallow-copy an ArrayBuffer,
+ // typed array or DataView to a new view, reusing the buffer.
+ function toBufferView(bufferSource) {
+ return new Uint8Array(
+ bufferSource.buffer || bufferSource,
+ bufferSource.byteOffset || 0,
+ getByteLength(bufferSource)
+ );
+ }
+
+ // We use this string twice, so give it a name for minification.
+ var tagDataView = '[object DataView]';
+
+ // Internal recursive comparison function for `_.isEqual`.
+ function eq(a, b, aStack, bStack) {
+ // Identical objects are equal. `0 === -0`, but they aren't identical.
+ // See the [Harmony `egal` proposal](https://wiki.ecmascript.org/doku.php?id=harmony:egal).
+ if (a === b) return a !== 0 || 1 / a === 1 / b;
+ // `null` or `undefined` only equal to itself (strict comparison).
+ if (a == null || b == null) return false;
+ // `NaN`s are equivalent, but non-reflexive.
+ if (a !== a) return b !== b;
+ // Exhaust primitive checks
+ var type = typeof a;
+ if (type !== 'function' && type !== 'object' && typeof b != 'object') return false;
+ return deepEq(a, b, aStack, bStack);
+ }
+
+ // Internal recursive comparison function for `_.isEqual`.
+ function deepEq(a, b, aStack, bStack) {
+ // Unwrap any wrapped objects.
+ if (a instanceof _$1) a = a._wrapped;
+ if (b instanceof _$1) b = b._wrapped;
+ // Compare `[[Class]]` names.
+ var className = toString.call(a);
+ if (className !== toString.call(b)) return false;
+ // Work around a bug in IE 10 - Edge 13.
+ if (hasStringTagBug && className == '[object Object]' && isDataView$1(a)) {
+ if (!isDataView$1(b)) return false;
+ className = tagDataView;
+ }
+ switch (className) {
+ // These types are compared by value.
+ case '[object RegExp]':
+ // RegExps are coerced to strings for comparison (Note: '' + /a/i === '/a/i')
+ case '[object String]':
+ // Primitives and their corresponding object wrappers are equivalent; thus, `"5"` is
+ // equivalent to `new String("5")`.
+ return '' + a === '' + b;
+ case '[object Number]':
+ // `NaN`s are equivalent, but non-reflexive.
+ // Object(NaN) is equivalent to NaN.
+ if (+a !== +a) return +b !== +b;
+ // An `egal` comparison is performed for other numeric values.
+ return +a === 0 ? 1 / +a === 1 / b : +a === +b;
+ case '[object Date]':
+ case '[object Boolean]':
+ // Coerce dates and booleans to numeric primitive values. Dates are compared by their
+ // millisecond representations. Note that invalid dates with millisecond representations
+ // of `NaN` are not equivalent.
+ return +a === +b;
+ case '[object Symbol]':
+ return SymbolProto.valueOf.call(a) === SymbolProto.valueOf.call(b);
+ case '[object ArrayBuffer]':
+ case tagDataView:
+ // Coerce to typed array so we can fall through.
+ return deepEq(toBufferView(a), toBufferView(b), aStack, bStack);
+ }
+
+ var areArrays = className === '[object Array]';
+ if (!areArrays && isTypedArray$1(a)) {
+ var byteLength = getByteLength(a);
+ if (byteLength !== getByteLength(b)) return false;
+ if (a.buffer === b.buffer && a.byteOffset === b.byteOffset) return true;
+ areArrays = true;
+ }
+ if (!areArrays) {
+ if (typeof a != 'object' || typeof b != 'object') return false;
+
+ // Objects with different constructors are not equivalent, but `Object`s or `Array`s
+ // from different frames are.
+ var aCtor = a.constructor, bCtor = b.constructor;
+ if (aCtor !== bCtor && !(isFunction$1(aCtor) && aCtor instanceof aCtor &&
+ isFunction$1(bCtor) && bCtor instanceof bCtor)
+ && ('constructor' in a && 'constructor' in b)) {
+ return false;
+ }
+ }
+ // Assume equality for cyclic structures. The algorithm for detecting cyclic
+ // structures is adapted from ES 5.1 section 15.12.3, abstract operation `JO`.
+
+ // Initializing stack of traversed objects.
+ // It's done here since we only need them for objects and arrays comparison.
+ aStack = aStack || [];
+ bStack = bStack || [];
+ var length = aStack.length;
+ while (length--) {
+ // Linear search. Performance is inversely proportional to the number of
+ // unique nested structures.
+ if (aStack[length] === a) return bStack[length] === b;
+ }
+
+ // Add the first object to the stack of traversed objects.
+ aStack.push(a);
+ bStack.push(b);
+
+ // Recursively compare objects and arrays.
+ if (areArrays) {
+ // Compare array lengths to determine if a deep comparison is necessary.
+ length = a.length;
+ if (length !== b.length) return false;
+ // Deep compare the contents, ignoring non-numeric properties.
+ while (length--) {
+ if (!eq(a[length], b[length], aStack, bStack)) return false;
+ }
+ } else {
+ // Deep compare objects.
+ var _keys = keys(a), key;
+ length = _keys.length;
+ // Ensure that both objects contain the same number of properties before comparing deep equality.
+ if (keys(b).length !== length) return false;
+ while (length--) {
+ // Deep compare each member
+ key = _keys[length];
+ if (!(has$1(b, key) && eq(a[key], b[key], aStack, bStack))) return false;
+ }
+ }
+ // Remove the first object from the stack of traversed objects.
+ aStack.pop();
+ bStack.pop();
+ return true;
+ }
+
+ // Perform a deep comparison to check if two objects are equal.
+ function isEqual(a, b) {
+ return eq(a, b);
+ }
+
+ // Retrieve all the enumerable property names of an object.
+ function allKeys(obj) {
+ if (!isObject(obj)) return [];
+ var keys = [];
+ for (var key in obj) keys.push(key);
+ // Ahem, IE < 9.
+ if (hasEnumBug) collectNonEnumProps(obj, keys);
+ return keys;
+ }
+
+ // Since the regular `Object.prototype.toString` type tests don't work for
+ // some types in IE 11, we use a fingerprinting heuristic instead, based
+ // on the methods. It's not great, but it's the best we got.
+ // The fingerprint method lists are defined below.
+ function ie11fingerprint(methods) {
+ var length = getLength(methods);
+ return function(obj) {
+ if (obj == null) return false;
+ // `Map`, `WeakMap` and `Set` have no enumerable keys.
+ var keys = allKeys(obj);
+ if (getLength(keys)) return false;
+ for (var i = 0; i < length; i++) {
+ if (!isFunction$1(obj[methods[i]])) return false;
+ }
+ // If we are testing against `WeakMap`, we need to ensure that
+ // `obj` doesn't have a `forEach` method in order to distinguish
+ // it from a regular `Map`.
+ return methods !== weakMapMethods || !isFunction$1(obj[forEachName]);
+ };
+ }
+
+ // In the interest of compact minification, we write
+ // each string in the fingerprints only once.
+ var forEachName = 'forEach',
+ hasName = 'has',
+ commonInit = ['clear', 'delete'],
+ mapTail = ['get', hasName, 'set'];
+
+ // `Map`, `WeakMap` and `Set` each have slightly different
+ // combinations of the above sublists.
+ var mapMethods = commonInit.concat(forEachName, mapTail),
+ weakMapMethods = commonInit.concat(mapTail),
+ setMethods = ['add'].concat(commonInit, forEachName, hasName);
+
+ var isMap = isIE11 ? ie11fingerprint(mapMethods) : tagTester('Map');
+
+ var isWeakMap = isIE11 ? ie11fingerprint(weakMapMethods) : tagTester('WeakMap');
+
+ var isSet = isIE11 ? ie11fingerprint(setMethods) : tagTester('Set');
+
+ var isWeakSet = tagTester('WeakSet');
+
+ // Retrieve the values of an object's properties.
+ function values(obj) {
+ var _keys = keys(obj);
+ var length = _keys.length;
+ var values = Array(length);
+ for (var i = 0; i < length; i++) {
+ values[i] = obj[_keys[i]];
+ }
+ return values;
+ }
+
+ // Convert an object into a list of `[key, value]` pairs.
+ // The opposite of `_.object` with one argument.
+ function pairs(obj) {
+ var _keys = keys(obj);
+ var length = _keys.length;
+ var pairs = Array(length);
+ for (var i = 0; i < length; i++) {
+ pairs[i] = [_keys[i], obj[_keys[i]]];
+ }
+ return pairs;
+ }
+
+ // Invert the keys and values of an object. The values must be serializable.
+ function invert(obj) {
+ var result = {};
+ var _keys = keys(obj);
+ for (var i = 0, length = _keys.length; i < length; i++) {
+ result[obj[_keys[i]]] = _keys[i];
+ }
+ return result;
+ }
+
+ // Return a sorted list of the function names available on the object.
+ function functions(obj) {
+ var names = [];
+ for (var key in obj) {
+ if (isFunction$1(obj[key])) names.push(key);
+ }
+ return names.sort();
+ }
+
+ // An internal function for creating assigner functions.
+ function createAssigner(keysFunc, defaults) {
+ return function(obj) {
+ var length = arguments.length;
+ if (defaults) obj = Object(obj);
+ if (length < 2 || obj == null) return obj;
+ for (var index = 1; index < length; index++) {
+ var source = arguments[index],
+ keys = keysFunc(source),
+ l = keys.length;
+ for (var i = 0; i < l; i++) {
+ var key = keys[i];
+ if (!defaults || obj[key] === void 0) obj[key] = source[key];
+ }
+ }
+ return obj;
+ };
+ }
+
+ // Extend a given object with all the properties in passed-in object(s).
+ var extend = createAssigner(allKeys);
+
+ // Assigns a given object with all the own properties in the passed-in
+ // object(s).
+ // (https://developer.mozilla.org/docs/Web/JavaScript/Reference/Global_Objects/Object/assign)
+ var extendOwn = createAssigner(keys);
+
+ // Fill in a given object with default properties.
+ var defaults = createAssigner(allKeys, true);
+
+ // Create a naked function reference for surrogate-prototype-swapping.
+ function ctor() {
+ return function(){};
+ }
+
+ // An internal function for creating a new object that inherits from another.
+ function baseCreate(prototype) {
+ if (!isObject(prototype)) return {};
+ if (nativeCreate) return nativeCreate(prototype);
+ var Ctor = ctor();
+ Ctor.prototype = prototype;
+ var result = new Ctor;
+ Ctor.prototype = null;
+ return result;
+ }
+
+ // Creates an object that inherits from the given prototype object.
+ // If additional properties are provided then they will be added to the
+ // created object.
+ function create(prototype, props) {
+ var result = baseCreate(prototype);
+ if (props) extendOwn(result, props);
+ return result;
+ }
+
+ // Create a (shallow-cloned) duplicate of an object.
+ function clone(obj) {
+ if (!isObject(obj)) return obj;
+ return isArray(obj) ? obj.slice() : extend({}, obj);
+ }
+
+ // Invokes `interceptor` with the `obj` and then returns `obj`.
+ // The primary purpose of this method is to "tap into" a method chain, in
+ // order to perform operations on intermediate results within the chain.
+ function tap(obj, interceptor) {
+ interceptor(obj);
+ return obj;
+ }
+
+ // Normalize a (deep) property `path` to array.
+ // Like `_.iteratee`, this function can be customized.
+ function toPath$1(path) {
+ return isArray(path) ? path : [path];
+ }
+ _$1.toPath = toPath$1;
+
+ // Internal wrapper for `_.toPath` to enable minification.
+ // Similar to `cb` for `_.iteratee`.
+ function toPath(path) {
+ return _$1.toPath(path);
+ }
+
+ // Internal function to obtain a nested property in `obj` along `path`.
+ function deepGet(obj, path) {
+ var length = path.length;
+ for (var i = 0; i < length; i++) {
+ if (obj == null) return void 0;
+ obj = obj[path[i]];
+ }
+ return length ? obj : void 0;
+ }
+
+ // Get the value of the (deep) property on `path` from `object`.
+ // If any property in `path` does not exist or if the value is
+ // `undefined`, return `defaultValue` instead.
+ // The `path` is normalized through `_.toPath`.
+ function get(object, path, defaultValue) {
+ var value = deepGet(object, toPath(path));
+ return isUndefined(value) ? defaultValue : value;
+ }
+
+ // Shortcut function for checking if an object has a given property directly on
+ // itself (in other words, not on a prototype). Unlike the internal `has`
+ // function, this public version can also traverse nested properties.
+ function has(obj, path) {
+ path = toPath(path);
+ var length = path.length;
+ for (var i = 0; i < length; i++) {
+ var key = path[i];
+ if (!has$1(obj, key)) return false;
+ obj = obj[key];
+ }
+ return !!length;
+ }
+
+ // Keep the identity function around for default iteratees.
+ function identity(value) {
+ return value;
+ }
+
+ // Returns a predicate for checking whether an object has a given set of
+ // `key:value` pairs.
+ function matcher(attrs) {
+ attrs = extendOwn({}, attrs);
+ return function(obj) {
+ return isMatch(obj, attrs);
+ };
+ }
+
+ // Creates a function that, when passed an object, will traverse that object’s
+ // properties down the given `path`, specified as an array of keys or indices.
+ function property(path) {
+ path = toPath(path);
+ return function(obj) {
+ return deepGet(obj, path);
+ };
+ }
+
+ // Internal function that returns an efficient (for current engines) version
+ // of the passed-in callback, to be repeatedly applied in other Underscore
+ // functions.
+ function optimizeCb(func, context, argCount) {
+ if (context === void 0) return func;
+ switch (argCount == null ? 3 : argCount) {
+ case 1: return function(value) {
+ return func.call(context, value);
+ };
+ // The 2-argument case is omitted because we’re not using it.
+ case 3: return function(value, index, collection) {
+ return func.call(context, value, index, collection);
+ };
+ case 4: return function(accumulator, value, index, collection) {
+ return func.call(context, accumulator, value, index, collection);
+ };
+ }
+ return function() {
+ return func.apply(context, arguments);
+ };
+ }
+
+ // An internal function to generate callbacks that can be applied to each
+ // element in a collection, returning the desired result — either `_.identity`,
+ // an arbitrary callback, a property matcher, or a property accessor.
+ function baseIteratee(value, context, argCount) {
+ if (value == null) return identity;
+ if (isFunction$1(value)) return optimizeCb(value, context, argCount);
+ if (isObject(value) && !isArray(value)) return matcher(value);
+ return property(value);
+ }
+
+ // External wrapper for our callback generator. Users may customize
+ // `_.iteratee` if they want additional predicate/iteratee shorthand styles.
+ // This abstraction hides the internal-only `argCount` argument.
+ function iteratee(value, context) {
+ return baseIteratee(value, context, Infinity);
+ }
+ _$1.iteratee = iteratee;
+
+ // The function we call internally to generate a callback. It invokes
+ // `_.iteratee` if overridden, otherwise `baseIteratee`.
+ function cb(value, context, argCount) {
+ if (_$1.iteratee !== iteratee) return _$1.iteratee(value, context);
+ return baseIteratee(value, context, argCount);
+ }
+
+ // Returns the results of applying the `iteratee` to each element of `obj`.
+ // In contrast to `_.map` it returns an object.
+ function mapObject(obj, iteratee, context) {
+ iteratee = cb(iteratee, context);
+ var _keys = keys(obj),
+ length = _keys.length,
+ results = {};
+ for (var index = 0; index < length; index++) {
+ var currentKey = _keys[index];
+ results[currentKey] = iteratee(obj[currentKey], currentKey, obj);
+ }
+ return results;
+ }
+
+ // Predicate-generating function. Often useful outside of Underscore.
+ function noop(){}
+
+ // Generates a function for a given object that returns a given property.
+ function propertyOf(obj) {
+ if (obj == null) return noop;
+ return function(path) {
+ return get(obj, path);
+ };
+ }
+
+ // Run a function **n** times.
+ function times(n, iteratee, context) {
+ var accum = Array(Math.max(0, n));
+ iteratee = optimizeCb(iteratee, context, 1);
+ for (var i = 0; i < n; i++) accum[i] = iteratee(i);
+ return accum;
+ }
+
+ // Return a random integer between `min` and `max` (inclusive).
+ function random(min, max) {
+ if (max == null) {
+ max = min;
+ min = 0;
+ }
+ return min + Math.floor(Math.random() * (max - min + 1));
+ }
+
+ // A (possibly faster) way to get the current timestamp as an integer.
+ var now = Date.now || function() {
+ return new Date().getTime();
+ };
+
+ // Internal helper to generate functions for escaping and unescaping strings
+ // to/from HTML interpolation.
+ function createEscaper(map) {
+ var escaper = function(match) {
+ return map[match];
+ };
+ // Regexes for identifying a key that needs to be escaped.
+ var source = '(?:' + keys(map).join('|') + ')';
+ var testRegexp = RegExp(source);
+ var replaceRegexp = RegExp(source, 'g');
+ return function(string) {
+ string = string == null ? '' : '' + string;
+ return testRegexp.test(string) ? string.replace(replaceRegexp, escaper) : string;
+ };
+ }
+
+ // Internal list of HTML entities for escaping.
+ var escapeMap = {
+ '&': '&',
+ '<': '<',
+ '>': '>',
+ '"': '"',
+ "'": ''',
+ '`': '`'
+ };
+
+ // Function for escaping strings to HTML interpolation.
+ var _escape = createEscaper(escapeMap);
+
+ // Internal list of HTML entities for unescaping.
+ var unescapeMap = invert(escapeMap);
+
+ // Function for unescaping strings from HTML interpolation.
+ var _unescape = createEscaper(unescapeMap);
+
+ // By default, Underscore uses ERB-style template delimiters. Change the
+ // following template settings to use alternative delimiters.
+ var templateSettings = _$1.templateSettings = {
+ evaluate: /<%([\s\S]+?)%>/g,
+ interpolate: /<%=([\s\S]+?)%>/g,
+ escape: /<%-([\s\S]+?)%>/g
+ };
+
+ // When customizing `_.templateSettings`, if you don't want to define an
+ // interpolation, evaluation or escaping regex, we need one that is
+ // guaranteed not to match.
+ var noMatch = /(.)^/;
+
+ // Certain characters need to be escaped so that they can be put into a
+ // string literal.
+ var escapes = {
+ "'": "'",
+ '\\': '\\',
+ '\r': 'r',
+ '\n': 'n',
+ '\u2028': 'u2028',
+ '\u2029': 'u2029'
+ };
+
+ var escapeRegExp = /\\|'|\r|\n|\u2028|\u2029/g;
+
+ function escapeChar(match) {
+ return '\\' + escapes[match];
+ }
+
+ // In order to prevent third-party code injection through
+ // `_.templateSettings.variable`, we test it against the following regular
+ // expression. It is intentionally a bit more liberal than just matching valid
+ // identifiers, but still prevents possible loopholes through defaults or
+ // destructuring assignment.
+ var bareIdentifier = /^\s*(\w|\$)+\s*$/;
+
+ // JavaScript micro-templating, similar to John Resig's implementation.
+ // Underscore templating handles arbitrary delimiters, preserves whitespace,
+ // and correctly escapes quotes within interpolated code.
+ // NB: `oldSettings` only exists for backwards compatibility.
+ function template(text, settings, oldSettings) {
+ if (!settings && oldSettings) settings = oldSettings;
+ settings = defaults({}, settings, _$1.templateSettings);
+
+ // Combine delimiters into one regular expression via alternation.
+ var matcher = RegExp([
+ (settings.escape || noMatch).source,
+ (settings.interpolate || noMatch).source,
+ (settings.evaluate || noMatch).source
+ ].join('|') + '|$', 'g');
+
+ // Compile the template source, escaping string literals appropriately.
+ var index = 0;
+ var source = "__p+='";
+ text.replace(matcher, function(match, escape, interpolate, evaluate, offset) {
+ source += text.slice(index, offset).replace(escapeRegExp, escapeChar);
+ index = offset + match.length;
+
+ if (escape) {
+ source += "'+\n((__t=(" + escape + "))==null?'':_.escape(__t))+\n'";
+ } else if (interpolate) {
+ source += "'+\n((__t=(" + interpolate + "))==null?'':__t)+\n'";
+ } else if (evaluate) {
+ source += "';\n" + evaluate + "\n__p+='";
+ }
+
+ // Adobe VMs need the match returned to produce the correct offset.
+ return match;
+ });
+ source += "';\n";
+
+ var argument = settings.variable;
+ if (argument) {
+ // Insure against third-party code injection. (CVE-2021-23358)
+ if (!bareIdentifier.test(argument)) throw new Error(
+ 'variable is not a bare identifier: ' + argument
+ );
+ } else {
+ // If a variable is not specified, place data values in local scope.
+ source = 'with(obj||{}){\n' + source + '}\n';
+ argument = 'obj';
+ }
+
+ source = "var __t,__p='',__j=Array.prototype.join," +
+ "print=function(){__p+=__j.call(arguments,'');};\n" +
+ source + 'return __p;\n';
+
+ var render;
+ try {
+ render = new Function(argument, '_', source);
+ } catch (e) {
+ e.source = source;
+ throw e;
+ }
+
+ var template = function(data) {
+ return render.call(this, data, _$1);
+ };
+
+ // Provide the compiled source as a convenience for precompilation.
+ template.source = 'function(' + argument + '){\n' + source + '}';
+
+ return template;
+ }
+
+ // Traverses the children of `obj` along `path`. If a child is a function, it
+ // is invoked with its parent as context. Returns the value of the final
+ // child, or `fallback` if any child is undefined.
+ function result(obj, path, fallback) {
+ path = toPath(path);
+ var length = path.length;
+ if (!length) {
+ return isFunction$1(fallback) ? fallback.call(obj) : fallback;
+ }
+ for (var i = 0; i < length; i++) {
+ var prop = obj == null ? void 0 : obj[path[i]];
+ if (prop === void 0) {
+ prop = fallback;
+ i = length; // Ensure we don't continue iterating.
+ }
+ obj = isFunction$1(prop) ? prop.call(obj) : prop;
+ }
+ return obj;
+ }
+
+ // Generate a unique integer id (unique within the entire client session).
+ // Useful for temporary DOM ids.
+ var idCounter = 0;
+ function uniqueId(prefix) {
+ var id = ++idCounter + '';
+ return prefix ? prefix + id : id;
+ }
+
+ // Start chaining a wrapped Underscore object.
+ function chain(obj) {
+ var instance = _$1(obj);
+ instance._chain = true;
+ return instance;
+ }
+
+ // Internal function to execute `sourceFunc` bound to `context` with optional
+ // `args`. Determines whether to execute a function as a constructor or as a
+ // normal function.
+ function executeBound(sourceFunc, boundFunc, context, callingContext, args) {
+ if (!(callingContext instanceof boundFunc)) return sourceFunc.apply(context, args);
+ var self = baseCreate(sourceFunc.prototype);
+ var result = sourceFunc.apply(self, args);
+ if (isObject(result)) return result;
+ return self;
+ }
+
+ // Partially apply a function by creating a version that has had some of its
+ // arguments pre-filled, without changing its dynamic `this` context. `_` acts
+ // as a placeholder by default, allowing any combination of arguments to be
+ // pre-filled. Set `_.partial.placeholder` for a custom placeholder argument.
+ var partial = restArguments(function(func, boundArgs) {
+ var placeholder = partial.placeholder;
+ var bound = function() {
+ var position = 0, length = boundArgs.length;
+ var args = Array(length);
+ for (var i = 0; i < length; i++) {
+ args[i] = boundArgs[i] === placeholder ? arguments[position++] : boundArgs[i];
+ }
+ while (position < arguments.length) args.push(arguments[position++]);
+ return executeBound(func, bound, this, this, args);
+ };
+ return bound;
+ });
+
+ partial.placeholder = _$1;
+
+ // Create a function bound to a given object (assigning `this`, and arguments,
+ // optionally).
+ var bind = restArguments(function(func, context, args) {
+ if (!isFunction$1(func)) throw new TypeError('Bind must be called on a function');
+ var bound = restArguments(function(callArgs) {
+ return executeBound(func, bound, context, this, args.concat(callArgs));
+ });
+ return bound;
+ });
+
+ // Internal helper for collection methods to determine whether a collection
+ // should be iterated as an array or as an object.
+ // Related: https://people.mozilla.org/~jorendorff/es6-draft.html#sec-tolength
+ // Avoids a very nasty iOS 8 JIT bug on ARM-64. #2094
+ var isArrayLike = createSizePropertyCheck(getLength);
+
+ // Internal implementation of a recursive `flatten` function.
+ function flatten$1(input, depth, strict, output) {
+ output = output || [];
+ if (!depth && depth !== 0) {
+ depth = Infinity;
+ } else if (depth <= 0) {
+ return output.concat(input);
+ }
+ var idx = output.length;
+ for (var i = 0, length = getLength(input); i < length; i++) {
+ var value = input[i];
+ if (isArrayLike(value) && (isArray(value) || isArguments$1(value))) {
+ // Flatten current level of array or arguments object.
+ if (depth > 1) {
+ flatten$1(value, depth - 1, strict, output);
+ idx = output.length;
+ } else {
+ var j = 0, len = value.length;
+ while (j < len) output[idx++] = value[j++];
+ }
+ } else if (!strict) {
+ output[idx++] = value;
+ }
+ }
+ return output;
+ }
+
+ // Bind a number of an object's methods to that object. Remaining arguments
+ // are the method names to be bound. Useful for ensuring that all callbacks
+ // defined on an object belong to it.
+ var bindAll = restArguments(function(obj, keys) {
+ keys = flatten$1(keys, false, false);
+ var index = keys.length;
+ if (index < 1) throw new Error('bindAll must be passed function names');
+ while (index--) {
+ var key = keys[index];
+ obj[key] = bind(obj[key], obj);
+ }
+ return obj;
+ });
+
+ // Memoize an expensive function by storing its results.
+ function memoize(func, hasher) {
+ var memoize = function(key) {
+ var cache = memoize.cache;
+ var address = '' + (hasher ? hasher.apply(this, arguments) : key);
+ if (!has$1(cache, address)) cache[address] = func.apply(this, arguments);
+ return cache[address];
+ };
+ memoize.cache = {};
+ return memoize;
+ }
+
+ // Delays a function for the given number of milliseconds, and then calls
+ // it with the arguments supplied.
+ var delay = restArguments(function(func, wait, args) {
+ return setTimeout(function() {
+ return func.apply(null, args);
+ }, wait);
+ });
+
+ // Defers a function, scheduling it to run after the current call stack has
+ // cleared.
+ var defer = partial(delay, _$1, 1);
+
+ // Returns a function, that, when invoked, will only be triggered at most once
+ // during a given window of time. Normally, the throttled function will run
+ // as much as it can, without ever going more than once per `wait` duration;
+ // but if you'd like to disable the execution on the leading edge, pass
+ // `{leading: false}`. To disable execution on the trailing edge, ditto.
+ function throttle(func, wait, options) {
+ var timeout, context, args, result;
+ var previous = 0;
+ if (!options) options = {};
+
+ var later = function() {
+ previous = options.leading === false ? 0 : now();
+ timeout = null;
+ result = func.apply(context, args);
+ if (!timeout) context = args = null;
+ };
+
+ var throttled = function() {
+ var _now = now();
+ if (!previous && options.leading === false) previous = _now;
+ var remaining = wait - (_now - previous);
+ context = this;
+ args = arguments;
+ if (remaining <= 0 || remaining > wait) {
+ if (timeout) {
+ clearTimeout(timeout);
+ timeout = null;
+ }
+ previous = _now;
+ result = func.apply(context, args);
+ if (!timeout) context = args = null;
+ } else if (!timeout && options.trailing !== false) {
+ timeout = setTimeout(later, remaining);
+ }
+ return result;
+ };
+
+ throttled.cancel = function() {
+ clearTimeout(timeout);
+ previous = 0;
+ timeout = context = args = null;
+ };
+
+ return throttled;
+ }
+
+ // When a sequence of calls of the returned function ends, the argument
+ // function is triggered. The end of a sequence is defined by the `wait`
+ // parameter. If `immediate` is passed, the argument function will be
+ // triggered at the beginning of the sequence instead of at the end.
+ function debounce(func, wait, immediate) {
+ var timeout, previous, args, result, context;
+
+ var later = function() {
+ var passed = now() - previous;
+ if (wait > passed) {
+ timeout = setTimeout(later, wait - passed);
+ } else {
+ timeout = null;
+ if (!immediate) result = func.apply(context, args);
+ // This check is needed because `func` can recursively invoke `debounced`.
+ if (!timeout) args = context = null;
+ }
+ };
+
+ var debounced = restArguments(function(_args) {
+ context = this;
+ args = _args;
+ previous = now();
+ if (!timeout) {
+ timeout = setTimeout(later, wait);
+ if (immediate) result = func.apply(context, args);
+ }
+ return result;
+ });
+
+ debounced.cancel = function() {
+ clearTimeout(timeout);
+ timeout = args = context = null;
+ };
+
+ return debounced;
+ }
+
+ // Returns the first function passed as an argument to the second,
+ // allowing you to adjust arguments, run code before and after, and
+ // conditionally execute the original function.
+ function wrap(func, wrapper) {
+ return partial(wrapper, func);
+ }
+
+ // Returns a negated version of the passed-in predicate.
+ function negate(predicate) {
+ return function() {
+ return !predicate.apply(this, arguments);
+ };
+ }
+
+ // Returns a function that is the composition of a list of functions, each
+ // consuming the return value of the function that follows.
+ function compose() {
+ var args = arguments;
+ var start = args.length - 1;
+ return function() {
+ var i = start;
+ var result = args[start].apply(this, arguments);
+ while (i--) result = args[i].call(this, result);
+ return result;
+ };
+ }
+
+ // Returns a function that will only be executed on and after the Nth call.
+ function after(times, func) {
+ return function() {
+ if (--times < 1) {
+ return func.apply(this, arguments);
+ }
+ };
+ }
+
+ // Returns a function that will only be executed up to (but not including) the
+ // Nth call.
+ function before(times, func) {
+ var memo;
+ return function() {
+ if (--times > 0) {
+ memo = func.apply(this, arguments);
+ }
+ if (times <= 1) func = null;
+ return memo;
+ };
+ }
+
+ // Returns a function that will be executed at most one time, no matter how
+ // often you call it. Useful for lazy initialization.
+ var once = partial(before, 2);
+
+ // Returns the first key on an object that passes a truth test.
+ function findKey(obj, predicate, context) {
+ predicate = cb(predicate, context);
+ var _keys = keys(obj), key;
+ for (var i = 0, length = _keys.length; i < length; i++) {
+ key = _keys[i];
+ if (predicate(obj[key], key, obj)) return key;
+ }
+ }
+
+ // Internal function to generate `_.findIndex` and `_.findLastIndex`.
+ function createPredicateIndexFinder(dir) {
+ return function(array, predicate, context) {
+ predicate = cb(predicate, context);
+ var length = getLength(array);
+ var index = dir > 0 ? 0 : length - 1;
+ for (; index >= 0 && index < length; index += dir) {
+ if (predicate(array[index], index, array)) return index;
+ }
+ return -1;
+ };
+ }
+
+ // Returns the first index on an array-like that passes a truth test.
+ var findIndex = createPredicateIndexFinder(1);
+
+ // Returns the last index on an array-like that passes a truth test.
+ var findLastIndex = createPredicateIndexFinder(-1);
+
+ // Use a comparator function to figure out the smallest index at which
+ // an object should be inserted so as to maintain order. Uses binary search.
+ function sortedIndex(array, obj, iteratee, context) {
+ iteratee = cb(iteratee, context, 1);
+ var value = iteratee(obj);
+ var low = 0, high = getLength(array);
+ while (low < high) {
+ var mid = Math.floor((low + high) / 2);
+ if (iteratee(array[mid]) < value) low = mid + 1; else high = mid;
+ }
+ return low;
+ }
+
+ // Internal function to generate the `_.indexOf` and `_.lastIndexOf` functions.
+ function createIndexFinder(dir, predicateFind, sortedIndex) {
+ return function(array, item, idx) {
+ var i = 0, length = getLength(array);
+ if (typeof idx == 'number') {
+ if (dir > 0) {
+ i = idx >= 0 ? idx : Math.max(idx + length, i);
+ } else {
+ length = idx >= 0 ? Math.min(idx + 1, length) : idx + length + 1;
+ }
+ } else if (sortedIndex && idx && length) {
+ idx = sortedIndex(array, item);
+ return array[idx] === item ? idx : -1;
+ }
+ if (item !== item) {
+ idx = predicateFind(slice.call(array, i, length), isNaN$1);
+ return idx >= 0 ? idx + i : -1;
+ }
+ for (idx = dir > 0 ? i : length - 1; idx >= 0 && idx < length; idx += dir) {
+ if (array[idx] === item) return idx;
+ }
+ return -1;
+ };
+ }
+
+ // Return the position of the first occurrence of an item in an array,
+ // or -1 if the item is not included in the array.
+ // If the array is large and already in sort order, pass `true`
+ // for **isSorted** to use binary search.
+ var indexOf = createIndexFinder(1, findIndex, sortedIndex);
+
+ // Return the position of the last occurrence of an item in an array,
+ // or -1 if the item is not included in the array.
+ var lastIndexOf = createIndexFinder(-1, findLastIndex);
+
+ // Return the first value which passes a truth test.
+ function find(obj, predicate, context) {
+ var keyFinder = isArrayLike(obj) ? findIndex : findKey;
+ var key = keyFinder(obj, predicate, context);
+ if (key !== void 0 && key !== -1) return obj[key];
+ }
+
+ // Convenience version of a common use case of `_.find`: getting the first
+ // object containing specific `key:value` pairs.
+ function findWhere(obj, attrs) {
+ return find(obj, matcher(attrs));
+ }
+
+ // The cornerstone for collection functions, an `each`
+ // implementation, aka `forEach`.
+ // Handles raw objects in addition to array-likes. Treats all
+ // sparse array-likes as if they were dense.
+ function each(obj, iteratee, context) {
+ iteratee = optimizeCb(iteratee, context);
+ var i, length;
+ if (isArrayLike(obj)) {
+ for (i = 0, length = obj.length; i < length; i++) {
+ iteratee(obj[i], i, obj);
+ }
+ } else {
+ var _keys = keys(obj);
+ for (i = 0, length = _keys.length; i < length; i++) {
+ iteratee(obj[_keys[i]], _keys[i], obj);
+ }
+ }
+ return obj;
+ }
+
+ // Return the results of applying the iteratee to each element.
+ function map(obj, iteratee, context) {
+ iteratee = cb(iteratee, context);
+ var _keys = !isArrayLike(obj) && keys(obj),
+ length = (_keys || obj).length,
+ results = Array(length);
+ for (var index = 0; index < length; index++) {
+ var currentKey = _keys ? _keys[index] : index;
+ results[index] = iteratee(obj[currentKey], currentKey, obj);
+ }
+ return results;
+ }
+
+ // Internal helper to create a reducing function, iterating left or right.
+ function createReduce(dir) {
+ // Wrap code that reassigns argument variables in a separate function than
+ // the one that accesses `arguments.length` to avoid a perf hit. (#1991)
+ var reducer = function(obj, iteratee, memo, initial) {
+ var _keys = !isArrayLike(obj) && keys(obj),
+ length = (_keys || obj).length,
+ index = dir > 0 ? 0 : length - 1;
+ if (!initial) {
+ memo = obj[_keys ? _keys[index] : index];
+ index += dir;
+ }
+ for (; index >= 0 && index < length; index += dir) {
+ var currentKey = _keys ? _keys[index] : index;
+ memo = iteratee(memo, obj[currentKey], currentKey, obj);
+ }
+ return memo;
+ };
+
+ return function(obj, iteratee, memo, context) {
+ var initial = arguments.length >= 3;
+ return reducer(obj, optimizeCb(iteratee, context, 4), memo, initial);
+ };
+ }
+
+ // **Reduce** builds up a single result from a list of values, aka `inject`,
+ // or `foldl`.
+ var reduce = createReduce(1);
+
+ // The right-associative version of reduce, also known as `foldr`.
+ var reduceRight = createReduce(-1);
+
+ // Return all the elements that pass a truth test.
+ function filter(obj, predicate, context) {
+ var results = [];
+ predicate = cb(predicate, context);
+ each(obj, function(value, index, list) {
+ if (predicate(value, index, list)) results.push(value);
+ });
+ return results;
+ }
+
+ // Return all the elements for which a truth test fails.
+ function reject(obj, predicate, context) {
+ return filter(obj, negate(cb(predicate)), context);
+ }
+
+ // Determine whether all of the elements pass a truth test.
+ function every(obj, predicate, context) {
+ predicate = cb(predicate, context);
+ var _keys = !isArrayLike(obj) && keys(obj),
+ length = (_keys || obj).length;
+ for (var index = 0; index < length; index++) {
+ var currentKey = _keys ? _keys[index] : index;
+ if (!predicate(obj[currentKey], currentKey, obj)) return false;
+ }
+ return true;
+ }
+
+ // Determine if at least one element in the object passes a truth test.
+ function some(obj, predicate, context) {
+ predicate = cb(predicate, context);
+ var _keys = !isArrayLike(obj) && keys(obj),
+ length = (_keys || obj).length;
+ for (var index = 0; index < length; index++) {
+ var currentKey = _keys ? _keys[index] : index;
+ if (predicate(obj[currentKey], currentKey, obj)) return true;
+ }
+ return false;
+ }
+
+ // Determine if the array or object contains a given item (using `===`).
+ function contains(obj, item, fromIndex, guard) {
+ if (!isArrayLike(obj)) obj = values(obj);
+ if (typeof fromIndex != 'number' || guard) fromIndex = 0;
+ return indexOf(obj, item, fromIndex) >= 0;
+ }
+
+ // Invoke a method (with arguments) on every item in a collection.
+ var invoke = restArguments(function(obj, path, args) {
+ var contextPath, func;
+ if (isFunction$1(path)) {
+ func = path;
+ } else {
+ path = toPath(path);
+ contextPath = path.slice(0, -1);
+ path = path[path.length - 1];
+ }
+ return map(obj, function(context) {
+ var method = func;
+ if (!method) {
+ if (contextPath && contextPath.length) {
+ context = deepGet(context, contextPath);
+ }
+ if (context == null) return void 0;
+ method = context[path];
+ }
+ return method == null ? method : method.apply(context, args);
+ });
+ });
+
+ // Convenience version of a common use case of `_.map`: fetching a property.
+ function pluck(obj, key) {
+ return map(obj, property(key));
+ }
+
+ // Convenience version of a common use case of `_.filter`: selecting only
+ // objects containing specific `key:value` pairs.
+ function where(obj, attrs) {
+ return filter(obj, matcher(attrs));
+ }
+
+ // Return the maximum element (or element-based computation).
+ function max(obj, iteratee, context) {
+ var result = -Infinity, lastComputed = -Infinity,
+ value, computed;
+ if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) {
+ obj = isArrayLike(obj) ? obj : values(obj);
+ for (var i = 0, length = obj.length; i < length; i++) {
+ value = obj[i];
+ if (value != null && value > result) {
+ result = value;
+ }
+ }
+ } else {
+ iteratee = cb(iteratee, context);
+ each(obj, function(v, index, list) {
+ computed = iteratee(v, index, list);
+ if (computed > lastComputed || computed === -Infinity && result === -Infinity) {
+ result = v;
+ lastComputed = computed;
+ }
+ });
+ }
+ return result;
+ }
+
+ // Return the minimum element (or element-based computation).
+ function min(obj, iteratee, context) {
+ var result = Infinity, lastComputed = Infinity,
+ value, computed;
+ if (iteratee == null || typeof iteratee == 'number' && typeof obj[0] != 'object' && obj != null) {
+ obj = isArrayLike(obj) ? obj : values(obj);
+ for (var i = 0, length = obj.length; i < length; i++) {
+ value = obj[i];
+ if (value != null && value < result) {
+ result = value;
+ }
+ }
+ } else {
+ iteratee = cb(iteratee, context);
+ each(obj, function(v, index, list) {
+ computed = iteratee(v, index, list);
+ if (computed < lastComputed || computed === Infinity && result === Infinity) {
+ result = v;
+ lastComputed = computed;
+ }
+ });
+ }
+ return result;
+ }
+
+ // Sample **n** random values from a collection using the modern version of the
+ // [Fisher-Yates shuffle](https://en.wikipedia.org/wiki/Fisher–Yates_shuffle).
+ // If **n** is not specified, returns a single random element.
+ // The internal `guard` argument allows it to work with `_.map`.
+ function sample(obj, n, guard) {
+ if (n == null || guard) {
+ if (!isArrayLike(obj)) obj = values(obj);
+ return obj[random(obj.length - 1)];
+ }
+ var sample = isArrayLike(obj) ? clone(obj) : values(obj);
+ var length = getLength(sample);
+ n = Math.max(Math.min(n, length), 0);
+ var last = length - 1;
+ for (var index = 0; index < n; index++) {
+ var rand = random(index, last);
+ var temp = sample[index];
+ sample[index] = sample[rand];
+ sample[rand] = temp;
+ }
+ return sample.slice(0, n);
+ }
+
+ // Shuffle a collection.
+ function shuffle(obj) {
+ return sample(obj, Infinity);
+ }
+
+ // Sort the object's values by a criterion produced by an iteratee.
+ function sortBy(obj, iteratee, context) {
+ var index = 0;
+ iteratee = cb(iteratee, context);
+ return pluck(map(obj, function(value, key, list) {
+ return {
+ value: value,
+ index: index++,
+ criteria: iteratee(value, key, list)
+ };
+ }).sort(function(left, right) {
+ var a = left.criteria;
+ var b = right.criteria;
+ if (a !== b) {
+ if (a > b || a === void 0) return 1;
+ if (a < b || b === void 0) return -1;
+ }
+ return left.index - right.index;
+ }), 'value');
+ }
+
+ // An internal function used for aggregate "group by" operations.
+ function group(behavior, partition) {
+ return function(obj, iteratee, context) {
+ var result = partition ? [[], []] : {};
+ iteratee = cb(iteratee, context);
+ each(obj, function(value, index) {
+ var key = iteratee(value, index, obj);
+ behavior(result, value, key);
+ });
+ return result;
+ };
+ }
+
+ // Groups the object's values by a criterion. Pass either a string attribute
+ // to group by, or a function that returns the criterion.
+ var groupBy = group(function(result, value, key) {
+ if (has$1(result, key)) result[key].push(value); else result[key] = [value];
+ });
+
+ // Indexes the object's values by a criterion, similar to `_.groupBy`, but for
+ // when you know that your index values will be unique.
+ var indexBy = group(function(result, value, key) {
+ result[key] = value;
+ });
+
+ // Counts instances of an object that group by a certain criterion. Pass
+ // either a string attribute to count by, or a function that returns the
+ // criterion.
+ var countBy = group(function(result, value, key) {
+ if (has$1(result, key)) result[key]++; else result[key] = 1;
+ });
+
+ // Split a collection into two arrays: one whose elements all pass the given
+ // truth test, and one whose elements all do not pass the truth test.
+ var partition = group(function(result, value, pass) {
+ result[pass ? 0 : 1].push(value);
+ }, true);
+
+ // Safely create a real, live array from anything iterable.
+ var reStrSymbol = /[^\ud800-\udfff]|[\ud800-\udbff][\udc00-\udfff]|[\ud800-\udfff]/g;
+ function toArray(obj) {
+ if (!obj) return [];
+ if (isArray(obj)) return slice.call(obj);
+ if (isString(obj)) {
+ // Keep surrogate pair characters together.
+ return obj.match(reStrSymbol);
+ }
+ if (isArrayLike(obj)) return map(obj, identity);
+ return values(obj);
+ }
+
+ // Return the number of elements in a collection.
+ function size(obj) {
+ if (obj == null) return 0;
+ return isArrayLike(obj) ? obj.length : keys(obj).length;
+ }
+
+ // Internal `_.pick` helper function to determine whether `key` is an enumerable
+ // property name of `obj`.
+ function keyInObj(value, key, obj) {
+ return key in obj;
+ }
+
+ // Return a copy of the object only containing the allowed properties.
+ var pick = restArguments(function(obj, keys) {
+ var result = {}, iteratee = keys[0];
+ if (obj == null) return result;
+ if (isFunction$1(iteratee)) {
+ if (keys.length > 1) iteratee = optimizeCb(iteratee, keys[1]);
+ keys = allKeys(obj);
+ } else {
+ iteratee = keyInObj;
+ keys = flatten$1(keys, false, false);
+ obj = Object(obj);
+ }
+ for (var i = 0, length = keys.length; i < length; i++) {
+ var key = keys[i];
+ var value = obj[key];
+ if (iteratee(value, key, obj)) result[key] = value;
+ }
+ return result;
+ });
+
+ // Return a copy of the object without the disallowed properties.
+ var omit = restArguments(function(obj, keys) {
+ var iteratee = keys[0], context;
+ if (isFunction$1(iteratee)) {
+ iteratee = negate(iteratee);
+ if (keys.length > 1) context = keys[1];
+ } else {
+ keys = map(flatten$1(keys, false, false), String);
+ iteratee = function(value, key) {
+ return !contains(keys, key);
+ };
+ }
+ return pick(obj, iteratee, context);
+ });
+
+ // Returns everything but the last entry of the array. Especially useful on
+ // the arguments object. Passing **n** will return all the values in
+ // the array, excluding the last N.
+ function initial(array, n, guard) {
+ return slice.call(array, 0, Math.max(0, array.length - (n == null || guard ? 1 : n)));
+ }
+
+ // Get the first element of an array. Passing **n** will return the first N
+ // values in the array. The **guard** check allows it to work with `_.map`.
+ function first(array, n, guard) {
+ if (array == null || array.length < 1) return n == null || guard ? void 0 : [];
+ if (n == null || guard) return array[0];
+ return initial(array, array.length - n);
+ }
+
+ // Returns everything but the first entry of the `array`. Especially useful on
+ // the `arguments` object. Passing an **n** will return the rest N values in the
+ // `array`.
+ function rest(array, n, guard) {
+ return slice.call(array, n == null || guard ? 1 : n);
+ }
+
+ // Get the last element of an array. Passing **n** will return the last N
+ // values in the array.
+ function last(array, n, guard) {
+ if (array == null || array.length < 1) return n == null || guard ? void 0 : [];
+ if (n == null || guard) return array[array.length - 1];
+ return rest(array, Math.max(0, array.length - n));
+ }
+
+ // Trim out all falsy values from an array.
+ function compact(array) {
+ return filter(array, Boolean);
+ }
+
+ // Flatten out an array, either recursively (by default), or up to `depth`.
+ // Passing `true` or `false` as `depth` means `1` or `Infinity`, respectively.
+ function flatten(array, depth) {
+ return flatten$1(array, depth, false);
+ }
+
+ // Take the difference between one array and a number of other arrays.
+ // Only the elements present in just the first array will remain.
+ var difference = restArguments(function(array, rest) {
+ rest = flatten$1(rest, true, true);
+ return filter(array, function(value){
+ return !contains(rest, value);
+ });
+ });
+
+ // Return a version of the array that does not contain the specified value(s).
+ var without = restArguments(function(array, otherArrays) {
+ return difference(array, otherArrays);
+ });
+
+ // Produce a duplicate-free version of the array. If the array has already
+ // been sorted, you have the option of using a faster algorithm.
+ // The faster algorithm will not work with an iteratee if the iteratee
+ // is not a one-to-one function, so providing an iteratee will disable
+ // the faster algorithm.
+ function uniq(array, isSorted, iteratee, context) {
+ if (!isBoolean(isSorted)) {
+ context = iteratee;
+ iteratee = isSorted;
+ isSorted = false;
+ }
+ if (iteratee != null) iteratee = cb(iteratee, context);
+ var result = [];
+ var seen = [];
+ for (var i = 0, length = getLength(array); i < length; i++) {
+ var value = array[i],
+ computed = iteratee ? iteratee(value, i, array) : value;
+ if (isSorted && !iteratee) {
+ if (!i || seen !== computed) result.push(value);
+ seen = computed;
+ } else if (iteratee) {
+ if (!contains(seen, computed)) {
+ seen.push(computed);
+ result.push(value);
+ }
+ } else if (!contains(result, value)) {
+ result.push(value);
+ }
+ }
+ return result;
+ }
+
+ // Produce an array that contains the union: each distinct element from all of
+ // the passed-in arrays.
+ var union = restArguments(function(arrays) {
+ return uniq(flatten$1(arrays, true, true));
+ });
+
+ // Produce an array that contains every item shared between all the
+ // passed-in arrays.
+ function intersection(array) {
+ var result = [];
+ var argsLength = arguments.length;
+ for (var i = 0, length = getLength(array); i < length; i++) {
+ var item = array[i];
+ if (contains(result, item)) continue;
+ var j;
+ for (j = 1; j < argsLength; j++) {
+ if (!contains(arguments[j], item)) break;
+ }
+ if (j === argsLength) result.push(item);
+ }
+ return result;
+ }
+
+ // Complement of zip. Unzip accepts an array of arrays and groups
+ // each array's elements on shared indices.
+ function unzip(array) {
+ var length = array && max(array, getLength).length || 0;
+ var result = Array(length);
+
+ for (var index = 0; index < length; index++) {
+ result[index] = pluck(array, index);
+ }
+ return result;
+ }
+
+ // Zip together multiple lists into a single array -- elements that share
+ // an index go together.
+ var zip = restArguments(unzip);
+
+ // Converts lists into objects. Pass either a single array of `[key, value]`
+ // pairs, or two parallel arrays of the same length -- one of keys, and one of
+ // the corresponding values. Passing by pairs is the reverse of `_.pairs`.
+ function object(list, values) {
+ var result = {};
+ for (var i = 0, length = getLength(list); i < length; i++) {
+ if (values) {
+ result[list[i]] = values[i];
+ } else {
+ result[list[i][0]] = list[i][1];
+ }
+ }
+ return result;
+ }
+
+ // Generate an integer Array containing an arithmetic progression. A port of
+ // the native Python `range()` function. See
+ // [the Python documentation](https://docs.python.org/library/functions.html#range).
+ function range(start, stop, step) {
+ if (stop == null) {
+ stop = start || 0;
+ start = 0;
+ }
+ if (!step) {
+ step = stop < start ? -1 : 1;
+ }
+
+ var length = Math.max(Math.ceil((stop - start) / step), 0);
+ var range = Array(length);
+
+ for (var idx = 0; idx < length; idx++, start += step) {
+ range[idx] = start;
+ }
+
+ return range;
+ }
+
+ // Chunk a single array into multiple arrays, each containing `count` or fewer
+ // items.
+ function chunk(array, count) {
+ if (count == null || count < 1) return [];
+ var result = [];
+ var i = 0, length = array.length;
+ while (i < length) {
+ result.push(slice.call(array, i, i += count));
+ }
+ return result;
+ }
+
+ // Helper function to continue chaining intermediate results.
+ function chainResult(instance, obj) {
+ return instance._chain ? _$1(obj).chain() : obj;
+ }
+
+ // Add your own custom functions to the Underscore object.
+ function mixin(obj) {
+ each(functions(obj), function(name) {
+ var func = _$1[name] = obj[name];
+ _$1.prototype[name] = function() {
+ var args = [this._wrapped];
+ push.apply(args, arguments);
+ return chainResult(this, func.apply(_$1, args));
+ };
+ });
+ return _$1;
+ }
+
+ // Add all mutator `Array` functions to the wrapper.
+ each(['pop', 'push', 'reverse', 'shift', 'sort', 'splice', 'unshift'], function(name) {
+ var method = ArrayProto[name];
+ _$1.prototype[name] = function() {
+ var obj = this._wrapped;
+ if (obj != null) {
+ method.apply(obj, arguments);
+ if ((name === 'shift' || name === 'splice') && obj.length === 0) {
+ delete obj[0];
+ }
+ }
+ return chainResult(this, obj);
+ };
+ });
+
+ // Add all accessor `Array` functions to the wrapper.
+ each(['concat', 'join', 'slice'], function(name) {
+ var method = ArrayProto[name];
+ _$1.prototype[name] = function() {
+ var obj = this._wrapped;
+ if (obj != null) obj = method.apply(obj, arguments);
+ return chainResult(this, obj);
+ };
+ });
+
+ // Named Exports
+
+ var allExports = {
+ __proto__: null,
+ VERSION: VERSION,
+ restArguments: restArguments,
+ isObject: isObject,
+ isNull: isNull,
+ isUndefined: isUndefined,
+ isBoolean: isBoolean,
+ isElement: isElement,
+ isString: isString,
+ isNumber: isNumber,
+ isDate: isDate,
+ isRegExp: isRegExp,
+ isError: isError,
+ isSymbol: isSymbol,
+ isArrayBuffer: isArrayBuffer,
+ isDataView: isDataView$1,
+ isArray: isArray,
+ isFunction: isFunction$1,
+ isArguments: isArguments$1,
+ isFinite: isFinite$1,
+ isNaN: isNaN$1,
+ isTypedArray: isTypedArray$1,
+ isEmpty: isEmpty,
+ isMatch: isMatch,
+ isEqual: isEqual,
+ isMap: isMap,
+ isWeakMap: isWeakMap,
+ isSet: isSet,
+ isWeakSet: isWeakSet,
+ keys: keys,
+ allKeys: allKeys,
+ values: values,
+ pairs: pairs,
+ invert: invert,
+ functions: functions,
+ methods: functions,
+ extend: extend,
+ extendOwn: extendOwn,
+ assign: extendOwn,
+ defaults: defaults,
+ create: create,
+ clone: clone,
+ tap: tap,
+ get: get,
+ has: has,
+ mapObject: mapObject,
+ identity: identity,
+ constant: constant,
+ noop: noop,
+ toPath: toPath$1,
+ property: property,
+ propertyOf: propertyOf,
+ matcher: matcher,
+ matches: matcher,
+ times: times,
+ random: random,
+ now: now,
+ escape: _escape,
+ unescape: _unescape,
+ templateSettings: templateSettings,
+ template: template,
+ result: result,
+ uniqueId: uniqueId,
+ chain: chain,
+ iteratee: iteratee,
+ partial: partial,
+ bind: bind,
+ bindAll: bindAll,
+ memoize: memoize,
+ delay: delay,
+ defer: defer,
+ throttle: throttle,
+ debounce: debounce,
+ wrap: wrap,
+ negate: negate,
+ compose: compose,
+ after: after,
+ before: before,
+ once: once,
+ findKey: findKey,
+ findIndex: findIndex,
+ findLastIndex: findLastIndex,
+ sortedIndex: sortedIndex,
+ indexOf: indexOf,
+ lastIndexOf: lastIndexOf,
+ find: find,
+ detect: find,
+ findWhere: findWhere,
+ each: each,
+ forEach: each,
+ map: map,
+ collect: map,
+ reduce: reduce,
+ foldl: reduce,
+ inject: reduce,
+ reduceRight: reduceRight,
+ foldr: reduceRight,
+ filter: filter,
+ select: filter,
+ reject: reject,
+ every: every,
+ all: every,
+ some: some,
+ any: some,
+ contains: contains,
+ includes: contains,
+ include: contains,
+ invoke: invoke,
+ pluck: pluck,
+ where: where,
+ max: max,
+ min: min,
+ shuffle: shuffle,
+ sample: sample,
+ sortBy: sortBy,
+ groupBy: groupBy,
+ indexBy: indexBy,
+ countBy: countBy,
+ partition: partition,
+ toArray: toArray,
+ size: size,
+ pick: pick,
+ omit: omit,
+ first: first,
+ head: first,
+ take: first,
+ initial: initial,
+ last: last,
+ rest: rest,
+ tail: rest,
+ drop: rest,
+ compact: compact,
+ flatten: flatten,
+ without: without,
+ uniq: uniq,
+ unique: uniq,
+ union: union,
+ intersection: intersection,
+ difference: difference,
+ unzip: unzip,
+ transpose: unzip,
+ zip: zip,
+ object: object,
+ range: range,
+ chunk: chunk,
+ mixin: mixin,
+ 'default': _$1
+ };
+
+ // Default Export
+
+ // Add all of the Underscore functions to the wrapper object.
+ var _ = mixin(allExports);
+ // Legacy Node.js API.
+ _._ = _;
+
+ return _;
+
+})));
+//# sourceMappingURL=underscore-umd.js.map
diff --git a/_static/underscore.js b/_static/underscore.js
new file mode 100644
index 00000000000..cf177d4285a
--- /dev/null
+++ b/_static/underscore.js
@@ -0,0 +1,6 @@
+!function(n,r){"object"==typeof exports&&"undefined"!=typeof module?module.exports=r():"function"==typeof define&&define.amd?define("underscore",r):(n="undefined"!=typeof globalThis?globalThis:n||self,function(){var t=n._,e=n._=r();e.noConflict=function(){return n._=t,e}}())}(this,(function(){
+// Underscore.js 1.13.1
+// https://underscorejs.org
+// (c) 2009-2021 Jeremy Ashkenas, Julian Gonggrijp, and DocumentCloud and Investigative Reporters & Editors
+// Underscore may be freely distributed under the MIT license.
+var n="1.13.1",r="object"==typeof self&&self.self===self&&self||"object"==typeof global&&global.global===global&&global||Function("return this")()||{},t=Array.prototype,e=Object.prototype,u="undefined"!=typeof Symbol?Symbol.prototype:null,o=t.push,i=t.slice,a=e.toString,f=e.hasOwnProperty,c="undefined"!=typeof ArrayBuffer,l="undefined"!=typeof DataView,s=Array.isArray,p=Object.keys,v=Object.create,h=c&&ArrayBuffer.isView,y=isNaN,d=isFinite,g=!{toString:null}.propertyIsEnumerable("toString"),b=["valueOf","isPrototypeOf","toString","propertyIsEnumerable","hasOwnProperty","toLocaleString"],m=Math.pow(2,53)-1;function j(n,r){return r=null==r?n.length-1:+r,function(){for(var t=Math.max(arguments.length-r,0),e=Array(t),u=0;u<t;u++)e[u]=arguments[u+r];switch(r){case 0:return n.call(this,e);case 1:return n.call(this,arguments[0],e);case 2:return n.call(this,arguments[0],arguments[1],e)}var o=Array(r+1);for(u=0;u<r;u++)o[u]=arguments[u];return o[r]=e,n.apply(this,o)}}function _(n){var r=typeof 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diff --git a/appveyor.yml b/appveyor.yml
deleted file mode 100644
index 05ad8a2820c..00000000000
--- a/appveyor.yml
+++ /dev/null
@@ -1,50 +0,0 @@
-os: Visual Studio 2022
-
-environment:
- global:
- # SDK v7.0 MSVC Express 2008's SetEnv.cmd script will fail if the
- # /E:ON and /V:ON options are not enabled in the batch script intepreter
- # See: https://stackoverflow.com/a/13751649/163740
- CMD_IN_ENV: "cmd /E:ON /V:ON /C .\\appveyor\\run_with_env.cmd"
-
- matrix:
- - PYTHON_DIR: C:\Python310-x64
-
-branches:
- only:
- - master
-
-init:
- - "ECHO %PYTHON_DIR%"
-
-install:
- # If there is a newer build queued for the same PR, cancel this one.
- # The AppVeyor 'rollout builds' option is supposed to serve the same
- # purpose but it is problematic because it tends to cancel builds pushed
- # directly to master instead of just PR builds (or the converse).
- # credits: JuliaLang developers.
- - ps: if ($env:APPVEYOR_PULL_REQUEST_NUMBER -and $env:APPVEYOR_BUILD_NUMBER -ne ((Invoke-RestMethod `
- https://ci.appveyor.com/api/projects/$env:APPVEYOR_ACCOUNT_NAME/$env:APPVEYOR_PROJECT_SLUG/history?recordsNumber=50).builds | `
- Where-Object pullRequestId -eq $env:APPVEYOR_PULL_REQUEST_NUMBER)[0].buildNumber) { `
- throw "There are newer queued builds for this pull request, failing early." }
- - ECHO "Filesystem root:"
- - ps: "ls \"C:/\""
-
- # Prepend newly installed Python to the PATH of this build (this cannot be
- # done from inside the powershell script as it would require to restart
- # the parent CMD process).
- - SET PATH=%PYTHON_DIR%;%PYTHON_DIR%\\Scripts;%PATH%
- - SET PATH=%PYTHON%;%PYTHON%\Scripts;%PYTHON%\Library\bin;%PATH%
- - SET PATH=%PATH%;C:\Program Files (x86)\Microsoft Visual Studio 14.0\VC\bin
- - "python -m pip install --upgrade pip"
- - "python -m pip install -r requirements/requirements.txt"
- - "python -m pip install pytest-xdist"
-
- # Check that we have the expected version and architecture for Python
- - "python --version"
- - "python -c \"import struct; print(struct.calcsize('P') * 8)\""
-
-build: off
-
-test_script:
- - "pytest tests -n auto -Werror --durations=0"
diff --git a/docs/Makefile b/docs/Makefile
deleted file mode 100644
index ae495eb36d2..00000000000
--- a/docs/Makefile
+++ /dev/null
@@ -1,21 +0,0 @@
-# Minimal makefile for Sphinx documentation
-#
-
-# You can set these variables from the command line.
-# SPHINXOPTS with -W means turn warnings into errors to fail the build when warnings are present.
-SPHINXOPTS = -W
-SPHINXBUILD = sphinx-build
-SPHINXPROJ = PythonRobotics
-SOURCEDIR = .
-BUILDDIR = _build
-
-# Put it first so that "make" without argument is like "make help".
-help:
- @$(SPHINXBUILD) -M help "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
-
-.PHONY: help Makefile
-
-# Catch-all target: route all unknown targets to Sphinx using the new
-# "make mode" option. $(O) is meant as a shortcut for $(SPHINXOPTS).
-%: Makefile
- @$(SPHINXBUILD) -M $@ "$(SOURCEDIR)" "$(BUILDDIR)" $(SPHINXOPTS) $(O)
\ No newline at end of file
diff --git a/docs/README.md b/docs/README.md
deleted file mode 100644
index fb7d4cc3bc7..00000000000
--- a/docs/README.md
+++ /dev/null
@@ -1,29 +0,0 @@
-## Python Robotics Documentation
-
-This folder contains documentation for the Python Robotics project.
-
-
-### Build the Documentation
-
-#### Install Sphinx and Theme
-
-```
-pip install sphinx sphinx-autobuild sphinx-rtd-theme sphinx_rtd_dark_mode sphinx_copybutton sphinx_rtd_dark_mode
-```
-
-#### Building the Docs
-
-In the `docs/` folder:
-```
-make html
-```
-
-if you want to building each time a file is changed:
-
-```
-sphinx-autobuild . _build/html
-```
-
-#### Check the generated doc
-
-Open the index.html file under docs/_build/
diff --git a/docs/_static/.gitkeep b/docs/_static/.gitkeep
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/docs/_templates/layout.html b/docs/_templates/layout.html
deleted file mode 100644
index 4b5b2789323..00000000000
--- a/docs/_templates/layout.html
+++ /dev/null
@@ -1,17 +0,0 @@
-{% extends "!layout.html" %}
-
-{% block sidebartitle %}
-{{ super() }}
-<script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-9612347954373886"
- crossorigin="anonymous"></script>
-<!-- PythonRoboticsDoc -->
-<ins class="adsbygoogle"
- style="display:block"
- data-ad-client="ca-pub-9612347954373886"
- data-ad-slot="1579532132"
- data-ad-format="auto"
- data-full-width-responsive="true"></ins>
-<script>
- (adsbygoogle = window.adsbygoogle || []).push({});
-</script>
-{% endblock %}
diff --git a/docs/conf.py b/docs/conf.py
deleted file mode 100644
index eeabab11b1c..00000000000
--- a/docs/conf.py
+++ /dev/null
@@ -1,230 +0,0 @@
-#
-# Configuration file for the Sphinx documentation builder.
-#
-# This file does only contain a selection of the most common options. For a
-# full list see the documentation:
-# https://www.sphinx-doc.org/en/master/config
-
-# -- Path setup --------------------------------------------------------------
-
-# If extensions (or modules to document with autodoc) are in another directory,
-# add these directories to sys.path here. If the directory is relative to the
-# documentation root, use os.path.abspath to make it absolute, like shown here.
-#
-import os
-import sys
-from pathlib import Path
-
-sys.path.insert(0, os.path.abspath('../'))
-
-
-# -- Project information -----------------------------------------------------
-
-project = 'PythonRobotics'
-copyright = '2018-now, Atsushi Sakai'
-author = 'Atsushi Sakai'
-
-# The short X.Y version
-version = ''
-# The full version, including alpha/beta/rc tags
-release = ''
-
-
-# -- General configuration ---------------------------------------------------
-
-# If your documentation needs a minimal Sphinx version, state it here.
-#
-# needs_sphinx = '1.0'
-
-# Add any Sphinx extension module names here, as strings. They can be
-# extensions coming with Sphinx (named 'sphinx.ext.*') or your custom
-# ones.
-extensions = [
- 'matplotlib.sphinxext.plot_directive',
- 'sphinx.ext.autodoc',
- 'sphinx.ext.mathjax',
- 'sphinx.ext.linkcode',
- 'sphinx.ext.napoleon',
- 'sphinx.ext.imgconverter',
- 'IPython.sphinxext.ipython_console_highlighting',
- 'sphinx_copybutton',
- 'sphinx_rtd_dark_mode',
-]
-
-# Add any paths that contain templates here, relative to this directory.
-templates_path = ['_templates']
-
-# The suffix(es) of source filenames.
-# You can specify multiple suffix as a list of string:
-#
-# source_suffix = ['.rst', '.md']
-source_suffix = '_main.rst'
-
-# The master toctree document.
-master_doc = 'index'
-
-# The language for content autogenerated by Sphinx. Refer to documentation
-# for a list of supported languages.
-#
-# This is also used if you do content translation via gettext catalogs.
-# Usually you set "language" from the command line for these cases.
-language = "en"
-
-# List of patterns, relative to source directory, that match files and
-# directories to ignore when looking for source files.
-# This pattern also affects html_static_path and html_extra_path .
-exclude_patterns = ['_build', 'Thumbs.db', '.DS_Store']
-
-# The name of the Pygments (syntax highlighting) style to use.
-pygments_style = 'sphinx'
-
-
-# -- Options for HTML output -------------------------------------------------
-
-# The theme to use for HTML and HTML Help pages. See the documentation for
-# a list of builtin themes.
-#
-# Fix for read the docs
-on_rtd = os.environ.get('READTHEDOCS') == 'True'
-if on_rtd:
- html_theme = 'default'
-else:
- html_theme = 'sphinx_rtd_light_them'
-
-# Theme options are theme-specific and customize the look and feel of a theme
-# further. For a list of options available for each theme, see the
-# documentation.
-#
-html_logo = '../icon.png'
-html_theme_options = {
- 'display_version': False,
-}
-
-# replace "view page source" with "edit on github" in Read The Docs theme
-# * https://github.com/readthedocs/sphinx_rtd_theme/issues/529
-html_context = {
- 'display_github': True,
- 'github_user': 'AtsushiSakai',
- 'github_repo': 'PythonRobotics',
- 'github_version': 'master',
- "conf_py_path": "/docs/",
- "source_suffix": source_suffix,
-}
-
-# Add any paths that contain custom static files (such as style sheets) here,
-# relative to this directory. They are copied after the builtin static files,
-# so a file named "default.css" will overwrite the builtin "default.css".
-html_static_path = ['_static']
-
-html_css_files = ['custom.css']
-
-# Custom sidebar templates, must be a dictionary that maps document names
-# to template names.
-#
-# The default sidebars (for documents that don't match any pattern) are
-# defined by theme itself. Builtin themes are using these templates by
-# default: ``['localtoc.html', 'relations.html', 'sourcelink.html',
-# 'searchbox.html']``.
-#
-# html_sidebars = {}
-
-
-# -- Options for HTMLHelp output ---------------------------------------------
-
-# Output file base name for HTML help builder.
-htmlhelp_basename = 'PythonRoboticsdoc'
-
-
-# -- Options for LaTeX output ------------------------------------------------
-
-latex_elements = {
- # The paper size ('letterpaper' or 'a4paper').
- #
- # 'papersize': 'letterpaper',
-
- # The font size ('10pt', '11pt' or '12pt').
- #
- # 'pointsize': '10pt',
-
- # Additional stuff for the LaTeX preamble.
- #
- # 'preamble': '',
-
- # Latex figure (float) alignment
- #
- # 'figure_align': 'htbp',
-}
-
-# Grouping the document tree into LaTeX files. List of tuples
-# (source start file, target name, title,
-# author, documentclass [howto, manual, or own class]).
-latex_documents = [
- (master_doc, 'PythonRobotics.tex', 'PythonRobotics Documentation',
- 'Atsushi Sakai', 'manual'),
-]
-
-
-# -- Options for manual page output ------------------------------------------
-
-# One entry per manual page. List of tuples
-# (source start file, name, description, authors, manual section).
-man_pages = [
- (master_doc, 'pythonrobotics', 'PythonRobotics Documentation',
- [author], 1)
-]
-
-
-# -- Options for Texinfo output ----------------------------------------------
-
-# Grouping the document tree into Texinfo files. List of tuples
-# (source start file, target name, title, author,
-# dir menu entry, description, category)
-texinfo_documents = [
- (master_doc, 'PythonRobotics', 'PythonRobotics Documentation',
- author, 'PythonRobotics', 'One line description of project.',
- 'Miscellaneous'),
-]
-
-
-# -- linkcode setting -------------------------------------------------
-
-import inspect
-import os
-import sys
-import functools
-
-GITHUB_REPO = "https://github.com/AtsushiSakai/PythonRobotics"
-GITHUB_BRANCH = "master"
-
-
-def linkcode_resolve(domain, info):
- if domain != "py":
- return None
-
- modname = info["module"]
- fullname = info["fullname"]
-
- try:
- module = __import__(modname, fromlist=[fullname])
- obj = functools.reduce(getattr, fullname.split("."), module)
- except (ImportError, AttributeError):
- return None
-
- try:
- srcfile = inspect.getsourcefile(obj)
- srcfile = get_relative_path_from_parent(srcfile, "PythonRobotics")
- lineno = inspect.getsourcelines(obj)[1]
- except Exception:
- return None
-
- return f"{GITHUB_REPO}/blob/{GITHUB_BRANCH}/{srcfile}#L{lineno}"
-
-
-def get_relative_path_from_parent(file_path: str, parent_dir: str):
- path = Path(file_path).resolve()
-
- try:
- parent_path = next(p for p in path.parents if p.name == parent_dir)
- return str(path.relative_to(parent_path))
- except StopIteration:
- raise ValueError(f"Parent directory '{parent_dir}' not found in {file_path}")
diff --git a/docs/doc_requirements.txt b/docs/doc_requirements.txt
deleted file mode 100644
index b29f4ba2891..00000000000
--- a/docs/doc_requirements.txt
+++ /dev/null
@@ -1,6 +0,0 @@
-sphinx == 7.2.6 # For sphinx documentation
-sphinx_rtd_theme == 2.0.0
-IPython == 8.20.0 # For sphinx documentation
-sphinxcontrib-napoleon == 0.7 # For auto doc
-sphinx-copybutton
-sphinx-rtd-dark-mode
diff --git a/docs/index_main.rst b/docs/index_main.rst
deleted file mode 100644
index 65634f32e81..00000000000
--- a/docs/index_main.rst
+++ /dev/null
@@ -1,57 +0,0 @@
-.. PythonRobotics documentation master file, created by
- sphinx-quickstart on Sat Sep 15 13:15:55 2018.
- You can adapt this file completely to your liking, but it should at least
- contain the root `toctree` directive.
-
-Welcome to PythonRobotics's documentation!
-==========================================
-
-"PythonRobotics" is a Python code collections and textbook
-(This document) for robotics algorithm, which is developed on `GitHub`_.
-
-See this section (:ref:`What is PythonRobotics?`) for more details of this project.
-
-This project is `the one of the most popular open-source software (OSS) in
-the field of robotics on GitHub`_.
-This is `user comments about this project`_, and
-this graph shows GitHub star history of this project:
-
-.. image:: https://api.star-history.com/svg?repos=AtsushiSakai/PythonRobotics&type=Date
- :alt: Star History
- :width: 80%
- :align: center
-
-
-.. _GitHub: https://github.com/AtsushiSakai/PythonRobotics
-.. _`user comments about this project`: https://github.com/AtsushiSakai/PythonRobotics/blob/master/users_comments.md
-.. _`MIT license`: https://github.com/AtsushiSakai/PythonRobotics/blob/master/LICENSE
-.. _`the one of the most popular open-source software (OSS) in the field of robotics on GitHub`: https://github.com/topics/robotics
-
-----------------------------------
-
-.. toctree::
- :maxdepth: 2
- :caption: Table of Contents
-
- modules/0_getting_started/0_getting_started
- modules/1_introduction/introduction
- modules/2_localization/localization
- modules/3_mapping/mapping
- modules/4_slam/slam
- modules/5_path_planning/path_planning
- modules/6_path_tracking/path_tracking
- modules/7_arm_navigation/arm_navigation
- modules/8_aerial_navigation/aerial_navigation
- modules/9_bipedal/bipedal
- modules/10_inverted_pendulum/inverted_pendulum
- modules/13_mission_planning/mission_planning
- modules/11_utils/utils
- modules/12_appendix/appendix
-
-
-Indices and tables
-==================
-
-* :ref:`genindex`
-* :ref:`modindex`
-* :ref:`search`
diff --git a/docs/make.bat b/docs/make.bat
deleted file mode 100644
index 07dcebea417..00000000000
--- a/docs/make.bat
+++ /dev/null
@@ -1,36 +0,0 @@
-@ECHO OFF
-
-pushd %~dp0
-
-REM Command file for Sphinx documentation
-
-if "%SPHINXBUILD%" == "" (
- set SPHINXBUILD=sphinx-build
-)
-set SOURCEDIR=.
-set BUILDDIR=_build
-set SPHINXPROJ=PythonRobotics
-
-if "%1" == "" goto help
-
-%SPHINXBUILD% >NUL 2>NUL
-if errorlevel 9009 (
- echo.
- echo.The 'sphinx-build' command was not found. Make sure you have Sphinx
- echo.installed, then set the SPHINXBUILD environment variable to point
- echo.to the full path of the 'sphinx-build' executable. Alternatively you
- echo.may add the Sphinx directory to PATH.
- echo.
- echo.If you don't have Sphinx installed, grab it from
- echo.https://sphinx-doc.org/
- exit /b 1
-)
-
-%SPHINXBUILD% -M %1 %SOURCEDIR% %BUILDDIR% %SPHINXOPTS%
-goto end
-
-:help
-%SPHINXBUILD% -M help %SOURCEDIR% %BUILDDIR% %SPHINXOPTS%
-
-:end
-popd
diff --git a/docs/modules/0_getting_started/0_getting_started_main.rst b/docs/modules/0_getting_started/0_getting_started_main.rst
deleted file mode 100644
index cb2cba47841..00000000000
--- a/docs/modules/0_getting_started/0_getting_started_main.rst
+++ /dev/null
@@ -1,13 +0,0 @@
-.. _`getting started`:
-
-Getting Started
-===============
-
-.. toctree::
- :maxdepth: 2
- :caption: Contents
-
- 1_what_is_python_robotics
- 2_how_to_run_sample_codes
- 3_how_to_contribute
- 4_how_to_read_textbook
diff --git a/docs/modules/0_getting_started/1_what_is_python_robotics_main.rst b/docs/modules/0_getting_started/1_what_is_python_robotics_main.rst
deleted file mode 100644
index 2a7bd574f0b..00000000000
--- a/docs/modules/0_getting_started/1_what_is_python_robotics_main.rst
+++ /dev/null
@@ -1,130 +0,0 @@
-.. _`What is PythonRobotics?`:
-
-What is PythonRobotics?
-------------------------
-
-This is an Open Source Software (OSS) project: PythonRobotics, which is a Python code collection of robotics algorithms.
-These codes are developed under `MIT license`_ and on `GitHub`_.
-
-.. _GitHub: https://github.com/AtsushiSakai/PythonRobotics
-.. _`MIT license`: https://github.com/AtsushiSakai/PythonRobotics/blob/master/LICENSE
-
-This project has three main philosophies below:
-
-Philosophy 1. Easy to understand each algorithm's basic idea.
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-The goal is for beginners in robotics to understand the basic ideas behind each algorithm.
-
-`Python`_ programming language is adopted in this project to achieve the goal.
-Python is a high-level programming language that is easy to read and write.
-If the code is not easy to read, it would be difficult to achieve our goal of
-allowing beginners to understand the algorithms.
-Python has great libraries for matrix operation, mathematical and scientific operation,
-and visualization, which makes code more readable because such operations
-don’t need to be re-implemented.
-Having the core Python packages allows the user to focus on the algorithms,
-rather than the implementations.
-
-PythonRobotics provides not only the code but also intuitive animations that
-visually demonstrate the process and behavior of each algorithm over time.
-This is an example of an animation gif file that shows the process of the
-path planning in a highway scenario for autonomous vehicle.
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/FrenetOptimalTrajectory/high_speed_and_velocity_keeping_frenet_path.gif
-
-This animation is a gif file and is created using the `Matplotlib`_ library.
-All animation gif files are stored in the `PythonRoboticsGifs`_ repository and
-all animation movies are also uploaded to this `YouTube channel`_.
-
-PythonRobotics also provides a textbook that explains the basic ideas of each algorithm.
-The PythonRobotics textbook allows you to learn fundamental algorithms used in
-robotics with minimal mathematical formulas and textual explanations,
-based on PythonRobotics’ sample codes and animations.
-The contents of this document, like the code, are managed in the PythonRobotics
-`GitHub`_ repository and converted into HTML-based online documents using `Sphinx`_,
-which is a Python-based documentation builder.
-Please refer to this section ":ref:`How to read this textbook`" for information on
-how to read this document for learning.
-
-
-.. _`Python`: https://www.python.org/
-.. _`PythonRoboticsGifs`: https://github.com/AtsushiSakai/PythonRoboticsGifs
-.. _`YouTube channel`: https://youtube.com/playlist?list=PL12URV8HFpCozuz0SDxke6b2ae5UZvIwa&si=AH2fNPPYufPtK20S
-
-
-Philosophy 2. Widely used and practical algorithms are selected.
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-The second philosophy is that implemented algorithms have to be practical
-and widely used in both academia and industry.
-We believe learning these algorithms will be useful in many applications.
-For example, Kalman filters and particle filter for localization,
-grid mapping for mapping,
-dynamic programming based approaches and sampling based approaches for path planning,
-and optimal control based approach for path tracking.
-These algorithms are implemented and explained in the textbook in this project.
-
-Philosophy 3. Minimum dependency.
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-Each sample code of PythonRobotics is written in Python3 and only depends on
-some standard modules for readability and ease to setup and use.
-
-
-.. _`Requirements`:
-
-Requirements
-============
-
-PythonRobotics depends only on the following five libraries,
-including Python itself, to run each sample code.
-
-- `Python 3.12.x`_ (for Python runtime)
-- `NumPy`_ (for matrix operation)
-- `SciPy`_ (for scientific operation)
-- `cvxpy`_ (for convex optimization)
-- `Matplotlib`_ (for visualization)
-
-If you only need to run the code, the five libraries mentioned above are sufficient.
-However, for code development or creating documentation for the textbook,
-the following additional libraries are required.
-
-- `pytest`_ (for unit tests)
-- `pytest-xdist`_ (for parallel unit tests)
-- `mypy`_ (for type check)
-- `Sphinx`_ (for document generation)
-- `ruff`_ (for code style check)
-
-.. _`Python 3.12.x`: https://www.python.org/
-.. _`NumPy`: https://numpy.org/
-.. _`SciPy`: https://scipy.org/
-.. _`Matplotlib`: https://matplotlib.org/
-.. _`cvxpy`: https://www.cvxpy.org/
-.. _`pytest`: https://docs.pytest.org/en/latest/
-.. _`pytest-xdist`: https://github.com/pytest-dev/pytest-xdist
-.. _`mypy`: https://mypy-lang.org/
-.. _`Sphinx`: https://www.sphinx-doc.org/en/master/index.html
-.. _`ruff`: https://github.com/astral-sh/ruff
-
-For instructions on installing the above libraries, please refer to
-this section ":ref:`How to run sample codes`".
-
-Audio overview of this project
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-For an audio overview of this project, please refer to this `YouTube video`_.
-
-.. _`YouTube video`: https://www.youtube.com/watch?v=uMeRnNoJAfU
-
-Arxiv paper
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-We have published a paper on this project on Arxiv in 2018.
-
-See this paper for more details about this Project:
-
-- `PythonRobotics: a Python code collection of robotics algorithms`_ (`BibTeX`_)
-
-.. _`PythonRobotics: a Python code collection of robotics algorithms`: https://arxiv.org/abs/1808.10703
-.. _`BibTeX`: https://github.com/AtsushiSakai/PythonRoboticsPaper/blob/master/python_robotics.bib
-
diff --git a/docs/modules/0_getting_started/2_how_to_run_sample_codes_main.rst b/docs/modules/0_getting_started/2_how_to_run_sample_codes_main.rst
deleted file mode 100644
index b92fc9bde0f..00000000000
--- a/docs/modules/0_getting_started/2_how_to_run_sample_codes_main.rst
+++ /dev/null
@@ -1,118 +0,0 @@
-.. _`How to run sample codes`:
-
-How to run sample codes
--------------------------
-
-In this chapter, we will explain the setup process for running each sample code
-in PythonRobotics and describe the contents of each directory.
-
-Steps to setup and run sample codes
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-1. Install `Python 3.12.x`_
-
-Note that older versions of Python3 might work, but we recommend using
-the specified version, because the sample codes are only tested with it.
-
-2. If you prefer to use conda for package management, install
-Anaconda or Miniconda to use `conda`_ command.
-
-3. Clone this repo and go into dir.
-
-.. code-block::
-
- >$ git clone https://github.com/AtsushiSakai/PythonRobotics.git
-
- >$ cd PythonRobotics
-
-
-4. Install the required libraries.
-
-We have prepared requirements management files for `conda`_ and `pip`_ under
-the requirements directory. Using these files makes it easy to install the necessary libraries.
-
-using conda :
-
-.. code-block::
-
- >$ conda env create -f requirements/environment.yml
-
-using pip :
-
-.. code-block::
-
- >$ pip install -r requirements/requirements.txt
-
-
-5. Execute python script in each directory.
-
-For example, to run the sample code of `Extented Kalman Filter` in the
-`localization` directory, execute the following command:
-
-.. code-block::
-
- >$ cd localization/extended_kalman_filter
-
- >$ python extended_kalman_filter.py
-
-Then, you can see this animation of the EKF algorithm based localization:
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/extended_kalman_filter/animation.gif
-
-Please refer to the `Directory structure`_ section for more details on the contents of each directory.
-
-6. Add star to this repo if you like it 😃.
-
-.. _`Python 3.12.x`: https://www.python.org/
-.. _`conda`: https://docs.conda.io/projects/conda/en/stable/user-guide/install/index.html
-.. _`pip`: https://pip.pypa.io/en/stable/
-.. _`the requirements directory`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/requirements
-
-.. _`Directory structure`:
-
-Directory structure
-~~~~~~~~~~~~~~~~~~~~
-
-The top-level directory structure of PythonRobotics is as follows:
-
-Sample codes directories:
-
-- `AerialNavigation`_ : the sample codes of aerial navigation algorithms for drones and rocket landing.
-- `ArmNavigation`_ : the sample codes of arm navigation algorithms for robotic arms.
-- `Localization`_ : the sample codes of localization algorithms.
-- `Bipedal`_ : the sample codes of bipedal walking algorithms for legged robots.
-- `Control`_ : the sample codes of control algorithms for robotic systems.
-- `Mapping`_ : the sample codes of mapping or obstacle shape recognition algorithms.
-- `PathPlanning`_ : the sample codes of path planning algorithms.
-- `PathTracking`_ : the sample codes of path tracking algorithms for car like robots.
-- `SLAM`_ : the sample codes of SLAM algorithms.
-
-Other directories:
-
-- `docs`_ : This directory contains the documentation of PythonRobotics.
-- `requirements`_ : This directory contains the requirements management files.
-- `tests`_ : This directory contains the unit test files.
-- `utils`_ : This directory contains utility functions used in some sample codes in common.
-- `.github`_ : This directory contains the GitHub Actions configuration files.
-- `.circleci`_ : This directory contains the CircleCI configuration files.
-
-The structure of this document is the same as that of the sample code
-directories mentioned above.
-For more details, please refer to the :ref:`How to read this textbook` section.
-
-
-.. _`AerialNavigation`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/AerialNavigation
-.. _`ArmNavigation`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/ArmNavigation
-.. _`Localization`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/Localization
-.. _`Bipedal`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/Bipedal
-.. _`Control`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/Control
-.. _`Mapping`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/Mapping
-.. _`PathPlanning`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/PathPlanning
-.. _`PathTracking`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/PathTracking
-.. _`SLAM`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/SLAM
-.. _`docs`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/docs
-.. _`requirements`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/requirements
-.. _`tests`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/tests
-.. _`utils`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/utils
-.. _`.github`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/.github
-.. _`.circleci`: https://github.com/AtsushiSakai/PythonRobotics/tree/master/.circleci
diff --git a/docs/modules/0_getting_started/4_how_to_read_textbook_main.rst b/docs/modules/0_getting_started/4_how_to_read_textbook_main.rst
deleted file mode 100644
index 1625c838afa..00000000000
--- a/docs/modules/0_getting_started/4_how_to_read_textbook_main.rst
+++ /dev/null
@@ -1,14 +0,0 @@
-.. _`How to read this textbook`:
-
-How to read this textbook
---------------------------
-
-This document is structured to help you learn the fundamental concepts
-behind each sample code in PythonRobotics.
-
-If you already have some knowledge of robotics technologies, you can start
-by reading any document that interests you.
-
-However, if you have no prior knowledge of robotics technologies, it is
-recommended that you first read the :ref:`Introduction` section and then proceed
-to the documents related to the technical fields that interest you.
\ No newline at end of file
diff --git a/docs/modules/12_appendix/external_sensors_main.rst b/docs/modules/12_appendix/external_sensors_main.rst
deleted file mode 100644
index 3597418150c..00000000000
--- a/docs/modules/12_appendix/external_sensors_main.rst
+++ /dev/null
@@ -1,62 +0,0 @@
-.. _`External Sensors for Robots`:
-
-External Sensors for Robots
-============================
-
-This project, `PythonRobotics`, focuses on algorithms, so hardware is not included.
-However, having basic knowledge of hardware in robotics is also important for understanding algorithms.
-Therefore, we will provide an overview.
-
-Introduction
-------------
-
-In recent years, the application of robotic technology has advanced,
-particularly in areas such as autonomous vehicles and disaster response robots.
-A crucial element in these technologies is external recognition—the robot's ability to understand its surrounding environment, identify safe zones, and detect moving objects using onboard sensors. Achieving effective external recognition involves various techniques, but equally important is the selection of appropriate sensors. Robots, like the sensors they employ, come in many forms, but external recognition sensors can be broadly categorized into three types. Developing an advanced external recognition system requires a thorough understanding of each sensor's principles and characteristics to determine their optimal application. This article summarizes the principles and features of these sensors for personal study purposes.
-
-Laser Sensors
--------------
-
-Laser sensors measure distances by utilizing light, commonly referred to as Light Detection and Ranging (LIDAR). They operate by emitting light towards an object and calculating the distance based on the time it takes for the reflected light to return, using the speed of light as a constant.
-
-Radar Sensors
--------------
-
-TBD
-
-
-Monocular Cameras
------------------
-
-Monocular cameras utilize a single camera to recognize the external environment. Compared to other sensors, they can detect color and brightness information, making them primarily useful for object recognition. However, they face challenges in independently measuring distances to surrounding objects and may struggle in low-light or dark conditions.
-
-Requirements for Cameras and Image Processing in Robotics
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-While camera sensors are widely used in applications like surveillance, deploying them in robotics necessitates meeting specific requirements:
-
-1. High dynamic range to adapt to various lighting conditions
-2. Wide measurement range
-3. Capability for three-dimensional measurement through techniques like motion stereo
-4. Real-time processing with high frame rates
-5. Cost-effectiveness
-
-Stereo Cameras
---------------
-
-Stereo cameras employ multiple cameras to measure distances to surrounding objects. By knowing the positions and orientations of each camera and analyzing the disparity in the images (parallax), the distance to a specific point (the object represented by a particular pixel) can be calculated.
-
-Characteristics of Stereo Cameras
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-Advantages of stereo cameras include the ability to obtain high-precision and high-density distance information at close range, depending on factors like camera resolution and the distance between cameras (baseline). This makes them suitable for indoor robots that require precise shape recognition of nearby objects. Additionally, stereo cameras are relatively cost-effective compared to other sensors, leading to their use in consumer products like Subaru's EyeSight system. However, stereo cameras are less effective for long-distance measurements due to a decrease in accuracy proportional to the square of the distance. They are also susceptible to environmental factors such as lighting conditions.
-
-Ultrasonic Sensors
-------------------
-
-Ultrasonic sensors are commonly used in indoor robots and some automotive autonomous driving systems. Their features include affordability compared to laser or radar sensors, the ability to detect very close objects, and the capability to sense materials like glass, which may be challenging for lasers or cameras. However, they have limitations such as shorter maximum measurement distances and lower resolution and accuracy.
-
-References
-----------
-
-TBD
diff --git a/docs/modules/12_appendix/internal_sensors_main.rst b/docs/modules/12_appendix/internal_sensors_main.rst
deleted file mode 100644
index 18f209098ea..00000000000
--- a/docs/modules/12_appendix/internal_sensors_main.rst
+++ /dev/null
@@ -1,34 +0,0 @@
-.. _`Internal Sensors for Robots`:
-
-Internal Sensors for Robots
-============================
-
-This project, `PythonRobotics`, focuses on algorithms, so hardware is not included.
-However, having basic knowledge of hardware in robotics is also important for understanding algorithms.
-Therefore, we will provide an overview.
-
-Introduction
-------------
-
-Global Navigation Satellite System (GNSS)
--------------------------------------------
-
-Gyroscope
-----------
-
-Accelerometer
---------------
-
-Magnetometer
---------------
-
-Inertial Measurement Unit (IMU)
---------------------------------
-
-Pressure Sensor
------------------
-
-Temperature Sensor
---------------------
-
-
diff --git a/docs/modules/12_appendix/steering_motion_model/steering_model.png b/docs/modules/12_appendix/steering_motion_model/steering_model.png
deleted file mode 100644
index c66dded87af..00000000000
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diff --git a/docs/modules/12_appendix/steering_motion_model/turning_radius_calc1.png b/docs/modules/12_appendix/steering_motion_model/turning_radius_calc1.png
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diff --git a/docs/modules/12_appendix/steering_motion_model/turning_radius_calc2.png b/docs/modules/12_appendix/steering_motion_model/turning_radius_calc2.png
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diff --git a/docs/modules/12_appendix/steering_motion_model_main.rst b/docs/modules/12_appendix/steering_motion_model_main.rst
deleted file mode 100644
index 6e444b7909b..00000000000
--- a/docs/modules/12_appendix/steering_motion_model_main.rst
+++ /dev/null
@@ -1,97 +0,0 @@
-
-Steering Motion Model
------------------------
-
-Turning radius calculation by steering motion model
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-The turning Radius represents the radius of the circle when the robot turns, as shown in the diagram below.
-
-.. image:: steering_motion_model/steering_model.png
-
-When the steering angle is tilted by :math:`\delta`,
-the turning radius :math:`R` can be calculated using the following equation,
-based on the geometric relationship between the wheelbase (WB),
-which is the distance between the rear wheel center and the front wheel center,
-and the assumption that the turning radius circle passes through the center of
-the rear wheels in the diagram above.
-
-:math:`R = \frac{WB}{tan\delta}`
-
-The curvature :math:`\kappa` is the reciprocal of the turning radius:
-
-:math:`\kappa = \frac{tan\delta}{WB}`
-
-In the diagram above, the angular difference :math:`\Delta \theta` in the vehicle’s heading between two points on the turning radius :math:`R`
-is the same as the angle of the vector connecting the two points from the center of the turn.
-
-From the formula for the length of an arc and the radius,
-
-:math:`\Delta \theta = \frac{s}{R}`
-
-Here, :math:`s` is the distance between two points on the turning radius.
-
-So, yaw rate :math:`\omega` can be calculated as follows.
-
-:math:`\omega = \frac{v}{R}`
-
-and
-
-:math:`\omega = v\kappa`
-
-here, :math:`v` is the velocity of the vehicle.
-
-
-Turning radius calculation by 2 consecutive positions of the robot trajectory
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-In this section, we will derive the formula for the turning radius from 2 consecutive positions of the robot trajectory.
-
-.. image:: steering_motion_model/turning_radius_calc1.png
-
-As shown in the upper diagram above, the robot moves from a point at time :math:`t` to a point at time :math:`t+1`.
-Each point is represented by a 2D position :math:`(x_t, y_t)` and an orientation :math:`\theta_t`.
-
-The distance between the two points is :math:`d = \sqrt{(x_{t+1} - x_t)^2 + (y_{t+1} - y_t)^2}`.
-
-The angle between the two vectors from the turning center to the two points is :math:`\theta = \theta_{t+1} - \theta_t`.
-Here, by drawing a perpendicular line from the center of the turning radius
-to a straight line of length :math:`d` connecting two points,
-the following equation can be derived from the resulting right triangle.
-
-:math:`sin\frac{\theta}{2} = \frac{d}{2R}`
-
-So, the turning radius :math:`R` can be calculated as follows.
-
-:math:`R = \frac{d}{2sin\frac{\theta}{2}}`
-
-The curvature :math:`\kappa` is the reciprocal of the turning radius.
-So, the curvature can be calculated as follows.
-
-:math:`\kappa = \frac{2sin\frac{\theta}{2}}{d}`
-
-Target speed by maximum steering speed
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-If the maximum steering speed is given as :math:`\dot{\delta}_{max}`,
-the maximum curvature change rate :math:`\dot{\kappa}_{max}` can be calculated as follows:
-
-:math:`\dot{\kappa}_{max} = \frac{tan\dot{\delta}_{max}}{WB}`
-
-From the curvature calculation by 2 consecutive positions of the robot trajectory,
-
-the maximum curvature change rate :math:`\dot{\kappa}_{max}` can be calculated as follows:
-
-:math:`\dot{\kappa}_{max} = \frac{\kappa_{t+1}-\kappa_{t}}{\Delta t}`
-
-If we can assume that the vehicle will not exceed the maximum curvature change rate,
-
-the target minimum velocity :math:`v_{min}` can be calculated as follows:
-
-:math:`v_{min} = \frac{d_{t+1}+d_{t}}{\Delta t} = \frac{d_{t+1}+d_{t}}{(\kappa_{t+1}-\kappa_{t})}\frac{tan\dot{\delta}_{max}}{WB}`
-
-
-References:
-~~~~~~~~~~~
-
-- `Vehicle Dynamics and Control <https://link.springer.com/book/10.1007/978-1-4614-1433-9>`_
diff --git a/docs/modules/13_mission_planning/behavior_tree/behavior_tree_main.rst b/docs/modules/13_mission_planning/behavior_tree/behavior_tree_main.rst
deleted file mode 100644
index ae3e16da818..00000000000
--- a/docs/modules/13_mission_planning/behavior_tree/behavior_tree_main.rst
+++ /dev/null
@@ -1,104 +0,0 @@
-Behavior Tree
--------------
-
-Behavior Tree is a modular, hierarchical decision model that is widely used in robot control, and game development.
-It present some similarities to hierarchical state machines with the key difference that the main building block of a behavior is a task rather than a state.
-Behavior Tree have been shown to generalize several other control architectures (https://ieeexplore.ieee.org/document/7790863)
-
-Core Concepts
-~~~~~~~~~~~~~
-
-Control Node
-++++++++++++
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.ControlNode
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.SequenceNode
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.SelectorNode
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.WhileDoElseNode
-
-Action Node
-++++++++++++
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.ActionNode
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.EchoNode
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.SleepNode
-
-Decorator Node
-++++++++++++++
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.DecoratorNode
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.InverterNode
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.TimeoutNode
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.DelayNode
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.ForceSuccessNode
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.ForceFailureNode
-
-Behavior Tree Factory
-+++++++++++++++++++++
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.BehaviorTreeFactory
- :members:
-
-Behavior Tree
-+++++++++++++
-
-.. autoclass:: MissionPlanning.BehaviorTree.behavior_tree.BehaviorTree
- :members:
-
-Example
-~~~~~~~
-
-Visualize the behavior tree by `xml-tree-visual <https://xml-tree-visual.vercel.app/>`_.
-
-.. image:: ./robot_behavior_case.svg
-
-Print the behavior tree
-
-.. code-block:: text
-
- Behavior Tree
- [Robot Main Controller]
- [Battery Management]
- (Low Battery Detection)
- <Check Battery>
- <Low Battery Warning>
- <Charge Battery>
- [Patrol Task]
- <Start Task>
- [Move to Position A]
- <Move to A>
- [Obstacle Handling A]
- [Obstacle Present]
- <Detect Obstacle>
- <Avoid Obstacle>
- <No Obstacle>
- <Position A Task>
- [Move to Position B]
- (Short Wait)
- <Prepare Movement>
- <Move to B>
- (Limited Time Obstacle Handling)
- [Obstacle Present]
- <Detect Obstacle>
- <Avoid Obstacle>
- <Position B Task>
- [Conditional Move to C]
- <Check Sufficient Battery>
- [Perform Position C Task]
- <Move to C>
- (Ensure Completion)
- <Position C Task>
- <Skip Position C>
- <Complete Patrol>
- <Return to Charging Station>
- Behavior Tree
diff --git a/docs/modules/13_mission_planning/behavior_tree/robot_behavior_case.svg b/docs/modules/13_mission_planning/behavior_tree/robot_behavior_case.svg
deleted file mode 100644
index a3d43aed525..00000000000
--- a/docs/modules/13_mission_planning/behavior_tree/robot_behavior_case.svg
+++ /dev/null
@@ -1,22 +0,0 @@
-<svg width="2870" height="795" id="tree-svg" style="overflow: visible;" xmlns="http://www.w3.org/2000/svg" viewBox="-1560 -65 4380 810"><style xmlns="http://www.w3.org/1999/xhtml">
- .node rect {
- fill: #fff;
- stroke-width: 1px;
- }
- .node text {
- font: 12px sans-serif;
- }
- .node-attributes {
- font: 10px sans-serif;
- fill: #666;
- }
- .link {
- fill: none;
- stroke: #999;
- stroke-width: 1px;
- }
- line {
- stroke: #444;
- stroke-width: 2px;
- }
- </style><g transform="translate(75,112) scale(0.8)"><path class="link" d="M0,0C0,60,-1125,60,-1125,120"/><path class="link" d="M0,0C0,60,1125,60,1125,120"/><path class="link" d="M-1125,120C-1125,180,-1395,180,-1395,240"/><path class="link" d="M-1125,120C-1125,180,-1125,180,-1125,240"/><path class="link" d="M-1125,120C-1125,180,-855,180,-855,240"/><path class="link" d="M1125,120C1125,180,-405,180,-405,240"/><path class="link" d="M1125,120C1125,180,-135,180,-135,240"/><path class="link" d="M1125,120C1125,180,990,180,990,240"/><path class="link" d="M1125,120C1125,180,2115,180,2115,240"/><path class="link" d="M1125,120C1125,180,2385,180,2385,240"/><path class="link" d="M1125,120C1125,180,2655,180,2655,240"/><path class="link" d="M-1395,240C-1395,300,-1395,300,-1395,360"/><path class="link" d="M-135,240C-135,300,-405,300,-405,360"/><path class="link" d="M-135,240C-135,300,-135,300,-135,360"/><path class="link" d="M-135,240C-135,300,135,300,135,360"/><path class="link" 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class="link" d="M2250,480C2250,540,2250,540,2250,600"/><g class="node" transform="translate(0,0)"><rect x="-115" y="-15" width="230" height="50" stroke="#4A90E2" style="stroke: rgb(74, 144, 226);"/><text dy="5" text-anchor="middle">Selector</text><line x1="-105" y1="10" x2="105" y2="10" stroke="#444" stroke-width="2"/><text class="node-attributes" dy="25" x="-105" text-anchor="start">name: Robot Main Controller</text><line x1="-105" y1="30" x2="105" y2="30" stroke="#ddd" stroke-width="1"/></g><g class="node" transform="translate(-1125,120)"><rect x="-115" y="-15" width="230" height="50" stroke="#4A90E2" style="stroke: rgb(74, 144, 226);"/><text dy="5" text-anchor="middle">Sequence</text><line x1="-105" y1="10" x2="105" y2="10" stroke="#444" stroke-width="2"/><text class="node-attributes" dy="25" x="-105" text-anchor="start">name: Battery Management</text><line x1="-105" y1="30" x2="105" y2="30" stroke="#ddd" stroke-width="1"/></g><g class="node" transform="translate(1125,120)"><rect 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\ No newline at end of file
diff --git a/docs/modules/13_mission_planning/mission_planning_main.rst b/docs/modules/13_mission_planning/mission_planning_main.rst
deleted file mode 100644
index c35eacd8d5e..00000000000
--- a/docs/modules/13_mission_planning/mission_planning_main.rst
+++ /dev/null
@@ -1,13 +0,0 @@
-.. _`Mission Planning`:
-
-Mission Planning
-================
-
-Mission planning includes tools such as finite state machines and behavior trees used to describe robot behavior and high level task planning.
-
-.. toctree::
- :maxdepth: 2
- :caption: Contents
-
- state_machine/state_machine
- behavior_tree/behavior_tree
diff --git a/docs/modules/13_mission_planning/state_machine/robot_behavior_case.png b/docs/modules/13_mission_planning/state_machine/robot_behavior_case.png
deleted file mode 100644
index fbc1369cbcd..00000000000
Binary files a/docs/modules/13_mission_planning/state_machine/robot_behavior_case.png and /dev/null differ
diff --git a/docs/modules/13_mission_planning/state_machine/state_machine_main.rst b/docs/modules/13_mission_planning/state_machine/state_machine_main.rst
deleted file mode 100644
index abaece1b115..00000000000
--- a/docs/modules/13_mission_planning/state_machine/state_machine_main.rst
+++ /dev/null
@@ -1,74 +0,0 @@
-State Machine
--------------
-
-A state machine is a model used to describe the transitions of an object between different states. It clearly shows how an object changes state based on events and may trigger corresponding actions.
-
-Core Concepts
-~~~~~~~~~~~~~
-
-- **State**: A distinct mode or condition of the system (e.g. "Idle", "Running"). Managed by State class with optional on_enter/on_exit callbacks
-- **Event**: A trigger signal that may cause state transitions (e.g. "start", "stop")
-- **Transition**: A state change path from source to destination state triggered by an event
-- **Action**: An operation executed during transition (before entering new state)
-- **Guard**: A precondition that must be satisfied to allow transition
-
-API
-~~~
-
-.. autoclass:: MissionPlanning.StateMachine.state_machine.StateMachine
- :members: add_transition, process, register_state
- :special-members: __init__
-
-PlantUML Support
-~~~~~~~~~~~~~~~~
-
-The ``generate_plantuml()`` method creates diagrams showing:
-
-- Current state (marked with [*] arrow)
-- All possible transitions
-- Guard conditions in [brackets]
-- Actions prefixed with /
-
-Example
-~~~~~~~
-
-state machine diagram:
-+++++++++++++++++++++++
-.. image:: robot_behavior_case.png
-
-state transition table:
-+++++++++++++++++++++++
-.. list-table:: State Transitions
- :header-rows: 1
- :widths: 20 15 20 20 20
-
- * - Source State
- - Event
- - Target State
- - Guard
- - Action
- * - patrolling
- - detect_task
- - executing_task
- -
- -
- * - executing_task
- - task_complete
- - patrolling
- -
- - reset_task
- * - executing_task
- - low_battery
- - returning_to_base
- - is_battery_low
- -
- * - returning_to_base
- - reach_base
- - charging
- -
- -
- * - charging
- - charge_complete
- - patrolling
- -
- -
\ No newline at end of file
diff --git a/docs/modules/1_introduction/1_definition_of_robotics/definition_of_robotics_main.rst b/docs/modules/1_introduction/1_definition_of_robotics/definition_of_robotics_main.rst
deleted file mode 100644
index ca595301a6f..00000000000
--- a/docs/modules/1_introduction/1_definition_of_robotics/definition_of_robotics_main.rst
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@@ -1,107 +0,0 @@
-Definition of Robotics
-----------------------
-
-This section explains the definition, history, key components, and applications of robotics.
-
-What is Robotics?
-^^^^^^^^^^^^^^^^^^
-
-Robot is a machine that can perform tasks automatically or semi-autonomously.
-Robotics is the study of robots.
-
-The word “robot” comes from the Czech word “robota,” which means “forced labor” or “drudgery.”
-It was first used in the 1920 science fiction play `R.U.R.`_ (Rossum’s Universal Robots)
-by the Czech writer `Karel Čapek`_.
-In the play, robots were artificial workers created to serve humans, but they eventually rebelled.
-
-Over time, “robot” came to refer to machines or automated systems that can perform tasks,
-often with some level of intelligence or autonomy.
-
-Currently, 2 millions robots are working in the world, and the number is increasing every year.
-In South Korea, where the adoption of robots is particularly rapid,
-50 robots are operating per 1,000 people.
-
-.. _`R.U.R.`: https://thereader.mitpress.mit.edu/origin-word-robot-rur/
-.. _`Karel Čapek`: https://en.wikipedia.org/wiki/Karel_%C4%8Capek
-
-The History of Robots
-^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-This timeline highlights key milestones in the history of robotics:
-
-Ancient and Early Concepts (Before 1500s)
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-The idea of **automated machines** has existed for thousands of years.
-Ancient civilizations imagined mechanical beings:
-
-- **Ancient Greece (4th Century BC)** – Greek engineer `Hero of Alexandria`_ designed early **automata** (self-operating machines) powered by water or air.
-- **Chinese and Arabic Automata (9th–13th Century)** – Inventors like `Ismail Al-Jazari`_ created intricate mechanical devices, including water clocks and automated moving peacocks driven by hydropower.
-
-.. _`Hero of Alexandria`: https://en.wikipedia.org/wiki/Hero_of_Alexandria
-.. _`Ismail Al-Jazari`: https://en.wikipedia.org/wiki/Ismail_al-Jazari
-
-The Birth of Modern Robotics (1500s–1800s)
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-- `Leonardo da Vinci’s Robot`_ (1495) – Designed a humanoid knight with mechanical movement.
-- `Jacques de Vaucanson’s Digesting Duck`_ (1738) – Created robotic figures like a mechanical duck that could "eat" and "digest."
-- `Industrial Revolution`_ (18th–19th Century) – Machines began replacing human labor in factories, setting the foundation for automation.
-
-.. _`Leonardo da Vinci’s Robot`: https://en.wikipedia.org/wiki/Leonardo%27s_robot
-.. _`Jacques de Vaucanson’s Digesting Duck`: https://en.wikipedia.org/wiki/Jacques_de_Vaucanson
-.. _`Industrial Revolution`: https://en.wikipedia.org/wiki/Industrial_Revolution
-
-The Rise of Industrial Robots (1900s–1950s)
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-- **The Term “Robot” (1921)** – Czech writer `Karel Čapek`_ introduced the word *“robot”* in his play `R.U.R.`_ (Rossum’s Universal Robots).
-- **Early Cybernetics (1940s–1950s)** – Scientists like `Norbert Wiener`_ developed theories of self-regulating machines, influencing modern robotics (Cybernetics).
-
-.. _`Norbert Wiener`: https://en.wikipedia.org/wiki/Norbert_Wiener
-
-The Birth of Modern Robotics (1950s–1980s)
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-- **First Industrial Robot (1961)** – `Unimate`_, created by `George Devol`_ and `Joseph Engelberger`_, was the first programmable robot used in a factory.
-- **Rise of AI & Autonomous Robots (1970s–1980s)** – Researchers developed mobile robots like `Shakey`_ (Stanford, 1966) and AI-based control systems.
-
-.. _`Unimate`: https://en.wikipedia.org/wiki/Unimate
-.. _`George Devol`: https://en.wikipedia.org/wiki/George_Devol
-.. _`Joseph Engelberger`: https://en.wikipedia.org/wiki/Joseph_Engelberger
-.. _`Shakey`: https://en.wikipedia.org/wiki/Shakey_the_robot
-
-Advanced Robotics and AI Integration (1990s–Present)
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-- **Industrial Robots** – Advanced robots like `Baxter`_ and `Amazon Robotics`_ revolutionized manufacturing and logistics.
-- **Autonomous Vehicles** – Self-driving cars for robo taxi like `Waymo`_ and autonomous haulage system in mining like `AHS`_ became more advanced and bisiness-ready.
-- **Exploration Robots** – Used for planetary exploration (e.g., NASA’s `Mars rovers`_).
-- **Medical Robotics** – Robots like `da Vinci Surgical System`_ revolutionized healthcare.
-- **Personal Robots** – Devices like `Roomba`_ (vacuum robot) and `Sophia`_ (AI humanoid) became popular.
-- **Service Robots** - Assistive robots like serving robots in restaurants and hotels like `Bellabot`_.
-- **Collaborative Robots (Drones)** – Collaborative robots like UAV (Unmanned Aerial Vehicle) in drone shows and delivery services.
-
-.. _`Baxter`: https://en.wikipedia.org/wiki/Baxter_(robot)
-.. _`Amazon Robotics`: https://en.wikipedia.org/wiki/Amazon_Robotics
-.. _`Mars rovers`: https://en.wikipedia.org/wiki/Mars_rover
-.. _`Waymo`: https://waymo.com/
-.. _`AHS`: https://www.futurebridge.com/industry/perspectives-industrial-manufacturing/autonomous-haulage-systems-the-future-of-mining-operations/
-.. _`da Vinci Surgical System`: https://en.wikipedia.org/wiki/Da_Vinci_Surgical_System
-.. _`Roomba`: https://en.wikipedia.org/wiki/Roomba
-.. _`Sophia`: https://en.wikipedia.org/wiki/Sophia_(robot)
-.. _`Bellabot`: https://www.pudurobotics.com/en
-
-Key Components of Robotics
-^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-Robotics consists of several essential components:
-
-#. Sensors – Gather information from the environment (e.g., Cameras, LiDAR, GNSS, Gyro, Accelerometer, Wheel encoders).
-#. Actuators – Enable movement and interaction with the world (e.g., Motors, Hydraulic systems).
-#. Computers – Process sensor data and make decisions (e.g., Micro-controllers, CPUs, GPUs).
-#. Power Supply – Provides energy to run the robot (e.g., Batteries, Solar power).
-#. Software & Algorithms – Allow the robot to function and make intelligent decisions (e.g., ROS, Machine learning models, Localization, Mapping, Path planning, Control).
-
-This project, `PythonRobotics`, focuses on the software and algorithms part of robotics.
-If you are interested in `Sensors` hardware, you can check :ref:`Internal Sensors for Robots` or :ref:`External Sensors for Robots`.
diff --git a/docs/modules/1_introduction/2_python_for_robotics/python_for_robotics_main.rst b/docs/modules/1_introduction/2_python_for_robotics/python_for_robotics_main.rst
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--- a/docs/modules/1_introduction/2_python_for_robotics/python_for_robotics_main.rst
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-Python for Robotics
-----------------------
-
-A programing language, Python is used for this `PythonRobotics` project
-to achieve the purposes of this project described in the :ref:`What is PythonRobotics?`.
-
-This section explains the Python itself and features for science computing and robotics.
-
-Python for general-purpose programming
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-`Python <https://www.python.org/>`_ is an general-purpose programming language developed by
-`Guido van Rossum <https://en.wikipedia.org/wiki/Guido_van_Rossum>`_ from the late 1980s.
-
-It features as follows:
-
-#. High-level
-#. Interpreted
-#. Dynamic type system (also type annotation is supported)
-#. Emphasizes code readability
-#. Rapid prototyping
-#. Batteries included
-#. Interoperability for C and Fortran
-
-Due to these features, Python is one of the most popular programming language
-for educational purposes for programming beginners.
-
-Python for Scientific Computing
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-Python itself was not designed for scientific computing.
-However, scientists quickly recognized its strengths.
-For example,
-
-#. High-level and interpreted features enable scientists to focus on their problems without dealing with low-level programming tasks like memory management.
-#. Code readability, rapid prototyping, and batteries included features enables scientists who are not professional programmers, to solve their problems easily.
-#. The interoperability to wrap C and Fortran libraries enables scientists to access already existed powerful and optimized scientific computing libraries.
-
-To address the more needs of scientific computing, many fundamental scientific computation libraries have been developed based on the upper features.
-
-- `NumPy <https://numpy.org/>`_ is the fundamental package for scientific computing with Python.
-- `SciPy <https://www.scipy.org/>`_ is a library that builds on NumPy and provides a large number of functions that operate on NumPy arrays and are useful for different types of scientific and engineering applications.
-- `Matplotlib <https://matplotlib.org/>`_ is a plotting library for the Python programming language and its numerical mathematics extension NumPy.
-- `Pandas <https://pandas.pydata.org/>`_ is a fast, powerful, flexible, and easy-to-use open-source data analysis and data manipulation library built on top of NumPy.
-- `SymPy <https://www.sympy.org/>`_ is a Python library for symbolic mathematics.
-- `CVXPy <https://www.cvxpy.org/>`_ is a Python-embedded modeling language for convex optimization problems.
-
-Also, more domain-specific libraries have been developed based on these fundamental libraries:
-
-- `Scikit-learn <https://scikit-learn.org/stable/>`_ is a free software machine learning library for the Python programming language.
-- `Scikit-image <https://scikit-image.org/>`_ is a collection of algorithms for image processing.
-- `Networkx <https://networkx.org/>`_ is a package for the creation, manipulation for complex networks.
-- `SunPy <https://sunpy.org/>`_ is a community-developed free and open-source software package for solar physics.
-- `Astropy <https://www.astropy.org/>`_ is a community-developed free and open-source software package for astronomy.
-
-Currently, Python is one of the most popular programming languages for scientific computing.
-
-Python for Robotics
-^^^^^^^^^^^^^^^^^^^^
-
-Python has become an increasingly popular language in robotics.
-
-These are advantages of Python for Robotics:
-
-Simplicity and Readability
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-Python's syntax is clear and concise, making it easier to learn and write code.
-This is crucial in robotics where complex algorithms and control logic are involved.
-
-
-Extensive libraries for scientific computation.
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-Scientific computation routine are fundamental for robotics.
-For example:
-
-- Matrix operation is needed for rigid body transformation, state estimation, and model based control.
-- Optimization is needed for optimization based SLAM, optimal path planning, and optimal control.
-- Visualization is needed for robot teleoperation, debugging, and simulation.
-
-ROS supports Python
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-`ROS`_ (Robot Operating System) is an open-source and widely used framework for robotics development.
-It is designed to help developping complicated robotic applications.
-ROS provides essential tools, libraries, and drivers to simplify robot programming and integration.
-
-Key Features of ROS:
-
-- Modular Architecture – Uses a node-based system where different components (nodes) communicate via messages.
-- Hardware Abstraction – Supports various robots, sensors, and actuators, making development more flexible.
-- Powerful Communication System – Uses topics, services, and actions for efficient data exchange between components.
-- Rich Ecosystem – Offers many pre-built packages for navigation, perception, and manipulation.
-- Multi-language Support – Primarily uses Python and C++, but also supports other languages.
-- Simulation & Visualization – Tools like Gazebo (for simulation) and RViz (for visualization) aid in development and testing.
-- Scalability & Community Support – Widely used in academia and industry, with a large open-source community.
-
-ROS has strong Python support (`rospy`_ for ROS1 and `rclpy`_ for ROS2).
-This allows developers to easily create nodes, manage communication between
-different parts of a robot system, and utilize various ROS tools.
-
-.. _`ROS`: https://www.ros.org/
-.. _`rospy`: http://wiki.ros.org/rospy
-.. _`rclpy`: https://docs.ros.org/en/jazzy/Tutorials/Beginner-Client-Libraries/Writing-A-Simple-Py-Publisher-And-Subscriber.html
-
-Cross-Platform Compatibility
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-Python code can run on various operating systems (Windows, macOS, Linux), providing flexibility in choosing hardware platforms for robotics projects.
-
-Large Community and Support
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-Python has a vast and active community, offering ample resources, tutorials, and support for developers. This is invaluable when tackling challenges in robotics development.
-
-Situations which Python is NOT suitable for Robotics
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-We explained the advantages of Python for robotics.
-However, Python is not always the best choice for robotics development.
-
-These are situations where Python is NOT suitable for robotics:
-
-High-speed real-time control
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-Python is an interpreted language, which means it is slower than compiled languages like C++.
-This can be a disadvantage when real-time control is required,
-such as in high-speed motion control or safety-critical systems.
-
-So, for these applications, we recommend to understand the each algorithm you
-needed using this project and implement it in other suitable languages like C++.
-
-Resource-constrained systems
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-Python is a high-level language that requires more memory and processing power
-compared to low-level languages.
-So, it is difficult to run Python on resource-constrained systems like
-microcontrollers or embedded devices.
-In such cases, C or C++ is more suitable for these applications.
diff --git a/docs/modules/1_introduction/3_technologies_for_robotics/technologies_for_robotics_main.rst b/docs/modules/1_introduction/3_technologies_for_robotics/technologies_for_robotics_main.rst
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-Technologies for Robotics
--------------------------
-
-The field of robotics needs wide areas of technologies such as mechanical engineering,
-electrical engineering, computer science, and artificial intelligence (AI).
-This project, `PythonRobotics`, only focus on computer science and artificial intelligence.
-
-The technologies for robotics are categorized as following 3 categories:
-
-#. `Autonomous Navigation`_
-#. `Manipulation`_
-#. `Robot type specific technologies`_
-
-.. _`Autonomous Navigation`:
-
-Autonomous Navigation
-^^^^^^^^^^^^^^^^^^^^^^^^
-Autonomous navigation is a capability that can move to a goal over long
-periods of time without any external control by an operator.
-
-To achieve autonomous navigation, the robot needs to have the following technologies:
-- It needs to know where it is (localization)
-- Where it is safe (mapping)
-- Where is is safe and where the robot is in the map (Simultaneous Localization and Mapping (SLAM))
-- Where and how to move (path planning)
-- How to control its motion (path following).
-
-The autonomous system would not work correctly if any of these technologies is missing.
-
-In recent years, autonomous navigation technologies have received huge
-attention in many fields.
-For example, self-driving cars, drones, and autonomous mobile robots in indoor and outdoor environments.
-
-In this project, we provide many algorithms, sample codes,
-and documentations for autonomous navigation.
-
-#. :ref:`Localization`
-#. :ref:`Mapping`
-#. :ref:`SLAM`
-#. :ref:`Path planning`
-#. :ref:`Path tracking`
-
-
-
-.. _`Manipulation`:
-
-Manipulation
-^^^^^^^^^^^^^^^^^^^^^^^^
-
-#. :ref:`Arm Navigation`
-
-.. _`Robot type specific technologies`:
-
-Robot type specific technologies
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-#. :ref:`Aerial Navigation`
-#. :ref:`Bipedal`
-#. :ref:`Inverted Pendulum`
-
-
-Additional Information
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-#. :ref:`utils`
-#. :ref:`Appendix`
-
-
diff --git a/docs/modules/1_introduction/introduction_main.rst b/docs/modules/1_introduction/introduction_main.rst
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-.. _Introduction:
-
-Introduction
-============
-
-PythonRobotics is composed of two words: "Python" and "Robotics".
-Therefore, I will first explain these two topics, Robotics and Python.
-After that, I will provide an overview of the robotics technologies
-covered in PythonRobotics.
-
-.. toctree::
- :maxdepth: 2
- :caption: Table of Contents
-
- 1_definition_of_robotics/definition_of_robotics
- 2_python_for_robotics/python_for_robotics
- 3_technologies_for_robotics/technologies_for_robotics
-
diff --git a/docs/modules/2_localization/extended_kalman_filter_localization_files/ekf_with_velocity_correction_1_0.png b/docs/modules/2_localization/extended_kalman_filter_localization_files/ekf_with_velocity_correction_1_0.png
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-Distance Map
-------------
-
-This is an implementation of the Distance Map algorithm for path planning.
-
-The Distance Map algorithm computes the unsigned distance field (UDF) and signed distance field (SDF) from a boolean field representing obstacles.
-
-The UDF gives the distance from each point to the nearest obstacle. The SDF gives positive distances for points outside obstacles and negative distances for points inside obstacles.
-
-Example
-~~~~~~~
-
-The algorithm is demonstrated on a simple 2D grid with obstacles:
-
-.. image:: distance_map.png
-
-API
-~~~
-
-.. autofunction:: Mapping.DistanceMap.distance_map.compute_sdf
-
-.. autofunction:: Mapping.DistanceMap.distance_map.compute_udf
-
-References
-~~~~~~~~~~
-
-- `Distance Transforms of Sampled Functions <https://cs.brown.edu/people/pfelzens/papers/dt-final.pdf>`_ paper by Pedro F. Felzenszwalb and Daniel P. Huttenlocher.
\ No newline at end of file
diff --git a/docs/modules/4_slam/graph_slam/graphSLAM_SE2_example.rst b/docs/modules/4_slam/graph_slam/graphSLAM_SE2_example.rst
deleted file mode 100644
index 15963aff79d..00000000000
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-Graph SLAM for a real-world SE(2) dataset
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. code:: ipython3
-
- from graphslam.graph import Graph
- from graphslam.load import load_g2o_se2
-
-Introduction
-^^^^^^^^^^^^
-
-For a complete derivation of the Graph SLAM algorithm, please see
-`Graph SLAM Formulation`_.
-
-This notebook illustrates the iterative optimization of a real-world
-:math:`SE(2)` dataset. The code can be found in the ``graphslam``
-folder. For simplicity, numerical differentiation is used in lieu of
-analytic Jacobians. This code originated from the
-`python-graphslam <https://github.com/JeffLIrion/python-graphslam>`__
-repo, which is a full-featured Graph SLAM solver. The dataset in this
-example is used with permission from Luca Carlone and was downloaded
-from his `website <https://lucacarlone.mit.edu/datasets/>`__.
-
-The Dataset
-^^^^^^^^^^^^
-
-.. code:: ipython3
-
- g = load_g2o_se2("data/input_INTEL.g2o")
-
- print("Number of edges: {}".format(len(g._edges)))
- print("Number of vertices: {}".format(len(g._vertices)))
-
-
-.. parsed-literal::
-
- Number of edges: 1483
- Number of vertices: 1228
-
-
-.. code:: ipython3
-
- g.plot(title=r"Original ($\chi^2 = {:.0f}$)".format(g.calc_chi2()))
-
-
-
-.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_4_0.png
-
-
-Each edge in this dataset is a constraint that compares the measured
-:math:`SE(2)` transformation between two poses to the expected
-:math:`SE(2)` transformation between them, as computed using the current
-pose estimates. These edges can be classified into two categories:
-
-1. Odometry edges constrain two consecutive vertices, and the
- measurement for the :math:`SE(2)` transformation comes directly from
- odometry data.
-2. Scan-matching edges constrain two non-consecutive vertices. These
- scan matches can be computed using, for example, 2-D LiDAR data or
- landmarks; the details of how these constraints are determined is
- beyond the scope of this example. This is often referred to as *loop
- closure* in the Graph SLAM literature.
-
-We can easily parse out the two different types of edges present in this
-dataset and plot them.
-
-.. code:: ipython3
-
- def parse_edges(g):
- """Split the graph `g` into two graphs, one with only odometry edges and the other with only scan-matching edges.
-
- Parameters
- ----------
- g : graphslam.graph.Graph
- The input graph
-
- Returns
- -------
- g_odom : graphslam.graph.Graph
- A graph consisting of the vertices and odometry edges from `g`
- g_scan : graphslam.graph.Graph
- A graph consisting of the vertices and scan-matching edges from `g`
-
- """
- edges_odom = []
- edges_scan = []
-
- for e in g._edges:
- if abs(e.vertex_ids[1] - e.vertex_ids[0]) == 1:
- edges_odom.append(e)
- else:
- edges_scan.append(e)
-
- g_odom = Graph(edges_odom, g._vertices)
- g_scan = Graph(edges_scan, g._vertices)
-
- return g_odom, g_scan
-
-.. code:: ipython3
-
- g_odom, g_scan = parse_edges(g)
-
- print("Number of odometry edges: {:4d}".format(len(g_odom._edges)))
- print("Number of scan-matching edges: {:4d}".format(len(g_scan._edges)))
-
- print("\nχ^2 error from odometry edges: {:11.3f}".format(g_odom.calc_chi2()))
- print("χ^2 error from scan-matching edges: {:11.3f}".format(g_scan.calc_chi2()))
-
-
-.. parsed-literal::
-
- Number of odometry edges: 1227
- Number of scan-matching edges: 256
-
- χ^2 error from odometry edges: 0.232
- χ^2 error from scan-matching edges: 7191686.151
-
-
-.. code:: ipython3
-
- g_odom.plot(title="Odometry edges")
-
-
-
-.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_8_0.png
-
-
-.. code:: ipython3
-
- g_scan.plot(title="Scan-matching edges")
-
-
-
-.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_9_0.png
-
-
-Optimization
-^^^^^^^^^^^^
-
-Initially, the pose estimates are consistent with the collected odometry
-measurements, and the odometry edges contribute almost zero towards the
-:math:`\chi^2` error. However, there are large discrepancies between the
-scan-matching constraints and the initial pose estimates. This is not
-surprising, since small errors in odometry readings that are propagated
-over time can lead to large errors in the robot’s trajectory. What makes
-Graph SLAM effective is that it allows incorporation of multiple
-different data sources into a single optimization problem.
-
-.. code:: ipython3
-
- g.optimize()
-
-
-.. parsed-literal::
-
-
- Iteration chi^2 rel. change
- --------- ----- -----------
- 0 7191686.3825
- 1 320031728.8624 43.500234
- 2 125083004.3299 -0.609154
- 3 338155.9074 -0.997297
- 4 735.1344 -0.997826
- 5 215.8405 -0.706393
- 6 215.8405 -0.000000
-
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/GraphBasedSLAM/Graph_SLAM_optimization.gif
-
-.. code:: ipython3
-
- g.plot(title="Optimized")
-
-
-
-.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_13_0.png
-
-
-.. code:: ipython3
-
- print("\nχ^2 error from odometry edges: {:7.3f}".format(g_odom.calc_chi2()))
- print("χ^2 error from scan-matching edges: {:7.3f}".format(g_scan.calc_chi2()))
-
-
-.. parsed-literal::
-
-
- χ^2 error from odometry edges: 142.189
- χ^2 error from scan-matching edges: 73.652
-
-
-.. code:: ipython3
-
- g_odom.plot(title="Odometry edges")
-
-
-
-.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_15_0.png
-
-
-.. code:: ipython3
-
- g_scan.plot(title="Scan-matching edges")
-
-
-
-.. image:: graphSLAM_SE2_example_files/graphSLAM_SE2_example_16_0.png
-
diff --git a/docs/modules/4_slam/graph_slam/graphSLAM_doc.rst b/docs/modules/4_slam/graph_slam/graphSLAM_doc.rst
deleted file mode 100644
index 5297604809b..00000000000
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+++ /dev/null
@@ -1,554 +0,0 @@
-
-Graph SLAM
-~~~~~~~~~~~~
-
-.. code:: ipython3
-
- import copy
- import math
- import itertools
- import numpy as np
- import matplotlib.pyplot as plt
- from graph_based_slam import calc_rotational_matrix, calc_jacobian, cal_observation_sigma, \
- calc_input, observation, motion_model, Edge, pi_2_pi
-
- %matplotlib inline
- np.set_printoptions(precision=3, suppress=True)
- np.random.seed(0)
-
-Introduction
-^^^^^^^^^^^^
-
-In contrast to the probabilistic approaches for solving SLAM, such as
-EKF, UKF, particle filters, and so on, the graph technique formulates
-the SLAM as an optimization problem. It is mostly used to solve the full
-SLAM problem in an offline fashion, i.e. optimize all the poses of the
-robot after the path has been traversed. However, some variants are
-available that uses graph-based approaches to perform online estimation
-or to solve for a subset of the poses.
-
-GraphSLAM uses the motion information as well as the observations of the
-environment to create least square problem that can be solved using
-standard optimization techniques.
-
-Minimal Example
-^^^^^^^^^^^^^^^
-
-The following example illustrates the main idea behind graphSLAM. A
-simple case of a 1D robot is considered that can only move in 1
-direction. The robot is commanded to move forward with a control input
-:math:`u_t=1`, however, the motion is not perfect and the measured
-odometry will deviate from the true path. At each time step the robot can
-observe its environment, for this simple case as well, there is only a
-single landmark at coordinates :math:`x=3`. The measured observations
-are the range between the robot and landmark. These measurements are
-also subjected to noise. No bearing information is required since this
-is a 1D problem.
-
-To solve this, graphSLAM creates what is called as the system
-information matrix :math:`\Omega` also referred to as :math:`H` and the
-information vector :math:`\xi` also known as :math:`b`. The entries are
-created based on the information of the motion and the observation.
-
-.. code:: ipython3
-
- R = 0.2
- Q = 0.2
- N = 3
- graphics_radius = 0.1
-
- odom = np.empty((N,1))
- obs = np.empty((N,1))
- x_true = np.empty((N,1))
-
- landmark = 3
- # Simulated readings of odometry and observations
- x_true[0], odom[0], obs[0] = 0.0, 0.0, 2.9
- x_true[1], odom[1], obs[1] = 1.0, 1.5, 2.0
- x_true[2], odom[2], obs[2] = 2.0, 2.4, 1.0
-
- hxDR = copy.deepcopy(odom)
- # Visualization
- plt.plot(landmark,0, '*k', markersize=30)
- for i in range(N):
- plt.plot(odom[i], 0, '.', markersize=50, alpha=0.8, color='steelblue')
- plt.plot([odom[i], odom[i] + graphics_radius],
- [0,0], 'r')
- plt.text(odom[i], 0.02, "X_{}".format(i), fontsize=12)
- plt.plot(obs[i]+odom[i],0,'.', markersize=25, color='brown')
- plt.plot(x_true[i],0,'.g', markersize=20)
- plt.grid()
- plt.show()
-
-
- # Defined as a function to facilitate iteration
- def get_H_b(odom, obs):
- """
- Create the information matrix and information vector. This implementation is
- based on the concept of virtual measurement i.e. the observations of the
- landmarks are converted into constraints (edges) between the nodes that
- have observed this landmark.
- """
- measure_constraints = {}
- omegas = {}
- zids = list(itertools.combinations(range(N),2))
- H = np.zeros((N,N))
- b = np.zeros((N,1))
- for (t1, t2) in zids:
- x1 = odom[t1]
- x2 = odom[t2]
- z1 = obs[t1]
- z2 = obs[t2]
-
- # Adding virtual measurement constraint
- measure_constraints[(t1,t2)] = (x2-x1-z1+z2)
- omegas[(t1,t2)] = (1 / (2*Q))
-
- # populate system's information matrix and vector
- H[t1,t1] += omegas[(t1,t2)]
- H[t2,t2] += omegas[(t1,t2)]
- H[t2,t1] -= omegas[(t1,t2)]
- H[t1,t2] -= omegas[(t1,t2)]
-
- b[t1] += omegas[(t1,t2)] * measure_constraints[(t1,t2)]
- b[t2] -= omegas[(t1,t2)] * measure_constraints[(t1,t2)]
-
- return H, b
-
-
- H, b = get_H_b(odom, obs)
- print("The determinant of H: ", np.linalg.det(H))
- H[0,0] += 1 # np.inf ?
- print("The determinant of H after anchoring constraint: ", np.linalg.det(H))
-
- for i in range(5):
- H, b = get_H_b(odom, obs)
- H[(0,0)] += 1
-
- # Recover the posterior over the path
- dx = np.linalg.inv(H) @ b
- odom += dx
- # repeat till convergence
- print("Running graphSLAM ...")
- print("Odometry values after optimzation: \n", odom)
-
- plt.figure()
- plt.plot(x_true, np.zeros(x_true.shape), '.', markersize=20, label='Ground truth')
- plt.plot(odom, np.zeros(x_true.shape), '.', markersize=20, label='Estimation')
- plt.plot(hxDR, np.zeros(x_true.shape), '.', markersize=20, label='Odom')
- plt.legend()
- plt.grid()
- plt.show()
-
-
-
-.. image:: graphSLAM_doc_files/graphSLAM_doc_2_0.png
-
-
-.. parsed-literal::
-
- The determinant of H: 0.0
- The determinant of H after anchoring constraint: 18.750000000000007
- Running graphSLAM ...
- Odometry values after optimzation:
- [[-0. ]
- [ 0.9]
- [ 1.9]]
-
-
-
-.. image:: graphSLAM_doc_files/graphSLAM_doc_2_2.png
-
-
-In particular, the tasks are split into 2 parts, graph construction, and
-graph optimization. ### Graph Construction
-
-Firstly the nodes are defined
-:math:`\boldsymbol{x} = \boldsymbol{x}_{1:n}` such that each node is the
-pose of the robot at time :math:`t_i` Secondly, the edges i.e. the
-constraints, are constructed according to the following conditions:
-
-- robot moves from :math:`\boldsymbol{x}_i` to
- :math:`\boldsymbol{x}_j`. This edge corresponds to the odometry
- measurement. Relative motion constraints (Not included in the
- previous minimal example).
-- Measurement constraints, this can be done in two ways:
-
- - The information matrix is set in such a way that it includes the
- landmarks in the map as well. Then the constraints can be entered
- in a straightforward fashion between a node
- :math:`\boldsymbol{x}_i` and some landmark :math:`m_k`
- - Through creating a virtual measurement among all the node that
- have observed the same landmark. More concretely, robot observes
- the same landmark from :math:`\boldsymbol{x}_i` and
- :math:`\boldsymbol{x}_j`. Relative measurement constraint. The
- “virtual measurement” :math:`\boldsymbol{z}_{ij}`, which is the
- estimated pose of :math:`\boldsymbol{x}_j` as seen from the node
- :math:`\boldsymbol{x}_i`. The virtual measurement can then be
- entered in the information matrix and vector in a similar fashion
- to the motion constraints.
-
-An edge is fully characterized by the values of the error (entry to
-information vector) and the local information matrix (entry to the
-system’s information vector). The larger the local information matrix
-(lower :math:`Q` or :math:`R`) the values that this edge will contribute
-with.
-
-Important Notes:
-
-- The addition to the information matrix and vector are added to the
- earlier values.
-- In the case of 2D robot, the constraints will be non-linear,
- therefore, a Jacobian of the error w.r.t the states is needed when
- updated :math:`H` and :math:`b`.
-- The anchoring constraint is needed in order to avoid having a
- singular information matri.
-
-Graph Optimization
-^^^^^^^^^^^^^^^^^^
-
-The result from this formulation yields an overdetermined system of
-equations. The goal after constructing the graph is to find:
-:math:`x^*=\underset{x}{\mathrm{argmin}}~\underset{ij}\Sigma~f(e_{ij})`,
-where :math:`f` is some error function that depends on the edges between
-to related nodes :math:`i` and :math:`j`. The derivation in the references
-arrive at the solution for :math:`x^* = H^{-1}b`
-
-Planar Example:
-^^^^^^^^^^^^^^^
-
-Now we will go through an example with a more realistic case of a 2D
-robot with 3DoF, namely, :math:`[x, y, \theta]^T`
-
-.. code:: ipython3
-
- # Simulation parameter
- Qsim = np.diag([0.01, np.deg2rad(0.010)])**2 # error added to range and bearing
- Rsim = np.diag([0.1, np.deg2rad(1.0)])**2 # error added to [v, w]
-
- DT = 2.0 # time tick [s]
- SIM_TIME = 100.0 # simulation time [s]
- MAX_RANGE = 30.0 # maximum observation range
- STATE_SIZE = 3 # State size [x,y,yaw]
-
- # TODO: Why not use Qsim ?
- # Covariance parameter of Graph Based SLAM
- C_SIGMA1 = 0.1
- C_SIGMA2 = 0.1
- C_SIGMA3 = np.deg2rad(1.0)
-
- MAX_ITR = 20 # Maximum iteration during optimization
- timesteps = 1
-
- # consider only 2 landmarks for simplicity
- # RFID positions [x, y, yaw]
- RFID = np.array([[10.0, -2.0, 0.0],
- # [15.0, 10.0, 0.0],
- # [3.0, 15.0, 0.0],
- # [-5.0, 20.0, 0.0],
- # [-5.0, 5.0, 0.0]
- ])
-
- # State Vector [x y yaw v]'
- xTrue = np.zeros((STATE_SIZE, 1))
- xDR = np.zeros((STATE_SIZE, 1)) # Dead reckoning
- xTrue[2] = np.deg2rad(45)
- xDR[2] = np.deg2rad(45)
- # history initial values
- hxTrue = xTrue
- hxDR = xTrue
- _, z, _, _ = observation(xTrue, xDR, np.array([[0,0]]).T, RFID)
- hz = [z]
-
- for i in range(timesteps):
- u = calc_input()
- xTrue, z, xDR, ud = observation(xTrue, xDR, u, RFID)
- hxDR = np.hstack((hxDR, xDR))
- hxTrue = np.hstack((hxTrue, xTrue))
- hz.append(z)
-
- # visualize
- graphics_radius = 0.3
- plt.plot(RFID[:, 0], RFID[:, 1], "*k", markersize=20)
- plt.plot(hxDR[0, :], hxDR[1, :], '.', markersize=50, alpha=0.8, label='Odom')
- plt.plot(hxTrue[0, :], hxTrue[1, :], '.', markersize=20, alpha=0.6, label='X_true')
-
- for i in range(hxDR.shape[1]):
- x = hxDR[0, i]
- y = hxDR[1, i]
- yaw = hxDR[2, i]
- plt.plot([x, x + graphics_radius * np.cos(yaw)],
- [y, y + graphics_radius * np.sin(yaw)], 'r')
- d = hz[i][:, 0]
- angle = hz[i][:, 1]
- plt.plot([x + d * np.cos(angle + yaw)], [y + d * np.sin(angle + yaw)], '.',
- markersize=20, alpha=0.7)
- plt.legend()
- plt.grid()
- plt.show()
-
-
-
-.. image:: graphSLAM_doc_files/graphSLAM_doc_4_0.png
-
-
-.. code:: ipython3
-
- # Copy the data to have a consistent naming with the .py file
- zlist = copy.deepcopy(hz)
- x_opt = copy.deepcopy(hxDR)
- xlist = copy.deepcopy(hxDR)
- number_of_nodes = x_opt.shape[1]
- n = number_of_nodes * STATE_SIZE
-
-After the data has been saved, the graph will be constructed by looking
-at each pair for nodes. The virtual measurement is only created if two
-nodes have observed the same landmark at different points in time. The
-next cells are a walk through for a single iteration of graph
-construction -> optimization -> estimate update.
-
-.. code:: ipython3
-
- # get all the possible combination of the different node
- zids = list(itertools.combinations(range(len(zlist)), 2))
- print("Node combinations: \n", zids)
-
- for i in range(xlist.shape[1]):
- print("Node {} observed landmark with ID {}".format(i, zlist[i][0, 3]))
-
-
-.. parsed-literal::
-
- Node combinations:
- [(0, 1)]
- Node 0 observed landmark with ID 0.0
- Node 1 observed landmark with ID 0.0
-
-
-In the following code snippet the error based on the virtual measurement
-between node 0 and 1 will be created. The equations for the error is as follows:
-:math:`e_{ij}^x = x_j + d_j cos(\psi_j +\theta_j) - x_i - d_i cos(\psi_i + \theta_i)`
-
-:math:`e_{ij}^y = y_j + d_j sin(\psi_j + \theta_j) - y_i - d_i sin(\psi_i + \theta_i)`
-
-:math:`e_{ij}^x = \psi_j + \theta_j - \psi_i - \theta_i`
-
-Where :math:`[x_i, y_i, \psi_i]` is the pose for node :math:`i` and
-similarly for node :math:`j`, :math:`d` is the measured distance at
-nodes :math:`i` and :math:`j`, and :math:`\theta` is the measured
-bearing to the landmark. The difference is visualized with the figure in
-the next cell.
-
-In case of perfect motion and perfect measurement the error shall be
-zero since :math:`x_j + d_j cos(\psi_j + \theta_j)` should equal
-:math:`x_i + d_i cos(\psi_i + \theta_i)`
-
-.. code:: ipython3
-
- # Initialize edges list
- edges = []
-
- # Go through all the different combinations
- for (t1, t2) in zids:
- x1, y1, yaw1 = xlist[0, t1], xlist[1, t1], xlist[2, t1]
- x2, y2, yaw2 = xlist[0, t2], xlist[1, t2], xlist[2, t2]
-
- # All nodes have valid observation with ID=0, therefore, no data association condition
- iz1 = 0
- iz2 = 0
-
- d1 = zlist[t1][iz1, 0]
- angle1, phi1 = zlist[t1][iz1, 1], zlist[t1][iz1, 2]
- d2 = zlist[t2][iz2, 0]
- angle2, phi2 = zlist[t2][iz2, 1], zlist[t2][iz2, 2]
-
- # find angle between observation and horizontal
- tangle1 = pi_2_pi(yaw1 + angle1)
- tangle2 = pi_2_pi(yaw2 + angle2)
-
- # project the observations
- tmp1 = d1 * math.cos(tangle1)
- tmp2 = d2 * math.cos(tangle2)
- tmp3 = d1 * math.sin(tangle1)
- tmp4 = d2 * math.sin(tangle2)
-
- edge = Edge()
- print(y1,y2, tmp3, tmp4)
- # calculate the error of the virtual measurement
- # node 1 as seen from node 2 throught the observations 1,2
- edge.e[0, 0] = x2 - x1 - tmp1 + tmp2
- edge.e[1, 0] = y2 - y1 - tmp3 + tmp4
- edge.e[2, 0] = pi_2_pi(yaw2 - yaw1 - tangle1 + tangle2)
-
- edge.d1, edge.d2 = d1, d2
- edge.yaw1, edge.yaw2 = yaw1, yaw2
- edge.angle1, edge.angle2 = angle1, angle2
- edge.id1, edge.id2 = t1, t2
-
- edges.append(edge)
-
- print("For nodes",(t1,t2))
- print("Added edge with errors: \n", edge.e)
-
- # Visualize measurement projections
- plt.plot(RFID[0, 0], RFID[0, 1], "*k", markersize=20)
- plt.plot([x1,x2],[y1,y2], '.', markersize=50, alpha=0.8)
- plt.plot([x1, x1 + graphics_radius * np.cos(yaw1)],
- [y1, y1 + graphics_radius * np.sin(yaw1)], 'r')
- plt.plot([x2, x2 + graphics_radius * np.cos(yaw2)],
- [y2, y2 + graphics_radius * np.sin(yaw2)], 'r')
-
- plt.plot([x1,x1+tmp1], [y1,y1], label="obs 1 x")
- plt.plot([x2,x2+tmp2], [y2,y2], label="obs 2 x")
- plt.plot([x1,x1], [y1,y1+tmp3], label="obs 1 y")
- plt.plot([x2,x2], [y2,y2+tmp4], label="obs 2 y")
- plt.plot(x1+tmp1, y1+tmp3, 'o')
- plt.plot(x2+tmp2, y2+tmp4, 'o')
- plt.legend()
- plt.grid()
- plt.show()
-
-
-.. parsed-literal::
-
- 0.0 1.427649841628278 -2.0126109674819155 -3.524048014922737
- For nodes (0, 1)
- Added edge with errors:
- [[-0.02 ]
- [-0.084]
- [ 0. ]]
-
-
-
-.. image:: graphSLAM_doc_files/graphSLAM_doc_9_1.png
-
-
-Since the constraints equations derived before are non-linear,
-linearization is needed before we can insert them into the information
-matrix and information vector. Two jacobians
-
-:math:`A = \frac{\partial e_{ij}}{\partial \boldsymbol{x}_i}` as
-:math:`\boldsymbol{x}_i` holds the three variabls x, y, and theta.
-Similarly, :math:`B = \frac{\partial e_{ij}}{\partial \boldsymbol{x}_j}`
-
-.. code:: ipython3
-
- # Initialize the system information matrix and information vector
- H = np.zeros((n, n))
- b = np.zeros((n, 1))
- x_opt = copy.deepcopy(hxDR)
-
- for edge in edges:
- id1 = edge.id1 * STATE_SIZE
- id2 = edge.id2 * STATE_SIZE
-
- t1 = edge.yaw1 + edge.angle1
- A = np.array([[-1.0, 0, edge.d1 * math.sin(t1)],
- [0, -1.0, -edge.d1 * math.cos(t1)],
- [0, 0, -1.0]])
-
- t2 = edge.yaw2 + edge.angle2
- B = np.array([[1.0, 0, -edge.d2 * math.sin(t2)],
- [0, 1.0, edge.d2 * math.cos(t2)],
- [0, 0, 1.0]])
-
- # TODO: use Qsim instead of sigma
- sigma = np.diag([C_SIGMA1, C_SIGMA2, C_SIGMA3])
- Rt1 = calc_rotational_matrix(tangle1)
- Rt2 = calc_rotational_matrix(tangle2)
- edge.omega = np.linalg.inv(Rt1 @ sigma @ Rt1.T + Rt2 @ sigma @ Rt2.T)
-
- # Fill in entries in H and b
- H[id1:id1 + STATE_SIZE, id1:id1 + STATE_SIZE] += A.T @ edge.omega @ A
- H[id1:id1 + STATE_SIZE, id2:id2 + STATE_SIZE] += A.T @ edge.omega @ B
- H[id2:id2 + STATE_SIZE, id1:id1 + STATE_SIZE] += B.T @ edge.omega @ A
- H[id2:id2 + STATE_SIZE, id2:id2 + STATE_SIZE] += B.T @ edge.omega @ B
-
- b[id1:id1 + STATE_SIZE] += (A.T @ edge.omega @ edge.e)
- b[id2:id2 + STATE_SIZE] += (B.T @ edge.omega @ edge.e)
-
-
- print("The determinant of H: ", np.linalg.det(H))
- plt.figure()
- plt.subplot(1,2,1)
- plt.imshow(H, extent=[0, n, 0, n])
- plt.subplot(1,2,2)
- plt.imshow(b, extent=[0, 1, 0, n])
- plt.show()
-
- # Fix the origin, multiply by large number gives same results but better visualization
- H[0:STATE_SIZE, 0:STATE_SIZE] += np.identity(STATE_SIZE)
- print("The determinant of H after origin constraint: ", np.linalg.det(H))
- plt.figure()
- plt.subplot(1,2,1)
- plt.imshow(H, extent=[0, n, 0, n])
- plt.subplot(1,2,2)
- plt.imshow(b, extent=[0, 1, 0, n])
- plt.show()
-
-
-.. parsed-literal::
-
- The determinant of H: 0.0
- The determinant of H after origin constraint: 716.1972439134893
-
-
-
-.. image:: graphSLAM_doc_files/graphSLAM_doc_11_1.png
-
-.. image:: graphSLAM_doc_files/graphSLAM_doc_11_2.png
-
-.. code:: ipython3
-
- # Find the solution (first iteration)
- dx = - np.linalg.inv(H) @ b
- for i in range(number_of_nodes):
- x_opt[0:3, i] += dx[i * 3:i * 3 + 3, 0]
- print("dx: \n",dx)
- print("ground truth: \n ",hxTrue)
- print("Odom: \n", hxDR)
- print("SLAM: \n", x_opt)
-
- # performance will improve with more iterations, nodes and landmarks.
- print("\ngraphSLAM localization error: ", np.sum((x_opt - hxTrue) ** 2))
- print("Odom localization error: ", np.sum((hxDR - hxTrue) ** 2))
-
-
-.. parsed-literal::
-
- dx:
- [[-0. ]
- [-0. ]
- [ 0. ]
- [ 0.02 ]
- [ 0.084]
- [-0. ]]
- ground truth:
- [[0. 1.414]
- [0. 1.414]
- [0.785 0.985]]
- Odom:
- [[0. 1.428]
- [0. 1.428]
- [0.785 0.976]]
- SLAM:
- [[-0. 1.448]
- [-0. 1.512]
- [ 0.785 0.976]]
-
- graphSLAM localization error: 0.010729072751057656
- Odom localization error: 0.0004460978857535104
-
-
-The references:
-^^^^^^^^^^^^^^^
-
-- `The GraphSLAM Algorithm with Applications to Large-Scale Mapping of Urban Structures <http://robots.stanford.edu/papers/thrun.graphslam.pdf>`_
-
-- `Introduction to Mobile Robotics Graph-Based SLAM <http://ais.informatik.uni-freiburg.de/teaching/ss13/robotics/slides/16-graph-slam.pdf>`_
-
-- `A Tutorial on Graph-Based SLAM <http://www2.informatik.uni-freiburg.de/~stachnis/pdf/grisetti10titsmag.pdf>`_
-
-N.B. An additional step is required that uses the estimated path to
-update the belief regarding the map.
-
diff --git a/docs/modules/4_slam/graph_slam/graphSLAM_formulation.rst b/docs/modules/4_slam/graph_slam/graphSLAM_formulation.rst
deleted file mode 100644
index 4978596c102..00000000000
--- a/docs/modules/4_slam/graph_slam/graphSLAM_formulation.rst
+++ /dev/null
@@ -1,218 +0,0 @@
-.. _Graph SLAM Formulation:
-
-Graph SLAM Formulation
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-Author Jeff Irion
-
-Problem Formulation
-^^^^^^^^^^^^^^^^^^^
-
-Let a robot’s trajectory through its environment be represented by a
-sequence of :math:`N` poses:
-:math:`\mathbf{p}_1, \mathbf{p}_2, \ldots, \mathbf{p}_N`. Each pose lies
-on a manifold: :math:`\mathbf{p}_i \in \mathcal{M}`. Simple examples of
-manifolds used in Graph SLAM include 1-D, 2-D, and 3-D space, i.e.,
-:math:`\mathbb{R}`, :math:`\mathbb{R}^2`, and :math:`\mathbb{R}^3`.
-These environments are *rectilinear*, meaning that there is no concept
-of orientation. By contrast, in :math:`SE(2)` problem settings a robot’s
-pose consists of its location in :math:`\mathbb{R}^2` and its
-orientation :math:`\theta`. Similarly, in :math:`SE(3)` a robot’s pose
-consists of its location in :math:`\mathbb{R}^3` and its orientation,
-which can be represented via Euler angles, quaternions, or :math:`SO(3)`
-rotation matrices.
-
-As the robot explores its environment, it collects a set of :math:`M`
-measurements :math:`\mathcal{Z} = \{\mathbf{z}_j\}`. Examples of such
-measurements include odometry, GPS, and IMU data. Given a set of poses
-:math:`\mathbf{p}_1, \ldots, \mathbf{p}_N`, we can compute the estimated
-measurement
-:math:`\hat{\mathbf{z}}_j(\mathbf{p}_1, \ldots, \mathbf{p}_N)`. We can
-then compute the *residual*
-:math:`\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j)` for measurement
-:math:`j`. The formula for the residual depends on the type of
-measurement. As an example, let :math:`\mathbf{z}_1` be an odometry
-measurement that was collected when the robot traveled from
-:math:`\mathbf{p}_1` to :math:`\mathbf{p}_2`. The expected measurement
-and the residual are computed as
-
-.. math::
-
- \begin{aligned}
- \hat{\mathbf{z}}_1(\mathbf{p}_1, \mathbf{p}_2) &= \mathbf{p}_2 \ominus \mathbf{p}_1 \\
- \mathbf{e}_1(\mathbf{z}_1, \hat{\mathbf{z}}_1) &= \mathbf{z}_1 \ominus \hat{\mathbf{z}}_1 = \mathbf{z}_1 \ominus (\mathbf{p}_2 \ominus \mathbf{p}_1),\end{aligned}
-
-where the :math:`\ominus` operator indicates inverse pose composition.
-We model measurement :math:`\mathbf{z}_j` as having independent Gaussian
-noise with zero mean and covariance matrix :math:`\Omega_j^{-1}`; we
-refer to :math:`\Omega_j` as the *information matrix* for measurement
-:math:`j`. That is,
-
-.. math::
- p(\mathbf{z}_j \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) = \eta_j \exp (-\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\mathsf{T}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j)
- :label: infomat
-
-where :math:`\eta_j` is the normalization constant.
-
-The objective of Graph SLAM is to find the maximum likelihood set of
-poses given the measurements :math:`\mathcal{Z} = \{\mathbf{z}_j\}`; in
-other words, we want to find
-
-.. math:: \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z})
-
-Using Bayes’ rule, we can write this probability as
-
-.. math::
- \begin{aligned}
- p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z}) &= \frac{p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) p(\mathbf{p}_1, \ldots, \mathbf{p}_N) }{ p(\mathcal{Z}) } \notag \\
- &\propto p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N)
- \end{aligned}
- :label: bayes
-
-since :math:`p(\mathcal{Z})` is a constant (albeit, an unknown constant)
-and we assume that :math:`p(\mathbf{p}_1, \ldots, \mathbf{p}_N)` is
-uniformly distributed. Therefore, we
-can use Eq. :eq:`infomat` and and Eq. :eq:`bayes` to simplify the Graph SLAM
-optimization as follows:
-
-.. math::
-
- \begin{aligned}
- \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z}) &= \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) \\
- &= \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \prod_{j=1}^M p(\mathbf{z}_j \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) \\
- &= \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \prod_{j=1}^M \exp \left( -(\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j) \right) \\
- &= \mathop{\mathrm{arg\,min}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \sum_{j=1}^M (\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j).\end{aligned}
-
-We define
-
-.. math:: \chi^2 := \sum_{j=1}^M (\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j),
-
-and this is what we seek to minimize.
-
-Dimensionality and Pose Representation
-^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^
-
-Before proceeding further, it is helpful to discuss the dimensionality
-of the problem. We have:
-
-- A set of :math:`N` poses
- :math:`\mathbf{p}_1, \mathbf{p}_2, \ldots, \mathbf{p}_N`, where each
- pose lies on the manifold :math:`\mathcal{M}`
-
- - Each pose :math:`\mathbf{p}_i` is represented as a vector in (a
- subset of) :math:`\mathbb{R}^d`. For example:
-
- - An :math:`SE(2)` pose is typically represented as
- :math:`(x, y, \theta)`, and thus :math:`d = 3`.
-
- - An :math:`SE(3)` pose is typically represented as
- :math:`(x, y, z, q_x, q_y, q_z, q_w)`, where :math:`(x, y, z)`
- is a point in :math:`\mathbb{R}^3` and
- :math:`(q_x, q_y, q_z, q_w)` is a *quaternion*, and so
- :math:`d = 7`. For more information about :math:`SE(3)`
- parameterization and pose transformations, see
- [blanco2010tutorial]_.
-
- - We also need to be able to represent each pose compactly as a
- vector in (a subset of) :math:`\mathbb{R}^c`.
-
- - Since an :math:`SE(2)` pose has three degrees of freedom, the
- :math:`(x, y, \theta)` representation is again sufficient and
- :math:`c=3`.
-
- - An :math:`SE(3)` pose only has six degrees of freedom, and we
- can represent it compactly as :math:`(x, y, z, q_x, q_y, q_z)`,
- and thus :math:`c=6`.
-
- - We use the :math:`\boxplus` operator to indicate pose composition
- when one or both of the poses are represented compactly. The
- output can be a pose in :math:`\mathcal{M}` or a vector in
- :math:`\mathbb{R}^c`, as required by context.
-
-- A set of :math:`M` measurements
- :math:`\mathcal{Z} = \{\mathbf{z}_1, \mathbf{z}_2, \ldots, \mathbf{z}_M\}`
-
- - Each measurement’s dimensionality can be unique, and we will use
- :math:`\bullet` to denote a “wildcard” variable.
-
- - Measurement :math:`\mathbf{z}_j \in \mathbb{R}^\bullet` has an
- associated information matrix
- :math:`\Omega_j \in \mathbb{R}^{\bullet \times \bullet}` and
- residual function
- :math:`\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j) = \mathbf{e}_j(\mathbf{z}_j, \mathbf{p}_1, \ldots, \mathbf{p}_N) \in \mathbb{R}^\bullet`.
-
- - A measurement could, in theory, constrain anywhere from 1 pose to
- all :math:`N` poses. In practice, each measurement usually
- constrains only 1 or 2 poses.
-
-Graph SLAM Algorithm
-^^^^^^^^^^^^^^^^^^^^
-
-The “Graph” in Graph SLAM refers to the fact that we view the problem as
-a graph. The graph has a set :math:`\mathcal{V}` of :math:`N` vertices,
-where each vertex :math:`v_i` has an associated pose
-:math:`\mathbf{p}_i`. Similarly, the graph has a set :math:`\mathcal{E}`
-of :math:`M` edges, where each edge :math:`e_j` has an associated
-measurement :math:`\mathbf{z}_j`. In practice, the edges in this graph
-are either unary (i.e., a loop) or binary. (Note: :math:`e_j` refers to
-the edge in the graph associated with measurement :math:`\mathbf{z}_j`,
-whereas :math:`\mathbf{e}_j` refers to the residual function associated
-with :math:`\mathbf{z}_j`.) For more information about the Graph SLAM
-algorithm, see [grisetti2010tutorial]_.
-
-We want to optimize
-
-.. math:: \chi^2 = \sum_{e_j \in \mathcal{E}} \mathbf{e}_j^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j.
-
-Let :math:`\mathbf{x}_i \in \mathbb{R}^c` be the compact representation
-of pose :math:`\mathbf{p}_i \in \mathcal{M}`, and let
-
-.. math:: \mathbf{x} := \begin{bmatrix} \mathbf{x}_1 \\ \mathbf{x}_2 \\ \vdots \\ \mathbf{x}_N \end{bmatrix} \in \mathbb{R}^{cN}
-
-We will solve this optimization problem iteratively. Let
-
-.. math:: \mathbf{x}^{k+1} := \mathbf{x}^k \boxplus \Delta \mathbf{x}^k = \begin{bmatrix} \mathbf{x}_1 \boxplus \Delta \mathbf{x}_1 \\ \mathbf{x}_2 \boxplus \Delta \mathbf{x}_2 \\ \vdots \\ \mathbf{x}_N \boxplus \Delta \mathbf{x}_2 \end{bmatrix}
- :label: update
-
-The :math:`\chi^2` error at iteration :math:`k+1` is
-
-.. math:: \chi_{k+1}^2 = \sum_{e_j \in \mathcal{E}} \underbrace{\left[ \mathbf{e}_j(\mathbf{x}^{k+1}) \right]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\mathbf{e}_j(\mathbf{x}^{k+1})}_{\bullet \times 1}.
- :label: chisq_at_kplusone
-
-We will linearize the residuals as:
-
-.. math::
- \begin{aligned}
- \mathbf{e}_j(\mathbf{x}^{k+1}) &= \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k) \\
- &\approx \mathbf{e}_j(\mathbf{x}^{k}) + \frac{\partial}{\partial \Delta \mathbf{x}^k} \left[ \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k) \right] \Delta \mathbf{x}^k \\
- &= \mathbf{e}_j(\mathbf{x}^{k}) + \left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right) \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \Delta \mathbf{x}^k.
- \end{aligned}
- :label: linearization
-
-Plugging :eq:`linearization` into :eq:`chisq_at_kplusone`, we get:
-
-.. math::
-
- \begin{aligned}
- \chi_{k+1}^2 &\approx \ \ \ \ \ \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x}^k)]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\mathbf{e}_j(\mathbf{x}^k)}_{\bullet \times 1} \notag \\
- &\hphantom{\approx} \ \ \ + \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x^k}) ]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \underbrace{\Delta \mathbf{x}^k}_{cN \times 1} \notag \\
- &\hphantom{\approx} \ \ \ + \sum_{e_j \in \mathcal{E}} \underbrace{(\Delta \mathbf{x}^k)^{\scriptstyle{\mathsf{T}}}}_{1 \times cN} \underbrace{ \left( \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \right)^{\scriptstyle{\mathsf{T}}}}_{cN \times dN} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)^{\scriptstyle{\mathsf{T}}}}_{dN \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \underbrace{\Delta \mathbf{x}^k}_{cN \times 1} \notag \\
- &= \chi_k^2 + 2 \mathbf{b}^{\scriptstyle{\mathsf{T}}}\Delta \mathbf{x}^k + (\Delta \mathbf{x}^k)^{\scriptstyle{\mathsf{T}}}H \Delta \mathbf{x}^k, \notag\end{aligned}
-
-where
-
-.. math::
-
- \begin{aligned}
- \mathbf{b}^{\scriptstyle{\mathsf{T}}}&= \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x^k}) ]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \\
- H &= \sum_{e_j \in \mathcal{E}} \underbrace{ \left( \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \right)^{\scriptstyle{\mathsf{T}}}}_{cN \times dN} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)^{\scriptstyle{\mathsf{T}}}}_{dN \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN}.\end{aligned}
-
-Using this notation, we obtain the optimal update as
-
-.. math:: \Delta \mathbf{x}^k = -H^{-1} \mathbf{b}. \label{eq:deltax}
-
-We apply this update to the poses via :eq:`update` and repeat until convergence.
-
-
-.. [blanco2010tutorial] Blanco, J.-L.A tutorial onSE(3) transformation parameterization and on-manifold optimization.University of Malaga, Tech. Rep 3(2010)
-.. [grisetti2010tutorial] Grisetti, G., Kummerle, R., Stachniss, C., and Burgard, W.A tutorial on graph-based SLAM.IEEE Intelligent Transportation Systems Magazine 2, 4 (2010), 31–43.
-
diff --git a/docs/modules/4_slam/slam_main.rst b/docs/modules/4_slam/slam_main.rst
deleted file mode 100644
index 98211986c2b..00000000000
--- a/docs/modules/4_slam/slam_main.rst
+++ /dev/null
@@ -1,18 +0,0 @@
-.. _`SLAM`:
-
-SLAM
-====
-
-Simultaneous Localization and Mapping(SLAM) examples
-Simultaneous Localization and Mapping (SLAM) is an ability to estimate the pose of a robot and the map of the environment at the same time. The SLAM problem is hard to
-solve, because a map is needed for localization and localization is needed for mapping. In this way, SLAM is often said to be similar to a ‘chicken-and-egg’ problem. Popular SLAM solution methods include the extended Kalman filter, particle filter, and Fast SLAM algorithm[31]. Fig.4 shows SLAM simulation results using extended Kalman filter and results using FastSLAM2.0[31].
-
-.. toctree::
- :maxdepth: 2
- :caption: Contents
-
- iterative_closest_point_matching/iterative_closest_point_matching
- ekf_slam/ekf_slam
- FastSLAM1/FastSLAM1
- FastSLAM2/FastSLAM2
- graph_slam/graph_slam
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-Catmull-Rom Spline Planning
-----------------------------
-
-.. image:: catmull_rom_path_planning.png
-
-This is a Catmull-Rom spline path planning routine.
-
-If you provide waypoints, the Catmull-Rom spline generates a smooth path that always passes through the control points,
-exhibits local control, and maintains 𝐶1 continuity.
-
-
-Catmull-Rom Spline Fundamentals
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-Catmull-Rom splines are a type of cubic spline that passes through a given set of points, known as control points.
-
-They are defined by the following equation for calculating a point on the spline:
-
-:math:`P(t) = 0.5 \times \left( 2P_1 + (-P_0 + P_2)t + (2P_0 - 5P_1 + 4P_2 - P_3)t^2 + (-P_0 + 3P_1 - 3P_2 + P_3)t^3 \right)`
-
-Where:
-
-* :math:`P(t)` is the point on the spline at parameter :math:`t`.
-* :math:`P_0, P_1, P_2, P_3` are the control points surrounding the parameter :math:`t`.
-
-Types of Catmull-Rom Splines
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-There are different types of Catmull-Rom splines based on the choice of the **tau** parameter, which influences how the curve
-behaves in relation to the control points:
-
-1. **Uniform Catmull-Rom Spline**:
- The standard implementation where the parameterization is uniform. Each segment of the spline is treated equally,
- regardless of the distances between control points.
-
-
-2. **Chordal Catmull-Rom Spline**:
- This spline type takes into account the distance between control points. The parameterization is based on the actual distance
- along the spline, ensuring smoother transitions. The equation can be modified to include the chord length :math:`L_i` between
- points :math:`P_i` and :math:`P_{i+1}`:
-
- .. math::
- \tau_i = \sqrt{(x_{i+1} - x_i)^2 + (y_{i+1} - y_i)^2}
-
-3. **Centripetal Catmull-Rom Spline**:
- This variation improves upon the chordal spline by using the square root of the distance to determine the parameterization,
- which avoids oscillations and creates a more natural curve. The parameter :math:`t_i` is adjusted using the following relation:
-
- .. math::
- t_i = \sqrt{(x_{i+1} - x_i)^2 + (y_{i+1} - y_i)^2}
-
-
-Blending Functions
-~~~~~~~~~~~~~~~~~~~~~
-
-In Catmull-Rom spline interpolation, blending functions are used to calculate the influence of each control point on the spline at a
-given parameter :math:`t`. The blending functions ensure that the spline is smooth and passes through the control points while
-maintaining continuity. The four blending functions used in Catmull-Rom splines are defined as follows:
-
-1. **Blending Function 1**:
-
- .. math::
- b_1(t) = -t + 2t^2 - t^3
-
-2. **Blending Function 2**:
-
- .. math::
- b_2(t) = 2 - 5t^2 + 3t^3
-
-3. **Blending Function 3**:
-
- .. math::
- b_3(t) = t + 4t^2 - 3t^3
-
-4. **Blending Function 4**:
-
- .. math::
- b_4(t) = -t^2 + t^3
-
-The blending functions are combined in the spline equation to create a smooth curve that reflects the influence of each control point.
-
-The following figure illustrates the blending functions over the interval :math:`[0, 1]`:
-
-.. image:: blending_functions.png
-
-Catmull-Rom Spline API
-~~~~~~~~~~~~~~~~~~~~~~~
-
-This section provides an overview of the functions used for Catmull-Rom spline path planning.
-
-API
-++++
-
-.. autofunction:: PathPlanning.Catmull_RomSplinePath.catmull_rom_spline_path.catmull_rom_point
-
-.. autofunction:: PathPlanning.Catmull_RomSplinePath.catmull_rom_spline_path.catmull_rom_spline
-
-
-References
-~~~~~~~~~~~~~~
-
-- `Catmull-Rom Spline - Wikipedia <https://en.wikipedia.org/wiki/Centripetal_Catmull%E2%80%93Rom_spline>`__
-- `Catmull-Rom Splines <http://graphics.cs.cmu.edu/nsp/course/15-462/Fall04/assts/catmullRom.pdf>`__
\ No newline at end of file
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diff --git a/docs/modules/5_path_planning/elastic_bands/elastic_bands_main.rst b/docs/modules/5_path_planning/elastic_bands/elastic_bands_main.rst
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-Elastic Bands
--------------
-
-This is a path planning with Elastic Bands.
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ElasticBands/animation.gif
-
-
-Core Concept
-~~~~~~~~~~~~
-- **Elastic Band**: A dynamically deformable collision-free path initialized by a global planner.
-- **Objective**:
-
- * Shorten and smooth the path.
- * Maximize obstacle clearance.
- * Maintain global path connectivity.
-
-Bubble Representation
-~~~~~~~~~~~~~~~~~~~~~~~~
-- **Definition**: A local free-space region around configuration :math:`b`:
-
- .. math::
- B(b) = \{ q: \|q - b\| < \rho(b) \},
-
- where :math:`\rho(b)` is the radius of the bubble.
-
-
-Force-Based Deformation
-~~~~~~~~~~~~~~~~~~~~~~~
-The elastic band deforms under artificial forces:
-
-Internal Contraction Force
-++++++++++++++++++++++++++
-- **Purpose**: Reduces path slack and length.
-- **Formula**: For node :math:`b_i`:
-
- .. math::
- f_c(b_i) = k_c \left( \frac{b_{i-1} - b_i}{\|b_{i-1} - b_i\|} + \frac{b_{i+1} - b_i}{\|b_{i+1} - b_i\|} \right)
-
- where :math:`k_c` is the contraction gain.
-
-External Repulsion Force
-+++++++++++++++++++++++++
-- **Purpose**: Pushes the path away from obstacles.
-- **Formula**: For node :math:`b_i`:
-
- .. math::
- f_r(b_i) = \begin{cases}
- k_r (\rho_0 - \rho(b_i)) \nabla \rho(b_i) & \text{if } \rho(b_i) < \rho_0, \\
- 0 & \text{otherwise}.
- \end{cases}
-
- where :math:`k_r` is the repulsion gain, :math:`\rho_0` is the maximum distance for applying repulsion force, and :math:`\nabla \rho(b_i)` is approximated via finite differences:
-
- .. math::
- \frac{\partial \rho}{\partial x} \approx \frac{\rho(b_i + h) - \rho(b_i - h)}{2h}.
-
-Dynamic Path Maintenance
-~~~~~~~~~~~~~~~~~~~~~~~~~~
-1. **Node Update**:
-
- .. math::
- b_i^{\text{new}} = b_i^{\text{old}} + \alpha (f_c + f_r),
-
- where :math:`\alpha` is a step-size parameter, which often proportional to :math:`\rho(b_i^{\text{old}})`
-
-2. **Overlap Enforcement**:
-- Insert new nodes if adjacent nodes are too far apart
-- Remove redundant nodes if adjacent nodes are too close
-
-References
-~~~~~~~~~~~~~~~~~~~~~~~
-
-- `Elastic Bands: Connecting Path Planning and Control <http://www8.cs.umu.se/research/ifor/dl/Control/elastic%20bands.pdf>`__
diff --git a/docs/modules/5_path_planning/frenet_frame_path/frenet_frame_path_main.rst b/docs/modules/5_path_planning/frenet_frame_path/frenet_frame_path_main.rst
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--- a/docs/modules/5_path_planning/frenet_frame_path/frenet_frame_path_main.rst
+++ /dev/null
@@ -1,46 +0,0 @@
-Optimal Trajectory in a Frenet Frame
-------------------------------------
-
-This is optimal trajectory generation in a Frenet Frame.
-
-The cyan line is the target course and black crosses are obstacles.
-
-The red line is predicted path.
-
-High Speed and Velocity Keeping Scenario
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/FrenetOptimalTrajectory/high_speed_and_velocity_keeping_frenet_path.gif
-
-This scenario shows how the trajectory is maintained at high speeds while keeping a consistent velocity.
-
-High Speed and Merging and Stopping Scenario
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/FrenetOptimalTrajectory/high_speed_and_merging_and_stopping_frenet_path.gif
-
-This scenario demonstrates the trajectory planning at high speeds with merging and stopping behaviors.
-
-Low Speed and Velocity Keeping Scenario
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/FrenetOptimalTrajectory/low_speed_and_velocity_keeping_frenet_path.gif
-
-This scenario demonstrates how the trajectory is managed at low speeds while maintaining a steady velocity.
-
-Low Speed and Merging and Stopping Scenario
-~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/FrenetOptimalTrajectory/low_speed_and_merging_and_stopping_frenet_path.gif
-
-This scenario illustrates the trajectory planning at low speeds with merging and stopping behaviors.
-
-Ref:
-
-- `Optimal Trajectory Generation for Dynamic Street Scenarios in a
- Frenet
- Frame <https://www.researchgate.net/profile/Moritz_Werling/publication/224156269_Optimal_Trajectory_Generation_for_Dynamic_Street_Scenarios_in_a_Frenet_Frame/links/54f749df0cf210398e9277af.pdf>`__
-
-- `Optimal trajectory generation for dynamic street scenarios in a
- Frenet Frame <https://www.youtube.com/watch?v=Cj6tAQe7UCY>`__
-
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-Reeds Shepp planning
---------------------
-
-A sample code with Reeds Shepp path planning.
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ReedsSheppPath/animation.gif?raw=true
-
-Mathematical Description of Individual Path Types
-=================================================
-Here is an overview of mathematical derivations of formulae for individual path types.
-
-In all the derivations below, radius of curvature of the vehicle is assumed to be of unit length and start pose is considered to be at origin. (*In code we are removing the offset due to start position and normalising the lengths before passing the values to these functions.*)
-
-Also, (t, u, v) respresent the measure of each motion requried. Thus, in case of a turning maneuver, they represent the angle inscribed at the centre of turning circle and in case of straight maneuver, they represent the distance to be travelled.
-
-1. **Left-Straight-Left**
-
-.. image:: LSL.png
-
-We can deduce the following facts using geometry.
-
-- AGHC is a rectangle.
-- :math:`∠LAC = ∠BAG = t`
-- :math:`t + v = φ`
-- :math:`C(x - sin(φ), y + cos(φ))`
-- :math:`A(0, 1)`
-- :math:`u, t = polar(vector<AC>)`
-
-Hence, we have:
-
-- :math:`u, t = polar(x - sin(φ), y + cos(φ) - 1)`
-- :math:`v = φ - t`
-
-
-2. **Left-Straight-Right**
-
-.. image:: LSR.png
-
-With followng notations:
-
-- :math:`∠MBD = t1`
-- :math:`∠BDF = θ`
-- :math:`BC = u1`
-
-We can deduce the following facts using geometry.
-
-- D is mid-point of BC and FG.
-- :math:`t - v = φ`
-- :math:`C(x + sin(φ), y - cos(φ))`
-- :math:`A(0, 1)`
-- :math:`u1, t1 = polar(vector<AC>)`
-- :math:`\frac{u1^2}{4} = 1 + \frac{u^2}{4}`
-- :math:`BF = 1` [Radius Of Curvature]
-- :math:`FD = \frac{u}{2}`
-- :math:`θ = arctan(\frac{BF}{FD})`
-- :math:`t1 + θ = t`
-
-Hence, we have:
-
-- :math:`u1, t1 = polar(x + sin(φ), y - cos(φ) - 1)`
-- :math:`u = \sqrt{u1^2 - 4}`
-- :math:`θ = arctan(\frac{2}{u})`
-- :math:`t = t1 + θ`
-- :math:`v = t - φ`
-
-3. **LeftxRightxLeft**
-
-.. image:: L_R_L.png
-
-With followng notations:
-
-- :math:`∠CBD = ∠CDB = A` [BCD is an isoceles triangle]
-- :math:`∠DBK = θ`
-- :math:`BD = u1`
-
-We can deduce the following facts using geometry.
-
-- :math:`t + u + v = φ`
-- :math:`D(x - sin(φ), y + cos(φ))`
-- :math:`B(0, 1)`
-- :math:`u1, θ = polar(vector<BD>)`
-- :math:`A = arccos(\frac{BD/2}{CD})`
-- :math:`u = (π - 2*A)`
-- :math:`∠ABK = \frac{π}{2}`
-- :math:`∠KBD = θ`
-- :math:`t = ∠ABK + ∠KBD + ∠DBC`
-
-Hence, we have:
-
-- :math:`u1, θ = polar(x - sin(φ), y + cos(φ) - 1)`
-- :math:`A = arccos(\frac{u1/2}{2})`
-- :math:`t = \frac{π}{2} + θ + A`
-- :math:`u = (π - 2*A)`
-- :math:`v = (φ - t - u)`
-
-4. **LeftxRight-Left**
-
-.. image:: L_RL.png
-
-With followng notations:
-
-- :math:`∠CBD = ∠CDB = A` [BCD is an isoceles triangle]
-- :math:`∠DBK = θ`
-- :math:`BD = u1`
-
-We can deduce the following facts using geometry.
-
-- :math:`t + u - v = φ`
-- :math:`D(x - sin(φ), y + cos(φ))`
-- :math:`B(0, 1)`
-- :math:`u1, θ = polar(vector<BD>)`
-- :math:`A = arccos(\frac{BD/2}{CD})`
-- :math:`u = (π - 2*A)`
-- :math:`∠ABK = \frac{π}{2}`
-- :math:`∠KBD = θ`
-- :math:`t = ∠ABK + ∠KBD + ∠DBC`
-
-Hence, we have:
-
-- :math:`u1, θ = polar(x - sin(φ), y + cos(φ) - 1)`
-- :math:`A = arccos(\frac{u1/2}{2})`
-- :math:`t = \frac{π}{2} + θ + A`
-- :math:`u = (π - 2*A)`
-- :math:`v = (-φ + t + u)`
-
-5. **Left-RightxLeft**
-
-.. image:: LR_L.png
-
-With followng notations:
-
-- :math:`∠CBD = ∠CDB = A` [BCD is an isoceles triangle]
-- :math:`∠DBK = θ`
-- :math:`BD = u1`
-
-We can deduce the following facts using geometry.
-
-- :math:`t - u - v = φ`
-- :math:`D(x - sin(φ), y + cos(φ))`
-- :math:`B(0, 1)`
-- :math:`u1, θ = polar(vector<BD>)`
-- :math:`BC = CD = 2` [2 * radius of curvature]
-- :math:`cos(2π - u) = \frac{BC^2 + CD^2 - BD^2}{2 * BC * CD}` [Cosine Rule]
-- :math:`\frac{sin(A)}{BC} = \frac{sin(u)}{u1}` [Sine Rule]
-- :math:`∠ABK = \frac{π}{2}`
-- :math:`∠KBD = θ`
-- :math:`t = ∠ABK + ∠KBD - ∠DBC`
-
-Hence, we have:
-
-- :math:`u1, θ = polar(x - sin(φ), y + cos(φ) - 1)`
-- :math:`u = arccos(1 - \frac{u1^2}{8})`
-- :math:`A = arcsin(\frac{sin(u)}{u1}*2)`
-- :math:`t = \frac{π}{2} + θ - A`
-- :math:`v = (t - u - φ)`
-
-6. **Left-RightxLeft-Right**
-
-.. image:: LR_LR.png
-
-With followng notations:
-
-- :math:`∠CLG = ∠BCL = ∠CBG = ∠LGB = A = u` [BGCL is an isoceles trapezium]
-- :math:`∠KBG = θ`
-- :math:`BG = u1`
-
-We can deduce the following facts using geometry.
-
-- :math:`t - 2u + v = φ`
-- :math:`G(x + sin(φ), y - cos(φ))`
-- :math:`B(0, 1)`
-- :math:`u1, θ = polar(vector<BG>)`
-- :math:`BC = CL = LG = 2` [2 * radius of curvature]
-- :math:`CG^2 = CL^2 + LG^2 - 2*CL*LG*cos(A)` [Cosine rule in LGC]
-- :math:`CG^2 = CL^2 + LG^2 - 2*CL*LG*cos(A)` [Cosine rule in LGC]
-- From the previous two equations: :math:`A = arccos(\frac{u1 + 2}{4})`
-- :math:`∠ABK = \frac{π}{2}`
-- :math:`t = ∠ABK + ∠KBG + ∠GBC`
-
-Hence, we have:
-
-- :math:`u1, θ = polar(x + sin(φ), y - cos(φ) - 1)`
-- :math:`u = arccos(\frac{u1 + 2}{4})`
-- :math:`t = \frac{π}{2} + θ + u`
-- :math:`v = (φ - t + 2u)`
-
-7. **LeftxRight-LeftxRight**
-
-.. image:: L_RL_R.png
-
-With followng notations:
-
-- :math:`∠GBC = A` [BGCL is an isoceles trapezium]
-- :math:`∠KBG = θ`
-- :math:`BG = u1`
-
-We can deduce the following facts using geometry.
-
-- :math:`t - v = φ`
-- :math:`G(x + sin(φ), y - cos(φ))`
-- :math:`B(0, 1)`
-- :math:`u1, θ = polar(vector<BG>)`
-- :math:`BC = CL = LG = 2` [2 * radius of curvature]
-- :math:`CD = 1` [radius of curvature]
-- D is midpoint of BG
-- :math:`BD = \frac{u1}{2}`
-- :math:`cos(u) = \frac{BC^2 + CD^2 - BD^2}{2*BC*CD}` [Cosine rule in BCD]
-- :math:`sin(A) = CD*\frac{sin(u)}{BD}` [Sine rule in BCD]
-- :math:`∠ABK = \frac{π}{2}`
-- :math:`t = ∠ABK + ∠KBG + ∠GBC`
-
-Hence, we have:
-
-- :math:`u1, θ = polar(x + sin(φ), y - cos(φ) - 1)`
-- :math:`u = arccos(\frac{20 - u1^2}{16})`
-- :math:`A = arcsin(2*\frac{sin(u)}{u1})`
-- :math:`t = \frac{π}{2} + θ + A`
-- :math:`v = (t - φ)`
-
-
-8. **LeftxRight90-Straight-Left**
-
-.. image:: L_R90SL.png
-
-With followng notations:
-
-- :math:`∠FBM = A` [BGCL is an isoceles trapezium]
-- :math:`∠KBF = θ`
-- :math:`BF = u1`
-
-We can deduce the following facts using geometry.
-
-- :math:`t + \frac{π}{2} - v = φ`
-- :math:`F(x - sin(φ), y + cos(φ))`
-- :math:`B(0, 1)`
-- :math:`u1, θ = polar(vector<BF>)`
-- :math:`BM = CB = 2` [2 * radius of curvature]
-- :math:`MD = CD = 1` [CGDM is a rectangle]
-- :math:`MC = GD = u` [CGDM is a rectangle]
-- :math:`MF = MD + DF = 2`
-- :math:`BM = \sqrt{BF^2 - MF^2}` [Pythagoras theorem on BFM]
-- :math:`tan(A) = \frac{MF}{BM}`
-- :math:`u = MC = BM - CB`
-- :math:`t = ∠ABK + ∠KBF + ∠FBC`
-
-Hence, we have:
-
-- :math:`u1, θ = polar(x - sin(φ), y + cos(φ) - 1)`
-- :math:`u = arccos(\sqrt{u1^2 - 4} - 2)`
-- :math:`A = arctan(\frac{2}{\sqrt{u1^2 - 4}})`
-- :math:`t = \frac{π}{2} + θ + A`
-- :math:`v = (t - φ + \frac{π}{2})`
-
-
-9. **Left-Straight-Right90xLeft**
-
-.. image:: LSR90_L.png
-
-With followng notations:
-
-- :math:`∠MBH = A` [BGCL is an isoceles trapezium]
-- :math:`∠KBH = θ`
-- :math:`BH = u1`
-
-We can deduce the following facts using geometry.
-
-- :math:`t - \frac{π}{2} - v = φ`
-- :math:`H(x - sin(φ), y + cos(φ))`
-- :math:`B(0, 1)`
-- :math:`u1, θ = polar(vector<BH>)`
-- :math:`GH = 2` [2 * radius of curvature]
-- :math:`CM = DG = 1` [CGDM is a rectangle]
-- :math:`CD = MG = u` [CGDM is a rectangle]
-- :math:`BM = BC + CM = 2`
-- :math:`MH = \sqrt{BH^2 - BM^2}` [Pythagoras theorem on BHM]
-- :math:`tan(A) = \frac{HM}{BM}`
-- :math:`u = MC = BM - CB`
-- :math:`t = ∠ABK + ∠KBH - ∠HBC`
-
-Hence, we have:
-
-- :math:`u1, θ = polar(x - sin(φ), y + cos(φ) - 1)`
-- :math:`u = arccos(\sqrt{u1^2 - 4} - 2)`
-- :math:`A = arctan(\frac{2}{\sqrt{u1^2 - 4}})`
-- :math:`t = \frac{π}{2} + θ - A`
-- :math:`v = (t - φ - \frac{π}{2})`
-
-
-10. **LeftxRight90-Straight-Right**
-
-.. image:: L_R90SR.png
-
-With followng notations:
-
-- :math:`∠KBG = θ`
-- :math:`BG = u1`
-
-We can deduce the following facts using geometry.
-
-- :math:`t - \frac{π}{2} - v = φ`
-- :math:`G(x + sin(φ), y - cos(φ))`
-- :math:`B(0, 1)`
-- :math:`u1, θ = polar(vector<BG>)`
-- :math:`BD = 2` [2 * radius of curvature]
-- :math:`DG = EF = u` [DGFE is a rectangle]
-- :math:`DG = BG - BD = 2`
-- :math:`∠ABK = \frac{π}{2}`
-- :math:`t = ∠ABK + ∠KBG`
-
-Hence, we have:
-
-- :math:`u1, θ = polar(x + sin(φ), y - cos(φ) - 1)`
-- :math:`u = u1 - 2`
-- :math:`t = \frac{π}{2} + θ`
-- :math:`v = (t - φ - \frac{π}{2})`
-
-
-11. **Left-Straight-Left90xRight**
-
-.. image:: LSL90xR.png
-
-With followng notations:
-
-- :math:`∠KBH = θ`
-- :math:`BH = u1`
-
-We can deduce the following facts using geometry.
-
-- :math:`t + \frac{π}{2} + v = φ`
-- :math:`H(x + sin(φ), y - cos(φ))`
-- :math:`B(0, 1)`
-- :math:`u1, θ = polar(vector<BH>)`
-- :math:`GH = 2` [2 * radius of curvature]
-- :math:`DC = BG = u` [DGBC is a rectangle]
-- :math:`BG = BH - GH`
-- :math:`∠ABC= ∠KBH`
-
-Hence, we have:
-
-- :math:`u1, θ = polar(x + sin(φ), y - cos(φ) - 1)`
-- :math:`u = u1 - 2`
-- :math:`t = θ`
-- :math:`v = (φ - t - \frac{π}{2})`
-
-
-12. **LeftxRight90-Straight-Left90xRight**
-
-.. image:: L_R90SL90_R.png
-
-With followng notations:
-
-- :math:`∠KBH = θ`
-- :math:`∠HBM = A`
-- :math:`BH = u1`
-
-We can deduce the following facts using geometry.
-
-- :math:`t - v = φ`
-- :math:`H(x + sin(φ), y - cos(φ))`
-- :math:`B(0, 1)`
-- :math:`u1, θ = polar(vector<BH>)`
-- :math:`GF = ED = 1` [radius of curvature]
-- :math:`BD = GH = 2` [2 * radius of curvature]
-- :math:`FN = GH = 2` [ENMD is a rectangle]
-- :math:`NH = GF = 1` [FNHG is a rectangle]
-- :math:`MN = ED = 1` [ENMD is a rectangle]
-- :math:`DO = EF = u` [DOFE is a rectangle]
-- :math:`MH = MN + NH = 2`
-- :math:`BM = \sqrt{BH^2 - MH^2}` [Pythagoras theorem on BHM]
-- :math:`DO = BM - BD - OM`
-- :math:`tan(A) = \frac{MH}{BM}`
-- :math:`∠ABC = ∠ABK + ∠KBH + ∠HBM`
-
-Hence, we have:
-
-- :math:`u1, θ = polar(x + sin(φ), y - cos(φ) - 1)`
-- :math:`u = /sqrt{u1^2 - 4} - 4`
-- :math:`A = arctan(\frac{2}{u1^2 - 4})`
-- :math:`t = \frac{π}{2} + θ + A`
-- :math:`v = (t - φ)`
-
-
-Ref:
-
-- `15.3.2 Reeds-Shepp
- Curves <https://lavalle.pl/planning/node822.html>`__
-
-- `optimal paths for a car that goes both forwards and
- backwards <https://pdfs.semanticscholar.org/932e/c495b1d0018fd59dee12a0bf74434fac7af4.pdf>`__
-
-- `ghliu/pyReedsShepp: Implementation of Reeds Shepp
- curve. <https://github.com/ghliu/pyReedsShepp>`__
diff --git a/docs/modules/5_path_planning/rrt/figure_1.png b/docs/modules/5_path_planning/rrt/figure_1.png
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diff --git a/docs/modules/5_path_planning/rrt/rrt_star.rst b/docs/modules/5_path_planning/rrt/rrt_star.rst
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index 6deb6b91726..00000000000
--- a/docs/modules/5_path_planning/rrt/rrt_star.rst
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@@ -1,21 +0,0 @@
-RRT\*
-~~~~~
-
-.. figure:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTstar/animation.gif
-
-This is a path planning code with RRT\*
-
-Black circles are obstacles, green line is a searched tree, red crosses are start and goal positions.
-
-Simulation
-^^^^^^^^^^
-
-.. image:: rrt_star/rrt_star_1_0.png
- :width: 600px
-
-
-Ref
-^^^
-- `Sampling-based Algorithms for Optimal Motion Planning <https://arxiv.org/pdf/1105.1186>`__
-- `Incremental Sampling-based Algorithms for Optimal Motion Planning <https://arxiv.org/abs/1005.0416>`__
-
diff --git a/docs/modules/5_path_planning/rrt/rrt_star_reeds_shepp/figure_1.png b/docs/modules/5_path_planning/rrt/rrt_star_reeds_shepp/figure_1.png
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diff --git a/docs/modules/5_path_planning/time_based_grid_search/time_based_grid_search_main.rst b/docs/modules/5_path_planning/time_based_grid_search/time_based_grid_search_main.rst
deleted file mode 100644
index 04001d45044..00000000000
--- a/docs/modules/5_path_planning/time_based_grid_search/time_based_grid_search_main.rst
+++ /dev/null
@@ -1,80 +0,0 @@
-Time based grid search
-----------------------
-
-Space-time astar
-~~~~~~~~~~~~~~~~~~~~~~
-
-This is an extension of A* algorithm that supports planning around dynamic obstacles.
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/TimeBasedPathPlanning/SpaceTimeAStar/path_animation.gif
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/TimeBasedPathPlanning/SpaceTimeAStar/path_animation2.gif
-
-The key difference of this algorithm compared to vanilla A* is that the cost and heuristic are now time-based instead of distance-based.
-Using a time-based cost and heuristic ensures the path found is optimal in terms of time to reach the goal.
-
-The cost is the amount of time it takes to reach a given node, and the heuristic is the minimum amount of time it could take to reach the goal from that node, disregarding all obstacles.
-For a simple scenario where the robot can move 1 cell per time step and stop and go as it pleases, the heuristic for time is equivalent to the heuristic for distance.
-
-One optimization that was added in `this PR <https://github.com/AtsushiSakai/PythonRobotics/pull/1183>`__ was to add an expanded set to the algorithm. The algorithm will not expand nodes that are already in that set. This greatly reduces the number of node expansions needed to find a path, since no duplicates are expanded. It also helps to reduce the amount of memory the algorithm uses.
-
-Before::
-
- Found path to goal after 204490 expansions
- Planning took: 1.72464 seconds
- Memory usage (RSS): 68.19 MB
-
-
-After::
-
- Found path to goal after 2348 expansions
- Planning took: 0.01550 seconds
- Memory usage (RSS): 64.85 MB
-
-When starting at (1, 11) in the structured obstacle arrangement (second of the two gifs above).
-
-
-Safe Interval Path Planning
-~~~~~~~~~~~~~~~~~~~~~~~~~~~
-
-The safe interval path planning algorithm is described in this paper:
-
-`SIPP: Safe Interval Path Planning for Dynamic Environments <https://www.cs.cmu.edu/~maxim/files/sipp_icra11.pdf>`__
-
-It is faster than space-time A* because it pre-computes the intervals of time that are unoccupied in each cell. This allows it to reduce the number of successor node it generates by avoiding nodes within the same interval.
-
-**Comparison with SpaceTime A*:**
-
-Arrangement 1 starting at (1, 18)
-
-SafeInterval planner::
-
- Found path to goal after 322 expansions
- Planning took: 0.00730 seconds
-
-SpaceTime A*::
-
- Found path to goal after 2717154 expansions
- Planning took: 20.51330 seconds
-
-**Benchmarking the Safe Interval Path Planner:**
-
-250 random obstacles::
-
- Found path to goal after 764 expansions
- Planning took: 0.60596 seconds
-
-.. image:: https://raw.githubusercontent.com/AtsushiSakai/PythonRoboticsGifs/refs/heads/master/PathPlanning/TimeBasedPathPlanning/SafeIntervalPathPlanner/path_animation.gif
-
-Arrangement 1 starting at (1, 18)::
-
- Found path to goal after 322 expansions
- Planning took: 0.00730 seconds
-
-.. image:: https://raw.githubusercontent.com/AtsushiSakai/PythonRoboticsGifs/refs/heads/master/PathPlanning/TimeBasedPathPlanning/SafeIntervalPathPlanner/path_animation2.gif
-
-References
-~~~~~~~~~~~
-
-- `Cooperative Pathfinding <https://www.davidsilver.uk/wp-content/uploads/2020/03/coop-path-AIWisdom.pdf>`__
-- `SIPP: Safe Interval Path Planning for Dynamic Environments <https://www.cs.cmu.edu/~maxim/files/sipp_icra11.pdf>`__
diff --git a/docs/modules/6_path_tracking/lqr_speed_and_steering_control/lqr_speed_and_steering_control_main.rst b/docs/modules/6_path_tracking/lqr_speed_and_steering_control/lqr_speed_and_steering_control_main.rst
deleted file mode 100644
index ded187e972d..00000000000
--- a/docs/modules/6_path_tracking/lqr_speed_and_steering_control/lqr_speed_and_steering_control_main.rst
+++ /dev/null
@@ -1,140 +0,0 @@
-.. _linearquadratic-regulator-(lqr)-speed-and-steering-control:
-
-Linear–quadratic regulator (LQR) speed and steering control
------------------------------------------------------------
-
-Path tracking simulation with LQR speed and steering control.
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/lqr_speed_steer_control/animation.gif
-
-`[Code Link] <https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py>`_
-
-Overview
-~~~~~~~~
-
-The LQR (Linear Quadratic Regulator) speed and steering control model implemented in `lqr_speed_steer_control.py` provides a simulation
-for an autonomous vehicle to track:
-
-1. A desired speed by adjusting acceleration based on feedback from the current state and the desired speed.
-
-2. A desired trajectory by adjusting steering angle based on feedback from the current state and the desired trajectory.
-
-by only using one LQT controller.
-
-Vehicle motion Model
-~~~~~~~~~~~~~~~~~~~~~
-
-The below figure shows the geometric model of the vehicle used in this simulation:
-
-.. image:: lqr_steering_control_model.jpg
- :width: 600px
-
-The `e`, :math:`{\theta}`, and :math:`\upsilon` represent the lateral error, orientation error, and velocity error, respectively, with respect to the desired trajectory and speed.
-And :math:`\dot{e}` and :math:`\dot{\theta}` represent the rates of change of these errors.
-
-The :math:`e_t` and :math:`\theta_t`, and :math:`\upsilon` are the updated values of `e`, :math:`\theta`, :math:`\upsilon` and at time `t`, respectively, and can be calculated using the following kinematic equations:
-
-.. math:: e_t = e_{t-1} + \dot{e}_{t-1} dt
-
-.. math:: \theta_t = \theta_{t-1} + \dot{\theta}_{t-1} dt
-
-.. math:: \upsilon_t = \upsilon_{t-1} + a_{t-1} dt
-
-Where `dt` is the time difference and :math:`a_t` is the acceleration at the time `t`.
-
-The change rate of the `e` can be calculated as:
-
-.. math:: \dot{e}_t = V \sin(\theta_{t-1})
-
-Where `V` is the current vehicle speed.
-
-If the :math:`\theta` is small,
-
-.. math:: \theta \approx 0
-
-the :math:`\sin(\theta)` can be approximated as :math:`\theta`:
-
-.. math:: \sin(\theta) = \theta
-
-So, the change rate of the `e` can be approximated as:
-
-.. math:: \dot{e}_t = V \theta_{t-1}
-
-The change rate of the :math:`\theta` can be calculated as:
-
-.. math:: \dot{\theta}_t = \frac{V}{L} \tan(\delta)
-
-where `L` is the wheelbase of the vehicle and :math:`\delta` is the steering angle.
-
-If the :math:`\delta` is small,
-
-.. math:: \delta \approx 0
-
-the :math:`\tan(\delta)` can be approximated as :math:`\delta`:
-
-.. math:: \tan(\delta) = \delta
-
-So, the change rate of the :math:`\theta` can be approximated as:
-
-.. math:: \dot{\theta}_t = \frac{V}{L} \delta
-
-The above equations can be used to update the state of the vehicle at each time step.
-
-Control Model
-~~~~~~~~~~~~~~
-
-To formulate the state-space representation of the vehicle dynamics as a linear model,
-the state vector `x` and control input vector `u` are defined as follows:
-
-.. math:: x_t = [e_t, \dot{e}_t, \theta_t, \dot{\theta}_t, \upsilon_t]^T
-
-.. math:: u_t = [\delta_t, a_t]^T
-
-The linear state transition equation can be represented as:
-
-.. math:: x_{t+1} = A x_t + B u_t
-
-where:
-
-:math:`\begin{equation*} A = \begin{bmatrix} 1 & dt & 0 & 0 & 0\\ 0 & 0 & v & 0 & 0\\ 0 & 0 & 1 & dt & 0\\ 0 & 0 & 0 & 0 & 0\\ 0 & 0 & 0 & 0 & 1\\\end{bmatrix} \end{equation*}`
-
-:math:`\begin{equation*} B = \begin{bmatrix} 0 & 0\\ 0 & 0\\ 0 & 0\\ \frac{v}{L} & 0\\ 0 & dt \\ \end{bmatrix} \end{equation*}`
-
-LQR controller
-~~~~~~~~~~~~~~~
-
-The Linear Quadratic Regulator (LQR) controller is used to calculate the optimal control input `u` that minimizes the quadratic cost function:
-
-:math:`J = \sum_{t=0}^{N} (x_t^T Q x_t + u_t^T R u_t)`
-
-where `Q` and `R` are the weighting matrices for the state and control input, respectively.
-
-for the linear model:
-
-:math:`x_{t+1} = A x_t + B u_t`
-
-The optimal control input `u` can be calculated as:
-
-:math:`u_t = -K x_t`
-
-where `K` is the feedback gain matrix obtained by solving the Riccati equation.
-
-Simulation results
-~~~~~~~~~~~~~~~~~~~
-
-
-.. image:: x-y.png
- :width: 600px
-
-.. image:: yaw.png
- :width: 600px
-
-.. image:: speed.png
- :width: 600px
-
-
-
-References:
-~~~~~~~~~~~
-
-- `Towards fully autonomous driving: Systems and algorithms <https://ieeexplore.ieee.org/document/5940562/>`__
diff --git a/docs/modules/6_path_tracking/lqr_speed_and_steering_control/lqr_steering_control_model.jpg b/docs/modules/6_path_tracking/lqr_speed_and_steering_control/lqr_steering_control_model.jpg
deleted file mode 100644
index 83754d5bb01..00000000000
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index bff3f1a786e..00000000000
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diff --git a/docs/modules/6_path_tracking/lqr_speed_and_steering_control/yaw.png b/docs/modules/6_path_tracking/lqr_speed_and_steering_control/yaw.png
deleted file mode 100644
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diff --git a/docs/modules/6_path_tracking/lqr_steering_control/lqr_steering_control_main.rst b/docs/modules/6_path_tracking/lqr_steering_control/lqr_steering_control_main.rst
deleted file mode 100644
index baca7a33fc4..00000000000
--- a/docs/modules/6_path_tracking/lqr_steering_control/lqr_steering_control_main.rst
+++ /dev/null
@@ -1,121 +0,0 @@
-.. _linearquadratic-regulator-(lqr)-steering-control:
-
-Linear–quadratic regulator (LQR) steering control
--------------------------------------------------
-
-Path tracking simulation with LQR steering control and PID speed
-control.
-
-.. image:: https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/lqr_steer_control/animation.gif
-
-`[Code Link] <https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/lqr_steer_control/lqr_steer_control.py>`_
-
-Overview
-~~~~~~~~
-
-The LQR (Linear Quadratic Regulator) steering control model implemented in lqr_steer_control.py provides a simulation
-for an autonomous vehicle to track a desired trajectory by adjusting steering angle based on feedback from the current state and the desired trajectory.
-This model utilizes a combination of PID speed control and LQR steering control to achieve smooth and accurate trajectory tracking.
-
-Vehicle motion Model
-~~~~~~~~~~~~~~~~~~~~~
-
-The below figure shows the geometric model of the vehicle used in this simulation:
-
-.. image:: lqr_steering_control_model.jpg
- :width: 600px
-
-The `e` and :math:`\theta` represent the lateral error and orientation error, respectively, with respect to the desired trajectory.
-And :math:`\dot{e}` and :math:`\dot{\theta}` represent the rates of change of these errors.
-
-The :math:`e_t` and :math:`\theta_t` are the updated values of `e` and :math:`\theta` at time `t`, respectively, and can be calculated using the following kinematic equations:
-
-.. math:: e_t = e_{t-1} + \dot{e}_{t-1} dt
-
-.. math:: \theta_t = \theta_{t-1} + \dot{\theta}_{t-1} dt
-
-Where `dt` is the time difference.
-
-The change rate of the `e` can be calculated as:
-
-.. math:: \dot{e}_t = V \sin(\theta_{t-1})
-
-Where `V` is the current vehicle speed.
-
-If the :math:`\theta` is small,
-
-.. math:: \theta \approx 0
-
-the :math:`\sin(\theta)` can be approximated as :math:`\theta`:
-
-.. math:: \sin(\theta) = \theta
-
-So, the change rate of the `e` can be approximated as:
-
-.. math:: \dot{e}_t = V \theta_{t-1}
-
-The change rate of the :math:`\theta` can be calculated as:
-
-.. math:: \dot{\theta}_t = \frac{V}{L} \tan(\delta)
-
-where `L` is the wheelbase of the vehicle and :math:`\delta` is the steering angle.
-
-If the :math:`\delta` is small,
-
-.. math:: \delta \approx 0
-
-the :math:`\tan(\delta)` can be approximated as :math:`\delta`:
-
-.. math:: \tan(\delta) = \delta
-
-So, the change rate of the :math:`\theta` can be approximated as:
-
-.. math:: \dot{\theta}_t = \frac{V}{L} \delta
-
-The above equations can be used to update the state of the vehicle at each time step.
-
-Control Model
-~~~~~~~~~~~~~~
-
-To formulate the state-space representation of the vehicle dynamics as a linear model,
-the state vector `x` and control input vector `u` are defined as follows:
-
-.. math:: x_t = [e_t, \dot{e}_t, \theta_t, \dot{\theta}_t]^T
-
-.. math:: u_t = \delta_t
-
-The linear state transition equation can be represented as:
-
-.. math:: x_{t+1} = A x_t + B u_t
-
-where:
-
-:math:`\begin{equation*} A = \begin{bmatrix} 1 & dt & 0 & 0\\ 0 & 0 & v & 0\\ 0 & 0 & 1 & dt\\ 0 & 0 & 0 & 0 \\ \end{bmatrix} \end{equation*}`
-
-:math:`\begin{equation*} B = \begin{bmatrix} 0\\ 0\\ 0\\ \frac{v}{L} \\ \end{bmatrix} \end{equation*}`
-
-LQR controller
-~~~~~~~~~~~~~~~
-
-The Linear Quadratic Regulator (LQR) controller is used to calculate the optimal control input `u` that minimizes the quadratic cost function:
-
-:math:`J = \sum_{t=0}^{N} (x_t^T Q x_t + u_t^T R u_t)`
-
-where `Q` and `R` are the weighting matrices for the state and control input, respectively.
-
-for the linear model:
-
-:math:`x_{t+1} = A x_t + B u_t`
-
-The optimal control input `u` can be calculated as:
-
-:math:`u_t = -K x_t`
-
-where `K` is the feedback gain matrix obtained by solving the Riccati equation.
-
-References:
-~~~~~~~~~~~
-- `ApolloAuto/apollo: An open autonomous driving platform <https://github.com/ApolloAuto/apollo>`_
-
-- `Linear Quadratic Regulator (LQR) <https://en.wikipedia.org/wiki/Linear%E2%80%93quadratic_regulator>`_
-
diff --git a/docs/modules/6_path_tracking/lqr_steering_control/lqr_steering_control_model.jpg b/docs/modules/6_path_tracking/lqr_steering_control/lqr_steering_control_model.jpg
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index 83754d5bb01..00000000000
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diff --git a/docs/modules/6_path_tracking/path_tracking_main.rst b/docs/modules/6_path_tracking/path_tracking_main.rst
deleted file mode 100644
index d98e3245835..00000000000
--- a/docs/modules/6_path_tracking/path_tracking_main.rst
+++ /dev/null
@@ -1,19 +0,0 @@
-.. _`Path Tracking`:
-
-Path Tracking
-=============
-
-Path tracking is the ability of a robot to follow the reference path generated by a path planner while simultaneously stabilizing the robot. The path tracking controller may need to account for modeling error and other forms of uncertainty. In path tracking, feedback control techniques and optimization based control techniques are widely used[22]. Fig.6 shows simulations using rear wheel feedback steering control and PID speed control, and iterative linear model predictive path tracking control[27].
-
-.. toctree::
- :maxdepth: 2
- :caption: Contents
-
- pure_pursuit_tracking/pure_pursuit_tracking
- stanley_control/stanley_control
- rear_wheel_feedback_control/rear_wheel_feedback_control
- lqr_steering_control/lqr_steering_control
- lqr_speed_and_steering_control/lqr_speed_and_steering_control
- model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control
- cgmres_nmpc/cgmres_nmpc
- move_to_a_pose_control/move_to_a_pose_control
diff --git a/genindex.html b/genindex.html
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+<html class="writer-html5" lang="en" >
+<head>
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+<li class="toctree-l1"><a class="reference internal" href="getting_started.html">Getting Started</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/introduction.html">Introduction</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/localization/localization.html">Localization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/slam/slam.html">SLAM</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="modules/arm_navigation/arm_navigation.html">Arm Navigation</a></li>
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+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+ <div itemprop="articleBody">
+
+
+<h1 id="index">Index</h1>
+
+<div class="genindex-jumpbox">
+ <a href="#A"><strong>A</strong></a>
+ | <a href="#C"><strong>C</strong></a>
+ | <a href="#D"><strong>D</strong></a>
+ | <a href="#E"><strong>E</strong></a>
+ | <a href="#F"><strong>F</strong></a>
+ | <a href="#G"><strong>G</strong></a>
+ | <a href="#I"><strong>I</strong></a>
+ | <a href="#L"><strong>L</strong></a>
+ | <a href="#M"><strong>M</strong></a>
+ | <a href="#N"><strong>N</strong></a>
+ | <a href="#P"><strong>P</strong></a>
+ | <a href="#R"><strong>R</strong></a>
+ | <a href="#V"><strong>V</strong></a>
+
+</div>
+<h2 id="A">A</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/path_planning/bspline_path/bspline_path.html#PathPlanning.BSplinePath.bspline_path.approximate_b_spline_path">approximate_b_spline_path() (in module PathPlanning.BSplinePath.bspline_path)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="C">C</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_curvature">calc_curvature() (PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D method)</a>
+</li>
+ <li><a href="modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_first_derivative">calc_first_derivative() (PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D method)</a>
+</li>
+ <li><a href="modules/mapping/normal_vector_estimation/normal_vector_estimation.html#Mapping.normal_vector_estimation.normal_vector_estimation.calc_normal_vector">calc_normal_vector() (in module Mapping.normal_vector_estimation.normal_vector_estimation)</a>
+</li>
+ <li><a href="modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_position">calc_position() (PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D method)</a>
+
+ <ul>
+ <li><a href="modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_position">(PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D method)</a>
+</li>
+ </ul></li>
+ <li><a href="modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_second_derivative">calc_second_derivative() (PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D method)</a>
+</li>
+ </ul></td>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_yaw">calc_yaw() (PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D method)</a>
+</li>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.center_grid_x">center_grid_x (Mapping.ndt_map.ndt_map.NDTMap.NDTGrid attribute)</a>
+</li>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.center_grid_y">center_grid_y (Mapping.ndt_map.ndt_map.NDTMap.NDTGrid attribute)</a>
+</li>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.covariance">covariance (Mapping.ndt_map.ndt_map.NDTMap.NDTGrid attribute)</a>
+</li>
+ <li><a href="modules/mapping/rectangle_fitting/rectangle_fitting.html#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.criteria">criteria (Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting attribute)</a>
+</li>
+ <li><a href="modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D">CubicSpline1D (class in PathPlanning.CubicSpline.cubic_spline_planner)</a>
+</li>
+ <li><a href="modules/path_planning/cubic_spline/cubic_spline.html#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D">CubicSpline2D (class in PathPlanning.CubicSpline.cubic_spline_planner)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="D">D</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/rectangle_fitting/rectangle_fitting.html#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.d_theta_deg_for_search">d_theta_deg_for_search (Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting attribute)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="E">E</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.eig_values">eig_values (Mapping.ndt_map.ndt_map.NDTMap.NDTGrid attribute)</a>
+</li>
+ </ul></td>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.eig_vec">eig_vec (Mapping.ndt_map.ndt_map.NDTMap.NDTGrid attribute)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="F">F</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/point_cloud_sampling/point_cloud_sampling.html#Mapping.point_cloud_sampling.point_cloud_sampling.farthest_point_sampling">farthest_point_sampling() (in module Mapping.point_cloud_sampling.point_cloud_sampling)</a>
+</li>
+ </ul></td>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/rectangle_fitting/rectangle_fitting.html#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.fitting">fitting() (Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting method)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="G">G</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.grid_index_map">grid_index_map (Mapping.ndt_map.ndt_map.NDTMap attribute)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="I">I</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/path_planning/bspline_path/bspline_path.html#PathPlanning.BSplinePath.bspline_path.interpolate_b_spline_path">interpolate_b_spline_path() (in module PathPlanning.BSplinePath.bspline_path)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="L">L</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/rectangle_fitting/rectangle_fitting.html#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting">LShapeFitting (class in Mapping.rectangle_fitting.rectangle_fitting)</a>
+</li>
+ </ul></td>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/rectangle_fitting/rectangle_fitting.html#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.Criteria">LShapeFitting.Criteria (class in Mapping.rectangle_fitting.rectangle_fitting)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="M">M</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.mean_x">mean_x (Mapping.ndt_map.ndt_map.NDTMap.NDTGrid attribute)</a>
+</li>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.mean_y">mean_y (Mapping.ndt_map.ndt_map.NDTMap.NDTGrid attribute)</a>
+</li>
+ </ul></td>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/rectangle_fitting/rectangle_fitting.html#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.min_dist_of_closeness_criteria">min_dist_of_closeness_criteria (Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting attribute)</a>
+</li>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.min_n_points">min_n_points (Mapping.ndt_map.ndt_map.NDTMap attribute)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="N">N</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.n_points">n_points (Mapping.ndt_map.ndt_map.NDTMap.NDTGrid attribute)</a>
+</li>
+ </ul></td>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap">NDTMap (class in Mapping.ndt_map.ndt_map)</a>
+</li>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid">NDTMap.NDTGrid (class in Mapping.ndt_map.ndt_map)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="P">P</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/path_planning/dubins_path/dubins_path.html#PathPlanning.DubinsPath.dubins_path_planner.plan_dubins_path">plan_dubins_path() (in module PathPlanning.DubinsPath.dubins_path_planner)</a>
+</li>
+ </ul></td>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/utils/plot/plot.html#utils.plot.plot_curvature">plot_curvature() (in module utils.plot)</a>
+</li>
+ <li><a href="modules/mapping/point_cloud_sampling/point_cloud_sampling.html#Mapping.point_cloud_sampling.point_cloud_sampling.poisson_disk_sampling">poisson_disk_sampling() (in module Mapping.point_cloud_sampling.point_cloud_sampling)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="R">R</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/rectangle_fitting/rectangle_fitting.html#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.R0">R0 (Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting attribute)</a>
+</li>
+ <li><a href="modules/mapping/normal_vector_estimation/normal_vector_estimation.html#Mapping.normal_vector_estimation.normal_vector_estimation.ransac_normal_vector_estimation">ransac_normal_vector_estimation() (in module Mapping.normal_vector_estimation.normal_vector_estimation)</a>
+</li>
+ </ul></td>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/rectangle_fitting/rectangle_fitting.html#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.Rd">Rd (Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting attribute)</a>
+</li>
+ <li><a href="modules/mapping/ndt_map/ndt_map.html#Mapping.ndt_map.ndt_map.NDTMap.resolution">resolution (Mapping.ndt_map.ndt_map.NDTMap attribute)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+<h2 id="V">V</h2>
+<table style="width: 100%" class="indextable genindextable"><tr>
+ <td style="width: 33%; vertical-align: top;"><ul>
+ <li><a href="modules/mapping/point_cloud_sampling/point_cloud_sampling.html#Mapping.point_cloud_sampling.point_cloud_sampling.voxel_point_sampling">voxel_point_sampling() (in module Mapping.point_cloud_sampling.point_cloud_sampling)</a>
+</li>
+ </ul></td>
+</tr></table>
+
+
+
+ </div>
+ </div>
+ <footer>
+
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+
+ <div role="contentinfo">
+ <p>© Copyright 2018-2021, Atsushi Sakai.</p>
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+ <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
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+ <p class="caption" role="heading"><span class="caption-text">Contents</span></p>
+<ul class="current">
+<li class="toctree-l1 current"><a class="current reference internal" href="#">Getting Started</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="#what-is-this">What is this?</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#requirements">Requirements</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#how-to-use">How to use</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/introduction.html">Introduction</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/localization/localization.html">Localization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/slam/slam.html">SLAM</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/path_planning/path_planning.html">Path Planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/bipedal/bipedal.html">Bipedal</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/control/control.html">Control</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/utils/utils.html">Utilities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/appendix/appendix.html">Appendix</a></li>
+<li class="toctree-l1"><a class="reference internal" href="how_to_contribute.html">How To Contribute</a></li>
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+ <li class="wy-breadcrumbs-aside">
+ <a href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/docs/getting_started_main.rst" class="fa fa-github"> Edit on GitHub</a>
+ </li>
+ </ul>
+ <hr/>
+</div>
+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+ <div itemprop="articleBody">
+
+ <section id="getting-started">
+<span id="id1"></span><h1>Getting Started<a class="headerlink" href="#getting-started" title="Permalink to this headline"></a></h1>
+<section id="what-is-this">
+<h2>What is this?<a class="headerlink" href="#what-is-this" title="Permalink to this headline"></a></h2>
+<p>This is an Open Source Software (OSS) project: PythonRobotics, which is a Python code collection of robotics algorithms.</p>
+<p>The focus of the project is on autonomous navigation, and the goal is for beginners in robotics to understand the basic ideas behind each algorithm.</p>
+<p>In this project, the algorithms which are practical and widely used in both academia and industry are selected.</p>
+<p>Each sample code is written in Python3 and only depends on some standard modules for readability and ease of use.</p>
+<p>It includes intuitive animations to understand the behavior of the simulation.</p>
+<p>See this paper for more details:</p>
+<ul class="simple">
+<li><p>PythonRobotics: a Python code collection of robotics algorithms: <a class="reference external" href="https://arxiv.org/abs/1808.10703">https://arxiv.org/abs/1808.10703</a></p></li>
+</ul>
+</section>
+<section id="requirements">
+<span id="id2"></span><h2>Requirements<a class="headerlink" href="#requirements" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://www.python.org/">Python 3.11.x</a></p></li>
+<li><p><a class="reference external" href="https://numpy.org/">NumPy</a></p></li>
+<li><p><a class="reference external" href="https://scipy.org/">SciPy</a></p></li>
+<li><p><a class="reference external" href="https://matplotlib.org/">Matplotlib</a></p></li>
+<li><p><a class="reference external" href="https://www.cvxpy.org/">cvxpy</a></p></li>
+</ul>
+<p>For development:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://docs.pytest.org/en/latest/">pytest</a> (for unit tests)</p></li>
+<li><p><a class="reference external" href="https://github.com/pytest-dev/pytest-xdist">pytest-xdist</a> (for parallel unit tests)</p></li>
+<li><p><a class="reference external" href="https://mypy-lang.org/">mypy</a> (for type check)</p></li>
+<li><p><a class="reference external" href="https://www.sphinx-doc.org/en/master/index.html">sphinx</a> (for document generation)</p></li>
+<li><p><a class="reference external" href="https://github.com/charliermarsh/ruff">ruff</a> (for code style check)</p></li>
+</ul>
+</section>
+<section id="how-to-use">
+<h2>How to use<a class="headerlink" href="#how-to-use" title="Permalink to this headline"></a></h2>
+<ol class="arabic simple">
+<li><p>Clone this repo and go into dir.</p></li>
+</ol>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>>$ git clone https://github.com/AtsushiSakai/PythonRobotics.git
+
+>$ cd PythonRobotics
+</pre></div>
+</div>
+<ol class="arabic simple" start="2">
+<li><p>Install the required libraries.</p></li>
+</ol>
+<p>using conda :</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>>$ conda env create -f requirements/environment.yml
+</pre></div>
+</div>
+<p>using pip :</p>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>>$ pip install -r requirements/requirements.txt
+</pre></div>
+</div>
+<ol class="arabic simple" start="3">
+<li><p>Execute python script in each directory.</p></li>
+<li><p>Add star to this repo if you like it 😃.</p></li>
+</ol>
+</section>
+</section>
+
+
+ </div>
+ </div>
+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+ <a href="index.html" class="btn btn-neutral float-left" title="Welcome to PythonRobotics’s documentation!" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
+ <a href="modules/introduction.html" class="btn btn-neutral float-right" title="Introduction" accesskey="n" rel="next">Next <span class="fa fa-arrow-circle-right" aria-hidden="true"></span></a>
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+
+ <div role="contentinfo">
+ <p>© Copyright 2018-2021, Atsushi Sakai.</p>
+ </div>
+
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+ <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
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diff --git a/how_to_contribute.html b/how_to_contribute.html
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+++ b/how_to_contribute.html
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+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
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+ <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
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+ <title>How To Contribute — PythonRobotics documentation</title>
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+ <form id="rtd-search-form" class="wy-form" action="search.html" method="get">
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+ crossorigin="anonymous"></script>
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+ </div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu">
+ <p class="caption" role="heading"><span class="caption-text">Contents</span></p>
+<ul class="current">
+<li class="toctree-l1"><a class="reference internal" href="getting_started.html">Getting Started</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/introduction.html">Introduction</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/localization/localization.html">Localization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/slam/slam.html">SLAM</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/path_planning/path_planning.html">Path Planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/bipedal/bipedal.html">Bipedal</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/control/control.html">Control</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/utils/utils.html">Utilities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/appendix/appendix.html">Appendix</a></li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">How To Contribute</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="#adding-a-new-algorithm-example">Adding a new algorithm example</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#step-1-choose-an-algorithm-to-implement">Step 1: Choose an algorithm to implement</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#step-2-implement-the-algorithm-with-matplotlib-based-animation">Step 2: Implement the algorithm with matplotlib based animation</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#step-3-add-a-unittest">Step 3: Add a unittest</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#step-4-write-a-document-about-the-algorithm">Step 4: Write a document about the algorithm</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#step-5-submit-a-pull-request-and-fix-codes-based-on-review">Step 5: Submit a pull request and fix codes based on review</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="#reporting-and-fixing-a-defect">Reporting and fixing a defect</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#adding-missed-documentations-for-existing-examples">Adding missed documentations for existing examples</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#supporting-this-project">Supporting this project</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#sponsors">Sponsors</a></li>
+</ul>
+</li>
+</ul>
+</li>
+</ul>
+
+ </div>
+ </div>
+ </nav>
+
+ <section data-toggle="wy-nav-shift" class="wy-nav-content-wrap"><nav class="wy-nav-top" aria-label="Mobile navigation menu" >
+ <i data-toggle="wy-nav-top" class="fa fa-bars"></i>
+ <a href="index.html">PythonRobotics</a>
+ </nav>
+
+ <div class="wy-nav-content">
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+ <div role="navigation" aria-label="Page navigation">
+ <ul class="wy-breadcrumbs">
+ <li><a href="index.html" class="icon icon-home"></a> »</li>
+ <li>How To Contribute</li>
+ <li class="wy-breadcrumbs-aside">
+ <a href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/docs/how_to_contribute_main.rst" class="fa fa-github"> Edit on GitHub</a>
+ </li>
+ </ul>
+ <hr/>
+</div>
+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+ <div itemprop="articleBody">
+
+ <section id="how-to-contribute">
+<h1>How To Contribute<a class="headerlink" href="#how-to-contribute" title="Permalink to this headline"></a></h1>
+<p>This document describes how to contribute this project.</p>
+<section id="adding-a-new-algorithm-example">
+<h2>Adding a new algorithm example<a class="headerlink" href="#adding-a-new-algorithm-example" title="Permalink to this headline"></a></h2>
+<p>This is a step by step manual to add a new algorithm example.</p>
+<section id="step-1-choose-an-algorithm-to-implement">
+<h3>Step 1: Choose an algorithm to implement<a class="headerlink" href="#step-1-choose-an-algorithm-to-implement" title="Permalink to this headline"></a></h3>
+<p>Before choosing an algorithm, please check the <a class="reference internal" href="getting_started.html#getting-started"><span class="std std-ref">Getting Started</span></a> doc to
+understand this project’s philosophy and setup your development environment.</p>
+<p>If an algorithm is widely used and successful, let’s create an issue to
+propose it for our community.</p>
+<p>If some people agree by thumbs up or posting positive comments, let go to next step.</p>
+<p>It is OK to just create an issue to propose adding an algorithm, someone might implement it.</p>
+<p>In that case, please share any papers or documentations to implement it.</p>
+</section>
+<section id="step-2-implement-the-algorithm-with-matplotlib-based-animation">
+<h3>Step 2: Implement the algorithm with matplotlib based animation<a class="headerlink" href="#step-2-implement-the-algorithm-with-matplotlib-based-animation" title="Permalink to this headline"></a></h3>
+<p>When you implement an algorithm, please keep the following items in mind.</p>
+<ol class="arabic simple">
+<li><p>Use only Python. Other language code is not acceptable.</p></li>
+<li><p>This project only accept codes for python 3.9 or higher.</p></li>
+<li><p>Use matplotlib based animation to show how the algorithm works.</p></li>
+<li><p>Only use current <a class="reference internal" href="getting_started.html#requirements"><span class="std std-ref">Requirements</span></a> libraries, not adding new dependencies.</p></li>
+<li><p>Keep simple your code. The main goal is to make it easy for users to understand the algorithm, not for practical usage.</p></li>
+</ol>
+</section>
+<section id="step-3-add-a-unittest">
+<h3>Step 3: Add a unittest<a class="headerlink" href="#step-3-add-a-unittest" title="Permalink to this headline"></a></h3>
+<p>If you add a new algorithm sample code, please add a unit test file under <a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/tree/master/tests">tests dir</a>.</p>
+<p>This sample test code might help you : <a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/tests/test_a_star.py">test_a_star.py</a>.</p>
+<p>At the least, try to run the example code without animation in the unit test.</p>
+<p>If you want to run the test suites locally, you can use the <cite>runtests.sh</cite> script by just executing it.</p>
+<p>The <a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/tests/test_codestyle.py">test_codestyle.py</a> check code style for your PR’s codes.</p>
+</section>
+<section id="step-4-write-a-document-about-the-algorithm">
+<span id="how-to-write-doc"></span><h3>Step 4: Write a document about the algorithm<a class="headerlink" href="#step-4-write-a-document-about-the-algorithm" title="Permalink to this headline"></a></h3>
+<p>Please add a document to describe the algorithm details, mathematical backgrounds and show graphs and animation gif.</p>
+<p>This project is using <a class="reference external" href="https://www.sphinx-doc.org/">Sphinx</a> as a document builder, all documentations are written by <a class="reference external" href="https://www.sphinx-doc.org/en/master/usage/restructuredtext/basics.html">reStructuredText</a>.</p>
+<p>You can add a new rst file under the subdirectory in <a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/tree/master/docs/modules">doc modules dir</a> and the top rst file can include it.</p>
+<p>Please check other documents for details.</p>
+<p>You can build the doc locally based on <a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/docs/README.md">doc README</a>.</p>
+<p>Note that the <a class="reference external" href="https://www.sphinx-doc.org/en/master/usage/restructuredtext/basics.html">reStructuredText</a> based doc should only focus on the mathematics and the algorithm of the example.</p>
+<p>Documentations related codes should be in the python script as the header comments of the script or docstrings of each function.</p>
+</section>
+<section id="step-5-submit-a-pull-request-and-fix-codes-based-on-review">
+<span id="submit-a-pull-request"></span><h3>Step 5: Submit a pull request and fix codes based on review<a class="headerlink" href="#step-5-submit-a-pull-request-and-fix-codes-based-on-review" title="Permalink to this headline"></a></h3>
+<p>Let’s submit a pull request when your code, test, and doc are ready.</p>
+<p>At first, please fix all CI errors before code review.</p>
+<p>You can check your PR doc from the CI panel.</p>
+<p>After the “ci/circleci: build_doc” CI is succeeded,
+you can access you PR doc with clicking the [Details] of the “ci/circleci: build_doc artifact” CI.</p>
+<img alt="_images/doc_ci.png" src="_images/doc_ci.png" />
+<p>After that, I will start the review.</p>
+<p>Note that this is my hobby project; I appreciate your patience during the review process.</p>
+</section>
+</section>
+<section id="reporting-and-fixing-a-defect">
+<h2>Reporting and fixing a defect<a class="headerlink" href="#reporting-and-fixing-a-defect" title="Permalink to this headline"></a></h2>
+<p>Reporting and fixing a defect is also great contribution.</p>
+<p>When you report an issue, please provide these information:</p>
+<ul class="simple">
+<li><p>A clear and concise description of what the bug is.</p></li>
+<li><p>A clear and concise description of what you expected to happen.</p></li>
+<li><p>Screenshots to help explain your problem if applicable.</p></li>
+<li><p>OS version</p></li>
+<li><p>Python version</p></li>
+<li><p>Each library versions</p></li>
+</ul>
+<p>If you want to fix any bug, you can find reported issues in <a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/issues?q=is%3Aissue+is%3Aopen+label%3Abug">bug labeled issues</a>.</p>
+<p>If you fix a bug of existing codes, please add a test function
+in the test code to show the issue was solved.</p>
+<p>This doc <a class="reference internal" href="#submit-a-pull-request">submit a pull request</a> can be helpful to submit a pull request.</p>
+</section>
+<section id="adding-missed-documentations-for-existing-examples">
+<h2>Adding missed documentations for existing examples<a class="headerlink" href="#adding-missed-documentations-for-existing-examples" title="Permalink to this headline"></a></h2>
+<p>Adding the missed documentations for existing examples is also great contribution.</p>
+<p>If you check the <a class="reference external" href="https://atsushisakai.github.io/PythonRobotics">Python Robotics Docs</a>, you can notice that some of the examples
+only have a simulation gif or short overview descriptions,
+but no detailed algorithm or mathematical description.</p>
+<p>This doc <a class="reference internal" href="#how-to-write-doc">how to write doc</a> can be helpful to write documents.</p>
+</section>
+<section id="supporting-this-project">
+<h2>Supporting this project<a class="headerlink" href="#supporting-this-project" title="Permalink to this headline"></a></h2>
+<p>Supporting this project financially is also a great contribution!!.</p>
+<p>If you or your company would like to support this project, please consider:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://github.com/sponsors/AtsushiSakai">Sponsor @AtsushiSakai on GitHub Sponsors</a></p></li>
+<li><p><a class="reference external" href="https://www.patreon.com/myenigma">Become a backer or sponsor on Patreon</a></p></li>
+<li><p><a class="reference external" href="https://www.paypal.me/myenigmapay/">One-time donation via PayPal</a></p></li>
+</ul>
+<p>If you would like to support us in some other way, please contact with creating an issue.</p>
+<section id="sponsors">
+<h3>Sponsors<a class="headerlink" href="#sponsors" title="Permalink to this headline"></a></h3>
+<ol class="arabic simple">
+<li><p><a class="reference external" href="https://www.jetbrains.com/">JetBrains</a> : They are providing a free license of their IDEs for this OSS development.</p></li>
+</ol>
+</section>
+</section>
+</section>
+
+
+ </div>
+ </div>
+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+ <a href="modules/appendix/Kalmanfilter_basics_2.html" class="btn btn-neutral float-left" title="KF Basics - Part 2" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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+
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+
+ <div role="contentinfo">
+ <p>© Copyright 2018-2021, Atsushi Sakai.</p>
+ </div>
+
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+ <a href="https://github.com/readthedocs/sphinx_rtd_theme">theme</a>
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+<html class="writer-html5" lang="en" >
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+<li class="toctree-l1"><a class="reference internal" href="getting_started.html">Getting Started</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/introduction.html">Introduction</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/localization/localization.html">Localization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/slam/slam.html">SLAM</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/path_planning/path_planning.html">Path Planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/bipedal/bipedal.html">Bipedal</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/control/control.html">Control</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/utils/utils.html">Utilities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="modules/appendix/appendix.html">Appendix</a></li>
+<li class="toctree-l1"><a class="reference internal" href="how_to_contribute.html">How To Contribute</a></li>
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+ <section id="welcome-to-pythonrobotics-s-documentation">
+<h1>Welcome to PythonRobotics’s documentation!<a class="headerlink" href="#welcome-to-pythonrobotics-s-documentation" title="Permalink to this headline"></a></h1>
+<p>Python codes for robotics algorithm. The project is on <a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics">GitHub</a>.</p>
+<p>This is a Python code collection of robotics algorithms.</p>
+<p>Features:</p>
+<ol class="arabic simple">
+<li><p>Easy to read for understanding each algorithm’s basic idea.</p></li>
+<li><p>Widely used and practical algorithms are selected.</p></li>
+<li><p>Minimum dependency.</p></li>
+</ol>
+<p>See this paper for more details:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://arxiv.org/abs/1808.10703">[1808.10703] PythonRobotics: a Python code collection of robotics
+algorithms</a> (<a class="reference external" href="https://github.com/AtsushiSakai/PythonRoboticsPaper/blob/master/python_robotics.bib">BibTeX</a>)</p></li>
+</ul>
+<div class="toctree-wrapper compound">
+<p class="caption" role="heading"><span class="caption-text">Contents</span></p>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="getting_started.html">Getting Started</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="getting_started.html#what-is-this">What is this?</a></li>
+<li class="toctree-l2"><a class="reference internal" href="getting_started.html#requirements">Requirements</a></li>
+<li class="toctree-l2"><a class="reference internal" href="getting_started.html#how-to-use">How to use</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/introduction.html">Introduction</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/introduction.html#definition-of-robotics">Definition Of Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/introduction.html#history-of-robotics">History Of Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/introduction.html#application-of-robotics">Application Of Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/introduction.html#software-for-robotics">Software for Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/introduction.html#id1">Software for Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/introduction.html#python-for-robotics">Python for Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/introduction.html#learning-robotics-algorithms">Learning Robotics Algorithms</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/localization/localization.html">Localization</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization.html">Extended Kalman Filter Localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/localization/ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization.html">Ensamble Kalman Filter Localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/localization/unscented_kalman_filter_localization/unscented_kalman_filter_localization.html">Unscented Kalman Filter localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/localization/histogram_filter_localization/histogram_filter_localization.html">Histogram filter localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/localization/particle_filter_localization/particle_filter_localization.html">Particle filter localization</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/mapping/mapping.html">Mapping</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/mapping/gaussian_grid_map/gaussian_grid_map.html">Gaussian grid map</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/mapping/ndt_map/ndt_map.html">Normal Distance Transform (NDT) map</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/mapping/ray_casting_grid_map/ray_casting_grid_map.html">Ray casting grid map</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/mapping/lidar_to_grid_map_tutorial/lidar_to_grid_map_tutorial.html">Lidar to grid map</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/mapping/point_cloud_sampling/point_cloud_sampling.html">Point cloud Sampling</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/mapping/k_means_object_clustering/k_means_object_clustering.html">k-means object clustering</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/mapping/circle_fitting/circle_fitting.html">Object shape recognition using circle fitting</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/mapping/rectangle_fitting/rectangle_fitting.html">Object shape recognition using rectangle fitting</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/mapping/normal_vector_estimation/normal_vector_estimation.html">Normal vector estimation</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/slam/slam.html">SLAM</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/slam/iterative_closest_point_matching/iterative_closest_point_matching.html">Iterative Closest Point (ICP) Matching</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/slam/ekf_slam/ekf_slam.html">EKF SLAM</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/slam/FastSLAM1/FastSLAM1.html">FastSLAM1.0</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/slam/FastSLAM2/FastSLAM2.html">FastSLAM 2.0</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/slam/graph_slam/graph_slam.html">Graph based SLAM</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/path_planning/path_planning.html">Path Planning</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/bugplanner/bugplanner.html">Bug planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/grid_base_search/grid_base_search.html">Grid based search</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/model_predictive_trajectory_generator/model_predictive_trajectory_generator.html">Model Predictive Trajectory Generator</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/state_lattice_planner/state_lattice_planner.html">State Lattice Planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/visibility_road_map_planner/visibility_road_map_planner.html">Visibility Road-Map planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_planning/coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/path_tracking/path_tracking.html">Path Tracking</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_tracking/pure_pursuit_tracking/pure_pursuit_tracking.html">Pure pursuit tracking</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_tracking/stanley_control/stanley_control.html">Stanley control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_tracking/rear_wheel_feedback_control/rear_wheel_feedback_control.html">Rear wheel feedback control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_tracking/lqr_steering_control/lqr_steering_control.html">Linear–quadratic regulator (LQR) steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_tracking/lqr_speed_and_steering_control/lqr_speed_and_steering_control.html">Linear–quadratic regulator (LQR) speed and steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_tracking/model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control.html">Model predictive speed and steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/path_tracking/cgmres_nmpc/cgmres_nmpc.html">Nonlinear Model Predictive Control with C-GMRES</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/arm_navigation/arm_navigation.html">Arm Navigation</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/arm_navigation/planar_two_link_ik.html">Two joint arm to point control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/arm_navigation/n_joint_arm_to_point_control.html">N joint arm to point control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/arm_navigation/obstacle_avoidance_arm_navigation.html">Arm navigation with obstacle avoidance</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/aerial_navigation/aerial_navigation.html">Aerial Navigation</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/aerial_navigation/drone_3d_trajectory_following/drone_3d_trajectory_following.html">Drone 3d trajectory following</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/aerial_navigation/rocket_powered_landing/rocket_powered_landing.html">Rocket powered landing</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/bipedal/bipedal.html">Bipedal</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/bipedal/bipedal_planner/bipedal_planner.html">Bipedal Planner</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/control/control.html">Control</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/control/inverted_pendulum_control/inverted_pendulum_control.html">Inverted Pendulum Control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/control/move_to_a_pose_control/move_to_a_pose_control.html">Move to a Pose Control</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/utils/utils.html">Utilities</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/utils/plot/plot.html">Plotting Utilities</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="modules/appendix/appendix.html">Appendix</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="modules/appendix/Kalmanfilter_basics.html">KF Basics - Part I</a></li>
+<li class="toctree-l2"><a class="reference internal" href="modules/appendix/Kalmanfilter_basics_2.html">KF Basics - Part 2</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="how_to_contribute.html">How To Contribute</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="how_to_contribute.html#adding-a-new-algorithm-example">Adding a new algorithm example</a></li>
+<li class="toctree-l2"><a class="reference internal" href="how_to_contribute.html#reporting-and-fixing-a-defect">Reporting and fixing a defect</a></li>
+<li class="toctree-l2"><a class="reference internal" href="how_to_contribute.html#adding-missed-documentations-for-existing-examples">Adding missed documentations for existing examples</a></li>
+<li class="toctree-l2"><a class="reference internal" href="how_to_contribute.html#supporting-this-project">Supporting this project</a></li>
+</ul>
+</li>
+</ul>
+</div>
+</section>
+<section id="indices-and-tables">
+<h1>Indices and tables<a class="headerlink" href="#indices-and-tables" title="Permalink to this headline"></a></h1>
+<ul class="simple">
+<li><p><a class="reference internal" href="genindex.html"><span class="std std-ref">Index</span></a></p></li>
+<li><p><a class="reference internal" href="py-modindex.html"><span class="std std-ref">Module Index</span></a></p></li>
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+ <p>© Copyright 2018-2021, Atsushi Sakai.</p>
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+<html class="writer-html5" lang="en" >
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+<li class="toctree-l1"><a class="reference internal" href="../localization/localization.html">Localization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../slam/slam.html">SLAM</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../path_planning/path_planning.html">Path Planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">Aerial Navigation</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="drone_3d_trajectory_following/drone_3d_trajectory_following.html">Drone 3d trajectory following</a></li>
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+ <section id="drone-3d-trajectory-following">
+<h1>Drone 3d trajectory following<a class="headerlink" href="#drone-3d-trajectory-following" title="Permalink to this headline"></a></h1>
+<p>This is a 3d trajectory following simulation for a quadrotor.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/AerialNavigation/drone_3d_trajectory_following/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/AerialNavigation/drone_3d_trajectory_following/animation.gif" />
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+
+ <section id="rocket-powered-landing">
+<h1>Rocket powered landing<a class="headerlink" href="#rocket-powered-landing" title="Permalink to this headline"></a></h1>
+<section id="simulation">
+<h2>Simulation<a class="headerlink" href="#simulation" title="Permalink to this headline"></a></h2>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">Image</span>
+<span class="n">Image</span><span class="p">(</span><span class="n">filename</span><span class="o">=</span><span class="s2">"figure.png"</span><span class="p">,</span><span class="n">width</span><span class="o">=</span><span class="mi">600</span><span class="p">)</span>
+<span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">display</span><span class="p">,</span> <span class="n">HTML</span>
+
+<span class="n">display</span><span class="p">(</span><span class="n">HTML</span><span class="p">(</span><span class="n">data</span><span class="o">=</span><span class="s2">"""</span>
+<span class="s2"><style></span>
+<span class="s2"> div#notebook-container { width: 95%; }</span>
+<span class="s2"> div#menubar-container { width: 65%; }</span>
+<span class="s2"> div#maintoolbar-container { width: 99%; }</span>
+<span class="s2"></style></span>
+<span class="s2">"""</span><span class="p">))</span>
+</pre></div>
+</div>
+<style>
+ div#notebook-container { width: 95%; }
+ div#menubar-container { width: 65%; }
+ div#maintoolbar-container { width: 99%; }
+</style><figure class="align-default">
+<img alt="gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/AerialNavigation/rocket_powered_landing/animation.gif" />
+</figure>
+</section>
+<section id="equation-generation">
+<h2>Equation generation<a class="headerlink" href="#equation-generation" title="Permalink to this headline"></a></h2>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">sympy</span> <span class="k">as</span> <span class="nn">sp</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">display</span>
+<span class="n">sp</span><span class="o">.</span><span class="n">init_printing</span><span class="p">(</span><span class="n">use_latex</span><span class="o">=</span><span class="s1">'mathjax'</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># parameters</span>
+<span class="c1"># Angular moment of inertia</span>
+<span class="n">J_B</span> <span class="o">=</span> <span class="mf">1e-2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">])</span>
+
+<span class="c1"># Gravity</span>
+<span class="n">g_I</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">))</span>
+
+<span class="c1"># Fuel consumption</span>
+<span class="n">alpha_m</span> <span class="o">=</span> <span class="mf">0.01</span>
+
+<span class="c1"># Vector from thrust point to CoM</span>
+<span class="n">r_T_B</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="o">-</span><span class="mf">1e-2</span><span class="p">,</span> <span class="mf">0.</span><span class="p">,</span> <span class="mf">0.</span><span class="p">])</span>
+
+
+<span class="k">def</span> <span class="nf">dir_cosine</span><span class="p">(</span><span class="n">q</span><span class="p">):</span>
+ <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">matrix</span><span class="p">([</span>
+ <span class="p">[</span><span class="mi">1</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">q</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span><span class="p">),</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">+</span>
+ <span class="n">q</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">3</span><span class="p">]),</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">-</span> <span class="n">q</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">2</span><span class="p">])],</span>
+ <span class="p">[</span><span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">-</span> <span class="n">q</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">3</span><span class="p">]),</span> <span class="mi">1</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span>
+ <span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">q</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span><span class="p">),</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">+</span> <span class="n">q</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">1</span><span class="p">])],</span>
+ <span class="p">[</span><span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">+</span> <span class="n">q</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">2</span><span class="p">]),</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">3</span><span class="p">]</span> <span class="o">-</span>
+ <span class="n">q</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">q</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="mi">1</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">q</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span> <span class="o">+</span> <span class="n">q</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)]</span>
+ <span class="p">])</span>
+
+<span class="k">def</span> <span class="nf">omega</span><span class="p">(</span><span class="n">w</span><span class="p">):</span>
+ <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">matrix</span><span class="p">([</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="n">w</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="o">-</span><span class="n">w</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="o">-</span><span class="n">w</span><span class="p">[</span><span class="mi">2</span><span class="p">]],</span>
+ <span class="p">[</span><span class="n">w</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">0</span><span class="p">,</span> <span class="n">w</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="o">-</span><span class="n">w</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
+ <span class="p">[</span><span class="n">w</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="o">-</span><span class="n">w</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="mi">0</span><span class="p">,</span> <span class="n">w</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="n">w</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">w</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="o">-</span><span class="n">w</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="p">])</span>
+
+<span class="k">def</span> <span class="nf">skew</span><span class="p">(</span><span class="n">v</span><span class="p">):</span>
+ <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">matrix</span><span class="p">([</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="n">v</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
+ <span class="p">[</span><span class="n">v</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="o">-</span><span class="n">v</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">v</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="p">])</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">f</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="mi">14</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+
+<span class="n">x</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">Matrix</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">symbols</span><span class="p">(</span>
+ <span class="s1">'m rx ry rz vx vy vz q0 q1 q2 q3 wx wy wz'</span><span class="p">,</span> <span class="n">real</span><span class="o">=</span><span class="kc">True</span><span class="p">))</span>
+<span class="n">u</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">Matrix</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">symbols</span><span class="p">(</span><span class="s1">'ux uy uz'</span><span class="p">,</span> <span class="n">real</span><span class="o">=</span><span class="kc">True</span><span class="p">))</span>
+
+<span class="n">g_I</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">Matrix</span><span class="p">(</span><span class="n">g_I</span><span class="p">)</span>
+<span class="n">r_T_B</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">Matrix</span><span class="p">(</span><span class="n">r_T_B</span><span class="p">)</span>
+<span class="n">J_B</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">Matrix</span><span class="p">(</span><span class="n">J_B</span><span class="p">)</span>
+
+<span class="n">C_B_I</span> <span class="o">=</span> <span class="n">dir_cosine</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">7</span><span class="p">:</span><span class="mi">11</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+<span class="n">C_I_B</span> <span class="o">=</span> <span class="n">C_B_I</span><span class="o">.</span><span class="n">transpose</span><span class="p">()</span>
+
+<span class="n">f</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="o">-</span> <span class="n">alpha_m</span> <span class="o">*</span> <span class="n">u</span><span class="o">.</span><span class="n">norm</span><span class="p">()</span>
+<span class="n">f</span><span class="p">[</span><span class="mi">1</span><span class="p">:</span><span class="mi">4</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">4</span><span class="p">:</span><span class="mi">7</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+<span class="n">f</span><span class="p">[</span><span class="mi">4</span><span class="p">:</span><span class="mi">7</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">C_I_B</span> <span class="o">*</span> <span class="n">u</span> <span class="o">+</span> <span class="n">g_I</span>
+<span class="n">f</span><span class="p">[</span><span class="mi">7</span><span class="p">:</span><span class="mi">11</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">/</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">omega</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">11</span><span class="p">:</span><span class="mi">14</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span> <span class="o">*</span> <span class="n">x</span><span class="p">[</span><span class="mi">7</span><span class="p">:</span> <span class="mi">11</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+<span class="n">f</span><span class="p">[</span><span class="mi">11</span><span class="p">:</span><span class="mi">14</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">J_B</span> <span class="o">**</span> <span class="o">-</span><span class="mi">1</span> <span class="o">*</span> \
+ <span class="p">(</span><span class="n">skew</span><span class="p">(</span><span class="n">r_T_B</span><span class="p">)</span> <span class="o">*</span> <span class="n">u</span> <span class="o">-</span> <span class="n">skew</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">11</span><span class="p">:</span><span class="mi">14</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span> <span class="o">*</span> <span class="n">J_B</span> <span class="o">*</span> <span class="n">x</span><span class="p">[</span><span class="mi">11</span><span class="p">:</span><span class="mi">14</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">display</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">simplify</span><span class="p">(</span><span class="n">f</span><span class="p">))</span> <span class="c1"># f</span>
+</pre></div>
+</div>
+<div class="math notranslate nohighlight">
+\[\begin{split}\left[\begin{matrix}- 0.01 \sqrt{ux^{2} + uy^{2} + uz^{2}}\\vx\\vy\\vz\\\frac{- 1.0 m - ux \left(2 q_{2}^{2} + 2 q_{3}^{2} - 1\right) - 2 uy \left(q_{0} q_{3} - q_{1} q_{2}\right) + 2 uz \left(q_{0} q_{2} + q_{1} q_{3}\right)}{m}\\\frac{2 ux \left(q_{0} q_{3} + q_{1} q_{2}\right) - uy \left(2 q_{1}^{2} + 2 q_{3}^{2} - 1\right) - 2 uz \left(q_{0} q_{1} - q_{2} q_{3}\right)}{m}\\\frac{- 2 ux \left(q_{0} q_{2} - q_{1} q_{3}\right) + 2 uy \left(q_{0} q_{1} + q_{2} q_{3}\right) - uz \left(2 q_{1}^{2} + 2 q_{2}^{2} - 1\right)}{m}\\- 0.5 q_{1} wx - 0.5 q_{2} wy - 0.5 q_{3} wz\\0.5 q_{0} wx + 0.5 q_{2} wz - 0.5 q_{3} wy\\0.5 q_{0} wy - 0.5 q_{1} wz + 0.5 q_{3} wx\\0.5 q_{0} wz + 0.5 q_{1} wy - 0.5 q_{2} wx\\0\\1.0 uz\\- 1.0 uy\end{matrix}\right]\end{split}\]</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">display</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">simplify</span><span class="p">(</span><span class="n">f</span><span class="o">.</span><span class="n">jacobian</span><span class="p">(</span><span class="n">x</span><span class="p">)))</span><span class="c1"># A</span>
+</pre></div>
+</div>
+<div class="math notranslate nohighlight">
+\[\begin{split}\left[\begin{array}{cccccccccccccc}0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 1 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\\frac{ux \left(2 q_{2}^{2} + 2 q_{3}^{2} - 1\right) + 2 uy \left(q_{0} q_{3} - q_{1} q_{2}\right) - 2 uz \left(q_{0} q_{2} + q_{1} q_{3}\right)}{m^{2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{2 \left(q_{2} uz - q_{3} uy\right)}{m} & \frac{2 \left(q_{2} uy + q_{3} uz\right)}{m} & \frac{2 \left(q_{0} uz + q_{1} uy - 2 q_{2} ux\right)}{m} & \frac{2 \left(- q_{0} uy + q_{1} uz - 2 q_{3} ux\right)}{m} & 0 & 0 & 0\\\frac{- 2 ux \left(q_{0} q_{3} + q_{1} q_{2}\right) + uy \left(2 q_{1}^{2} + 2 q_{3}^{2} - 1\right) + 2 uz \left(q_{0} q_{1} - q_{2} q_{3}\right)}{m^{2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{2 \left(- q_{1} uz + q_{3} ux\right)}{m} & \frac{2 \left(- q_{0} uz - 2 q_{1} uy + q_{2} ux\right)}{m} & \frac{2 \left(q_{1} ux + q_{3} uz\right)}{m} & \frac{2 \left(q_{0} ux + q_{2} uz - 2 q_{3} uy\right)}{m} & 0 & 0 & 0\\\frac{2 ux \left(q_{0} q_{2} - q_{1} q_{3}\right) - 2 uy \left(q_{0} q_{1} + q_{2} q_{3}\right) + uz \left(2 q_{1}^{2} + 2 q_{2}^{2} - 1\right)}{m^{2}} & 0 & 0 & 0 & 0 & 0 & 0 & \frac{2 \left(q_{1} uy - q_{2} ux\right)}{m} & \frac{2 \left(q_{0} uy - 2 q_{1} uz + q_{3} ux\right)}{m} & \frac{2 \left(- q_{0} ux - 2 q_{2} uz + q_{3} uy\right)}{m} & \frac{2 \left(q_{1} ux + q_{2} uy\right)}{m} & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & - 0.5 wx & - 0.5 wy & - 0.5 wz & - 0.5 q_{1} & - 0.5 q_{2} & - 0.5 q_{3}\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.5 wx & 0 & 0.5 wz & - 0.5 wy & 0.5 q_{0} & - 0.5 q_{3} & 0.5 q_{2}\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.5 wy & - 0.5 wz & 0 & 0.5 wx & 0.5 q_{3} & 0.5 q_{0} & - 0.5 q_{1}\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0.5 wz & 0.5 wy & - 0.5 wx & 0 & - 0.5 q_{2} & 0.5 q_{1} & 0.5 q_{0}\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\\0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0\end{array}\right]\end{split}\]</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">sp</span><span class="o">.</span><span class="n">simplify</span><span class="p">(</span><span class="n">f</span><span class="o">.</span><span class="n">jacobian</span><span class="p">(</span><span class="n">u</span><span class="p">))</span> <span class="c1"># B</span>
+</pre></div>
+</div>
+<div class="math notranslate nohighlight">
+\[\begin{split}\left[\begin{matrix}- \frac{0.01 ux}{\sqrt{ux^{2} + uy^{2} + uz^{2}}} & - \frac{0.01 uy}{\sqrt{ux^{2} + uy^{2} + uz^{2}}} & - \frac{0.01 uz}{\sqrt{ux^{2} + uy^{2} + uz^{2}}}\\0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\\\frac{- 2 q_{2}^{2} - 2 q_{3}^{2} + 1}{m} & \frac{2 \left(- q_{0} q_{3} + q_{1} q_{2}\right)}{m} & \frac{2 \left(q_{0} q_{2} + q_{1} q_{3}\right)}{m}\\\frac{2 \left(q_{0} q_{3} + q_{1} q_{2}\right)}{m} & \frac{- 2 q_{1}^{2} - 2 q_{3}^{2} + 1}{m} & \frac{2 \left(- q_{0} q_{1} + q_{2} q_{3}\right)}{m}\\\frac{2 \left(- q_{0} q_{2} + q_{1} q_{3}\right)}{m} & \frac{2 \left(q_{0} q_{1} + q_{2} q_{3}\right)}{m} & \frac{- 2 q_{1}^{2} - 2 q_{2}^{2} + 1}{m}\\0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 0\\0 & 0 & 1.0\\0 & -1.0 & 0\end{matrix}\right]\end{split}\]</div>
+</section>
+<section id="references">
+<h2>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p>Python implementation of ‘Successive Convexification for 6-DoF Mars
+Rocket Powered Landing with Free-Final-Time’ paper by Michael Szmuk
+and Behçet Açıkmeşe.</p></li>
+<li><p>inspired by EmbersArc/SuccessiveConvexificationFreeFinalTime:
+Implementation of “Successive Convexification for 6-DoF Mars Rocket
+Powered Landing with Free-Final-Time”
+<a class="reference external" href="https://github.com/EmbersArc/SuccessiveConvexificationFreeFinalTime">https://github.com/EmbersArc/SuccessiveConvexificationFreeFinalTime</a></p></li>
+</ul>
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+<li class="toctree-l4"><a class="reference internal" href="#what-is-expectation-of-a-random-variables">What is Expectation of a Random Variables?</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#what-is-the-advantage-of-representing-the-belief-as-a-unimodal-as-opposed-to-multimodal">What is the advantage of representing the belief as a unimodal as opposed to multimodal?</a></li>
+</ul>
+</li>
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+</li>
+<li class="toctree-l3"><a class="reference internal" href="#gaussians">Gaussians</a><ul>
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+
+ <section id="kf-basics-part-i">
+<h1>KF Basics - Part I<a class="headerlink" href="#kf-basics-part-i" title="Permalink to this headline"></a></h1>
+<section id="introduction">
+<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
+<section id="what-is-the-need-to-describe-belief-in-terms-of-pdfs">
+<h3>What is the need to describe belief in terms of PDF’s?<a class="headerlink" href="#what-is-the-need-to-describe-belief-in-terms-of-pdfs" title="Permalink to this headline"></a></h3>
+<p>This is because robot environments are stochastic. A robot environment
+may have cows with Tesla by side. That is a robot and it’s environment
+cannot be deterministically modelled(e.g as a function of something like
+time t). In the real world sensors are also error prone, and hence
+there’ll be a set of values with a mean and variance that it can take.
+Hence, we always have to model around some mean and variances
+associated.</p>
+</section>
+<section id="what-is-expectation-of-a-random-variables">
+<h3>What is Expectation of a Random Variables?<a class="headerlink" href="#what-is-expectation-of-a-random-variables" title="Permalink to this headline"></a></h3>
+<p>Expectation is nothing but an average of the probabilites</p>
+<div class="math notranslate nohighlight">
+\[\mathbb E[X] = \sum_{i=1}^n p_ix_i\]</div>
+<p>In the continous form,</p>
+<div class="math notranslate nohighlight">
+\[\mathbb E[X] = \int_{-\infty}^\infty x\, f(x) \,dx\]</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">random</span>
+<span class="n">x</span><span class="o">=</span><span class="p">[</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">]</span>
+<span class="n">p</span><span class="o">=</span><span class="p">[</span><span class="mf">0.1</span><span class="p">,</span><span class="mf">0.3</span><span class="p">,</span><span class="mf">0.4</span><span class="p">]</span>
+<span class="n">E_x</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">p</span><span class="p">))</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">E_x</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">1.4000000000000001</span>
+</pre></div>
+</div>
+</section>
+<section id="what-is-the-advantage-of-representing-the-belief-as-a-unimodal-as-opposed-to-multimodal">
+<h3>What is the advantage of representing the belief as a unimodal as opposed to multimodal?<a class="headerlink" href="#what-is-the-advantage-of-representing-the-belief-as-a-unimodal-as-opposed-to-multimodal" title="Permalink to this headline"></a></h3>
+<p>Obviously, it makes sense because we can’t multiple probabilities to a
+car moving for two locations. This would be too confusing and the
+information will not be useful.</p>
+</section>
+</section>
+<section id="variance-covariance-and-correlation">
+<h2>Variance, Covariance and Correlation<a class="headerlink" href="#variance-covariance-and-correlation" title="Permalink to this headline"></a></h2>
+<section id="variance">
+<h3>Variance<a class="headerlink" href="#variance" title="Permalink to this headline"></a></h3>
+<p>Variance is the spread of the data. The mean does’nt tell much <strong>about</strong>
+the data. Therefore the variance tells us about the <strong>story</strong> about the
+data meaning the spread of the data.</p>
+<div class="math notranslate nohighlight">
+\[\mathit{VAR}(X) = \frac{1}{n}\sum_{i=1}^n (x_i - \mu)^2\]</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">10</span><span class="p">)</span>
+<span class="n">np</span><span class="o">.</span><span class="n">var</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">1.0224618077401504</span>
+</pre></div>
+</div>
+</section>
+<section id="covariance">
+<h3>Covariance<a class="headerlink" href="#covariance" title="Permalink to this headline"></a></h3>
+<p>This is for a multivariate distribution. For example, a robot in 2-D
+space can take values in both x and y. To describe them, a normal
+distribution with mean in both x and y is needed.</p>
+<p>For a multivariate distribution, mean <span class="math notranslate nohighlight">\(\mu\)</span> can be represented as
+a matrix,</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\mu = \begin{bmatrix}\mu_1\\\mu_2\\ \vdots \\\mu_n\end{bmatrix}\end{split}\]</div>
+<p>Similarly, variance can also be represented.</p>
+<p>But an important concept is that in the same way as every variable or
+dimension has a variation in its values, it is also possible that there
+will be values on how they <strong>together vary</strong>. This is also a measure of
+how two datasets are related to each other or <strong>correlation</strong>.</p>
+<p>For example, as height increases weight also generally increases. These
+variables are correlated. They are positively correlated because as one
+variable gets larger so does the other.</p>
+<p>We use a <strong>covariance matrix</strong> to denote covariances of a multivariate
+normal distribution:</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\Sigma = \begin{bmatrix}
+ \sigma_1^2 & \sigma_{12} & \cdots & \sigma_{1n} \\
+ \sigma_{21} &\sigma_2^2 & \cdots & \sigma_{2n} \\
+ \vdots & \vdots & \ddots & \vdots \\
+ \sigma_{n1} & \sigma_{n2} & \cdots & \sigma_n^2
+ \end{bmatrix}\end{split}\]</div>
+<p><strong>Diagonal</strong> - Variance of each variable associated.</p>
+<p><strong>Off-Diagonal</strong> - covariance between ith and jth variables.</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\begin{aligned}VAR(X) = \sigma_x^2 &= \frac{1}{n}\sum_{i=1}^n(X - \mu)^2\\
+COV(X, Y) = \sigma_{xy} &= \frac{1}{n}\sum_{i=1}^n[(X-\mu_x)(Y-\mu_y)\big]\end{aligned}\end{split}\]</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span><span class="mi">3</span><span class="p">))</span>
+<span class="n">np</span><span class="o">.</span><span class="n">cov</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([[</span><span class="mf">0.08868895</span><span class="p">,</span> <span class="mf">0.05064471</span><span class="p">,</span> <span class="mf">0.08855629</span><span class="p">],</span>
+ <span class="p">[</span><span class="mf">0.05064471</span><span class="p">,</span> <span class="mf">0.06219243</span><span class="p">,</span> <span class="mf">0.11555291</span><span class="p">],</span>
+ <span class="p">[</span><span class="mf">0.08855629</span><span class="p">,</span> <span class="mf">0.11555291</span><span class="p">,</span> <span class="mf">0.21534324</span><span class="p">]])</span>
+</pre></div>
+</div>
+<p>Covariance taking the data as <strong>sample</strong> with <span class="math notranslate nohighlight">\(\frac{1}{N-1}\)</span></p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">x_cor</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">10</span><span class="p">)</span>
+<span class="n">y_cor</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">10</span><span class="p">)</span>
+<span class="n">np</span><span class="o">.</span><span class="n">cov</span><span class="p">(</span><span class="n">x_cor</span><span class="p">,</span><span class="n">y_cor</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([[</span> <span class="mf">0.1571437</span> <span class="p">,</span> <span class="o">-</span><span class="mf">0.00766623</span><span class="p">],</span>
+ <span class="p">[</span><span class="o">-</span><span class="mf">0.00766623</span><span class="p">,</span> <span class="mf">0.13957621</span><span class="p">]])</span>
+</pre></div>
+</div>
+<p>Covariance taking the data as <strong>population</strong> with <span class="math notranslate nohighlight">\(\frac{1}{N}\)</span></p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">np</span><span class="o">.</span><span class="n">cov</span><span class="p">(</span><span class="n">x_cor</span><span class="p">,</span><span class="n">y_cor</span><span class="p">,</span><span class="n">bias</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([[</span> <span class="mf">0.14142933</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.0068996</span> <span class="p">],</span>
+ <span class="p">[</span><span class="o">-</span><span class="mf">0.0068996</span> <span class="p">,</span> <span class="mf">0.12561859</span><span class="p">]])</span>
+</pre></div>
+</div>
+</section>
+</section>
+<section id="gaussians">
+<h2>Gaussians<a class="headerlink" href="#gaussians" title="Permalink to this headline"></a></h2>
+<section id="central-limit-theorem">
+<h3>Central Limit Theorem<a class="headerlink" href="#central-limit-theorem" title="Permalink to this headline"></a></h3>
+<p>According to this theorem, the average of n samples of random and
+independent variables tends to follow a normal distribution as we
+increase the sample size.(Generally, for n>=30)</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">import</span> <span class="nn">random</span>
+<span class="n">a</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">100</span><span class="p">,))</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">100</span><span class="p">):</span>
+ <span class="n">x</span><span class="o">=</span><span class="p">[</span><span class="n">random</span><span class="o">.</span><span class="n">uniform</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">10</span><span class="p">)</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">1000</span><span class="p">)]</span>
+ <span class="n">a</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">axis</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span><span class="o">/</span><span class="mi">1000</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">(</span><span class="n">array</span><span class="p">([</span> <span class="mf">1.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">,</span> <span class="mf">9.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">,</span> <span class="mf">12.</span><span class="p">,</span> <span class="mf">20.</span><span class="p">,</span> <span class="mf">16.</span><span class="p">,</span> <span class="mf">16.</span><span class="p">,</span> <span class="mf">4.</span><span class="p">,</span> <span class="mf">6.</span><span class="p">]),</span>
+ <span class="n">array</span><span class="p">([</span><span class="mf">5.30943011</span><span class="p">,</span> <span class="mf">5.34638597</span><span class="p">,</span> <span class="mf">5.38334183</span><span class="p">,</span> <span class="mf">5.42029769</span><span class="p">,</span> <span class="mf">5.45725355</span><span class="p">,</span>
+ <span class="mf">5.49420941</span><span class="p">,</span> <span class="mf">5.53116527</span><span class="p">,</span> <span class="mf">5.56812114</span><span class="p">,</span> <span class="mf">5.605077</span> <span class="p">,</span> <span class="mf">5.64203286</span><span class="p">,</span>
+ <span class="mf">5.67898872</span><span class="p">]),</span>
+ <span class="o"><</span><span class="n">a</span> <span class="nb">list</span> <span class="n">of</span> <span class="mi">10</span> <span class="n">Patch</span> <span class="n">objects</span><span class="o">></span><span class="p">)</span>
+</pre></div>
+</div>
+<img alt="../../_images/Kalmanfilter_basics_14_1.png" src="../../_images/Kalmanfilter_basics_14_1.png" />
+</section>
+<section id="gaussian-distribution">
+<h3>Gaussian Distribution<a class="headerlink" href="#gaussian-distribution" title="Permalink to this headline"></a></h3>
+<p>A Gaussian is a <em>continuous probability distribution</em> that is completely
+described with two parameters, the mean (<span class="math notranslate nohighlight">\(\mu\)</span>) and the variance
+(<span class="math notranslate nohighlight">\(\sigma^2\)</span>). It is defined as:</p>
+<div class="math notranslate nohighlight">
+\[f(x, \mu, \sigma) = \frac{1}{\sigma\sqrt{2\pi}} \exp\big [{-\frac{(x-\mu)^2}{2\sigma^2} }\big ]\]</div>
+<p>Range is <span class="math notranslate nohighlight">\([-\inf,\inf]\)</span></p>
+<p>This is just a function of mean(<span class="math notranslate nohighlight">\(\mu\)</span>) and standard deviation
+(<span class="math notranslate nohighlight">\(\sigma\)</span>) and what gives the normal distribution the
+charecteristic <strong>bell curve</strong>.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.mlab</span> <span class="k">as</span> <span class="nn">mlab</span>
+<span class="kn">import</span> <span class="nn">math</span>
+<span class="kn">import</span> <span class="nn">scipy.stats</span>
+
+<span class="n">mu</span> <span class="o">=</span> <span class="mi">0</span>
+<span class="n">variance</span> <span class="o">=</span> <span class="mi">5</span>
+<span class="n">sigma</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">variance</span><span class="p">)</span>
+<span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">mu</span> <span class="o">-</span> <span class="mi">5</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="n">mu</span> <span class="o">+</span> <span class="mi">5</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span><span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span> <span class="n">sigma</span><span class="p">))</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../_images/Kalmanfilter_basics_16_0.png" src="../../_images/Kalmanfilter_basics_16_0.png" />
+</section>
+<section id="why-do-we-need-gaussian-distributions">
+<h3>Why do we need Gaussian distributions?<a class="headerlink" href="#why-do-we-need-gaussian-distributions" title="Permalink to this headline"></a></h3>
+<p>Since it becomes really difficult in the real world to deal with
+multimodal distribution as we cannot put the belief in two seperate
+location of the robots. This becomes really confusing and in practice
+impossible to comprehend. Gaussian probability distribution allows us to
+drive the robots using only one mode with peak at the mean with some
+variance.</p>
+</section>
+</section>
+<section id="gaussian-properties">
+<h2>Gaussian Properties<a class="headerlink" href="#gaussian-properties" title="Permalink to this headline"></a></h2>
+<p><strong>Multiplication</strong></p>
+<p>For the measurement update in a Bayes Filter, the algorithm tells us to
+multiply the Prior P(X_t) and measurement P(Z_t|X_t) to calculate the
+posterior:</p>
+<div class="math notranslate nohighlight">
+\[P(X \mid Z) = \frac{P(Z \mid X)P(X)}{P(Z)}\]</div>
+<p>Here for the numerator, <span class="math notranslate nohighlight">\(P(Z \mid X),P(X)\)</span> both are gaussian.</p>
+<p><span class="math notranslate nohighlight">\(N(\bar\mu, \bar\sigma^1)\)</span> and <span class="math notranslate nohighlight">\(N(\bar\mu, \bar\sigma^2)\)</span>
+are their mean and variances.</p>
+<p>New mean is</p>
+<div class="math notranslate nohighlight">
+\[\mu_\mathtt{new} = \frac{\sigma_z^2\bar\mu + \bar\sigma^2z}{\bar\sigma^2+\sigma_z^2}\]</div>
+<p>New variance is</p>
+<div class="math notranslate nohighlight">
+\[\sigma_\mathtt{new} = \frac{\sigma_z^2\bar\sigma^2}{\bar\sigma^2+\sigma_z^2}\]</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.mlab</span> <span class="k">as</span> <span class="nn">mlab</span>
+<span class="kn">import</span> <span class="nn">math</span>
+<span class="n">mu1</span> <span class="o">=</span> <span class="mi">0</span>
+<span class="n">variance1</span> <span class="o">=</span> <span class="mi">2</span>
+<span class="n">sigma</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">variance1</span><span class="p">)</span>
+<span class="n">x1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">mu1</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="n">mu1</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span><span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">mu1</span><span class="p">,</span> <span class="n">sigma</span><span class="p">),</span><span class="n">label</span><span class="o">=</span><span class="s1">'prior'</span><span class="p">)</span>
+
+<span class="n">mu2</span> <span class="o">=</span> <span class="mi">10</span>
+<span class="n">variance2</span> <span class="o">=</span> <span class="mi">2</span>
+<span class="n">sigma</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">variance2</span><span class="p">)</span>
+<span class="n">x2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">mu2</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="n">mu2</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x2</span><span class="p">,</span><span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x2</span><span class="p">,</span> <span class="n">mu2</span><span class="p">,</span> <span class="n">sigma</span><span class="p">),</span><span class="s2">"g-"</span><span class="p">,</span><span class="n">label</span><span class="o">=</span><span class="s1">'measurement'</span><span class="p">)</span>
+
+
+<span class="n">mu_new</span><span class="o">=</span><span class="p">(</span><span class="n">mu1</span><span class="o">*</span><span class="n">variance2</span><span class="o">+</span><span class="n">mu2</span><span class="o">*</span><span class="n">variance1</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">variance1</span><span class="o">+</span><span class="n">variance2</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"New mean is at: "</span><span class="p">,</span><span class="n">mu_new</span><span class="p">)</span>
+<span class="n">var_new</span><span class="o">=</span><span class="p">(</span><span class="n">variance1</span><span class="o">*</span><span class="n">variance2</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">variance1</span><span class="o">+</span><span class="n">variance2</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"New variance is: "</span><span class="p">,</span><span class="n">var_new</span><span class="p">)</span>
+<span class="n">sigma</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">var_new</span><span class="p">)</span>
+<span class="n">x3</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">mu_new</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="n">mu_new</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x3</span><span class="p">,</span><span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x3</span><span class="p">,</span> <span class="n">mu_new</span><span class="p">,</span> <span class="n">var_new</span><span class="p">),</span><span class="n">label</span><span class="o">=</span><span class="s2">"posterior"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">'upper left'</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span><span class="mi">20</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">New</span> <span class="n">mean</span> <span class="ow">is</span> <span class="n">at</span><span class="p">:</span> <span class="mf">5.0</span>
+<span class="n">New</span> <span class="n">variance</span> <span class="ow">is</span><span class="p">:</span> <span class="mf">1.0</span>
+</pre></div>
+</div>
+<img alt="../../_images/Kalmanfilter_basics_19_1.png" src="../../_images/Kalmanfilter_basics_19_1.png" />
+<p><strong>Addition</strong></p>
+<p>The motion step involves a case of adding up probability (Since it has
+to abide the Law of Total Probability). This means their beliefs are to
+be added and hence two gaussians. They are simply arithmetic additions
+of the two.</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\begin{gathered}\mu_x = \mu_p + \mu_z \\
+\sigma_x^2 = \sigma_z^2+\sigma_p^2\, \end{gathered}\end{split}\]</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">matplotlib.mlab</span> <span class="k">as</span> <span class="nn">mlab</span>
+<span class="kn">import</span> <span class="nn">math</span>
+<span class="n">mu1</span> <span class="o">=</span> <span class="mi">5</span>
+<span class="n">variance1</span> <span class="o">=</span> <span class="mi">1</span>
+<span class="n">sigma</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">variance1</span><span class="p">)</span>
+<span class="n">x1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">mu1</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="n">mu1</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span><span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x1</span><span class="p">,</span> <span class="n">mu1</span><span class="p">,</span> <span class="n">sigma</span><span class="p">),</span><span class="n">label</span><span class="o">=</span><span class="s1">'prior'</span><span class="p">)</span>
+
+<span class="n">mu2</span> <span class="o">=</span> <span class="mi">10</span>
+<span class="n">variance2</span> <span class="o">=</span> <span class="mi">1</span>
+<span class="n">sigma</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">variance2</span><span class="p">)</span>
+<span class="n">x2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">mu2</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="n">mu2</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x2</span><span class="p">,</span><span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x2</span><span class="p">,</span> <span class="n">mu2</span><span class="p">,</span> <span class="n">sigma</span><span class="p">),</span><span class="s2">"g-"</span><span class="p">,</span><span class="n">label</span><span class="o">=</span><span class="s1">'measurement'</span><span class="p">)</span>
+
+
+<span class="n">mu_new</span><span class="o">=</span><span class="n">mu1</span><span class="o">+</span><span class="n">mu2</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"New mean is at: "</span><span class="p">,</span><span class="n">mu_new</span><span class="p">)</span>
+<span class="n">var_new</span><span class="o">=</span><span class="p">(</span><span class="n">variance1</span><span class="o">+</span><span class="n">variance2</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"New variance is: "</span><span class="p">,</span><span class="n">var_new</span><span class="p">)</span>
+<span class="n">sigma</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">var_new</span><span class="p">)</span>
+<span class="n">x3</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="n">mu_new</span> <span class="o">-</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="n">mu_new</span> <span class="o">+</span> <span class="mi">3</span><span class="o">*</span><span class="n">sigma</span><span class="p">,</span> <span class="mi">100</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x3</span><span class="p">,</span><span class="n">scipy</span><span class="o">.</span><span class="n">stats</span><span class="o">.</span><span class="n">norm</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">x3</span><span class="p">,</span> <span class="n">mu_new</span><span class="p">,</span> <span class="n">var_new</span><span class="p">),</span><span class="n">label</span><span class="o">=</span><span class="s2">"posterior"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">(</span><span class="n">loc</span><span class="o">=</span><span class="s1">'upper left'</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">xlim</span><span class="p">(</span><span class="o">-</span><span class="mi">10</span><span class="p">,</span><span class="mi">20</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">New</span> <span class="n">mean</span> <span class="ow">is</span> <span class="n">at</span><span class="p">:</span> <span class="mi">15</span>
+<span class="n">New</span> <span class="n">variance</span> <span class="ow">is</span><span class="p">:</span> <span class="mi">2</span>
+</pre></div>
+</div>
+<img alt="../../_images/Kalmanfilter_basics_21_1.png" src="../../_images/Kalmanfilter_basics_21_1.png" />
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1">#Example from:</span>
+<span class="c1">#https://scipython.com/blog/visualizing-the-bivariate-gaussian-distribution/</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">matplotlib</span> <span class="kn">import</span> <span class="n">cm</span>
+<span class="kn">from</span> <span class="nn">mpl_toolkits.mplot3d</span> <span class="kn">import</span> <span class="n">Axes3D</span>
+
+<span class="c1"># Our 2-dimensional distribution will be over variables X and Y</span>
+<span class="n">N</span> <span class="o">=</span> <span class="mi">60</span>
+<span class="n">X</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
+<span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="n">N</span><span class="p">)</span>
+<span class="n">X</span><span class="p">,</span> <span class="n">Y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">meshgrid</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">)</span>
+
+<span class="c1"># Mean vector and covariance matrix</span>
+<span class="n">mu</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mf">0.</span><span class="p">,</span> <span class="mf">1.</span><span class="p">])</span>
+<span class="n">Sigma</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span> <span class="mf">1.</span> <span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">],</span> <span class="p">[</span><span class="o">-</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">]])</span>
+
+<span class="c1"># Pack X and Y into a single 3-dimensional array</span>
+<span class="n">pos</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">X</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="p">(</span><span class="mi">2</span><span class="p">,))</span>
+<span class="n">pos</span><span class="p">[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">X</span>
+<span class="n">pos</span><span class="p">[:,</span> <span class="p">:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">Y</span>
+
+<span class="k">def</span> <span class="nf">multivariate_gaussian</span><span class="p">(</span><span class="n">pos</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span> <span class="n">Sigma</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""Return the multivariate Gaussian distribution on array pos.</span>
+
+<span class="sd"> pos is an array constructed by packing the meshed arrays of variables</span>
+<span class="sd"> x_1, x_2, x_3, ..., x_k into its _last_ dimension.</span>
+
+<span class="sd"> """</span>
+
+ <span class="n">n</span> <span class="o">=</span> <span class="n">mu</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+ <span class="n">Sigma_det</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">det</span><span class="p">(</span><span class="n">Sigma</span><span class="p">)</span>
+ <span class="n">Sigma_inv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">Sigma</span><span class="p">)</span>
+ <span class="n">N</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">((</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span><span class="o">**</span><span class="n">n</span> <span class="o">*</span> <span class="n">Sigma_det</span><span class="p">)</span>
+ <span class="c1"># This einsum call calculates (x-mu)T.Sigma-1.(x-mu) in a vectorized</span>
+ <span class="c1"># way across all the input variables.</span>
+ <span class="n">fac</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s1">'...k,kl,...l->...'</span><span class="p">,</span> <span class="n">pos</span><span class="o">-</span><span class="n">mu</span><span class="p">,</span> <span class="n">Sigma_inv</span><span class="p">,</span> <span class="n">pos</span><span class="o">-</span><span class="n">mu</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">fac</span> <span class="o">/</span> <span class="mi">2</span><span class="p">)</span> <span class="o">/</span> <span class="n">N</span>
+
+<span class="c1"># The distribution on the variables X, Y packed into pos.</span>
+<span class="n">Z</span> <span class="o">=</span> <span class="n">multivariate_gaussian</span><span class="p">(</span><span class="n">pos</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span> <span class="n">Sigma</span><span class="p">)</span>
+
+<span class="c1"># Create a surface plot and projected filled contour plot under it.</span>
+<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">gca</span><span class="p">(</span><span class="n">projection</span><span class="o">=</span><span class="s1">'3d'</span><span class="p">)</span>
+<span class="n">ax</span><span class="o">.</span><span class="n">plot_surface</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">rstride</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">cstride</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">antialiased</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span>
+ <span class="n">cmap</span><span class="o">=</span><span class="n">cm</span><span class="o">.</span><span class="n">viridis</span><span class="p">)</span>
+
+<span class="n">cset</span> <span class="o">=</span> <span class="n">ax</span><span class="o">.</span><span class="n">contourf</span><span class="p">(</span><span class="n">X</span><span class="p">,</span> <span class="n">Y</span><span class="p">,</span> <span class="n">Z</span><span class="p">,</span> <span class="n">zdir</span><span class="o">=</span><span class="s1">'z'</span><span class="p">,</span> <span class="n">offset</span><span class="o">=-</span><span class="mf">0.15</span><span class="p">,</span> <span class="n">cmap</span><span class="o">=</span><span class="n">cm</span><span class="o">.</span><span class="n">viridis</span><span class="p">)</span>
+
+<span class="c1"># Adjust the limits, ticks and view angle</span>
+<span class="n">ax</span><span class="o">.</span><span class="n">set_zlim</span><span class="p">(</span><span class="o">-</span><span class="mf">0.15</span><span class="p">,</span><span class="mf">0.2</span><span class="p">)</span>
+<span class="n">ax</span><span class="o">.</span><span class="n">set_zticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="mf">0.2</span><span class="p">,</span><span class="mi">5</span><span class="p">))</span>
+<span class="n">ax</span><span class="o">.</span><span class="n">view_init</span><span class="p">(</span><span class="mi">27</span><span class="p">,</span> <span class="o">-</span><span class="mi">21</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../_images/Kalmanfilter_basics_22_0.png" src="../../_images/Kalmanfilter_basics_22_0.png" />
+<p>This is a 3D projection of the gaussians involved with the lower surface
+showing the 2D projection of the 3D projection above. The innermost
+ellipse represents the highest peak, that is the maximum probability for
+a given (X,Y) value.</p>
+<p>** numpy einsum examples **</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">25</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">5</span><span class="p">,</span><span class="mi">5</span><span class="p">)</span>
+<span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">6</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">3</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="n">c</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span> <span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span>
+ <span class="p">[</span> <span class="mi">5</span> <span class="mi">6</span> <span class="mi">7</span> <span class="mi">8</span> <span class="mi">9</span><span class="p">]</span>
+ <span class="p">[</span><span class="mi">10</span> <span class="mi">11</span> <span class="mi">12</span> <span class="mi">13</span> <span class="mi">14</span><span class="p">]</span>
+ <span class="p">[</span><span class="mi">15</span> <span class="mi">16</span> <span class="mi">17</span> <span class="mi">18</span> <span class="mi">19</span><span class="p">]</span>
+ <span class="p">[</span><span class="mi">20</span> <span class="mi">21</span> <span class="mi">22</span> <span class="mi">23</span> <span class="mi">24</span><span class="p">]]</span>
+<span class="p">[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span> <span class="mi">3</span> <span class="mi">4</span><span class="p">]</span>
+<span class="p">[[</span><span class="mi">0</span> <span class="mi">1</span> <span class="mi">2</span><span class="p">]</span>
+ <span class="p">[</span><span class="mi">3</span> <span class="mi">4</span> <span class="mi">5</span><span class="p">]]</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1">#this is the diagonal sum, i repeated means the diagonal</span>
+<span class="n">np</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s1">'ij'</span><span class="p">,</span> <span class="n">a</span><span class="p">)</span>
+<span class="c1">#this takes the output ii which is the diagonal and outputs to a</span>
+<span class="n">np</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s1">'ii->i'</span><span class="p">,</span><span class="n">a</span><span class="p">)</span>
+<span class="c1">#this takes in the array A represented by their axes 'ij' and B by its only axes'j'</span>
+<span class="c1">#and multiples them element wise</span>
+<span class="n">np</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s1">'ij,j'</span><span class="p">,</span><span class="n">a</span><span class="p">,</span> <span class="n">b</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([</span> <span class="mi">30</span><span class="p">,</span> <span class="mi">80</span><span class="p">,</span> <span class="mi">130</span><span class="p">,</span> <span class="mi">180</span><span class="p">,</span> <span class="mi">230</span><span class="p">])</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">B</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span>
+ <span class="p">[</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">],</span>
+ <span class="p">[</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">]])</span>
+<span class="n">C</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">multiply</span><span class="p">(</span><span class="n">A</span><span class="p">,</span><span class="n">B</span><span class="p">)</span>
+<span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">C</span><span class="p">,</span><span class="n">axis</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">22</span><span class="p">,</span> <span class="mi">76</span><span class="p">])</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">D</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">])</span>
+<span class="n">E</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">],</span>
+ <span class="p">[</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">6</span><span class="p">,</span> <span class="mi">7</span><span class="p">],</span>
+ <span class="p">[</span> <span class="mi">8</span><span class="p">,</span> <span class="mi">9</span><span class="p">,</span> <span class="mi">10</span><span class="p">,</span> <span class="mi">11</span><span class="p">]])</span>
+
+<span class="n">np</span><span class="o">.</span><span class="n">einsum</span><span class="p">(</span><span class="s1">'i,ij->i'</span><span class="p">,</span><span class="n">D</span><span class="p">,</span><span class="n">E</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">array</span><span class="p">([</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">22</span><span class="p">,</span> <span class="mi">76</span><span class="p">])</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">scipy.stats</span> <span class="kn">import</span> <span class="n">multivariate_normal</span>
+<span class="n">x</span><span class="p">,</span> <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">mgrid</span><span class="p">[</span><span class="o">-</span><span class="mi">5</span><span class="p">:</span><span class="mi">5</span><span class="p">:</span><span class="mf">.1</span><span class="p">,</span> <span class="o">-</span><span class="mi">5</span><span class="p">:</span><span class="mi">5</span><span class="p">:</span><span class="mf">.1</span><span class="p">]</span>
+<span class="n">pos</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="p">(</span><span class="mi">2</span><span class="p">,))</span>
+<span class="n">pos</span><span class="p">[:,</span> <span class="p">:,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span><span class="p">;</span> <span class="n">pos</span><span class="p">[:,</span> <span class="p">:,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">y</span>
+<span class="n">rv</span> <span class="o">=</span> <span class="n">multivariate_normal</span><span class="p">([</span><span class="mf">0.5</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.2</span><span class="p">],</span> <span class="p">[[</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">],</span> <span class="p">[</span><span class="mf">0.9</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">]])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">contourf</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">rv</span><span class="o">.</span><span class="n">pdf</span><span class="p">(</span><span class="n">pos</span><span class="p">))</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o"><</span><span class="n">matplotlib</span><span class="o">.</span><span class="n">contour</span><span class="o">.</span><span class="n">QuadContourSet</span> <span class="n">at</span> <span class="mh">0x139196438</span><span class="o">></span>
+</pre></div>
+</div>
+<img alt="../../_images/Kalmanfilter_basics_28_1.png" src="../../_images/Kalmanfilter_basics_28_1.png" />
+</section>
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ol class="arabic simple">
+<li><p>Roger Labbe’s
+<a class="reference external" href="https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python">repo</a>
+on Kalman Filters. (Majority of the examples in the notes are from
+this)</p></li>
+<li><p>Probabilistic Robotics by Sebastian Thrun, Wolfram Burgard and Dieter
+Fox, MIT Press.</p></li>
+<li><p>Scipy
+<a class="reference external" href="https://scipython.com/blog/visualizing-the-bivariate-gaussian-distribution/">Documentation</a></p></li>
+</ol>
+</section>
+</section>
+
+
+ </div>
+ </div>
+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+ <a href="appendix.html" class="btn btn-neutral float-left" title="Appendix" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics.html">KF Basics - Part I</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">KF Basics - Part 2</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#probabilistic-generative-laws">Probabilistic Generative Laws</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#st-law">1st Law:</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#nd-law">2nd Law:</a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="#conditional-dependence-and-independence-example">Conditional dependence and independence example:</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#bayes-rule">Bayes Rule:</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#bayes-filter-algorithm">Bayes Filter Algorithm</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#bayes-filter-localization-example">Bayes filter localization example:</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#bayes-and-kalman-filter-structure">Bayes and Kalman filter structure</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#kalman-gain">Kalman Gain</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#kalman-filter-univariate-and-multivariate">Kalman Filter - Univariate and Multivariate</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#references">References:</a></li>
+</ul>
+</li>
+</ul>
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+
+ <section id="kf-basics-part-2">
+<h1>KF Basics - Part 2<a class="headerlink" href="#kf-basics-part-2" title="Permalink to this headline"></a></h1>
+<section id="probabilistic-generative-laws">
+<h2>Probabilistic Generative Laws<a class="headerlink" href="#probabilistic-generative-laws" title="Permalink to this headline"></a></h2>
+<section id="st-law">
+<h3>1st Law:<a class="headerlink" href="#st-law" title="Permalink to this headline"></a></h3>
+<p>The belief representing the state <span class="math notranslate nohighlight">\(x_{t}\)</span>, is conditioned on all
+past states, measurements and controls. This can be shown mathematically
+by the conditional probability shown below:</p>
+<div class="math notranslate nohighlight">
+\[p(x_{t} | x_{0:t-1},z_{1:t-1},u_{1:t})\]</div>
+<ol class="arabic simple">
+<li><p><span class="math notranslate nohighlight">\(z_{t}\)</span> represents the <strong>measurement</strong></p></li>
+<li><p><span class="math notranslate nohighlight">\(u_{t}\)</span> the <strong>motion command</strong></p></li>
+<li><p><span class="math notranslate nohighlight">\(x_{t}\)</span> the <strong>state</strong> (can be the position, velocity, etc) of
+the robot or its environment at time t.</p></li>
+</ol>
+<p>‘If we know the state <span class="math notranslate nohighlight">\(x_{t-1}\)</span> and <span class="math notranslate nohighlight">\(u_{t}\)</span>, then knowing
+the states <span class="math notranslate nohighlight">\(x_{0:t-2}\)</span>, <span class="math notranslate nohighlight">\(z_{1:t-1}\)</span> becomes immaterial
+through the property of <strong>conditional independence</strong>’. The state
+<span class="math notranslate nohighlight">\(x_{t-1}\)</span> introduces a conditional independence between
+<span class="math notranslate nohighlight">\(x_{t}\)</span> and <span class="math notranslate nohighlight">\(z_{1:t-1}\)</span>, <span class="math notranslate nohighlight">\(u_{1:t-1}\)</span></p>
+<p>Therefore the law now holds as:</p>
+<div class="math notranslate nohighlight">
+\[p(x_{t} | x_{0:t-1},z_{1:t-1},u_{1:t})=p(x_{t} | x_{t-1},u_{t})\]</div>
+</section>
+<section id="nd-law">
+<h3>2nd Law:<a class="headerlink" href="#nd-law" title="Permalink to this headline"></a></h3>
+<p>If <span class="math notranslate nohighlight">\(x_{t}\)</span> is complete, then:</p>
+<div class="math notranslate nohighlight">
+\[p(z_{t} | x-_{0:t},z_{1:t-1},u_{1:t})=p(z_{t} | x_{t})\]</div>
+<p><span class="math notranslate nohighlight">\(x_{t}\)</span> is <strong>complete</strong> means that the past states, controls or
+measurements carry no additional information to predict future.</p>
+<p><span class="math notranslate nohighlight">\(x_{0:t-1}\)</span>, <span class="math notranslate nohighlight">\(z_{1:t-1}\)</span> and <span class="math notranslate nohighlight">\(u_{1:t}\)</span> are
+<strong>conditionally independent</strong> of <span class="math notranslate nohighlight">\(z_{t}\)</span> given <span class="math notranslate nohighlight">\(x_{t}\)</span> of
+complete.</p>
+<p>The filter works in two parts:</p>
+<p><span class="math notranslate nohighlight">\(p(x_{t} | x_{t-1},u_{t})\)</span> -> <strong>State Transition Probability</strong></p>
+<p><span class="math notranslate nohighlight">\(p(z_{t} | x_{t})\)</span> -> <strong>Measurement Probability</strong></p>
+</section>
+</section>
+<section id="conditional-dependence-and-independence-example">
+<h2>Conditional dependence and independence example:<a class="headerlink" href="#conditional-dependence-and-independence-example" title="Permalink to this headline"></a></h2>
+<p><span class="math notranslate nohighlight">\(\bullet\)</span><strong>Independent but conditionally dependent</strong></p>
+<p>Let’s say you flip two fair coins</p>
+<p>A - Your first coin flip is heads</p>
+<p>B - Your second coin flip is heads</p>
+<p>C - Your first two flips were the same</p>
+<p>A and B here are independent. However, A and B are conditionally
+dependent given C, since if you know C then your first coin flip will
+inform the other one.</p>
+<p><span class="math notranslate nohighlight">\(\bullet\)</span><strong>Dependent but conditionally independent</strong></p>
+<p>A box contains two coins: a regular coin and one fake two-headed coin
+((P(H)=1). I choose a coin at random and toss it twice. Define the
+following events.</p>
+<p>A= First coin toss results in an H.</p>
+<p>B= Second coin toss results in an H.</p>
+<p>C= Coin 1 (regular) has been selected.</p>
+<p>If we know A has occurred (i.e., the first coin toss has resulted in
+heads), we would guess that it is more likely that we have chosen Coin 2
+than Coin 1. This in turn increases the conditional probability that B
+occurs. This suggests that A and B are not independent. On the other
+hand, given C (Coin 1 is selected), A and B are independent.</p>
+</section>
+<section id="bayes-rule">
+<h2>Bayes Rule:<a class="headerlink" href="#bayes-rule" title="Permalink to this headline"></a></h2>
+<p>Posterior =</p>
+<div class="math notranslate nohighlight">
+\[\frac{Likelihood*Prior}{Marginal}\]</div>
+<p>Here,</p>
+<p><strong>Posterior</strong> = Probability of an event occurring based on certain
+evidence.</p>
+<p><strong>Likelihood</strong> = How probable is the evidence given the event.</p>
+<p><strong>Prior</strong> = Probability of the just the event occurring without having
+any evidence.</p>
+<p><strong>Marginal</strong> = Probability of the evidence given all the instances of
+events possible.</p>
+<p>Example:</p>
+<p>1% of women have breast cancer (and therefore 99% do not). 80% of
+mammograms detect breast cancer when it is there (and therefore 20% miss
+it). 9.6% of mammograms detect breast cancer when its not there (and
+therefore 90.4% correctly return a negative result).</p>
+<p>We can turn the process above into an equation, which is Bayes Theorem.
+Here is the equation:</p>
+<p><span class="math notranslate nohighlight">\(\displaystyle{\Pr(\mathrm{A}|\mathrm{X}) = \frac{\Pr(\mathrm{X}|\mathrm{A})\Pr(\mathrm{A})}{\Pr(\mathrm{X|A})\Pr(\mathrm{A})+ \Pr(\mathrm{X | not \ A})\Pr(\mathrm{not \ A})}}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\bullet\)</span>Pr(A|X) = Chance of having cancer (A) given a positive
+test (X). This is what we want to know: How likely is it to have cancer
+with a positive result? In our case it was 7.8%.</p>
+<p><span class="math notranslate nohighlight">\(\bullet\)</span>Pr(X|A) = Chance of a positive test (X) given that you
+had cancer (A). This is the chance of a true positive, 80% in our case.</p>
+<p><span class="math notranslate nohighlight">\(\bullet\)</span>Pr(A) = Chance of having cancer (1%).</p>
+<p><span class="math notranslate nohighlight">\(\bullet\)</span>Pr(not A) = Chance of not having cancer (99%).</p>
+<p><span class="math notranslate nohighlight">\(\bullet\)</span>Pr(X|not A) = Chance of a positive test (X) given that
+you didn’t have cancer (~A). This is a false positive, 9.6% in our case.</p>
+</section>
+<section id="bayes-filter-algorithm">
+<h2>Bayes Filter Algorithm<a class="headerlink" href="#bayes-filter-algorithm" title="Permalink to this headline"></a></h2>
+<p>The basic filter algorithm is:</p>
+<p>for all <span class="math notranslate nohighlight">\(x_{t}\)</span>:</p>
+<ol class="arabic simple">
+<li><p><span class="math notranslate nohighlight">\(\overline{bel}(x_t) = \int p(x_t | u_t, x_{t-1}) bel(x_{t-1})dx\)</span></p></li>
+<li><p><span class="math notranslate nohighlight">\(bel(x_t) = \eta p(z_t | x_t) \overline{bel}(x_t)\)</span></p></li>
+</ol>
+<p>end.</p>
+<p><span class="math notranslate nohighlight">\(\rightarrow\)</span>The first step in filter is to calculate the prior
+for the next step that uses the bayes theorem. This is the
+<strong>Prediction</strong> step. The belief, <span class="math notranslate nohighlight">\(\overline{bel}(x_t)\)</span>, is
+<strong>before</strong> incorporating measurement(<span class="math notranslate nohighlight">\(z_{t}\)</span>) at time t=t. This
+is the step where the motion occurs and information is lost because the
+means and covariances of the gaussians are added. The RHS of the
+equation incorporates the law of total probability for prior
+calculation.</p>
+<p><span class="math notranslate nohighlight">\(\rightarrow\)</span> This is the <strong>Correction</strong> or update step that
+calculates the belief of the robot <strong>after</strong> taking into account the
+measurement(<span class="math notranslate nohighlight">\(z_{t}\)</span>) at time t=t. This is where we incorporate
+the sensor information for the whereabouts of the robot. We gain
+information here as the gaussians get multiplied here. (Multiplication
+of gaussian values allows the resultant to lie in between these numbers
+and the resultant covariance is smaller.</p>
+</section>
+<section id="bayes-filter-localization-example">
+<h2>Bayes filter localization example:<a class="headerlink" href="#bayes-filter-localization-example" title="Permalink to this headline"></a></h2>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">IPython.display</span> <span class="kn">import</span> <span class="n">Image</span>
+<span class="n">Image</span><span class="p">(</span><span class="n">filename</span><span class="o">=</span><span class="s2">"bayes_filter.png"</span><span class="p">,</span><span class="n">width</span><span class="o">=</span><span class="mi">400</span><span class="p">)</span>
+</pre></div>
+</div>
+<a class="reference internal image-reference" href="../../_images/Kalmanfilter_basics_2_5_0.png"><img alt="../../_images/Kalmanfilter_basics_2_5_0.png" src="../../_images/Kalmanfilter_basics_2_5_0.png" style="width: 400px;" /></a>
+<p>Given - A robot with a sensor to detect doorways along a hallway. Also,
+the robot knows how the hallway looks like but doesn’t know where it is
+in the map.</p>
+<ol class="arabic simple">
+<li><p>Initially(first scenario), it doesn’t know where it is with respect
+to the map and hence the belief assigns equal probability to each
+location in the map.</p></li>
+<li><p>The first sensor reading is incorporated and it shows the presence of
+a door. Now the robot knows how the map looks like but cannot
+localize yet as map has 3 doors present. Therefore it assigns equal
+probability to each door present.</p></li>
+<li><p>The robot now moves forward. This is the prediction step and the
+motion causes the robot to lose some of the information and hence the
+variance of the gaussians increase (diagram 4.). The final belief is
+<strong>convolution</strong> of posterior from previous step and the current state
+after motion. Also, the means shift on the right due to the motion.</p></li>
+<li><p>Again, incorporating the measurement, the sensor senses a door and
+this time too the possibility of door is equal for the three door.
+This is where the filter’s magic kicks in. For the final belief
+(diagram 5.), the posterior calculated after sensing is mixed or
+<strong>convolution</strong> of previous posterior and measurement. It improves
+the robot’s belief at location near to the second door. The variance
+<strong>decreases</strong> and <strong>peaks</strong>.</p></li>
+<li><p>Finally after series of iterations of motion and correction, the
+robot is able to localize itself with respect to the
+environment.(diagram 6.)</p></li>
+</ol>
+<p>Do note that the robot knows the map but doesn’t know where exactly it
+is on the map.</p>
+</section>
+<section id="bayes-and-kalman-filter-structure">
+<h2>Bayes and Kalman filter structure<a class="headerlink" href="#bayes-and-kalman-filter-structure" title="Permalink to this headline"></a></h2>
+<p>The basic structure and the concept remains the same as bayes filter for
+Kalman. The only key difference is the mathematical representation of
+Kalman filter. The Kalman filter is nothing but a bayesian filter that
+uses Gaussians.</p>
+<p>For a bayes filter to be a Kalman filter, <strong>each term of belief is now a
+gaussian</strong>, unlike histograms. The basic formulation for the <strong>bayes
+filter</strong> algorithm is:</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\begin{aligned}
+\bar {\mathbf x} &= \mathbf x \ast f_{\mathbf x}(\bullet)\, \, &\text{Prediction} \\
+\mathbf x &= \mathcal L \cdot \bar{\mathbf x}\, \, &\text{Correction}
+\end{aligned}\end{split}\]</div>
+<p><span class="math notranslate nohighlight">\(\bar{\mathbf x}\)</span> is the <em>prior</em></p>
+<p><span class="math notranslate nohighlight">\(\mathcal L\)</span> is the <em>likelihood</em> of a measurement given the prior
+<span class="math notranslate nohighlight">\(\bar{\mathbf x}\)</span></p>
+<p><span class="math notranslate nohighlight">\(f_{\mathbf x}(\bullet)\)</span> is the <em>process model</em> or the gaussian
+term that helps predict the next state like velocity to track position
+or acceleration.</p>
+<p><span class="math notranslate nohighlight">\(\ast\)</span> denotes <em>convolution</em>.</p>
+</section>
+<section id="kalman-gain">
+<h2>Kalman Gain<a class="headerlink" href="#kalman-gain" title="Permalink to this headline"></a></h2>
+<div class="math notranslate nohighlight">
+\[x = (\mathcal L \bar x)\]</div>
+<p>Where x is posterior and <span class="math notranslate nohighlight">\(\mathcal L\)</span> and <span class="math notranslate nohighlight">\(\bar x\)</span> are
+gaussians.</p>
+<p>Therefore the mean of the posterior is given by:</p>
+<div class="math notranslate nohighlight">
+\[\mu=\frac{\bar\sigma^2\, \mu_z + \sigma_z^2 \, \bar\mu} {\bar\sigma^2 + \sigma_z^2}\]</div>
+<div class="math notranslate nohighlight">
+\[\mu = \left( \frac{\bar\sigma^2}{\bar\sigma^2 + \sigma_z^2}\right) \mu_z + \left(\frac{\sigma_z^2}{\bar\sigma^2 + \sigma_z^2}\right)\bar\mu\]</div>
+<p>In this form it is easy to see that we are scaling the measurement and
+the prior by weights:</p>
+<div class="math notranslate nohighlight">
+\[\mu = W_1 \mu_z + W_2 \bar\mu\]</div>
+<p>The weights sum to one because the denominator is a normalization term.
+We introduce a new term, <span class="math notranslate nohighlight">\(K=W_1\)</span>, giving us:</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\begin{aligned}
+\mu &= K \mu_z + (1-K) \bar\mu\\
+&= \bar\mu + K(\mu_z - \bar\mu)
+\end{aligned}\end{split}\]</div>
+<p>where</p>
+<div class="math notranslate nohighlight">
+\[K = \frac {\bar\sigma^2}{\bar\sigma^2 + \sigma_z^2}\]</div>
+<p>The variance in terms of the Kalman gain:</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\begin{aligned}
+\sigma^2 &= \frac{\bar\sigma^2 \sigma_z^2 } {\bar\sigma^2 + \sigma_z^2} \\
+&= K\sigma_z^2 \\
+&= (1-K)\bar\sigma^2
+\end{aligned}\end{split}\]</div>
+<p><span class="math notranslate nohighlight">\(K\)</span> is the <em>Kalman gain</em>. It’s the crux of the Kalman filter. It
+is a scaling term that chooses a value partway between <span class="math notranslate nohighlight">\(\mu_z\)</span> and
+<span class="math notranslate nohighlight">\(\bar\mu\)</span>.</p>
+</section>
+<section id="kalman-filter-univariate-and-multivariate">
+<h2>Kalman Filter - Univariate and Multivariate<a class="headerlink" href="#kalman-filter-univariate-and-multivariate" title="Permalink to this headline"></a></h2>
+<p><strong>Prediction</strong></p>
+<p><span class="math notranslate nohighlight">\(\begin{array}{|l|l|l|} \hline \text{Univariate} & \text{Univariate} & \text{Multivariate}\\ & \text{(Kalman form)} & \\ \hline \bar \mu = \mu + \mu_{f_x} & \bar x = x + dx & \bar{\mathbf x} = \mathbf{Fx} + \mathbf{Bu}\\ \bar\sigma^2 = \sigma_x^2 + \sigma_{f_x}^2 & \bar P = P + Q & \bar{\mathbf P} = \mathbf{FPF}^\mathsf T + \mathbf Q \\ \hline \end{array}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\mathbf x,\, \mathbf P\)</span> are the state mean and covariance. They
+correspond to <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(\sigma^2\)</span>.</p>
+<p><span class="math notranslate nohighlight">\(\mathbf F\)</span> is the <em>state transition function</em>. When multiplied by
+<span class="math notranslate nohighlight">\(\bf x\)</span> it computes the prior.</p>
+<p><span class="math notranslate nohighlight">\(\mathbf Q\)</span> is the process covariance. It corresponds to
+<span class="math notranslate nohighlight">\(\sigma^2_{f_x}\)</span>.</p>
+<p><span class="math notranslate nohighlight">\(\mathbf B\)</span> and <span class="math notranslate nohighlight">\(\mathbf u\)</span> are model control inputs to the
+system.</p>
+<p><strong>Correction</strong></p>
+<p><span class="math notranslate nohighlight">\(\begin{array}{|l|l|l|} \hline \text{Univariate} & \text{Univariate} & \text{Multivariate}\\ & \text{(Kalman form)} & \\ \hline & y = z - \bar x & \mathbf y = \mathbf z - \mathbf{H\bar x} \\ & K = \frac{\bar P}{\bar P+R}& \mathbf K = \mathbf{\bar{P}H}^\mathsf T (\mathbf{H\bar{P}H}^\mathsf T + \mathbf R)^{-1} \\ \mu=\frac{\bar\sigma^2\, \mu_z + \sigma_z^2 \, \bar\mu} {\bar\sigma^2 + \sigma_z^2} & x = \bar x + Ky & \mathbf x = \bar{\mathbf x} + \mathbf{Ky} \\ \sigma^2 = \frac{\sigma_1^2\sigma_2^2}{\sigma_1^2+\sigma_2^2} & P = (1-K)\bar P & \mathbf P = (\mathbf I - \mathbf{KH})\mathbf{\bar{P}} \\ \hline \end{array}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\mathbf H\)</span> is the measurement function.</p>
+<p><span class="math notranslate nohighlight">\(\mathbf z,\, \mathbf R\)</span> are the measurement mean and noise
+covariance. They correspond to <span class="math notranslate nohighlight">\(z\)</span> and <span class="math notranslate nohighlight">\(\sigma_z^2\)</span> in the
+univariate filter. <span class="math notranslate nohighlight">\(\mathbf y\)</span> and <span class="math notranslate nohighlight">\(\mathbf K\)</span> are the
+residual and Kalman gain.</p>
+<p>The details will be different than the univariate filter because these
+are vectors and matrices, but the concepts are exactly the same:</p>
+<ul class="simple">
+<li><p>Use a Gaussian to represent our estimate of the state and error</p></li>
+<li><p>Use a Gaussian to represent the measurement and its error</p></li>
+<li><p>Use a Gaussian to represent the process model</p></li>
+<li><p>Use the process model to predict the next state (the prior)</p></li>
+<li><p>Form an estimate part way between the measurement and the prior</p></li>
+</ul>
+</section>
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ol class="arabic simple">
+<li><p>Roger Labbe’s
+<a class="reference external" href="https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python">repo</a>
+on Kalman Filters. (Majority of text in the notes are from this)</p></li>
+<li><p>Probabilistic Robotics by Sebastian Thrun, Wolfram Burgard and Dieter
+Fox, MIT Press.</p></li>
+</ol>
+</section>
+</section>
+
+
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+<div class="toctree-wrapper compound">
+<p class="caption" role="heading"><span class="caption-text">Contents</span></p>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="Kalmanfilter_basics.html">KF Basics - Part I</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics.html#introduction">Introduction</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics.html#variance-covariance-and-correlation">Variance, Covariance and Correlation</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics.html#gaussians">Gaussians</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics.html#gaussian-properties">Gaussian Properties</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics.html#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="Kalmanfilter_basics_2.html">KF Basics - Part 2</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics_2.html#probabilistic-generative-laws">Probabilistic Generative Laws</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics_2.html#conditional-dependence-and-independence-example">Conditional dependence and independence example:</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics_2.html#bayes-rule">Bayes Rule:</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics_2.html#bayes-filter-algorithm">Bayes Filter Algorithm</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics_2.html#bayes-filter-localization-example">Bayes filter localization example:</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics_2.html#bayes-and-kalman-filter-structure">Bayes and Kalman filter structure</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics_2.html#kalman-gain">Kalman Gain</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics_2.html#kalman-filter-univariate-and-multivariate">Kalman Filter - Univariate and Multivariate</a></li>
+<li class="toctree-l2"><a class="reference internal" href="Kalmanfilter_basics_2.html#references">References:</a></li>
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+</li>
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new file mode 100644
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+<li class="toctree-l1 current"><a class="reference internal" href="arm_navigation.html">Arm Navigation</a><ul class="current">
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+<li class="toctree-l2 current"><a class="current reference internal" href="#">N joint arm to point control</a></li>
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+
+ <section id="n-joint-arm-to-point-control">
+<h1>N joint arm to point control<a class="headerlink" href="#n-joint-arm-to-point-control" title="Permalink to this headline"></a></h1>
+<p>N joint arm to a point control simulation.</p>
+<p>This is a interactive simulation.</p>
+<p>You can set the goal position of the end effector with left-click on the
+plotting area.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/ArmNavigation/n_joint_arm_to_point_control/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/ArmNavigation/n_joint_arm_to_point_control/animation.gif" />
+<p>In this simulation N = 10, however, you can change it.</p>
+</section>
+
+
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+ </div>
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+<li class="toctree-l1 current"><a class="reference internal" href="arm_navigation.html">Arm Navigation</a><ul class="current">
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+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
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+
+ <section id="arm-navigation-with-obstacle-avoidance">
+<h1>Arm navigation with obstacle avoidance<a class="headerlink" href="#arm-navigation-with-obstacle-avoidance" title="Permalink to this headline"></a></h1>
+<p>Arm navigation with obstacle avoidance simulation.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/ArmNavigation/arm_obstacle_navigation/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/ArmNavigation/arm_obstacle_navigation/animation.gif" />
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+
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+<html class="writer-html5" lang="en" >
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+<li class="toctree-l1 current"><a class="reference internal" href="arm_navigation.html">Arm Navigation</a><ul class="current">
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Two joint arm to point control</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#inverse-kinematics-for-a-planar-two-link-robotic-arm">Inverse Kinematics for a Planar Two-Link Robotic Arm</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="n_joint_arm_to_point_control.html">N joint arm to point control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="obstacle_avoidance_arm_navigation.html">Arm navigation with obstacle avoidance</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="../control/control.html">Control</a></li>
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+ <section id="two-joint-arm-to-point-control">
+<h1>Two joint arm to point control<a class="headerlink" href="#two-joint-arm-to-point-control" title="Permalink to this headline"></a></h1>
+<figure class="align-default">
+<img alt="TwoJointArmToPointControl" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/ArmNavigation/two_joint_arm_to_point_control/animation.gif" />
+</figure>
+<p>This is two joint arm to a point control simulation.</p>
+<p>This is a interactive simulation.</p>
+<p>You can set the goal position of the end effector with left-click on the plotting area.</p>
+<section id="inverse-kinematics-for-a-planar-two-link-robotic-arm">
+<h2>Inverse Kinematics for a Planar Two-Link Robotic Arm<a class="headerlink" href="#inverse-kinematics-for-a-planar-two-link-robotic-arm" title="Permalink to this headline"></a></h2>
+<p>A classic problem with robotic arms is getting the end-effector, the
+mechanism at the end of the arm responsible for manipulating the
+environment, to where you need it to be. Maybe the end-effector is a
+gripper and maybe you want to pick up an object and maybe you know where
+that object is relative to the robot - but you cannot tell the
+end-effector where to go directly. Instead, you have to determine the
+joint angles that get the end-effector to where you want it to be. This
+problem is known as inverse kinematics.</p>
+<p>Credit for this solution goes to:
+<a class="reference external" href="https://robotacademy.net.au/lesson/inverse-kinematics-for-a-2-joint-robot-arm-using-geometry/">https://robotacademy.net.au/lesson/inverse-kinematics-for-a-2-joint-robot-arm-using-geometry/</a></p>
+<p>First, let’s define a class to make plotting our arm easier.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> inline
+<span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">cos</span><span class="p">,</span> <span class="n">sin</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+
+<span class="k">class</span> <span class="nc">TwoLinkArm</span><span class="p">:</span>
+ <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">joint_angles</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]):</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">shoulder</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">link_lengths</span> <span class="o">=</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">update_joints</span><span class="p">(</span><span class="n">joint_angles</span><span class="p">)</span>
+
+ <span class="k">def</span> <span class="nf">update_joints</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">joint_angles</span><span class="p">):</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">joint_angles</span> <span class="o">=</span> <span class="n">joint_angles</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">forward_kinematics</span><span class="p">()</span>
+
+ <span class="k">def</span> <span class="nf">forward_kinematics</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+ <span class="n">theta0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">joint_angles</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+ <span class="n">theta1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">joint_angles</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+ <span class="n">l0</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">link_lengths</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+ <span class="n">l1</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">link_lengths</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">elbow</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">shoulder</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">l0</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">theta0</span><span class="p">),</span> <span class="n">l0</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">theta0</span><span class="p">)])</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">wrist</span> <span class="o">=</span> <span class="bp">self</span><span class="o">.</span><span class="n">elbow</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">l1</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">theta0</span> <span class="o">+</span> <span class="n">theta1</span><span class="p">),</span> <span class="n">l1</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">theta0</span> <span class="o">+</span> <span class="n">theta1</span><span class="p">)])</span>
+
+ <span class="k">def</span> <span class="nf">plot</span><span class="p">(</span><span class="bp">self</span><span class="p">):</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">shoulder</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">shoulder</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
+ <span class="s1">'r-'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="bp">self</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="bp">self</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
+ <span class="s1">'r-'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">shoulder</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">shoulder</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="s1">'ko'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="s1">'ko'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="bp">self</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="bp">self</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="s1">'ko'</span><span class="p">)</span>
+</pre></div>
+</div>
+<p>Let’s also define a function to make it easier to draw an angle on our
+diagram.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">sqrt</span>
+
+<span class="k">def</span> <span class="nf">transform_points</span><span class="p">(</span><span class="n">points</span><span class="p">,</span> <span class="n">theta</span><span class="p">,</span> <span class="n">origin</span><span class="p">):</span>
+ <span class="n">T</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">cos</span><span class="p">(</span><span class="n">theta</span><span class="p">),</span> <span class="o">-</span><span class="n">sin</span><span class="p">(</span><span class="n">theta</span><span class="p">),</span> <span class="n">origin</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="n">sin</span><span class="p">(</span><span class="n">theta</span><span class="p">),</span> <span class="n">cos</span><span class="p">(</span><span class="n">theta</span><span class="p">),</span> <span class="n">origin</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">]])</span>
+ <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">matmul</span><span class="p">(</span><span class="n">T</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">points</span><span class="p">))</span>
+
+<span class="k">def</span> <span class="nf">draw_angle</span><span class="p">(</span><span class="n">angle</span><span class="p">,</span> <span class="n">offset</span><span class="o">=</span><span class="mi">0</span><span class="p">,</span> <span class="n">origin</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">r</span><span class="o">=</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">n_points</span><span class="o">=</span><span class="mi">100</span><span class="p">):</span>
+ <span class="n">x_start</span> <span class="o">=</span> <span class="n">r</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">angle</span><span class="p">)</span>
+ <span class="n">x_end</span> <span class="o">=</span> <span class="n">r</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="p">(</span><span class="n">x_end</span> <span class="o">-</span> <span class="n">x_start</span><span class="p">)</span><span class="o">/</span><span class="p">(</span><span class="n">n_points</span><span class="o">-</span><span class="mi">1</span><span class="p">)</span>
+ <span class="n">coords</span> <span class="o">=</span> <span class="p">[[</span><span class="mi">0</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_points</span><span class="p">)]</span> <span class="k">for</span> <span class="n">_</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">3</span><span class="p">)]</span>
+ <span class="n">x</span> <span class="o">=</span> <span class="n">x_start</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n_points</span><span class="o">-</span><span class="mi">1</span><span class="p">):</span>
+ <span class="n">y</span> <span class="o">=</span> <span class="n">sqrt</span><span class="p">(</span><span class="n">r</span><span class="o">**</span><span class="mi">2</span> <span class="o">-</span> <span class="n">x</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+ <span class="n">coords</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span>
+ <span class="n">coords</span><span class="p">[</span><span class="mi">1</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">y</span>
+ <span class="n">coords</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
+ <span class="n">x</span> <span class="o">+=</span> <span class="n">dx</span>
+ <span class="n">coords</span><span class="p">[</span><span class="mi">0</span><span class="p">][</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">r</span>
+ <span class="n">coords</span><span class="p">[</span><span class="mi">2</span><span class="p">][</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
+ <span class="n">coords</span> <span class="o">=</span> <span class="n">transform_points</span><span class="p">(</span><span class="n">coords</span><span class="p">,</span> <span class="n">offset</span><span class="p">,</span> <span class="n">origin</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">coords</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">coords</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="s1">'k-'</span><span class="p">)</span>
+</pre></div>
+</div>
+<p>Okay, we now have a TwoLinkArm class to help us draw the arm, which
+we’ll do several times during our derivation. Notice there is a method
+called forward_kinematics - forward kinematics specifies the
+end-effector position given the joint angles and link lengths. Forward
+kinematics is easier than inverse kinematics.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">arm</span> <span class="o">=</span> <span class="n">TwoLinkArm</span><span class="p">()</span>
+
+<span class="n">theta0</span> <span class="o">=</span> <span class="mf">0.5</span>
+<span class="n">theta1</span> <span class="o">=</span> <span class="mi">1</span>
+
+<span class="n">arm</span><span class="o">.</span><span class="n">update_joints</span><span class="p">([</span><span class="n">theta0</span><span class="p">,</span> <span class="n">theta1</span><span class="p">])</span>
+<span class="n">arm</span><span class="o">.</span><span class="n">plot</span><span class="p">()</span>
+
+<span class="k">def</span> <span class="nf">label_diagram</span><span class="p">():</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="s1">'k--'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">+</span><span class="mf">0.5</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">theta0</span><span class="p">)],</span>
+ <span class="p">[</span><span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span><span class="o">+</span><span class="mf">0.5</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">theta0</span><span class="p">)],</span>
+ <span class="s1">'k--'</span><span class="p">)</span>
+
+ <span class="n">draw_angle</span><span class="p">(</span><span class="n">theta0</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="mf">0.25</span><span class="p">)</span>
+ <span class="n">draw_angle</span><span class="p">(</span><span class="n">theta1</span><span class="p">,</span> <span class="n">offset</span><span class="o">=</span><span class="n">theta0</span><span class="p">,</span> <span class="n">origin</span><span class="o">=</span><span class="p">[</span><span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span> <span class="n">r</span><span class="o">=</span><span class="mf">0.25</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s2">"$l_0$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"r"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s2">"$l_1$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.8</span><span class="p">,</span> <span class="mi">1</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"r"</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\theta_0$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.35</span><span class="p">,</span> <span class="mf">0.05</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\theta_1$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.8</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">)</span>
+
+<span class="n">label_diagram</span><span class="p">()</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s2">"Shoulder"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="n">arm</span><span class="o">.</span><span class="n">shoulder</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">arm</span><span class="o">.</span><span class="n">shoulder</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="mf">0.15</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">),</span>
+ <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.05</span><span class="p">))</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s2">"Elbow"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="mf">1.25</span><span class="p">,</span> <span class="mf">0.25</span><span class="p">),</span>
+ <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.05</span><span class="p">))</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s2">"Wrist"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">1</span><span class="p">]),</span> <span class="n">xytext</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">1.75</span><span class="p">),</span>
+ <span class="n">arrowprops</span><span class="o">=</span><span class="nb">dict</span><span class="p">(</span><span class="n">facecolor</span><span class="o">=</span><span class="s1">'black'</span><span class="p">,</span> <span class="n">shrink</span><span class="o">=</span><span class="mf">0.05</span><span class="p">))</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../_images/Planar_Two_Link_IK_5_0.png" src="../../_images/Planar_Two_Link_IK_5_0.png" />
+<p>It’s common to name arm joints anatomically, hence the names shoulder,
+elbow, and wrist. In this example, the wrist is not itself a joint, but
+we can consider it to be our end-effector. If we constrain the shoulder
+to the origin, we can write the forward kinematics for the elbow and the
+wrist.</p>
+<div class="line-block">
+<div class="line"><span class="math notranslate nohighlight">\(elbow_x = l_0\cos(\theta_0)\)</span></div>
+<div class="line"><span class="math notranslate nohighlight">\(elbow_y = l_0\sin(\theta_0)\)</span></div>
+</div>
+<div class="line-block">
+<div class="line"><span class="math notranslate nohighlight">\(wrist_x = elbow_x + l_1\cos(\theta_0+\theta_1) = l_0\cos(\theta_0) + l_1\cos(\theta_0+\theta_1)\)</span></div>
+<div class="line"><span class="math notranslate nohighlight">\(wrist_y = elbow_y + l_1\sin(\theta_0+\theta_1) = l_0\sin(\theta_0) + l_1\sin(\theta_0+\theta_1)\)</span></div>
+</div>
+<p>Since the wrist is our end-effector, let’s just call its coordinates
+<span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span>. The forward kinematics for our
+end-effector is then</p>
+<div class="line-block">
+<div class="line"><span class="math notranslate nohighlight">\(x = l_0\cos(\theta_0) + l_1\cos(\theta_0+\theta_1)\)</span></div>
+<div class="line"><span class="math notranslate nohighlight">\(y = l_0\sin(\theta_0) + l_1\sin(\theta_0+\theta_1)\)</span></div>
+</div>
+<p>A first attempt to find the joint angles <span class="math notranslate nohighlight">\(\theta_0\)</span> and
+<span class="math notranslate nohighlight">\(\theta_1\)</span> that would get our end-effector to the desired
+coordinates <span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> might be to try solving the forward
+kinematics for <span class="math notranslate nohighlight">\(\theta_0\)</span> and <span class="math notranslate nohighlight">\(\theta_1\)</span>, but that would be
+the wrong move. An easier path involves going back to the geometry of
+the arm.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">pi</span>
+
+<span class="n">arm</span><span class="o">.</span><span class="n">plot</span><span class="p">()</span>
+<span class="n">label_diagram</span><span class="p">()</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
+ <span class="s1">'k--'</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
+ <span class="s1">'b--'</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="s1">'b--'</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s2">"$x$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.05</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"b"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s2">"$y$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"b"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s2">"$r$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.45</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\alpha$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.75</span><span class="p">,</span> <span class="mf">0.6</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">)</span>
+
+<span class="n">alpha</span> <span class="o">=</span> <span class="n">pi</span><span class="o">-</span><span class="n">theta1</span>
+<span class="n">draw_angle</span><span class="p">(</span><span class="n">alpha</span><span class="p">,</span> <span class="n">offset</span><span class="o">=</span><span class="n">theta0</span><span class="o">+</span><span class="n">theta1</span><span class="p">,</span> <span class="n">origin</span><span class="o">=</span><span class="p">[</span><span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span> <span class="n">r</span><span class="o">=</span><span class="mf">0.1</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../_images/Planar_Two_Link_IK_7_0.png" src="../../_images/Planar_Two_Link_IK_7_0.png" />
+<p>The distance from the end-effector to the robot base (shoulder joint) is
+<span class="math notranslate nohighlight">\(r\)</span> and can be written in terms of the end-effector position using
+the Pythagorean Theorem.</p>
+<p><span class="math notranslate nohighlight">\(r^2\)</span> = <span class="math notranslate nohighlight">\(x^2 + y^2\)</span></p>
+<p>Then, by the law of cosines, <span class="math notranslate nohighlight">\(r\)</span>2 can also be written as:</p>
+<p><span class="math notranslate nohighlight">\(r^2\)</span> = <span class="math notranslate nohighlight">\(l_0^2 + l_1^2 - 2l_0l_1\cos(\alpha)\)</span></p>
+<p>Because <span class="math notranslate nohighlight">\(\alpha\)</span> can be written as <span class="math notranslate nohighlight">\(\pi - \theta_1\)</span>, we can
+relate the desired end-effector position to one of our joint angles,
+<span class="math notranslate nohighlight">\(\theta_1\)</span>.</p>
+<p><span class="math notranslate nohighlight">\(x^2 + y^2\)</span> = <span class="math notranslate nohighlight">\(l_0^2 + l_1^2 - 2l_0l_1\cos(\alpha)\)</span></p>
+<p><span class="math notranslate nohighlight">\(x^2 + y^2\)</span> = <span class="math notranslate nohighlight">\(l_0^2 + l_1^2 - 2l_0l_1\cos(\pi-\theta_1)\)</span></p>
+<p><span class="math notranslate nohighlight">\(2l_0l_1\cos(\pi-\theta_1) = l_0^2 + l_1^2 - x^2 - y^2\)</span></p>
+<div class="line-block">
+<div class="line"><span class="math notranslate nohighlight">\(\cos(\pi-\theta_1) = \frac{l_0^2 + l_1^2 - x^2 - y^2}{2l_0l_1}\)</span></div>
+<div class="line"><span class="math notranslate nohighlight">\(~\)</span></div>
+<div class="line"><span class="math notranslate nohighlight">\(~\)</span></div>
+<div class="line"><span class="math notranslate nohighlight">\(\cos(\pi-\theta_1) = -cos(\theta_1)\)</span> is a trigonometric
+identity, so we can also write</div>
+</div>
+<p><span class="math notranslate nohighlight">\(\cos(\theta_1) = \frac{x^2 + y^2 - l_0^2 - l_1^2}{2l_0l_1}\)</span></p>
+<p>which leads us to an equation for <span class="math notranslate nohighlight">\(\theta_1\)</span> in terms of the link
+lengths and the desired end-effector position!</p>
+<p><span class="math notranslate nohighlight">\(\theta_1 = \cos^{-1}(\frac{x^2 + y^2 - l_0^2 - l_1^2}{2l_0l_1})\)</span></p>
+<p>This is actually one of two possible solutions for <span class="math notranslate nohighlight">\(\theta_1\)</span>, but
+we’ll ignore the other possibility for now. This solution will lead us
+to the “arm-down” configuration of the arm, which is what’s shown in the
+diagram. Now we’ll derive an equation for <span class="math notranslate nohighlight">\(\theta_0\)</span> that depends
+on this value of <span class="math notranslate nohighlight">\(\theta_1\)</span>.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">atan2</span>
+
+<span class="n">arm</span><span class="o">.</span><span class="n">plot</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
+ <span class="s1">'k--'</span><span class="p">)</span>
+
+<span class="n">p</span> <span class="o">=</span> <span class="mi">1</span> <span class="o">+</span> <span class="n">cos</span><span class="p">(</span><span class="n">theta1</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">p</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">theta0</span><span class="p">)],</span>
+ <span class="p">[</span><span class="n">arm</span><span class="o">.</span><span class="n">elbow</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">p</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">theta0</span><span class="p">)],</span>
+ <span class="s1">'b--'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">p</span><span class="o">*</span><span class="n">cos</span><span class="p">(</span><span class="n">theta0</span><span class="p">)],</span>
+ <span class="p">[</span><span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">p</span><span class="o">*</span><span class="n">sin</span><span class="p">(</span><span class="n">theta0</span><span class="p">)],</span>
+ <span class="s1">'b--'</span><span class="p">,</span> <span class="n">linewidth</span><span class="o">=</span><span class="mi">5</span><span class="p">)</span>
+
+<span class="n">beta</span> <span class="o">=</span> <span class="n">atan2</span><span class="p">(</span><span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span><span class="o">-</span><span class="n">theta0</span>
+<span class="n">draw_angle</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">offset</span><span class="o">=</span><span class="n">theta0</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="mf">0.45</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\beta$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.35</span><span class="p">,</span> <span class="mf">0.35</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s2">"$r$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.45</span><span class="p">,</span> <span class="mf">0.9</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$l_1sin(\theta_1)$"</span><span class="p">,</span><span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">1.25</span><span class="p">,</span> <span class="mf">1.1</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"b"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$l_1cos(\theta_1)$"</span><span class="p">,</span><span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">1.1</span><span class="p">,</span> <span class="mf">0.4</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"b"</span><span class="p">)</span>
+
+<span class="n">label_diagram</span><span class="p">()</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../_images/Planar_Two_Link_IK_9_0.png" src="../../_images/Planar_Two_Link_IK_9_0.png" />
+<p>Consider the angle between the displacement vector <span class="math notranslate nohighlight">\(r\)</span> and the
+first link <span class="math notranslate nohighlight">\(l_0\)</span>; let’s call it <span class="math notranslate nohighlight">\(\beta\)</span>. If we extend the
+first link to include the component of the second link in the same
+direction as the first, we form a right triangle with components
+<span class="math notranslate nohighlight">\(l_0+l_1cos(\theta_1)\)</span> and <span class="math notranslate nohighlight">\(l_1sin(\theta_1)\)</span>, allowing us
+to express <span class="math notranslate nohighlight">\(\beta\)</span> as</p>
+<p><span class="math notranslate nohighlight">\(\beta = \tan^{-1}(\frac{l_1\sin(\theta_1)}{l_0+l_1\cos(\theta_1)})\)</span></p>
+<p>We now have an expression for this angle <span class="math notranslate nohighlight">\(\beta\)</span> in terms of one
+of our arm’s joint angles. Now, can we relate <span class="math notranslate nohighlight">\(\beta\)</span> to
+<span class="math notranslate nohighlight">\(\theta_0\)</span>? Yes!</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">arm</span><span class="o">.</span><span class="n">plot</span><span class="p">()</span>
+<span class="n">label_diagram</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
+ <span class="s1">'k--'</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">1</span><span class="p">]],</span>
+ <span class="s1">'b--'</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="mi">0</span><span class="p">,</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="s1">'b--'</span><span class="p">)</span>
+
+<span class="n">gamma</span> <span class="o">=</span> <span class="n">atan2</span><span class="p">(</span><span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">arm</span><span class="o">.</span><span class="n">wrist</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+<span class="n">draw_angle</span><span class="p">(</span><span class="n">beta</span><span class="p">,</span> <span class="n">offset</span><span class="o">=</span><span class="n">theta0</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="mf">0.2</span><span class="p">)</span>
+<span class="n">draw_angle</span><span class="p">(</span><span class="n">gamma</span><span class="p">,</span> <span class="n">r</span><span class="o">=</span><span class="mf">0.6</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s2">"$x$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.7</span><span class="p">,</span> <span class="mf">0.05</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"b"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="s2">"$y$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"b"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\beta$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.2</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">annotate</span><span class="p">(</span><span class="sa">r</span><span class="s2">"$\gamma$"</span><span class="p">,</span> <span class="n">xy</span><span class="o">=</span><span class="p">(</span><span class="mf">0.6</span><span class="p">,</span> <span class="mf">0.2</span><span class="p">),</span> <span class="n">size</span><span class="o">=</span><span class="mi">15</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../_images/Planar_Two_Link_IK_12_0.png" src="../../_images/Planar_Two_Link_IK_12_0.png" />
+<p>Our first joint angle <span class="math notranslate nohighlight">\(\theta_0\)</span> added to <span class="math notranslate nohighlight">\(\beta\)</span> gives us
+the angle between the positive <span class="math notranslate nohighlight">\(x\)</span>-axis and the displacement
+vector <span class="math notranslate nohighlight">\(r\)</span>; let’s call this angle <span class="math notranslate nohighlight">\(\gamma\)</span>.</p>
+<p><span class="math notranslate nohighlight">\(\gamma = \theta_0+\beta\)</span></p>
+<p><span class="math notranslate nohighlight">\(\theta_0\)</span>, our remaining joint angle, can then be expressed as</p>
+<p><span class="math notranslate nohighlight">\(\theta_0 = \gamma-\beta\)</span></p>
+<p>We already know <span class="math notranslate nohighlight">\(\beta\)</span>. <span class="math notranslate nohighlight">\(\gamma\)</span> is simply the inverse
+tangent of <span class="math notranslate nohighlight">\(\frac{y}{x}\)</span>, so we have an equation of
+<span class="math notranslate nohighlight">\(\theta_0\)</span>!</p>
+<p><span class="math notranslate nohighlight">\(\theta_0 = \tan^{-1}(\frac{y}{x})-\tan^{-1}(\frac{l_1\sin(\theta_1)}{l_0+l_1\cos(\theta_1)})\)</span></p>
+<p>We now have the inverse kinematics for a planar two-link robotic arm. If
+you’re planning on implementing this in a programming language, it’s
+best to use the atan2 function, which is included in most math libraries
+and correctly accounts for the signs of <span class="math notranslate nohighlight">\(y\)</span> and <span class="math notranslate nohighlight">\(x\)</span>. Notice
+that <span class="math notranslate nohighlight">\(\theta_1\)</span> must be calculated before <span class="math notranslate nohighlight">\(\theta_0\)</span>.</p>
+<div class="line-block">
+<div class="line"><span class="math notranslate nohighlight">\(\theta_1 = \cos^{-1}(\frac{x^2 + y^2 - l_0^2 - l_1^2}{2l_0l_1})\)</span></div>
+<div class="line"><span class="math notranslate nohighlight">\(\theta_0 = atan2(y, x)-atan2(l_1\sin(\theta_1), l_0+l_1\cos(\theta_1))\)</span></div>
+</div>
+</section>
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+<li class="toctree-l2"><a class="reference internal" href="inverted_pendulum_control/inverted_pendulum_control.html#lqr-control">LQR control</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="move_to_a_pose_control/move_to_a_pose_control.html">Move to a Pose Control</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="move_to_a_pose_control/move_to_a_pose_control.html#position-control-of-non-holonomic-systems">Position Control of non-Holonomic Systems</a></li>
+<li class="toctree-l2"><a class="reference internal" href="move_to_a_pose_control/move_to_a_pose_control.html#pathfindercontroller-class">PathFinderController class</a></li>
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+<li class="toctree-l1 current"><a class="reference internal" href="../control.html">Control</a><ul class="current">
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Inverted Pendulum Control</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#modeling">Modeling</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#lqr-control">LQR control</a></li>
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+
+ <section id="inverted-pendulum-control">
+<h1>Inverted Pendulum Control<a class="headerlink" href="#inverted-pendulum-control" title="Permalink to this headline"></a></h1>
+<p>An inverted pendulum on a cart consists of a mass <span class="math notranslate nohighlight">\(m\)</span> at the top of a pole of length <span class="math notranslate nohighlight">\(l\)</span> pivoted on a
+horizontally moving base as shown in the adjacent.</p>
+<p>The objective of the control system is to balance the inverted pendulum by applying a force to the cart that the pendulum is attached to.</p>
+<section id="modeling">
+<h2>Modeling<a class="headerlink" href="#modeling" title="Permalink to this headline"></a></h2>
+<img alt="../../../_images/inverted-pendulum.png" class="align-center" src="../../../_images/inverted-pendulum.png" />
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(M\)</span>: mass of the cart</p></li>
+<li><p><span class="math notranslate nohighlight">\(m\)</span>: mass of the load on the top of the rod</p></li>
+<li><p><span class="math notranslate nohighlight">\(l\)</span>: length of the rod</p></li>
+<li><p><span class="math notranslate nohighlight">\(u\)</span>: force applied to the cart</p></li>
+<li><p><span class="math notranslate nohighlight">\(x\)</span>: cart position coordinate</p></li>
+<li><p><span class="math notranslate nohighlight">\(\theta\)</span>: pendulum angle from vertical</p></li>
+</ul>
+<p>Using Lagrange’s equations:</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}& (M + m)\ddot{x} - ml\ddot{\theta}cos{\theta} + ml\dot{\theta^2}\sin{\theta} = u \\
+& l\ddot{\theta} - g\sin{\theta} = \ddot{x}\cos{\theta}\end{split}\]</div>
+<p>See this <a class="reference external" href="https://en.wikipedia.org/wiki/Inverted_pendulum#From_Lagrange's_equations">link</a> for more details.</p>
+<p>So</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}& \ddot{x} = \frac{m(gcos{\theta} - \dot{\theta}^2l)sin{\theta} + u}{M + m - mcos^2{\theta}} \\
+& \ddot{\theta} = \frac{g(M + m)sin{\theta} - \dot{\theta}^2lmsin{\theta}cos{\theta} + ucos{\theta}}{l(M + m - mcos^2{\theta})}\end{split}\]</div>
+<p>Linearized model when <span class="math notranslate nohighlight">\(\theta\)</span> small, <span class="math notranslate nohighlight">\(cos{\theta} \approx 1\)</span>, <span class="math notranslate nohighlight">\(sin{\theta} \approx \theta\)</span>, <span class="math notranslate nohighlight">\(\dot{\theta}^2 \approx 0\)</span>.</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}& \ddot{x} = \frac{gm}{M}\theta + \frac{1}{M}u\\
+& \ddot{\theta} = \frac{g(M + m)}{Ml}\theta + \frac{1}{Ml}u\end{split}\]</div>
+<p>State space:</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}& \dot{x} = Ax + Bu \\
+& y = Cx + Du\end{split}\]</div>
+<p>where</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}& x = [x, \dot{x}, \theta,\dot{\theta}]\\
+& A = \begin{bmatrix} 0 & 1 & 0 & 0\\0 & 0 & \frac{gm}{M} & 0\\0 & 0 & 0 & 1\\0 & 0 & \frac{g(M + m)}{Ml} & 0 \end{bmatrix}\\
+& B = \begin{bmatrix} 0 \\ \frac{1}{M} \\ 0 \\ \frac{1}{Ml} \end{bmatrix}\end{split}\]</div>
+<p>If control only theta</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}& C = \begin{bmatrix} 0 & 0 & 1 & 0 \end{bmatrix}\\
+& D = [0]\end{split}\]</div>
+<p>If control x and theta</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}& C = \begin{bmatrix} 1 & 0 & 0 & 0\\0 & 0 & 1 & 0 \end{bmatrix}\\
+& D = \begin{bmatrix} 0 \\ 0 \end{bmatrix}\end{split}\]</div>
+</section>
+<section id="lqr-control">
+<h2>LQR control<a class="headerlink" href="#lqr-control" title="Permalink to this headline"></a></h2>
+<p>The LQR controller minimize this cost function defined as:</p>
+<div class="math notranslate nohighlight">
+\[J = x^T Q x + u^T R u\]</div>
+<p>the feedback control law that minimizes the value of the cost is:</p>
+<div class="math notranslate nohighlight">
+\[u = -K x\]</div>
+<p>where:</p>
+<div class="math notranslate nohighlight">
+\[K = (B^T P B + R)^{-1} B^T P A\]</div>
+<p>and <span class="math notranslate nohighlight">\(P\)</span> is the unique positive definite solution to the discrete time
+<a class="reference external" href="https://en.wikipedia.org/wiki/Inverted_pendulum#From_Lagrange's_equations">algebraic Riccati equation</a> (DARE):</p>
+<div class="math notranslate nohighlight">
+\[P = A^T P A - A^T P B ( R + B^T P B )^{-1} B^T P A + Q\]</div>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Control/InvertedPendulumCart/animation_lqr.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Control/InvertedPendulumCart/animation_lqr.gif" />
+</section>
+<section id="mpc-control">
+<h2>MPC control<a class="headerlink" href="#mpc-control" title="Permalink to this headline"></a></h2>
+<p>The MPC controller minimize this cost function defined as:</p>
+<div class="math notranslate nohighlight">
+\[J = x^T Q x + u^T R u\]</div>
+<p>subject to:</p>
+<ul class="simple">
+<li><p>Linearized Inverted Pendulum model</p></li>
+<li><p>Initial state</p></li>
+</ul>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Control/InvertedPendulumCart/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Control/InvertedPendulumCart/animation.gif" />
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+<li class="toctree-l1"><a class="reference internal" href="../../mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../slam/slam.html">SLAM</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_planning/path_planning.html">Path Planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../inverted_pendulum_control/inverted_pendulum_control.html">Inverted Pendulum Control</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Move to a Pose Control</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#position-control-of-non-holonomic-systems">Position Control of non-Holonomic Systems</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#pathfindercontroller-class">PathFinderController class</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#constructor">Constructor</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#member-function-s">Member function(s)</a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="#how-does-the-algorithm-work">How does the Algorithm Work</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#move-to-a-pose-robot-class">Move to a Pose Robot (Class)</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#robot-class">Robot Class</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#id1">Constructor</a></li>
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+
+ <section id="move-to-a-pose-control">
+<h1>Move to a Pose Control<a class="headerlink" href="#move-to-a-pose-control" title="Permalink to this headline"></a></h1>
+<p>In this section, we present the logic of PathFinderController that drives a car from a start pose (x, y, theta) to a goal pose. A simulation of moving to a pose control is presented below.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/move_to_pose/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/move_to_pose/animation.gif" />
+<section id="position-control-of-non-holonomic-systems">
+<h2>Position Control of non-Holonomic Systems<a class="headerlink" href="#position-control-of-non-holonomic-systems" title="Permalink to this headline"></a></h2>
+<p>This section explains the logic of a position controller for systems with constraint (non-Holonomic system).</p>
+<p>The position control of a 1-DOF (Degree of Freedom) system is quite straightforward. We only need to compute a position error and multiply it with a proportional gain to create a command. The actuator of the system takes this command and drive the system to the target position. This controller can be easily extended to higher dimensions (e.g., using Kp_x and Kp_y gains for a 2D position control). In these systems, the number of control commands is equal to the number of degrees of freedom (Holonomic system).</p>
+<p>To describe the configuration of a car on a 2D plane, we need three DOFs (i.e., x, y, and theta). But to drive a car we only need two control commands (theta_engine and theta_steering_wheel). This difference is because of a constraint between the x and y DOFs. The relationship between the delta_x and delta_y is governed by the theta_steering_wheel.</p>
+<p>Note that a car is normally a non-Holonomic system but if the road is slippery, the car turns into a Holonomic system and thus it needs three independent commands to be controlled.</p>
+</section>
+<section id="pathfindercontroller-class">
+<h2>PathFinderController class<a class="headerlink" href="#pathfindercontroller-class" title="Permalink to this headline"></a></h2>
+<section id="constructor">
+<h3>Constructor<a class="headerlink" href="#constructor" title="Permalink to this headline"></a></h3>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">PathFinderController</span><span class="p">(</span><span class="n">Kp_rho</span><span class="p">,</span> <span class="n">Kp_alpha</span><span class="p">,</span> <span class="n">Kp_beta</span><span class="p">)</span>
+</pre></div>
+</div>
+<p>Constructs an instantiate of the PathFinderController for navigating a 3-DOF wheeled robot on a 2D plane.</p>
+<p>Parameters:</p>
+<ul>
+<li><div class="line-block">
+<div class="line"><strong>Kp_rho</strong> : The linear velocity gain to translate the robot along a line towards the goal</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>Kp_alpha</strong> : The angular velocity gain to rotate the robot towards the goal</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>Kp_beta</strong> : The offset angular velocity gain accounting for smooth merging to the goal angle (i.e., it helps the robot heading to be parallel to the target angle.)</div>
+</div>
+</li>
+</ul>
+</section>
+<section id="member-function-s">
+<h3>Member function(s)<a class="headerlink" href="#member-function-s" title="Permalink to this headline"></a></h3>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">calc_control_command</span><span class="p">(</span><span class="n">x_diff</span><span class="p">,</span> <span class="n">y_diff</span><span class="p">,</span> <span class="n">theta</span><span class="p">,</span> <span class="n">theta_goal</span><span class="p">)</span>
+</pre></div>
+</div>
+<p>Returns the control command for the linear and angular velocities as well as the distance to goal</p>
+<p>Parameters:</p>
+<ul>
+<li><div class="line-block">
+<div class="line"><strong>x_diff</strong> : The position of target with respect to current robot position in x direction</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>y_diff</strong> : The position of target with respect to current robot position in y direction</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>theta</strong> : The current heading angle of robot with respect to x axis</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>theta_goal</strong> : The target angle of robot with respect to x axis</div>
+</div>
+</li>
+</ul>
+<p>Returns:</p>
+<ul>
+<li><div class="line-block">
+<div class="line"><strong>rho</strong> : The distance between the robot and the goal position</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>v</strong> : Command linear velocity</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>w</strong> : Command angular velocity</div>
+</div>
+</li>
+</ul>
+</section>
+</section>
+<section id="how-does-the-algorithm-work">
+<h2>How does the Algorithm Work<a class="headerlink" href="#how-does-the-algorithm-work" title="Permalink to this headline"></a></h2>
+<p>The distance between the robot and the goal position, <span class="math notranslate nohighlight">\(\rho\)</span>, is computed as</p>
+<div class="math notranslate nohighlight">
+\[\rho = \sqrt{(x_{robot} - x_{target})^2 + (y_{robot} - y_{target})^2}.\]</div>
+<p>The distance <span class="math notranslate nohighlight">\(\rho\)</span> is used to determine the robot speed. The idea is to slow down the robot as it gets closer to the target.</p>
+<div class="math notranslate nohighlight" id="equation-move-to-a-pose-eq1">
+<span class="eqno">(1)<a class="headerlink" href="#equation-move-to-a-pose-eq1" title="Permalink to this equation"></a></span>\[v = K_P{_\rho} \times \rho\qquad\]</div>
+<p>Note that for your applications, you need to tune the speed gain, <span class="math notranslate nohighlight">\(K_P{_\rho}\)</span> to a proper value.</p>
+<p>To turn the robot and align its heading, <span class="math notranslate nohighlight">\(\theta\)</span>, toward the target position (not orientation), <span class="math notranslate nohighlight">\(\rho \vec{u}\)</span>, we need to compute the angle difference <span class="math notranslate nohighlight">\(\alpha\)</span>.</p>
+<div class="math notranslate nohighlight">
+\[\alpha = (\arctan2(y_{diff}, x_{diff}) - \theta + \pi) mod (2\pi) - \pi\]</div>
+<p>The term <span class="math notranslate nohighlight">\(mod(2\pi)\)</span> is used to map the angle to <span class="math notranslate nohighlight">\([-\pi, \pi)\)</span> range.</p>
+<p>Lastly to correct the orientation of the robot, we need to compute the orientation error, <span class="math notranslate nohighlight">\(\beta\)</span>, of the robot.</p>
+<div class="math notranslate nohighlight">
+\[\beta = (\theta_{goal} - \theta - \alpha + \pi) mod (2\pi) - \pi\]</div>
+<p>Note that to cancel out the effect of <span class="math notranslate nohighlight">\(\alpha\)</span> when the robot is at the vicinity of the target, the term</p>
+<p><span class="math notranslate nohighlight">\(-\alpha\)</span> is included.</p>
+<p>The final angular speed command is given by</p>
+<div class="math notranslate nohighlight" id="equation-move-to-a-pose-eq2">
+<span class="eqno">(2)<a class="headerlink" href="#equation-move-to-a-pose-eq2" title="Permalink to this equation"></a></span>\[\omega = K_P{_\alpha} \alpha - K_P{_\beta} \beta\qquad\]</div>
+<p>The linear and angular speeds (Equations <a class="reference internal" href="#equation-move-to-a-pose-eq1">(1)</a> and <a class="reference internal" href="#equation-move-to-a-pose-eq2">(2)</a>) are the output of the algorithm.</p>
+</section>
+<section id="move-to-a-pose-robot-class">
+<h2>Move to a Pose Robot (Class)<a class="headerlink" href="#move-to-a-pose-robot-class" title="Permalink to this headline"></a></h2>
+<p>This program (move_to_pose_robot.py) provides a Robot class to define different robots with different specifications.
+Using this class, you can simulate different robots simultaneously and compare the effect of your parameter settings.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Control/move_to_pos_robot_class/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Control/move_to_pos_robot_class/animation.gif" />
+<p>Note: The robot class is based on PathFinderController class in ‘the move_to_pose.py’.</p>
+<section id="robot-class">
+<h3>Robot Class<a class="headerlink" href="#robot-class" title="Permalink to this headline"></a></h3>
+</section>
+<section id="id1">
+<h3>Constructor<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h3>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">Robot</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">color</span><span class="p">,</span> <span class="n">max_linear_speed</span><span class="p">,</span> <span class="n">max_angular_speed</span><span class="p">,</span> <span class="n">path_finder_controller</span><span class="p">)</span>
+</pre></div>
+</div>
+<p>Constructs an instantiate of the 3-DOF wheeled Robot navigating on a 2D plane</p>
+<p>Parameters:</p>
+<ul>
+<li><div class="line-block">
+<div class="line"><strong>name</strong> : (string) The name of the robot</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>color</strong> : (string) The color of the robot</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>max_linear_speed</strong> : (float) The maximum linear speed that the robot can go</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>max_angular_speed</strong> : (float) The maximum angular speed that the robot can rotate about its vertical axis</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>path_finder_controller</strong> : (PathFinderController) A configurable controller to finds the path and calculates command linear and angular velocities.</div>
+</div>
+</li>
+</ul>
+</section>
+<section id="id2">
+<h3>Member function(s)<a class="headerlink" href="#id2" title="Permalink to this headline"></a></h3>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">set_start_target_poses</span><span class="p">(</span><span class="n">pose_start</span><span class="p">,</span> <span class="n">pose_target</span><span class="p">)</span>
+</pre></div>
+</div>
+<p>Sets the start and target positions of the robot.</p>
+<p>Parameters:</p>
+<ul>
+<li><div class="line-block">
+<div class="line"><strong>pose_start</strong> : (Pose) Start postion of the robot (see the Pose class)</div>
+</div>
+</li>
+<li><div class="line-block">
+<div class="line"><strong>pose_target</strong> : (Pose) Target postion of the robot (see the Pose class)</div>
+</div>
+</li>
+</ul>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">move</span><span class="p">(</span><span class="n">dt</span><span class="p">)</span>
+</pre></div>
+</div>
+<p>Move the robot for one time step increment</p>
+<p>Parameters:</p>
+<ul>
+<li><div class="line-block">
+<div class="line"><strong>dt</strong> : <float> time increment</div>
+</div>
+</li>
+</ul>
+</section>
+</section>
+<section id="references">
+<h2>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p>PathFinderController class</p></li>
+<li><p><a class="reference external" href="https://link.springer.com/book/10.1007/978-3-642-20144-8">P. I. Corke, “Robotics, Vision and Control” | SpringerLink
+p102</a></p></li>
+</ul>
+</section>
+</section>
+
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diff --git a/modules/introduction.html b/modules/introduction.html
new file mode 100644
index 00000000000..802694e74ac
--- /dev/null
+++ b/modules/introduction.html
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+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
+<head>
+ <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
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+ <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+ <title>Introduction — PythonRobotics documentation</title>
+ <link rel="stylesheet" href="../_static/pygments.css" type="text/css" />
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+ crossorigin="anonymous"></script>
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+ <p class="caption" role="heading"><span class="caption-text">Contents</span></p>
+<ul class="current">
+<li class="toctree-l1"><a class="reference internal" href="../getting_started.html">Getting Started</a></li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">Introduction</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="#definition-of-robotics">Definition Of Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#history-of-robotics">History Of Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#application-of-robotics">Application Of Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#software-for-robotics">Software for Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#id1">Software for Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#python-for-robotics">Python for Robotics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="#learning-robotics-algorithms">Learning Robotics Algorithms</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="localization/localization.html">Localization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="slam/slam.html">SLAM</a></li>
+<li class="toctree-l1"><a class="reference internal" href="path_planning/path_planning.html">Path Planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="bipedal/bipedal.html">Bipedal</a></li>
+<li class="toctree-l1"><a class="reference internal" href="control/control.html">Control</a></li>
+<li class="toctree-l1"><a class="reference internal" href="utils/utils.html">Utilities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="appendix/appendix.html">Appendix</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../how_to_contribute.html">How To Contribute</a></li>
+</ul>
+
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+ <div class="rst-content">
+ <div role="navigation" aria-label="Page navigation">
+ <ul class="wy-breadcrumbs">
+ <li><a href="../index.html" class="icon icon-home"></a> »</li>
+ <li>Introduction</li>
+ <li class="wy-breadcrumbs-aside">
+ <a href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/docs/modules/introduction_main.rst" class="fa fa-github"> Edit on GitHub</a>
+ </li>
+ </ul>
+ <hr/>
+</div>
+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+ <div itemprop="articleBody">
+
+ <section id="introduction">
+<h1>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h1>
+<p>TBD</p>
+<section id="definition-of-robotics">
+<h2>Definition Of Robotics<a class="headerlink" href="#definition-of-robotics" title="Permalink to this headline"></a></h2>
+<p>TBD</p>
+</section>
+<section id="history-of-robotics">
+<h2>History Of Robotics<a class="headerlink" href="#history-of-robotics" title="Permalink to this headline"></a></h2>
+<p>TBD</p>
+</section>
+<section id="application-of-robotics">
+<h2>Application Of Robotics<a class="headerlink" href="#application-of-robotics" title="Permalink to this headline"></a></h2>
+<p>TBD</p>
+</section>
+<section id="software-for-robotics">
+<h2>Software for Robotics<a class="headerlink" href="#software-for-robotics" title="Permalink to this headline"></a></h2>
+<p>TBD</p>
+</section>
+<section id="id1">
+<h2>Software for Robotics<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h2>
+<p>TBD</p>
+</section>
+<section id="python-for-robotics">
+<h2>Python for Robotics<a class="headerlink" href="#python-for-robotics" title="Permalink to this headline"></a></h2>
+<p>TBD</p>
+</section>
+<section id="learning-robotics-algorithms">
+<h2>Learning Robotics Algorithms<a class="headerlink" href="#learning-robotics-algorithms" title="Permalink to this headline"></a></h2>
+<p>TBD</p>
+</section>
+</section>
+
+
+ </div>
+ </div>
+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+ <a href="../getting_started.html" class="btn btn-neutral float-left" title="Getting Started" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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diff --git a/modules/localization/ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization.html b/modules/localization/ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization.html
new file mode 100644
index 00000000000..4dd3ad27196
--- /dev/null
+++ b/modules/localization/ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization.html
@@ -0,0 +1,153 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
+<head>
+ <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
+
+ <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+ <title>Ensamble Kalman Filter Localization — PythonRobotics documentation</title>
+ <link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
+ <link rel="stylesheet" href="../../../_static/css/theme.css" type="text/css" />
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+ <script src="../../../_static/js/theme.js"></script>
+ <link rel="index" title="Index" href="../../../genindex.html" />
+ <link rel="search" title="Search" href="../../../search.html" />
+ <link rel="next" title="Unscented Kalman Filter localization" href="../unscented_kalman_filter_localization/unscented_kalman_filter_localization.html" />
+ <link rel="prev" title="Extended Kalman Filter Localization" href="../extended_kalman_filter_localization_files/extended_kalman_filter_localization.html" />
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+<li class="toctree-l1"><a class="reference internal" href="../../introduction.html">Introduction</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../localization.html">Localization</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../extended_kalman_filter_localization_files/extended_kalman_filter_localization.html">Extended Kalman Filter Localization</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Ensamble Kalman Filter Localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../unscented_kalman_filter_localization/unscented_kalman_filter_localization.html">Unscented Kalman Filter localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../histogram_filter_localization/histogram_filter_localization.html">Histogram filter localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../particle_filter_localization/particle_filter_localization.html">Particle filter localization</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../../mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../slam/slam.html">SLAM</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_planning/path_planning.html">Path Planning</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="../../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="../../control/control.html">Control</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../utils/utils.html">Utilities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../appendix/appendix.html">Appendix</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../how_to_contribute.html">How To Contribute</a></li>
+</ul>
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+ <li><a href="../../../index.html" class="icon icon-home"></a> »</li>
+ <li><a href="../localization.html">Localization</a> »</li>
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+ <li class="wy-breadcrumbs-aside">
+ <a href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/docs/modules/localization/ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization_main.rst" class="fa fa-github"> Edit on GitHub</a>
+ </li>
+ </ul>
+ <hr/>
+</div>
+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+ <div itemprop="articleBody">
+
+ <section id="ensamble-kalman-filter-localization">
+<h1>Ensamble Kalman Filter Localization<a class="headerlink" href="#ensamble-kalman-filter-localization" title="Permalink to this headline"></a></h1>
+<figure class="align-default">
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/ensamble_kalman_filter/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/ensamble_kalman_filter/animation.gif" />
+</figure>
+<p>This is a sensor fusion localization with Ensamble Kalman Filter(EnKF).</p>
+</section>
+
+
+ </div>
+ </div>
+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+ <a href="../extended_kalman_filter_localization_files/extended_kalman_filter_localization.html" class="btn btn-neutral float-left" title="Extended Kalman Filter Localization" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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diff --git a/modules/localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization.html b/modules/localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization.html
new file mode 100644
index 00000000000..3713fd728b9
--- /dev/null
+++ b/modules/localization/extended_kalman_filter_localization_files/extended_kalman_filter_localization.html
@@ -0,0 +1,253 @@
+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
+<head>
+ <meta charset="utf-8" /><meta name="generator" content="Docutils 0.17.1: http://docutils.sourceforge.net/" />
+
+ <meta name="viewport" content="width=device-width, initial-scale=1.0" />
+ <title>Extended Kalman Filter Localization — PythonRobotics documentation</title>
+ <link rel="stylesheet" href="../../../_static/pygments.css" type="text/css" />
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+ <link rel="stylesheet" href="../../../_static/plot_directive.css" type="text/css" />
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+ <link rel="stylesheet" href="../../../_static/custom.css" type="text/css" />
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+ </form>
+</div>
+<script async src="https://pagead2.googlesyndication.com/pagead/js/adsbygoogle.js?client=ca-pub-9612347954373886"
+ crossorigin="anonymous"></script>
+<!-- PythonRoboticsDoc -->
+<ins class="adsbygoogle"
+ style="display:block"
+ data-ad-client="ca-pub-9612347954373886"
+ data-ad-slot="1579532132"
+ data-ad-format="auto"
+ data-full-width-responsive="true"></ins>
+<script>
+ (adsbygoogle = window.adsbygoogle || []).push({});
+</script>
+
+ </div><div class="wy-menu wy-menu-vertical" data-spy="affix" role="navigation" aria-label="Navigation menu">
+ <p class="caption" role="heading"><span class="caption-text">Contents</span></p>
+<ul class="current">
+<li class="toctree-l1"><a class="reference internal" href="../../../getting_started.html">Getting Started</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../introduction.html">Introduction</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../localization.html">Localization</a><ul class="current">
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Extended Kalman Filter Localization</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#filter-design">Filter design</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#motion-model">Motion Model</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#observation-model">Observation Model</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#extended-kalman-filter">Extended Kalman Filter</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#ref">Ref:</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization.html">Ensamble Kalman Filter Localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../unscented_kalman_filter_localization/unscented_kalman_filter_localization.html">Unscented Kalman Filter localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../histogram_filter_localization/histogram_filter_localization.html">Histogram filter localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../particle_filter_localization/particle_filter_localization.html">Particle filter localization</a></li>
+</ul>
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+ <section id="extended-kalman-filter-localization">
+<h1>Extended Kalman Filter Localization<a class="headerlink" href="#extended-kalman-filter-localization" title="Permalink to this headline"></a></h1>
+<a class="reference internal image-reference" href="../../../_images/extended_kalman_filter_localization_1_0.png"><img alt="../../../_images/extended_kalman_filter_localization_1_0.png" src="../../../_images/extended_kalman_filter_localization_1_0.png" style="width: 600px;" /></a>
+<figure class="align-default">
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/extended_kalman_filter/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/extended_kalman_filter/animation.gif" />
+</figure>
+<p>This is a sensor fusion localization with Extended Kalman Filter(EKF).</p>
+<p>The blue line is true trajectory, the black line is dead reckoning
+trajectory,</p>
+<p>the green point is positioning observation (ex. GPS), and the red line
+is estimated trajectory with EKF.</p>
+<p>The red ellipse is estimated covariance ellipse with EKF.</p>
+<p>Code: <a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/Localization/extended_kalman_filter/extended_kalman_filter.py">PythonRobotics/extended_kalman_filter.py at master ·
+AtsushiSakai/PythonRobotics</a></p>
+<section id="filter-design">
+<h2>Filter design<a class="headerlink" href="#filter-design" title="Permalink to this headline"></a></h2>
+<p>In this simulation, the robot has a state vector includes 4 states at
+time <span class="math notranslate nohighlight">\(t\)</span>.</p>
+<div class="math notranslate nohighlight">
+\[\textbf{x}_t=[x_t, y_t, \phi_t, v_t]\]</div>
+<p>x, y are a 2D x-y position, <span class="math notranslate nohighlight">\(\phi\)</span> is orientation, and v is
+velocity.</p>
+<p>In the code, “xEst” means the state vector.
+<a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/blob/916b4382de090de29f54538b356cef1c811aacce/Localization/extended_kalman_filter/extended_kalman_filter.py#L168">code</a></p>
+<p>And, <span class="math notranslate nohighlight">\(P_t\)</span> is covariace matrix of the state,</p>
+<p><span class="math notranslate nohighlight">\(Q\)</span> is covariance matrix of process noise,</p>
+<p><span class="math notranslate nohighlight">\(R\)</span> is covariance matrix of observation noise at time <span class="math notranslate nohighlight">\(t\)</span></p>
+<p>The robot has a speed sensor and a gyro sensor.</p>
+<p>So, the input vecor can be used as each time step</p>
+<div class="math notranslate nohighlight">
+\[\textbf{u}_t=[v_t, \omega_t]\]</div>
+<p>Also, the robot has a GNSS sensor, it means that the robot can observe
+x-y position at each time.</p>
+<div class="math notranslate nohighlight">
+\[\textbf{z}_t=[x_t,y_t]\]</div>
+<p>The input and observation vector includes sensor noise.</p>
+<p>In the code, “observation” function generates the input and observation
+vector with noise
+<a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/blob/916b4382de090de29f54538b356cef1c811aacce/Localization/extended_kalman_filter/extended_kalman_filter.py#L34-L50">code</a></p>
+</section>
+<section id="motion-model">
+<h2>Motion Model<a class="headerlink" href="#motion-model" title="Permalink to this headline"></a></h2>
+<p>The robot model is</p>
+<div class="math notranslate nohighlight">
+\[\dot{x} = v \cos(\phi)\]</div>
+<div class="math notranslate nohighlight">
+\[\dot{y} = v \sin(\phi)\]</div>
+<div class="math notranslate nohighlight">
+\[\dot{\phi} = \omega\]</div>
+<p>So, the motion model is</p>
+<div class="math notranslate nohighlight">
+\[\textbf{x}_{t+1} = f(\textbf{x}_t, \textbf{u}_t) = F\textbf{x}_t+B\textbf{u}_t\]</div>
+<p>where</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} F= \begin{bmatrix} 1 & 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \\ \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} B= \begin{bmatrix} cos(\phi) \Delta t & 0\\ sin(\phi) \Delta t & 0\\ 0 & \Delta t\\ 1 & 0\\ \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\Delta t\)</span> is a time interval.</p>
+<p>This is implemented at
+<a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/blob/916b4382de090de29f54538b356cef1c811aacce/Localization/extended_kalman_filter/extended_kalman_filter.py#L53-L67">code</a></p>
+<p>The motion function is that</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} \begin{bmatrix} x' \\ y' \\ w' \\ v' \end{bmatrix} = f(\textbf{x}, \textbf{u}) = \begin{bmatrix} x + v\cos(\phi)\Delta t \\ y + v\sin(\phi)\Delta t \\ \phi + \omega \Delta t \\ v \end{bmatrix} \end{equation*}\)</span></p>
+<p>Its Jacobian matrix is</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} J_f = \begin{bmatrix} \frac{\partial x'}{\partial x}& \frac{\partial x'}{\partial y} & \frac{\partial x'}{\partial \phi} & \frac{\partial x'}{\partial v}\\ \frac{\partial y'}{\partial x}& \frac{\partial y'}{\partial y} & \frac{\partial y'}{\partial \phi} & \frac{\partial y'}{\partial v}\\ \frac{\partial \phi'}{\partial x}& \frac{\partial \phi'}{\partial y} & \frac{\partial \phi'}{\partial \phi} & \frac{\partial \phi'}{\partial v}\\ \frac{\partial v'}{\partial x}& \frac{\partial v'}{\partial y} & \frac{\partial v'}{\partial \phi} & \frac{\partial v'}{\partial v} \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} = \begin{bmatrix} 1& 0 & -v \sin(\phi) \Delta t & \cos(\phi) \Delta t\\ 0 & 1 & v \cos(\phi) \Delta t & \sin(\phi) \Delta t\\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 1 \end{bmatrix} \end{equation*}\)</span></p>
+</section>
+<section id="observation-model">
+<h2>Observation Model<a class="headerlink" href="#observation-model" title="Permalink to this headline"></a></h2>
+<p>The robot can get x-y position infomation from GPS.</p>
+<p>So GPS Observation model is</p>
+<div class="math notranslate nohighlight">
+\[\textbf{z}_{t} = g(\textbf{x}_t) = H \textbf{x}_t\]</div>
+<p>where</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} H = \begin{bmatrix} 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ \end{bmatrix} \end{equation*}\)</span></p>
+<p>The observation function states that</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} \begin{bmatrix} x' \\ y' \end{bmatrix} = g(\textbf{x}) = \begin{bmatrix} x \\ y \end{bmatrix} \end{equation*}\)</span></p>
+<p>Its Jacobian matrix is</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} J_g = \begin{bmatrix} \frac{\partial x'}{\partial x} & \frac{\partial x'}{\partial y} & \frac{\partial x'}{\partial \phi} & \frac{\partial x'}{\partial v}\\ \frac{\partial y'}{\partial x}& \frac{\partial y'}{\partial y} & \frac{\partial y'}{\partial \phi} & \frac{\partial y'}{ \partial v}\\ \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} = \begin{bmatrix} 1& 0 & 0 & 0\\ 0 & 1 & 0 & 0\\ \end{bmatrix} \end{equation*}\)</span></p>
+</section>
+<section id="extended-kalman-filter">
+<h2>Extended Kalman Filter<a class="headerlink" href="#extended-kalman-filter" title="Permalink to this headline"></a></h2>
+<p>Localization process using Extended Kalman Filter:EKF is</p>
+<p>=== Predict ===</p>
+<p><span class="math notranslate nohighlight">\(x_{Pred} = Fx_t+Bu_t\)</span></p>
+<p><span class="math notranslate nohighlight">\(P_{Pred} = J_f P_t J_f^T + Q\)</span></p>
+<p>=== Update ===</p>
+<p><span class="math notranslate nohighlight">\(z_{Pred} = Hx_{Pred}\)</span></p>
+<p><span class="math notranslate nohighlight">\(y = z - z_{Pred}\)</span></p>
+<p><span class="math notranslate nohighlight">\(S = J_g P_{Pred}.J_g^T + R\)</span></p>
+<p><span class="math notranslate nohighlight">\(K = P_{Pred}.J_g^T S^{-1}\)</span></p>
+<p><span class="math notranslate nohighlight">\(x_{t+1} = x_{Pred} + Ky\)</span></p>
+<p><span class="math notranslate nohighlight">\(P_{t+1} = ( I - K J_g) P_{Pred}\)</span></p>
+</section>
+<section id="ref">
+<h2>Ref:<a class="headerlink" href="#ref" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="http://www.probabilistic-robotics.org/">PROBABILISTIC-ROBOTICS.ORG</a></p></li>
+</ul>
+</section>
+</section>
+
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+<li class="toctree-l1"><a class="reference internal" href="../../../getting_started.html">Getting Started</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../introduction.html">Introduction</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../localization.html">Localization</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../extended_kalman_filter_localization_files/extended_kalman_filter_localization.html">Extended Kalman Filter Localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization.html">Ensamble Kalman Filter Localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../unscented_kalman_filter_localization/unscented_kalman_filter_localization.html">Unscented Kalman Filter localization</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Histogram filter localization</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#filtering-algorithm">Filtering algorithm</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#step1-filter-initialization">Step1: Filter initialization</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#step2-predict-probability-by-motion">Step2: Predict probability by motion</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#step3-update-probability-by-observation">Step3: Update probability by observation</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#step4-estimate-position-from-probability">Step4: Estimate position from probability</a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../particle_filter_localization/particle_filter_localization.html">Particle filter localization</a></li>
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+
+ <section id="histogram-filter-localization">
+<h1>Histogram filter localization<a class="headerlink" href="#histogram-filter-localization" title="Permalink to this headline"></a></h1>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/histogram_filter/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/histogram_filter/animation.gif" />
+<p>This is a 2D localization example with Histogram filter.</p>
+<p>The red cross is true position, black points are RFID positions.</p>
+<p>The blue grid shows a position probability of histogram filter.</p>
+<p>In this simulation, we assume the robot’s yaw orientation and RFID’s positions are known,
+but x,y positions are unknown.</p>
+<p>The filter uses speed input and range observations from RFID for localization.</p>
+<p>Initial position information is not needed.</p>
+<section id="filtering-algorithm">
+<h2>Filtering algorithm<a class="headerlink" href="#filtering-algorithm" title="Permalink to this headline"></a></h2>
+<p>Histogram filter is a discrete Bayes filter in continuous space.</p>
+<p>It uses regular girds to manage probability of the robot existence.</p>
+<p>If a grid has higher probability, it means that the robot is likely to be there.</p>
+<p>In the simulation, we want to estimate x-y position, so we use 2D grid data.</p>
+<p>There are 4 steps for the histogram filter to estimate the probability distribution.</p>
+<section id="step1-filter-initialization">
+<h3>Step1: Filter initialization<a class="headerlink" href="#step1-filter-initialization" title="Permalink to this headline"></a></h3>
+<p>Histogram filter does not need initial position information.</p>
+<p>In that case, we can initialize each grid probability as a same value.</p>
+<p>If we can use initial position information, we can set initial probabilities based on it.</p>
+<p><a class="reference internal" href="../../mapping/gaussian_grid_map/gaussian_grid_map.html#gaussian-grid-map"><span class="std std-ref">Gaussian grid map</span></a> might be useful when the initial position information is provided as gaussian distribution.</p>
+</section>
+<section id="step2-predict-probability-by-motion">
+<h3>Step2: Predict probability by motion<a class="headerlink" href="#step2-predict-probability-by-motion" title="Permalink to this headline"></a></h3>
+<p>In histogram filter, when a robot move to a next grid,
+all probability information of each grid are shifted towards the movement direction.</p>
+<p>This process represents the change in the probability distribution as the robot moves.</p>
+<p>After the robot has moved, the probability distribution needs reflect
+the estimation error due to the movement.</p>
+<p>For example, the position probability is peaky with observations:</p>
+<a class="reference internal image-reference" href="../../../_images/1.png"><img alt="../../../_images/1.png" src="../../../_images/1.png" style="width: 400px;" /></a>
+<p>But, the probability is getting uncertain without observations:</p>
+<a class="reference internal image-reference" href="../../../_images/2.png"><img alt="../../../_images/2.png" src="../../../_images/2.png" style="width: 400px;" /></a>
+<p>The <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.ndimage.gaussian_filter.html">gaussian filter</a>
+is used in the simulation for adding noize.</p>
+</section>
+<section id="step3-update-probability-by-observation">
+<h3>Step3: Update probability by observation<a class="headerlink" href="#step3-update-probability-by-observation" title="Permalink to this headline"></a></h3>
+<p>In this step, all probabilities are updated by observations,
+this is the update step of bayesian filter.</p>
+<p>The probability update formula is different by the used sensor model.</p>
+<p>This simulation uses range observation model.</p>
+<p>The probability of each grid is updated by this formula:</p>
+<div class="math notranslate nohighlight">
+\[p_t=p_{t-1}*h(z)\]</div>
+<div class="math notranslate nohighlight">
+\[h(z)=\frac{\exp \left(-(d - z)^{2} / 2\right)}{\sqrt{2 \pi}}\]</div>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(p_t\)</span> is the probability at the time <cite>t</cite>.</p></li>
+<li><p><span class="math notranslate nohighlight">\(h(z)\)</span> is the observation probability with the observation <cite>z</cite>.</p></li>
+<li><p><span class="math notranslate nohighlight">\(d\)</span> is the known distance from the RD-ID to the grid center.</p></li>
+</ul>
+<p>When the <cite>d</cite> is 3.0, the <cite>h(z)</cite> distribution is:</p>
+<a class="reference internal image-reference" href="../../../_images/4.png"><img alt="../../../_images/4.png" src="../../../_images/4.png" style="width: 400px;" /></a>
+<p>The observation probability distribution looks a circle when a RF-ID is observed:</p>
+<a class="reference internal image-reference" href="../../../_images/3.png"><img alt="../../../_images/3.png" src="../../../_images/3.png" style="width: 400px;" /></a>
+</section>
+<section id="step4-estimate-position-from-probability">
+<h3>Step4: Estimate position from probability<a class="headerlink" href="#step4-estimate-position-from-probability" title="Permalink to this headline"></a></h3>
+<p>In each time step, we can calculate the final robot position from the current probability distribution.
+There are two ways to calculate the final positions:</p>
+<ol class="arabic simple">
+<li><p>Using the maximum probability grid position.</p></li>
+<li><p>Using the average of probability weighted grind position.</p></li>
+</ol>
+</section>
+</section>
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="http://www.probabilistic-robotics.org">_PROBABILISTIC ROBOTICS:</a></p></li>
+<li><p><a class="reference external" href="http://driving.stanford.edu/papers/ICRA2010.pdf">Robust Vehicle Localization in Urban Environments Using Probabilistic Maps</a></p></li>
+</ul>
+</section>
+</section>
+
+
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+<li class="toctree-l2"><a class="reference internal" href="extended_kalman_filter_localization_files/extended_kalman_filter_localization.html">Extended Kalman Filter Localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization.html">Ensamble Kalman Filter Localization</a></li>
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+<span id="id1"></span><h1>Localization<a class="headerlink" href="#localization" title="Permalink to this headline"></a></h1>
+<div class="toctree-wrapper compound">
+<p class="caption" role="heading"><span class="caption-text">Contents</span></p>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="extended_kalman_filter_localization_files/extended_kalman_filter_localization.html">Extended Kalman Filter Localization</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="extended_kalman_filter_localization_files/extended_kalman_filter_localization.html#filter-design">Filter design</a></li>
+<li class="toctree-l2"><a class="reference internal" href="extended_kalman_filter_localization_files/extended_kalman_filter_localization.html#motion-model">Motion Model</a></li>
+<li class="toctree-l2"><a class="reference internal" href="extended_kalman_filter_localization_files/extended_kalman_filter_localization.html#observation-model">Observation Model</a></li>
+<li class="toctree-l2"><a class="reference internal" href="extended_kalman_filter_localization_files/extended_kalman_filter_localization.html#extended-kalman-filter">Extended Kalman Filter</a></li>
+<li class="toctree-l2"><a class="reference internal" href="extended_kalman_filter_localization_files/extended_kalman_filter_localization.html#ref">Ref:</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization.html">Ensamble Kalman Filter Localization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="unscented_kalman_filter_localization/unscented_kalman_filter_localization.html">Unscented Kalman Filter localization</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="unscented_kalman_filter_localization/unscented_kalman_filter_localization.html#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="histogram_filter_localization/histogram_filter_localization.html">Histogram filter localization</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="histogram_filter_localization/histogram_filter_localization.html#filtering-algorithm">Filtering algorithm</a></li>
+<li class="toctree-l2"><a class="reference internal" href="histogram_filter_localization/histogram_filter_localization.html#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="particle_filter_localization/particle_filter_localization.html">Particle filter localization</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="particle_filter_localization/particle_filter_localization.html#how-to-calculate-covariance-matrix-from-particles">How to calculate covariance matrix from particles</a></li>
+<li class="toctree-l2"><a class="reference internal" href="particle_filter_localization/particle_filter_localization.html#references">References:</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization.html">Ensamble Kalman Filter Localization</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../histogram_filter_localization/histogram_filter_localization.html">Histogram filter localization</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Particle filter localization</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#how-to-calculate-covariance-matrix-from-particles">How to calculate covariance matrix from particles</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#references">References:</a></li>
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+ <section id="particle-filter-localization">
+<h1>Particle filter localization<a class="headerlink" href="#particle-filter-localization" title="Permalink to this headline"></a></h1>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/particle_filter/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/particle_filter/animation.gif" />
+<p>This is a sensor fusion localization with Particle Filter(PF).</p>
+<p>The blue line is true trajectory, the black line is dead reckoning
+trajectory,</p>
+<p>and the red line is estimated trajectory with PF.</p>
+<p>It is assumed that the robot can measure a distance from landmarks
+(RFID).</p>
+<p>This measurements are used for PF localization.</p>
+<section id="how-to-calculate-covariance-matrix-from-particles">
+<h2>How to calculate covariance matrix from particles<a class="headerlink" href="#how-to-calculate-covariance-matrix-from-particles" title="Permalink to this headline"></a></h2>
+<p>The covariance matrix <span class="math notranslate nohighlight">\(\Xi\)</span> from particle information is calculated by the following equation:</p>
+<div class="math notranslate nohighlight">
+\[\Xi_{j,k}=\frac{1}{1-\sum^N_{i=1}(w^i)^2}\sum^N_{i=1}w^i(x^i_j-\mu_j)(x^i_k-\mu_k)\]</div>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(\Xi_{j,k}\)</span> is covariance matrix element at row <span class="math notranslate nohighlight">\(i\)</span> and column <span class="math notranslate nohighlight">\(k\)</span>.</p></li>
+<li><p><span class="math notranslate nohighlight">\(w^i\)</span> is the weight of the <span class="math notranslate nohighlight">\(i\)</span> th particle.</p></li>
+<li><p><span class="math notranslate nohighlight">\(x^i_j\)</span> is the <span class="math notranslate nohighlight">\(j\)</span> th state of the <span class="math notranslate nohighlight">\(i\)</span> th particle.</p></li>
+<li><p><span class="math notranslate nohighlight">\(\mu_j\)</span> is the <span class="math notranslate nohighlight">\(j\)</span> th mean state of particles.</p></li>
+</ul>
+</section>
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="http://www.probabilistic-robotics.org">_PROBABILISTIC ROBOTICS:</a></p></li>
+<li><p><a class="reference external" href="https://arxiv.org/pdf/1801.07000.pdf">Improving the particle filter in high dimensions using conjugate artificial process noise</a></p></li>
+</ul>
+</section>
+</section>
+
+
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+<li class="toctree-l2"><a class="reference internal" href="../extended_kalman_filter_localization_files/extended_kalman_filter_localization.html">Extended Kalman Filter Localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../ensamble_kalman_filter_localization_files/ensamble_kalman_filter_localization.html">Ensamble Kalman Filter Localization</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Unscented Kalman Filter localization</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../histogram_filter_localization/histogram_filter_localization.html">Histogram filter localization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../particle_filter_localization/particle_filter_localization.html">Particle filter localization</a></li>
+</ul>
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+<li class="toctree-l1"><a class="reference internal" href="../../mapping/mapping.html">Mapping</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="../../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
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+ </li>
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+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+ <div itemprop="articleBody">
+
+ <section id="unscented-kalman-filter-localization">
+<h1>Unscented Kalman Filter localization<a class="headerlink" href="#unscented-kalman-filter-localization" title="Permalink to this headline"></a></h1>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/unscented_kalman_filter/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Localization/unscented_kalman_filter/animation.gif" />
+<p>This is a sensor fusion localization with Unscented Kalman Filter(UKF).</p>
+<p>The lines and points are same meaning of the EKF simulation.</p>
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://www.researchgate.net/publication/267963417_Discriminatively_Trained_Unscented_Kalman_Filter_for_Mobile_Robot_Localization">Discriminatively Trained Unscented Kalman Filter for Mobile Robot Localization</a></p></li>
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+
+ <section id="object-shape-recognition-using-circle-fitting">
+<h1>Object shape recognition using circle fitting<a class="headerlink" href="#object-shape-recognition-using-circle-fitting" title="Permalink to this headline"></a></h1>
+<p>This is an object shape recognition using circle fitting.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/circle_fitting/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/circle_fitting/animation.gif" />
+<p>The blue circle is the true object shape.</p>
+<p>The red crosses are observations from a ranging sensor.</p>
+<p>The red circle is the estimated object shape using circle fitting.</p>
+</section>
+
+
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+<span id="id1"></span><h1>Gaussian grid map<a class="headerlink" href="#gaussian-grid-map" title="Permalink to this headline"></a></h1>
+<p>This is a 2D Gaussian grid mapping example.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/gaussian_grid_map/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/gaussian_grid_map/animation.gif" />
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+<h1>k-means object clustering<a class="headerlink" href="#k-means-object-clustering" title="Permalink to this headline"></a></h1>
+<p>This is a 2D object clustering with k-means algorithm.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/kmeans_clustering/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/kmeans_clustering/animation.gif" />
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+<li class="toctree-l2"><a class="reference internal" href="../ndt_map/ndt_map.html">Normal Distance Transform (NDT) map</a></li>
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+<li class="toctree-l2 current"><a class="current reference internal" href="#">Lidar to grid map</a></li>
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+
+ <section id="lidar-to-grid-map">
+<h1>Lidar to grid map<a class="headerlink" href="#lidar-to-grid-map" title="Permalink to this headline"></a></h1>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/lidar_to_grid_map/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/lidar_to_grid_map/animation.gif" />
+<p>This simple tutorial shows how to read LIDAR (range) measurements from a
+file and convert it to occupancy grid.</p>
+<p>Occupancy grid maps (<em>Hans Moravec, A.E. Elfes: High resolution maps
+from wide angle sonar, Proc. IEEE Int. Conf. Robotics Autom. (1985)</em>)
+are a popular, probabilistic approach to represent the environment. The
+grid is basically discrete representation of the environment, which
+shows if a grid cell is occupied or not. Here the map is represented as
+a <code class="docutils literal notranslate"><span class="pre">numpy</span> <span class="pre">array</span></code>, and numbers close to 1 means the cell is occupied
+(<em>marked with red on the next image</em>), numbers close to 0 means they are
+free (<em>marked with green</em>). The grid has the ability to represent
+unknown (unobserved) areas, which are close to 0.5.</p>
+<figure class="align-default">
+<img alt="../../../_images/grid_map_example.png" src="../../../_images/grid_map_example.png" />
+</figure>
+<p>In order to construct the grid map from the measurement we need to
+discretise the values. But, first let’s need to <code class="docutils literal notranslate"><span class="pre">import</span></code> some
+necessary packages.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">math</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">math</span> <span class="kn">import</span> <span class="n">cos</span><span class="p">,</span> <span class="n">sin</span><span class="p">,</span> <span class="n">radians</span><span class="p">,</span> <span class="n">pi</span>
+</pre></div>
+</div>
+<p>The measurement file contains the distances and the corresponding angles
+in a <code class="docutils literal notranslate"><span class="pre">csv</span></code> (comma separated values) format. Let’s write the
+<code class="docutils literal notranslate"><span class="pre">file_read</span></code> method:</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">file_read</span><span class="p">(</span><span class="n">f</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Reading LIDAR laser beams (angles and corresponding distance data)</span>
+<span class="sd"> """</span>
+ <span class="n">measures</span> <span class="o">=</span> <span class="p">[</span><span class="n">line</span><span class="o">.</span><span class="n">split</span><span class="p">(</span><span class="s2">","</span><span class="p">)</span> <span class="k">for</span> <span class="n">line</span> <span class="ow">in</span> <span class="nb">open</span><span class="p">(</span><span class="n">f</span><span class="p">)]</span>
+ <span class="n">angles</span> <span class="o">=</span> <span class="p">[]</span>
+ <span class="n">distances</span> <span class="o">=</span> <span class="p">[]</span>
+ <span class="k">for</span> <span class="n">measure</span> <span class="ow">in</span> <span class="n">measures</span><span class="p">:</span>
+ <span class="n">angles</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">measure</span><span class="p">[</span><span class="mi">0</span><span class="p">]))</span>
+ <span class="n">distances</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">float</span><span class="p">(</span><span class="n">measure</span><span class="p">[</span><span class="mi">1</span><span class="p">]))</span>
+ <span class="n">angles</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">angles</span><span class="p">)</span>
+ <span class="n">distances</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">distances</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">angles</span><span class="p">,</span> <span class="n">distances</span>
+</pre></div>
+</div>
+<p>From the distances and the angles it is easy to determine the <code class="docutils literal notranslate"><span class="pre">x</span></code> and
+<code class="docutils literal notranslate"><span class="pre">y</span></code> coordinates with <code class="docutils literal notranslate"><span class="pre">sin</span></code> and <code class="docutils literal notranslate"><span class="pre">cos</span></code>. In order to display it
+<code class="docutils literal notranslate"><span class="pre">matplotlib.pyplot</span></code> (<code class="docutils literal notranslate"><span class="pre">plt</span></code>) is used.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">ang</span><span class="p">,</span> <span class="n">dist</span> <span class="o">=</span> <span class="n">file_read</span><span class="p">(</span><span class="s2">"lidar01.csv"</span><span class="p">)</span>
+<span class="n">ox</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">ang</span><span class="p">)</span> <span class="o">*</span> <span class="n">dist</span>
+<span class="n">oy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">ang</span><span class="p">)</span> <span class="o">*</span> <span class="n">dist</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">6</span><span class="p">,</span><span class="mi">10</span><span class="p">))</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">oy</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">oy</span><span class="p">))],</span> <span class="p">[</span><span class="n">ox</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">size</span><span class="p">(</span><span class="n">oy</span><span class="p">))],</span> <span class="s2">"ro-"</span><span class="p">)</span> <span class="c1"># lines from 0,0 to the</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+<span class="n">bottom</span><span class="p">,</span> <span class="n">top</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">()</span> <span class="c1"># return the current ylim</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">ylim</span><span class="p">((</span><span class="n">top</span><span class="p">,</span> <span class="n">bottom</span><span class="p">))</span> <span class="c1"># rescale y axis, to match the grid orientation</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../../_images/lidar_to_grid_map_tutorial_5_0.png" src="../../../_images/lidar_to_grid_map_tutorial_5_0.png" />
+<p>The <code class="docutils literal notranslate"><span class="pre">lidar_to_grid_map.py</span></code> contains handy functions which can used to
+convert a 2D range measurement to a grid map. For example the
+<code class="docutils literal notranslate"><span class="pre">bresenham</span></code> gives the a straight line between two points in a grid
+map. Let’s see how this works.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">lidar_to_grid_map</span> <span class="k">as</span> <span class="nn">lg</span>
+<span class="n">map1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="mi">50</span><span class="p">,</span> <span class="mi">50</span><span class="p">))</span> <span class="o">*</span> <span class="mf">0.5</span>
+<span class="n">line</span> <span class="o">=</span> <span class="n">lg</span><span class="o">.</span><span class="n">bresenham</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">),</span> <span class="p">(</span><span class="mi">40</span><span class="p">,</span> <span class="mi">30</span><span class="p">))</span>
+<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">line</span><span class="p">:</span>
+ <span class="n">map1</span><span class="p">[</span><span class="n">l</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="n">l</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="o">=</span> <span class="mi">1</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">map1</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../../_images/lidar_to_grid_map_tutorial_7_0.png" src="../../../_images/lidar_to_grid_map_tutorial_7_0.png" />
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">line</span> <span class="o">=</span> <span class="n">lg</span><span class="o">.</span><span class="n">bresenham</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">30</span><span class="p">),</span> <span class="p">(</span><span class="mi">40</span><span class="p">,</span> <span class="mi">30</span><span class="p">))</span>
+<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">line</span><span class="p">:</span>
+ <span class="n">map1</span><span class="p">[</span><span class="n">l</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="n">l</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="o">=</span> <span class="mi">1</span>
+<span class="n">line</span> <span class="o">=</span> <span class="n">lg</span><span class="o">.</span><span class="n">bresenham</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">30</span><span class="p">),</span> <span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
+<span class="k">for</span> <span class="n">l</span> <span class="ow">in</span> <span class="n">line</span><span class="p">:</span>
+ <span class="n">map1</span><span class="p">[</span><span class="n">l</span><span class="p">[</span><span class="mi">0</span><span class="p">]][</span><span class="n">l</span><span class="p">[</span><span class="mi">1</span><span class="p">]]</span> <span class="o">=</span> <span class="mi">1</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">map1</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../../_images/lidar_to_grid_map_tutorial_8_0.png" src="../../../_images/lidar_to_grid_map_tutorial_8_0.png" />
+<p>To fill empty areas, a queue-based algorithm can be used that can be
+used on an initialized occupancy map. The center point is given: the
+algorithm checks for neighbour elements in each iteration, and stops
+expansion on obstacles and free boundaries.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">collections</span> <span class="kn">import</span> <span class="n">deque</span>
+<span class="k">def</span> <span class="nf">flood_fill</span><span class="p">(</span><span class="n">cpoint</span><span class="p">,</span> <span class="n">pmap</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> cpoint: starting point (x,y) of fill</span>
+<span class="sd"> pmap: occupancy map generated from Bresenham ray-tracing</span>
+<span class="sd"> """</span>
+ <span class="c1"># Fill empty areas with queue method</span>
+ <span class="n">sx</span><span class="p">,</span> <span class="n">sy</span> <span class="o">=</span> <span class="n">pmap</span><span class="o">.</span><span class="n">shape</span>
+ <span class="n">fringe</span> <span class="o">=</span> <span class="n">deque</span><span class="p">()</span>
+ <span class="n">fringe</span><span class="o">.</span><span class="n">appendleft</span><span class="p">(</span><span class="n">cpoint</span><span class="p">)</span>
+ <span class="k">while</span> <span class="n">fringe</span><span class="p">:</span>
+ <span class="n">n</span> <span class="o">=</span> <span class="n">fringe</span><span class="o">.</span><span class="n">pop</span><span class="p">()</span>
+ <span class="n">nx</span><span class="p">,</span> <span class="n">ny</span> <span class="o">=</span> <span class="n">n</span>
+ <span class="c1"># West</span>
+ <span class="k">if</span> <span class="n">nx</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
+ <span class="k">if</span> <span class="n">pmap</span><span class="p">[</span><span class="n">nx</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">ny</span><span class="p">]</span> <span class="o">==</span> <span class="mf">0.5</span><span class="p">:</span>
+ <span class="n">pmap</span><span class="p">[</span><span class="n">nx</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">ny</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="n">fringe</span><span class="o">.</span><span class="n">appendleft</span><span class="p">((</span><span class="n">nx</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">ny</span><span class="p">))</span>
+ <span class="c1"># East</span>
+ <span class="k">if</span> <span class="n">nx</span> <span class="o"><</span> <span class="n">sx</span> <span class="o">-</span> <span class="mi">1</span><span class="p">:</span>
+ <span class="k">if</span> <span class="n">pmap</span><span class="p">[</span><span class="n">nx</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">ny</span><span class="p">]</span> <span class="o">==</span> <span class="mf">0.5</span><span class="p">:</span>
+ <span class="n">pmap</span><span class="p">[</span><span class="n">nx</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">ny</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="n">fringe</span><span class="o">.</span><span class="n">appendleft</span><span class="p">((</span><span class="n">nx</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">ny</span><span class="p">))</span>
+ <span class="c1"># North</span>
+ <span class="k">if</span> <span class="n">ny</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
+ <span class="k">if</span> <span class="n">pmap</span><span class="p">[</span><span class="n">nx</span><span class="p">,</span> <span class="n">ny</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="mf">0.5</span><span class="p">:</span>
+ <span class="n">pmap</span><span class="p">[</span><span class="n">nx</span><span class="p">,</span> <span class="n">ny</span> <span class="o">-</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="n">fringe</span><span class="o">.</span><span class="n">appendleft</span><span class="p">((</span><span class="n">nx</span><span class="p">,</span> <span class="n">ny</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))</span>
+ <span class="c1"># South</span>
+ <span class="k">if</span> <span class="n">ny</span> <span class="o"><</span> <span class="n">sy</span> <span class="o">-</span> <span class="mi">1</span><span class="p">:</span>
+ <span class="k">if</span> <span class="n">pmap</span><span class="p">[</span><span class="n">nx</span><span class="p">,</span> <span class="n">ny</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="mf">0.5</span><span class="p">:</span>
+ <span class="n">pmap</span><span class="p">[</span><span class="n">nx</span><span class="p">,</span> <span class="n">ny</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="n">fringe</span><span class="o">.</span><span class="n">appendleft</span><span class="p">((</span><span class="n">nx</span><span class="p">,</span> <span class="n">ny</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
+</pre></div>
+</div>
+<p>This algotihm will fill the area bounded by the yellow lines starting
+from a center point (e.g. (10, 20)) with zeros:</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">flood_fill</span><span class="p">((</span><span class="mi">10</span><span class="p">,</span> <span class="mi">20</span><span class="p">),</span> <span class="n">map1</span><span class="p">)</span>
+<span class="n">map_float</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">map1</span><span class="p">)</span><span class="o">/</span><span class="mf">10.0</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">map1</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../../_images/lidar_to_grid_map_tutorial_12_0.png" src="../../../_images/lidar_to_grid_map_tutorial_12_0.png" />
+<p>Let’s use this flood fill on real data:</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">xyreso</span> <span class="o">=</span> <span class="mf">0.02</span> <span class="c1"># x-y grid resolution</span>
+<span class="n">yawreso</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">radians</span><span class="p">(</span><span class="mf">3.1</span><span class="p">)</span> <span class="c1"># yaw angle resolution [rad]</span>
+<span class="n">ang</span><span class="p">,</span> <span class="n">dist</span> <span class="o">=</span> <span class="n">file_read</span><span class="p">(</span><span class="s2">"lidar01.csv"</span><span class="p">)</span>
+<span class="n">ox</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">ang</span><span class="p">)</span> <span class="o">*</span> <span class="n">dist</span>
+<span class="n">oy</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">ang</span><span class="p">)</span> <span class="o">*</span> <span class="n">dist</span>
+<span class="n">pmap</span><span class="p">,</span> <span class="n">minx</span><span class="p">,</span> <span class="n">maxx</span><span class="p">,</span> <span class="n">miny</span><span class="p">,</span> <span class="n">maxy</span><span class="p">,</span> <span class="n">xyreso</span> <span class="o">=</span> <span class="n">lg</span><span class="o">.</span><span class="n">generate_ray_casting_grid_map</span><span class="p">(</span><span class="n">ox</span><span class="p">,</span> <span class="n">oy</span><span class="p">,</span> <span class="n">xyreso</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span>
+<span class="n">xyres</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">pmap</span><span class="p">)</span><span class="o">.</span><span class="n">shape</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">(</span><span class="n">figsize</span><span class="o">=</span><span class="p">(</span><span class="mi">20</span><span class="p">,</span><span class="mi">8</span><span class="p">))</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">122</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">pmap</span><span class="p">,</span> <span class="n">cmap</span> <span class="o">=</span> <span class="s2">"PiYG_r"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">clim</span><span class="p">(</span><span class="o">-</span><span class="mf">0.4</span><span class="p">,</span> <span class="mf">1.4</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span><span class="o">.</span><span class="n">set_xticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mf">.5</span><span class="p">,</span> <span class="n">xyres</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="mi">1</span><span class="p">),</span> <span class="n">minor</span> <span class="o">=</span> <span class="kc">True</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">gca</span><span class="p">()</span><span class="o">.</span><span class="n">set_yticks</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="o">-</span><span class="mf">.5</span><span class="p">,</span> <span class="n">xyres</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="mi">1</span><span class="p">),</span> <span class="n">minor</span> <span class="o">=</span> <span class="kc">True</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">,</span> <span class="n">which</span><span class="o">=</span><span class="s2">"minor"</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s2">"w"</span><span class="p">,</span> <span class="n">linewidth</span> <span class="o">=</span> <span class="mf">.6</span><span class="p">,</span> <span class="n">alpha</span> <span class="o">=</span> <span class="mf">0.5</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">The</span> <span class="n">grid</span> <span class="nb">map</span> <span class="ow">is</span> <span class="mi">150</span> <span class="n">x</span> <span class="mi">100</span> <span class="o">.</span>
+</pre></div>
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+<li class="toctree-l1 current"><a class="current reference internal" href="#">Mapping</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="gaussian_grid_map/gaussian_grid_map.html">Gaussian grid map</a></li>
+<li class="toctree-l2"><a class="reference internal" href="ndt_map/ndt_map.html">Normal Distance Transform (NDT) map</a></li>
+<li class="toctree-l2"><a class="reference internal" href="ray_casting_grid_map/ray_casting_grid_map.html">Ray casting grid map</a></li>
+<li class="toctree-l2"><a class="reference internal" href="lidar_to_grid_map_tutorial/lidar_to_grid_map_tutorial.html">Lidar to grid map</a></li>
+<li class="toctree-l2"><a class="reference internal" href="point_cloud_sampling/point_cloud_sampling.html">Point cloud Sampling</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="normal_vector_estimation/normal_vector_estimation.html">Normal vector estimation</a></li>
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+<span id="id1"></span><h1>Mapping<a class="headerlink" href="#mapping" title="Permalink to this headline"></a></h1>
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+<ul>
+<li class="toctree-l1"><a class="reference internal" href="gaussian_grid_map/gaussian_grid_map.html">Gaussian grid map</a></li>
+<li class="toctree-l1"><a class="reference internal" href="ndt_map/ndt_map.html">Normal Distance Transform (NDT) map</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="ndt_map/ndt_map.html#normal-distribution">Normal Distribution</a></li>
+<li class="toctree-l2"><a class="reference internal" href="ndt_map/ndt_map.html#normal-distance-transform-mapping-steps">Normal Distance Transform mapping steps</a></li>
+<li class="toctree-l2"><a class="reference internal" href="ndt_map/ndt_map.html#api">API</a></li>
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+</li>
+<li class="toctree-l1"><a class="reference internal" href="ray_casting_grid_map/ray_casting_grid_map.html">Ray casting grid map</a></li>
+<li class="toctree-l1"><a class="reference internal" href="lidar_to_grid_map_tutorial/lidar_to_grid_map_tutorial.html">Lidar to grid map</a></li>
+<li class="toctree-l1"><a class="reference internal" href="point_cloud_sampling/point_cloud_sampling.html">Point cloud Sampling</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="point_cloud_sampling/point_cloud_sampling.html#voxel-point-sampling">Voxel Point Sampling</a></li>
+<li class="toctree-l2"><a class="reference internal" href="point_cloud_sampling/point_cloud_sampling.html#farthest-point-sampling">Farthest Point Sampling</a></li>
+<li class="toctree-l2"><a class="reference internal" href="point_cloud_sampling/point_cloud_sampling.html#poisson-disk-sampling">Poisson Disk Sampling</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="circle_fitting/circle_fitting.html">Object shape recognition using circle fitting</a></li>
+<li class="toctree-l1"><a class="reference internal" href="rectangle_fitting/rectangle_fitting.html">Object shape recognition using rectangle fitting</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="rectangle_fitting/rectangle_fitting.html#step1-adaptive-range-segmentation">Step1: Adaptive range segmentation</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rectangle_fitting/rectangle_fitting.html#step2-rectangle-search">Step2: Rectangle search</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rectangle_fitting/rectangle_fitting.html#api">API</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rectangle_fitting/rectangle_fitting.html#references">References</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="normal_vector_estimation/normal_vector_estimation.html">Normal vector estimation</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="normal_vector_estimation/normal_vector_estimation.html#normal-vector-calculation-of-a-3d-triangle">Normal vector calculation of a 3D triangle</a></li>
+<li class="toctree-l2"><a class="reference internal" href="normal_vector_estimation/normal_vector_estimation.html#normal-vector-estimation-with-randam-sampling-consensus-ransac">Normal vector estimation with RANdam SAmpling Consensus(RANSAC)</a></li>
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+<li class="toctree-l2 current"><a class="current reference internal" href="#">Normal Distance Transform (NDT) map</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#normal-distribution">Normal Distribution</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#normal-distance-transform-mapping-steps">Normal Distance Transform mapping steps</a></li>
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+ <li>Normal Distance Transform (NDT) map</li>
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+
+ <section id="normal-distance-transform-ndt-map">
+<span id="ndt-map"></span><h1>Normal Distance Transform (NDT) map<a class="headerlink" href="#normal-distance-transform-ndt-map" title="Permalink to this headline"></a></h1>
+<p>This is a NDT mapping example.</p>
+<p>Normal Distribution Transform (NDT) is a map representation that uses normal distribution for observation point modeling.</p>
+<section id="normal-distribution">
+<h2>Normal Distribution<a class="headerlink" href="#normal-distribution" title="Permalink to this headline"></a></h2>
+<p>Normal distribution consists of two parameters: mean <span class="math notranslate nohighlight">\(\mu\)</span> and covariance <span class="math notranslate nohighlight">\(\Sigma\)</span>.</p>
+<p><span class="math notranslate nohighlight">\(\mathbf{X} \sim \mathcal{N}(\boldsymbol{\mu}, \boldsymbol{\Sigma})\)</span></p>
+<p>In the 2D case, <span class="math notranslate nohighlight">\(\boldsymbol{\mu}\)</span> is a 2D vector and <span class="math notranslate nohighlight">\(\boldsymbol{\Sigma}\)</span> is a 2x2 matrix.</p>
+<p>In the matrix form, the probability density function of thr normal distribution is:</p>
+<p><span class="math notranslate nohighlight">\(X=\frac{1}{\sqrt{(2 \pi)^2|\Sigma|}} \exp \left\{-\frac{1}{2}^t(x-\mu) \sum^{-1}(x-\mu)\right\}\)</span></p>
+</section>
+<section id="normal-distance-transform-mapping-steps">
+<h2>Normal Distance Transform mapping steps<a class="headerlink" href="#normal-distance-transform-mapping-steps" title="Permalink to this headline"></a></h2>
+<p>NDT mapping consists of two steps:</p>
+<p>When we have a new observation like this:</p>
+<figure class="align-default">
+<img alt="../../../_images/raw_observations.png" src="../../../_images/raw_observations.png" />
+</figure>
+<p>First, we need to cluster the observation points.
+This is done by using a grid based clustering algorithm.</p>
+<p>The result is:</p>
+<figure class="align-default">
+<img alt="../../../_images/grid_clustering.png" src="../../../_images/grid_clustering.png" />
+</figure>
+<p>Then, we need to fit a normal distribution to each grid cluster.</p>
+<p>Black ellipse shows each NDT grid like this:</p>
+<figure class="align-default">
+<img alt="../../../_images/ndt_map1.png" src="../../../_images/ndt_map1.png" />
+</figure>
+<figure class="align-default">
+<img alt="../../../_images/ndt_map2.png" src="../../../_images/ndt_map2.png" />
+</figure>
+</section>
+<section id="api">
+<h2>API<a class="headerlink" href="#api" title="Permalink to this headline"></a></h2>
+<dl class="py class">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">Mapping.ndt_map.ndt_map.</span></span><span class="sig-name descname"><span class="pre">NDTMap</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ox</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">oy</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">resolution</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/Mapping/ndt_map/ndt_map.html#NDTMap"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap" title="Permalink to this definition"></a></dt>
+<dd><p>Normal Distribution Transform (NDT) map class</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>ox</strong> – obstacle x position list</p></li>
+<li><p><strong>oy</strong> – obstacle y position list</p></li>
+<li><p><strong>resolution</strong> – grid resolution [m]</p></li>
+</ul>
+</dd>
+</dl>
+<dl class="py class">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.NDTGrid">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">NDTGrid</span></span><a class="reference internal" href="../../../_modules/Mapping/ndt_map/ndt_map.html#NDTMap.NDTGrid"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid" title="Permalink to this definition"></a></dt>
+<dd><p>NDT grid</p>
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.center_grid_x">
+<span class="sig-name descname"><span class="pre">center_grid_x</span></span><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.center_grid_x" title="Permalink to this definition"></a></dt>
+<dd><p>Center x position of the NDT grid</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.center_grid_y">
+<span class="sig-name descname"><span class="pre">center_grid_y</span></span><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.center_grid_y" title="Permalink to this definition"></a></dt>
+<dd><p>Center y position of the NDT grid</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.covariance">
+<span class="sig-name descname"><span class="pre">covariance</span></span><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.covariance" title="Permalink to this definition"></a></dt>
+<dd><p>Covariance matrix of the NDT grid</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.eig_values">
+<span class="sig-name descname"><span class="pre">eig_values</span></span><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.eig_values" title="Permalink to this definition"></a></dt>
+<dd><p>Eigen values of the NDT grid</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.eig_vec">
+<span class="sig-name descname"><span class="pre">eig_vec</span></span><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.eig_vec" title="Permalink to this definition"></a></dt>
+<dd><p>Eigen vectors of the NDT grid</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.mean_x">
+<span class="sig-name descname"><span class="pre">mean_x</span></span><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.mean_x" title="Permalink to this definition"></a></dt>
+<dd><p>Mean x position of points in the NDTGrid cell</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.mean_y">
+<span class="sig-name descname"><span class="pre">mean_y</span></span><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.mean_y" title="Permalink to this definition"></a></dt>
+<dd><p>Mean y position of points in the NDTGrid cell</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.n_points">
+<span class="sig-name descname"><span class="pre">n_points</span></span><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.NDTGrid.n_points" title="Permalink to this definition"></a></dt>
+<dd><p>Number of points in the NDTGrid grid</p>
+</dd></dl>
+
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.grid_index_map">
+<span class="sig-name descname"><span class="pre">grid_index_map</span></span><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.grid_index_map" title="Permalink to this definition"></a></dt>
+<dd><p>NDT grid index map</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.min_n_points">
+<span class="sig-name descname"><span class="pre">min_n_points</span></span><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.min_n_points" title="Permalink to this definition"></a></dt>
+<dd><p>Minimum number of points in the NDT grid</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.ndt_map.ndt_map.NDTMap.resolution">
+<span class="sig-name descname"><span class="pre">resolution</span></span><a class="headerlink" href="#Mapping.ndt_map.ndt_map.NDTMap.resolution" title="Permalink to this definition"></a></dt>
+<dd><p>Resolution of the NDT grid [m]</p>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+</section>
+
+
+ </div>
+ </div>
+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
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+<li class="toctree-l2 current"><a class="current reference internal" href="#">Normal vector estimation</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#normal-vector-calculation-of-a-3d-triangle">Normal vector calculation of a 3D triangle</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#api">API</a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="#normal-vector-estimation-with-randam-sampling-consensus-ransac">Normal vector estimation with RANdam SAmpling Consensus(RANSAC)</a><ul>
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+ <section id="normal-vector-estimation">
+<h1>Normal vector estimation<a class="headerlink" href="#normal-vector-estimation" title="Permalink to this headline"></a></h1>
+<section id="normal-vector-calculation-of-a-3d-triangle">
+<h2>Normal vector calculation of a 3D triangle<a class="headerlink" href="#normal-vector-calculation-of-a-3d-triangle" title="Permalink to this headline"></a></h2>
+<p>A 3D point is as a vector:</p>
+<div class="math notranslate nohighlight">
+\[p = [x, y, z]\]</div>
+<p>When there are 3 points in 3D space, <span class="math notranslate nohighlight">\(p_1, p_2, p_3\)</span>,</p>
+<p>we can calculate a normal vector n of a 3D triangle which is consisted of the points.</p>
+<div class="math notranslate nohighlight">
+\[n = \frac{v1 \times v2}{|v1 \times v2|}\]</div>
+<p>where</p>
+<div class="math notranslate nohighlight">
+\[v1 = p2 - p1\]</div>
+<div class="math notranslate nohighlight">
+\[v2 = p3 - p1\]</div>
+<p>This is an example of normal vector calculation:</p>
+<figure class="align-default">
+<img alt="../../../_images/normal_vector_calc.png" src="../../../_images/normal_vector_calc.png" />
+</figure>
+<section id="api">
+<h3>API<a class="headerlink" href="#api" title="Permalink to this headline"></a></h3>
+<dl class="py function">
+<dt class="sig sig-object py" id="Mapping.normal_vector_estimation.normal_vector_estimation.calc_normal_vector">
+<span class="sig-prename descclassname"><span class="pre">Mapping.normal_vector_estimation.normal_vector_estimation.</span></span><span class="sig-name descname"><span class="pre">calc_normal_vector</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">p1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p2</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p3</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/Mapping/normal_vector_estimation/normal_vector_estimation.html#calc_normal_vector"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Mapping.normal_vector_estimation.normal_vector_estimation.calc_normal_vector" title="Permalink to this definition"></a></dt>
+<dd><p>Calculate normal vector of triangle</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>p1</strong> (<em>np.array</em>) – 3D point</p></li>
+<li><p><strong>p2</strong> (<em>np.array</em>) – 3D point</p></li>
+<li><p><strong>p3</strong> (<em>np.array</em>) – 3D point</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>normal_vector</strong> – normal vector (3,)</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>np.array</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+</section>
+<section id="normal-vector-estimation-with-randam-sampling-consensus-ransac">
+<h2>Normal vector estimation with RANdam SAmpling Consensus(RANSAC)<a class="headerlink" href="#normal-vector-estimation-with-randam-sampling-consensus-ransac" title="Permalink to this headline"></a></h2>
+<p>Consider the problem of estimating the normal vector of a plane based on a
+set of N 3D points where a plane can be observed.</p>
+<p>There is a way that uses all point cloud data to estimate a plane and
+a normal vector using the <a class="reference external" href="https://stackoverflow.com/a/44315221/8387766">least-squares method</a></p>
+<p>However, this method is vulnerable to noise of the point cloud.</p>
+<p>In this document, we will use a method that uses
+<a class="reference external" href="https://en.wikipedia.org/wiki/Random_sample_consensus">RANdam SAmpling Consensus(RANSAC)</a>
+to estimate a plane and a normal vector.</p>
+<p>RANSAC is a robust estimation methods for data set with outliers.</p>
+<p>This RANSAC based normal vector estimation method is as follows:</p>
+<ol class="arabic simple">
+<li><p>Select 3 points randomly from the point cloud.</p></li>
+<li><p>Calculate a normal vector of a plane which is consists of the sampled 3 points.</p></li>
+<li><p>Calculate the distance between the calculated plane and the all point cloud.</p></li>
+<li><p>If the distance is less than a threshold, the point is considered to be an inlier.</p></li>
+<li><p>Repeat the above steps until the inlier ratio is greater than a threshold.</p></li>
+</ol>
+<p>This is an example of RANSAC based normal vector estimation:</p>
+<figure class="align-default">
+<img alt="../../../_images/ransac_normal_vector_estimation.png" src="../../../_images/ransac_normal_vector_estimation.png" />
+</figure>
+<section id="id1">
+<h3>API<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h3>
+<dl class="py function">
+<dt class="sig sig-object py" id="Mapping.normal_vector_estimation.normal_vector_estimation.ransac_normal_vector_estimation">
+<span class="sig-prename descclassname"><span class="pre">Mapping.normal_vector_estimation.normal_vector_estimation.</span></span><span class="sig-name descname"><span class="pre">ransac_normal_vector_estimation</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">points_3d</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inlier_radio_th</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.7</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">inlier_dist</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">p</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.99</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/Mapping/normal_vector_estimation/normal_vector_estimation.html#ransac_normal_vector_estimation"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Mapping.normal_vector_estimation.normal_vector_estimation.ransac_normal_vector_estimation" title="Permalink to this definition"></a></dt>
+<dd><p>RANSAC based normal vector estimation</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>points_3d</strong> (<em>np.array</em>) – 3D points (N, 3)</p></li>
+<li><p><strong>inlier_radio_th</strong> (<em>float</em>) – Inlier ratio threshold. If inlier ratio is larger than this value,
+the iteration is stopped. Default is 0.7.</p></li>
+<li><p><strong>inlier_dist</strong> (<em>float</em>) – Inlier distance threshold. If distance between points and estimated
+plane is smaller than this value, the point is inlier. Default is 0.1.</p></li>
+<li><p><strong>p</strong> (<em>float</em>) – Probability that at least one of the sets of random samples does not
+include an outlier. If this probability is near 1, the iteration
+number is large. Default is 0.99.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><ul class="simple">
+<li><p><strong>center_vector</strong> (<em>np.array</em>) – Center of estimated plane. (3,)</p></li>
+<li><p><strong>normal_vector</strong> (<em>np.array</em>) – Normal vector of estimated plane. (3,)</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+</section>
+</section>
+
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+<li class="toctree-l1"><a class="reference internal" href="../../localization/localization.html">Localization</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../mapping.html">Mapping</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../gaussian_grid_map/gaussian_grid_map.html">Gaussian grid map</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../ndt_map/ndt_map.html">Normal Distance Transform (NDT) map</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../ray_casting_grid_map/ray_casting_grid_map.html">Ray casting grid map</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lidar_to_grid_map_tutorial/lidar_to_grid_map_tutorial.html">Lidar to grid map</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Point cloud Sampling</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#voxel-point-sampling">Voxel Point Sampling</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#api">API</a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="#farthest-point-sampling">Farthest Point Sampling</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#id2">API</a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="#poisson-disk-sampling">Poisson Disk Sampling</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#id3">API</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../k_means_object_clustering/k_means_object_clustering.html">k-means object clustering</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../normal_vector_estimation/normal_vector_estimation.html">Normal vector estimation</a></li>
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+
+ <section id="point-cloud-sampling">
+<span id="id1"></span><h1>Point cloud Sampling<a class="headerlink" href="#point-cloud-sampling" title="Permalink to this headline"></a></h1>
+<p>This sections explains point cloud sampling algorithms in PythonRobotics.</p>
+<p>Point clouds are two-dimensional and three-dimensional based data
+acquired by external sensors like LIDAR, cameras, etc.
+In general, Point Cloud data is very large in number of data.
+So, if you process all the data, computation time might become an issue.</p>
+<p>Point cloud sampling is a technique for solving this computational complexity
+issue by extracting only representative point data and thinning the point
+cloud data without compromising the performance of processing using the point
+cloud data.</p>
+<section id="voxel-point-sampling">
+<h2>Voxel Point Sampling<a class="headerlink" href="#voxel-point-sampling" title="Permalink to this headline"></a></h2>
+<figure class="align-default">
+<img alt="../../../_images/voxel_point_sampling.png" src="../../../_images/voxel_point_sampling.png" />
+</figure>
+<p>Voxel grid sampling is a method of reducing point cloud data by using the
+<a class="reference external" href="https://en.wikipedia.org/wiki/Voxel">Voxel grids</a> which is regular grids
+in three-dimensional space.</p>
+<p>This method determines which each point is in a grid, and replaces the point
+clouds that are in the same Voxel with their average to reduce the number of
+points.</p>
+<section id="api">
+<h3>API<a class="headerlink" href="#api" title="Permalink to this headline"></a></h3>
+<dl class="py function">
+<dt class="sig sig-object py" id="Mapping.point_cloud_sampling.point_cloud_sampling.voxel_point_sampling">
+<span class="sig-prename descclassname"><span class="pre">Mapping.point_cloud_sampling.point_cloud_sampling.</span></span><span class="sig-name descname"><span class="pre">voxel_point_sampling</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">original_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">numpy.ndarray</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">numpy.dtype</span><span class="p"><span class="pre">[</span></span><span class="pre">numpy._typing._array_like._ScalarType_co</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">voxel_size</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/Mapping/point_cloud_sampling/point_cloud_sampling.html#voxel_point_sampling"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Mapping.point_cloud_sampling.point_cloud_sampling.voxel_point_sampling" title="Permalink to this definition"></a></dt>
+<dd><p>Voxel Point Sampling function.
+This function sample N-dimensional points with voxel grid.
+Points in a same voxel grid will be merged by mean operation for sampling.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>original_points</strong> (<em>(</em><em>M</em><em>, </em><em>N</em><em>) </em><em>N-dimensional points for sampling.</em>) – The number of points is M.</p></li>
+<li><p><strong>voxel_size</strong> (<em>voxel grid size</em>) – </p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p></p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>sampled points (M’, N)</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+</section>
+<section id="farthest-point-sampling">
+<h2>Farthest Point Sampling<a class="headerlink" href="#farthest-point-sampling" title="Permalink to this headline"></a></h2>
+<figure class="align-default">
+<img alt="../../../_images/farthest_point_sampling.png" src="../../../_images/farthest_point_sampling.png" />
+</figure>
+<p>Farthest Point Sampling is a point cloud sampling method by a specified
+number of points so that the distance between points is as far from as
+possible.</p>
+<p>This method is useful for machine learning and other situations where
+you want to obtain a specified number of points from point cloud.</p>
+<section id="id2">
+<h3>API<a class="headerlink" href="#id2" title="Permalink to this headline"></a></h3>
+<dl class="py function">
+<dt class="sig sig-object py" id="Mapping.point_cloud_sampling.point_cloud_sampling.farthest_point_sampling">
+<span class="sig-prename descclassname"><span class="pre">Mapping.point_cloud_sampling.point_cloud_sampling.</span></span><span class="sig-name descname"><span class="pre">farthest_point_sampling</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">orig_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">numpy.ndarray</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">numpy.dtype</span><span class="p"><span class="pre">[</span></span><span class="pre">numpy._typing._array_like._ScalarType_co</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seed</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/Mapping/point_cloud_sampling/point_cloud_sampling.html#farthest_point_sampling"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Mapping.point_cloud_sampling.point_cloud_sampling.farthest_point_sampling" title="Permalink to this definition"></a></dt>
+<dd><p>Farthest point sampling function
+This function sample N-dimensional points with the farthest point policy.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>orig_points</strong> (<em>(</em><em>M</em><em>, </em><em>N</em><em>) </em><em>N-dimensional points for sampling.</em>) – The number of points is M.</p></li>
+<li><p><strong>n_points</strong> (<em>number of points for sampling</em>) – </p></li>
+<li><p><strong>seed</strong> (<em>random seed number</em>) – </p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p></p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>sampled points (n_points, N)</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+</section>
+<section id="poisson-disk-sampling">
+<h2>Poisson Disk Sampling<a class="headerlink" href="#poisson-disk-sampling" title="Permalink to this headline"></a></h2>
+<figure class="align-default">
+<img alt="../../../_images/poisson_disk_sampling.png" src="../../../_images/poisson_disk_sampling.png" />
+</figure>
+<p>Poisson disk sample is a point cloud sampling method by a specified
+number of points so that the algorithm selects points where the distance
+from selected points is greater than a certain distance.</p>
+<p>Although this method does not have good performance comparing the Farthest
+distance sample where each point is distributed farther from each other,
+this is suitable for real-time processing because of its fast computation time.</p>
+<section id="id3">
+<h3>API<a class="headerlink" href="#id3" title="Permalink to this headline"></a></h3>
+<dl class="py function">
+<dt class="sig sig-object py" id="Mapping.point_cloud_sampling.point_cloud_sampling.poisson_disk_sampling">
+<span class="sig-prename descclassname"><span class="pre">Mapping.point_cloud_sampling.point_cloud_sampling.</span></span><span class="sig-name descname"><span class="pre">poisson_disk_sampling</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">orig_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">numpy.ndarray</span><span class="p"><span class="pre">[</span></span><span class="pre">Any</span><span class="p"><span class="pre">,</span></span><span class="w"> </span><span class="pre">numpy.dtype</span><span class="p"><span class="pre">[</span></span><span class="pre">numpy._typing._array_like._ScalarType_co</span><span class="p"><span class="pre">]</span></span><span class="p"><span class="pre">]</span></span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">min_distance</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">float</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">seed</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">MAX_ITER</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/Mapping/point_cloud_sampling/point_cloud_sampling.html#poisson_disk_sampling"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Mapping.point_cloud_sampling.point_cloud_sampling.poisson_disk_sampling" title="Permalink to this definition"></a></dt>
+<dd><p>Poisson disk sampling function
+This function sample N-dimensional points randomly until the number of
+points keeping minimum distance between selected points.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>orig_points</strong> (<em>(</em><em>M</em><em>, </em><em>N</em><em>) </em><em>N-dimensional points for sampling.</em>) – The number of points is M.</p></li>
+<li><p><strong>n_points</strong> (<em>number of points for sampling</em>) – </p></li>
+<li><p><strong>min_distance</strong> (<em>minimum distance between selected points.</em>) – </p></li>
+<li><p><strong>seed</strong> (<em>random seed number</em>) – </p></li>
+<li><p><strong>MAX_ITER</strong> (<em>Maximum number of iteration. Default is 1000.</em>) – </p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p></p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>sampled points (n_points or less, N)</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+</section>
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+<h1>Ray casting grid map<a class="headerlink" href="#ray-casting-grid-map" title="Permalink to this headline"></a></h1>
+<p>This is a 2D ray casting grid mapping example.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/raycasting_grid_map/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/raycasting_grid_map/animation.gif" />
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+<li class="toctree-l3"><a class="reference internal" href="#step1-adaptive-range-segmentation">Step1: Adaptive range segmentation</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#step2-rectangle-search">Step2: Rectangle search</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#rectangle-area-minimization-criteria">1. Rectangle Area Minimization criteria</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#closeness-criteria">2. Closeness criteria</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#variance-criteria">3. Variance criteria</a></li>
+</ul>
+</li>
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+ <section id="object-shape-recognition-using-rectangle-fitting">
+<h1>Object shape recognition using rectangle fitting<a class="headerlink" href="#object-shape-recognition-using-rectangle-fitting" title="Permalink to this headline"></a></h1>
+<p>This is an object shape recognition using rectangle fitting.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/rectangle_fitting/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/Mapping/rectangle_fitting/animation.gif" />
+<p>This example code is based on this paper algorithm:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://www.ri.cmu.edu/publications/efficient-l-shape-fitting-for-vehicle-detection-using-laser-scanners">Efficient L-Shape Fitting for Vehicle Detection Using Laser Scanners - The Robotics Institute Carnegie Mellon University</a></p></li>
+</ul>
+<p>The algorithm consists of 2 steps as below.</p>
+<section id="step1-adaptive-range-segmentation">
+<h2>Step1: Adaptive range segmentation<a class="headerlink" href="#step1-adaptive-range-segmentation" title="Permalink to this headline"></a></h2>
+<p>In the first step, all range data points are segmented into some clusters.</p>
+<p>We calculate the distance between each range data and the nearest range data, and if this distance is below a certain threshold, it is judged to be in the same cluster.
+This distance threshold is determined in proportion to the distance from the sensor.
+This is taking advantage of the general model of distance sensors, which tends to have sparser data distribution as the distance from the sensor increases.</p>
+<p>The threshold range is calculated by:</p>
+<div class="math notranslate nohighlight">
+\[r_{th} = R_0 + R_d * r_{origin}\]</div>
+<p>where</p>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(r_{th}\)</span>: Threashold range</p></li>
+<li><p><span class="math notranslate nohighlight">\(R_0, R_d\)</span>: Constant parameters</p></li>
+<li><p><span class="math notranslate nohighlight">\(r_{origin}\)</span>: Distance from the sensor for a range data.</p></li>
+</ul>
+</section>
+<section id="step2-rectangle-search">
+<h2>Step2: Rectangle search<a class="headerlink" href="#step2-rectangle-search" title="Permalink to this headline"></a></h2>
+<p>In the second step, for each cluster calculated in the previous step, rectangular fittings will be applied.
+In this rectangular fitting, each cluster’s distance data is rotated at certain angle intervals.
+It is evaluated by one of the three evaluation functions below, then best angle parameter one is selected as the rectangle shape.</p>
+<section id="rectangle-area-minimization-criteria">
+<h3>1. Rectangle Area Minimization criteria<a class="headerlink" href="#rectangle-area-minimization-criteria" title="Permalink to this headline"></a></h3>
+<p>This evaluation function calculates the area of the smallest rectangle that includes all the points, derived from the difference between the maximum and minimum values on the x-y axis for all distance data points.
+This allows for fitting a rectangle in a direction that encompasses as much of the smallest rectangular shape as possible.</p>
+</section>
+<section id="closeness-criteria">
+<h3>2. Closeness criteria<a class="headerlink" href="#closeness-criteria" title="Permalink to this headline"></a></h3>
+<p>This evaluation function uses the distances between the top and bottom vertices on the right side of the rectangle and each point in the distance data as evaluation values.
+If there are points on the rectangle edges, this evaluation value decreases.</p>
+</section>
+<section id="variance-criteria">
+<h3>3. Variance criteria<a class="headerlink" href="#variance-criteria" title="Permalink to this headline"></a></h3>
+<p>This evaluation function uses the squreed distances between the edges of the rectangle (horizontal and vertical) and each point.
+Calculating the squared error is the same as calculating the variance.
+The smaller this variance, the more it signifies that the points fit within the rectangle.</p>
+</section>
+</section>
+<section id="api">
+<h2>API<a class="headerlink" href="#api" title="Permalink to this headline"></a></h2>
+<dl class="py class">
+<dt class="sig sig-object py" id="Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">Mapping.rectangle_fitting.rectangle_fitting.</span></span><span class="sig-name descname"><span class="pre">LShapeFitting</span></span><a class="reference internal" href="../../../_modules/Mapping/rectangle_fitting/rectangle_fitting.html#LShapeFitting"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting" title="Permalink to this definition"></a></dt>
+<dd><p>LShapeFitting class. You can use this class by initializing the class and
+changing the parameters, and then calling the fitting method.</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.Criteria">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-name descname"><span class="pre">Criteria</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">value</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/Mapping/rectangle_fitting/rectangle_fitting.html#LShapeFitting.Criteria"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.Criteria" title="Permalink to this definition"></a></dt>
+<dd><p>An enumeration.</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.R0">
+<span class="sig-name descname"><span class="pre">R0</span></span><a class="headerlink" href="#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.R0" title="Permalink to this definition"></a></dt>
+<dd><p>Range segmentation parameter [m]</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.Rd">
+<span class="sig-name descname"><span class="pre">Rd</span></span><a class="headerlink" href="#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.Rd" title="Permalink to this definition"></a></dt>
+<dd><p>Range segmentation parameter [m]</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.criteria">
+<span class="sig-name descname"><span class="pre">criteria</span></span><a class="headerlink" href="#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.criteria" title="Permalink to this definition"></a></dt>
+<dd><p>Fitting criteria parameter</p>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.d_theta_deg_for_search">
+<span class="sig-name descname"><span class="pre">d_theta_deg_for_search</span></span><a class="headerlink" href="#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.d_theta_deg_for_search" title="Permalink to this definition"></a></dt>
+<dd><p>Angle difference parameter [deg]</p>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.fitting">
+<span class="sig-name descname"><span class="pre">fitting</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">ox</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">oy</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/Mapping/rectangle_fitting/rectangle_fitting.html#LShapeFitting.fitting"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.fitting" title="Permalink to this definition"></a></dt>
+<dd><p>Fitting L-shape model to object points</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>ox</strong> (<em>x positions of range points from an object</em>) – </p></li>
+<li><p><strong>oy</strong> (<em>y positions of range points from an object</em>) – </p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><ul class="simple">
+<li><p><strong>rects</strong> (<em>Fitting rectangles</em>)</p></li>
+<li><p><strong>id_sets</strong> (<em>id sets of each cluster</em>)</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py attribute">
+<dt class="sig sig-object py" id="Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.min_dist_of_closeness_criteria">
+<span class="sig-name descname"><span class="pre">min_dist_of_closeness_criteria</span></span><a class="headerlink" href="#Mapping.rectangle_fitting.rectangle_fitting.LShapeFitting.min_dist_of_closeness_criteria" title="Permalink to this definition"></a></dt>
+<dd><p>Minimum distance for closeness criteria parameter [m]</p>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+<section id="references">
+<h2>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://www.ri.cmu.edu/publications/efficient-l-shape-fitting-for-vehicle-detection-using-laser-scanners">Efficient L-Shape Fitting for Vehicle Detection Using Laser Scanners - The Robotics Institute Carnegie Mellon University</a></p></li>
+</ul>
+</section>
+</section>
+
+
+ </div>
+ </div>
+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+ <a href="../circle_fitting/circle_fitting.html" class="btn btn-neutral float-left" title="Object shape recognition using circle fitting" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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+ <section id="bezier-path-planning">
+<h1>Bezier path planning<a class="headerlink" href="#bezier-path-planning" title="Permalink to this headline"></a></h1>
+<p>A sample code of Bezier path planning.</p>
+<p>It is based on 4 control points Beizer path.</p>
+<img alt="../../../_images/Figure_1.png" src="../../../_images/Figure_1.png" />
+<p>If you change the offset distance from start and end point,</p>
+<p>You can get different Beizer course:</p>
+<img alt="../../../_images/Figure_2.png" src="../../../_images/Figure_2.png" />
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.294.6438&rep=rep1&type=pdf">Continuous Curvature Path Generation Based on Bezier Curves for
+Autonomous
+Vehicles</a></p></li>
+</ul>
+</section>
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+
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+<li class="toctree-l2 current"><a class="current reference internal" href="#">B-Spline planning</a><ul>
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+ <section id="b-spline-planning">
+<h1>B-Spline planning<a class="headerlink" href="#b-spline-planning" title="Permalink to this headline"></a></h1>
+<img alt="../../../_images/bspline_path_planning.png" src="../../../_images/bspline_path_planning.png" />
+<p>This is a B-Spline path planning routines.</p>
+<p>If you input waypoints, it generates a smooth path with B-Spline curve.</p>
+<p>This codes provide two types of B-Spline curve generations:</p>
+<ol class="arabic simple">
+<li><p>Interpolation: generate a curve that passes through all waypoints.</p></li>
+<li><p>Approximation: generate a curve that approximates the waypoints. (Not passing through all waypoints)</p></li>
+</ol>
+<section id="bspline-basics">
+<h2>Bspline basics<a class="headerlink" href="#bspline-basics" title="Permalink to this headline"></a></h2>
+<p>BSpline (Basis-Spline) is a piecewise polynomial spline curve.</p>
+<p>It is expressed by the following equation.</p>
+<p><span class="math notranslate nohighlight">\(\mathbf{S}(x)=\sum_{i=k-p}^k \mathbf{c}_i B_{i, p}(x)\)</span></p>
+<p>here:</p>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(S(x)\)</span> is the curve point on the spline at x.</p></li>
+<li><p><span class="math notranslate nohighlight">\(c_i\)</span> is the representative point generating the spline, called the control point.</p></li>
+<li><p><span class="math notranslate nohighlight">\(p+1\)</span> is the dimension of the BSpline.</p></li>
+<li><p><span class="math notranslate nohighlight">\(k\)</span> is the number of knots.</p></li>
+<li><p><span class="math notranslate nohighlight">\(B_{i,p}(x)\)</span> is a function called Basis Function.</p></li>
+</ul>
+<p>The the basis function can be calculated by the following <a class="reference external" href="https://en.wikipedia.org/wiki/De_Boor%27s_algorithm">De Boor recursion formula</a>:</p>
+<p><span class="math notranslate nohighlight">\(B_{i, 0}(x):= \begin{cases}1 & \text { if } \quad t_i \leq x<t_{i+1} \\ 0 & \text { otherwise }\end{cases}\)</span></p>
+<p><span class="math notranslate nohighlight">\(B_{i, p}(x):=\frac{x-t_i}{t_{i+p}-t_i} B_{i, p-1}(x)+\frac{t_{i+p+1}-x}{t_{i+p+1}-t_{i+1}} B_{i+1, p-1}(x)\)</span></p>
+<p>here:</p>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(t_i\)</span> is each element of the knot vector.</p></li>
+</ul>
+<p>This figure shows the BSpline basis functions for each of <span class="math notranslate nohighlight">\(i\)</span>:</p>
+<img alt="../../../_images/basis_functions.png" src="../../../_images/basis_functions.png" />
+<p>Note that when all the basis functions are added together, summation is 1.0 for any x value.</p>
+<p>This means that the result curve is smooth when each control point is weighted addition by this basis function,</p>
+<p>This code is for generating the upper basis function graph using <a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.BSpline.html">scipy</a>.</p>
+<div class="highlight-python notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">scipy.interpolate</span> <span class="kn">import</span> <span class="n">BSpline</span>
+
+<span class="k">def</span> <span class="nf">B_orig</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
+ <span class="k">if</span> <span class="n">k</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+ <span class="k">return</span> <span class="mf">1.0</span> <span class="k">if</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o"><=</span> <span class="n">x</span> <span class="o"><</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="k">else</span> <span class="mf">0.0</span>
+ <span class="k">if</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="n">k</span><span class="p">]</span> <span class="o">==</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">]:</span>
+ <span class="n">c1</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">c1</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">/</span> <span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="n">k</span><span class="p">]</span> <span class="o">-</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span><span class="p">])</span> <span class="o">*</span> <span class="n">B</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">t</span><span class="p">)</span>
+
+ <span class="k">if</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">==</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]:</span>
+ <span class="n">c2</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">c2</span> <span class="o">=</span> <span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">x</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="n">k</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">t</span><span class="p">[</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">])</span> <span class="o">*</span> <span class="n">B</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">k</span> <span class="o">-</span> <span class="mi">1</span><span class="p">,</span> <span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">,</span> <span class="n">t</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">c1</span> <span class="o">+</span> <span class="n">c2</span>
+
+
+<span class="k">def</span> <span class="nf">B</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">t</span><span class="p">):</span>
+ <span class="n">c</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros_like</span><span class="p">(</span><span class="n">t</span><span class="p">)</span>
+ <span class="n">c</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="mi">1</span>
+ <span class="k">return</span> <span class="n">BSpline</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">c</span><span class="p">,</span> <span class="n">k</span><span class="p">)(</span><span class="n">x</span><span class="p">)</span>
+
+
+<span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
+ <span class="n">k</span> <span class="o">=</span> <span class="mi">3</span> <span class="c1"># degree of the spline</span>
+ <span class="n">t</span> <span class="o">=</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">4</span><span class="p">,</span> <span class="mi">5</span><span class="p">]</span> <span class="c1"># knots vector</span>
+
+ <span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mi">1000</span><span class="p">,</span> <span class="n">endpoint</span><span class="o">=</span><span class="kc">False</span><span class="p">)</span>
+ <span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">r_</span><span class="p">[[</span><span class="n">np</span><span class="o">.</span><span class="n">min</span><span class="p">(</span><span class="n">t</span><span class="p">)]</span><span class="o">*</span><span class="n">k</span><span class="p">,</span> <span class="n">t</span><span class="p">,</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">max</span><span class="p">(</span><span class="n">t</span><span class="p">)]</span><span class="o">*</span><span class="n">k</span><span class="p">]</span>
+
+ <span class="n">n</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">t</span><span class="p">)</span> <span class="o">-</span> <span class="n">k</span> <span class="o">-</span> <span class="mi">1</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">n</span><span class="p">):</span>
+ <span class="n">y</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">B</span><span class="p">(</span><span class="n">ix</span><span class="p">,</span> <span class="n">k</span><span class="p">,</span> <span class="n">i</span><span class="p">,</span> <span class="n">t</span><span class="p">)</span> <span class="k">for</span> <span class="n">ix</span> <span class="ow">in</span> <span class="n">x</span><span class="p">])</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="sa">f</span><span class="s1">'i = </span><span class="si">{</span><span class="n">i</span><span class="si">}</span><span class="s1">'</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">title</span><span class="p">(</span><span class="sa">f</span><span class="s1">'Basis functions (k = </span><span class="si">{</span><span class="n">k</span><span class="si">}</span><span class="s1">, knots = </span><span class="si">{</span><span class="n">t</span><span class="si">}</span><span class="s1">)'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+</section>
+<section id="bspline-interpolation-planning">
+<h2>Bspline interpolation planning<a class="headerlink" href="#bspline-interpolation-planning" title="Permalink to this headline"></a></h2>
+<p><a class="reference internal" href="#PathPlanning.BSplinePath.bspline_path.interpolate_b_spline_path" title="PathPlanning.BSplinePath.bspline_path.interpolate_b_spline_path"><code class="xref py py-meth docutils literal notranslate"><span class="pre">PathPlanning.BSplinePath.bspline_path.interpolate_b_spline_path()</span></code></a> generates a curve that passes through all waypoints.</p>
+<p>This is a simple example of the interpolation planning:</p>
+<img alt="../../../_images/interpolation1.png" src="../../../_images/interpolation1.png" />
+<p>This figure also shows curvatures of each path point using <a class="reference internal" href="../../utils/plot/plot.html#plot-curvature"><span class="std std-ref">utils.plot.plot_curvature</span></a>.</p>
+<p>The default spline degree is 3, so curvature changes smoothly.</p>
+<img alt="../../../_images/interp_and_curvature.png" src="../../../_images/interp_and_curvature.png" />
+<section id="api">
+<h3>API<a class="headerlink" href="#api" title="Permalink to this headline"></a></h3>
+<dl class="py function">
+<dt class="sig sig-object py" id="PathPlanning.BSplinePath.bspline_path.interpolate_b_spline_path">
+<span class="sig-prename descclassname"><span class="pre">PathPlanning.BSplinePath.bspline_path.</span></span><span class="sig-name descname"><span class="pre">interpolate_b_spline_path</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_path_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">degree</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">3</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">tuple</span></span></span><a class="reference internal" href="../../../_modules/PathPlanning/BSplinePath/bspline_path.html#interpolate_b_spline_path"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#PathPlanning.BSplinePath.bspline_path.interpolate_b_spline_path" title="Permalink to this definition"></a></dt>
+<dd><p>Interpolate x-y points with a B-Spline path</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>x</strong> (<em>array_like</em>) – x positions of interpolated points</p></li>
+<li><p><strong>y</strong> (<em>array_like</em>) – y positions of interpolated points</p></li>
+<li><p><strong>n_path_points</strong> (<em>int</em>) – number of path points</p></li>
+<li><p><strong>degree</strong> (<em>int</em><em>, </em><em>optional</em>) – B-Spline degree. Must be 2<= k <= 5. Default: 3</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><ul class="simple">
+<li><p><strong>x</strong> (<em>array</em>) – x positions of the result path</p></li>
+<li><p><strong>y</strong> (<em>array</em>) – y positions of the result path</p></li>
+<li><p><strong>heading</strong> (<em>array</em>) – heading of the result path</p></li>
+<li><p><strong>curvature</strong> (<em>array</em>) – curvature of the result path</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+</section>
+<section id="bspline-approximation-planning">
+<h2>Bspline approximation planning<a class="headerlink" href="#bspline-approximation-planning" title="Permalink to this headline"></a></h2>
+<p><a class="reference internal" href="#PathPlanning.BSplinePath.bspline_path.approximate_b_spline_path" title="PathPlanning.BSplinePath.bspline_path.approximate_b_spline_path"><code class="xref py py-meth docutils literal notranslate"><span class="pre">PathPlanning.BSplinePath.bspline_path.approximate_b_spline_path()</span></code></a>
+generates a curve that approximates the waypoints, which means that
+the curve might not pass through waypoints.</p>
+<p>Users can adjust path smoothness by the smoothing parameter <cite>s</cite>. If this
+value is bigger, the path will be smoother, but it will be less accurate.
+If this value is smaller, the path will be more accurate, but it will be
+less smooth.</p>
+<p>This is a simple example of the approximation planning:</p>
+<img alt="../../../_images/approximation1.png" src="../../../_images/approximation1.png" />
+<p>This figure also shows curvatures of each path point using <a class="reference internal" href="../../utils/plot/plot.html#plot-curvature"><span class="std std-ref">utils.plot.plot_curvature</span></a>.</p>
+<p>The default spline degree is 3, so curvature changes smoothly.</p>
+<img alt="../../../_images/approx_and_curvature.png" src="../../../_images/approx_and_curvature.png" />
+<section id="id1">
+<h3>API<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h3>
+<dl class="py function">
+<dt class="sig sig-object py" id="PathPlanning.BSplinePath.bspline_path.approximate_b_spline_path">
+<span class="sig-prename descclassname"><span class="pre">PathPlanning.BSplinePath.bspline_path.</span></span><span class="sig-name descname"><span class="pre">approximate_b_spline_path</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">list</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">list</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n_path_points</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">degree</span></span><span class="p"><span class="pre">:</span></span><span class="w"> </span><span class="n"><span class="pre">int</span></span><span class="w"> </span><span class="o"><span class="pre">=</span></span><span class="w"> </span><span class="default_value"><span class="pre">3</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span> <span class="sig-return"><span class="sig-return-icon">→</span> <span class="sig-return-typehint"><span class="pre">tuple</span></span></span><a class="reference internal" href="../../../_modules/PathPlanning/BSplinePath/bspline_path.html#approximate_b_spline_path"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#PathPlanning.BSplinePath.bspline_path.approximate_b_spline_path" title="Permalink to this definition"></a></dt>
+<dd><p>Approximate points with a B-Spline path</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>x</strong> (<em>array_like</em>) – x position list of approximated points</p></li>
+<li><p><strong>y</strong> (<em>array_like</em>) – y position list of approximated points</p></li>
+<li><p><strong>n_path_points</strong> (<em>int</em>) – number of path points</p></li>
+<li><p><strong>degree</strong> (<em>int</em><em>, </em><em>optional</em>) – B Spline curve degree. Must be 2<= k <= 5. Default: 3.</p></li>
+<li><p><strong>s</strong> (<em>int</em><em>, </em><em>optional</em>) – smoothing parameter. If this value is bigger, the path will be
+smoother, but it will be less accurate. If this value is smaller,
+the path will be more accurate, but it will be less smooth.
+When <cite>s</cite> is 0, it is equivalent to the interpolation. Default is None,
+in this case <cite>s</cite> will be <cite>len(x)</cite>.</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><ul class="simple">
+<li><p><strong>x</strong> (<em>array</em>) – x positions of the result path</p></li>
+<li><p><strong>y</strong> (<em>array</em>) – y positions of the result path</p></li>
+<li><p><strong>heading</strong> (<em>array</em>) – heading of the result path</p></li>
+<li><p><strong>curvature</strong> (<em>array</em>) – curvature of the result path</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+</dd></dl>
+
+</section>
+</section>
+<section id="references">
+<h2>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/B-spline">B-spline - Wikipedia</a></p></li>
+<li><p><a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.UnivariateSpline.html">scipy.interpolate.UnivariateSpline</a></p></li>
+</ul>
+</section>
+</section>
+
+
+ </div>
+ </div>
+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+ <a href="../cubic_spline/cubic_spline.html" class="btn btn-neutral float-left" title="Cubic spline planning" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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+<li class="toctree-l2"><a class="reference internal" href="../vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
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+</ul>
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+<h1>Bug planner<a class="headerlink" href="#bug-planner" title="Permalink to this headline"></a></h1>
+<p>This is a 2D planning with Bug algorithm.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/BugPlanner/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/BugPlanner/animation.gif" />
+<ul class="simple">
+<li><p><a class="reference external" href="https://sites.google.com/site/ece452bugalgorithms/">ECE452 Bug Algorithms</a></p></li>
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+<li class="toctree-l2"><a class="reference internal" href="../vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Clothoid path planning</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#step1-solve-g-function">Step1: Solve g function</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#step2-calculate-path-parameters">Step2: Calculate path parameters</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#step3-construct-a-path-with-fresnel-integral">Step3: Construct a path with Fresnel integral</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#references">References</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
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+
+ <section id="clothoid-path-planning">
+<span id="id1"></span><h1>Clothoid path planning<a class="headerlink" href="#clothoid-path-planning" title="Permalink to this headline"></a></h1>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ClothoidPath/animation1.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ClothoidPath/animation1.gif" />
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ClothoidPath/animation2.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ClothoidPath/animation2.gif" />
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ClothoidPath/animation3.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ClothoidPath/animation3.gif" />
+<p>This is a clothoid path planning sample code.</p>
+<p>This can interpolate two 2D pose (x, y, yaw) with a clothoid path,
+which its curvature is linearly continuous.
+In other words, this is G1 Hermite interpolation with a single clothoid segment.</p>
+<p>This path planning algorithm as follows:</p>
+<section id="step1-solve-g-function">
+<h2>Step1: Solve g function<a class="headerlink" href="#step1-solve-g-function" title="Permalink to this headline"></a></h2>
+<p>Solve the g(A) function with a nonlinear optimization solver.</p>
+<div class="math notranslate nohighlight">
+\[g(A):=Y(2A, \delta-A, \phi_{s})\]</div>
+<p>Where</p>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(\delta\)</span>: the orientation difference between start and goal pose.</p></li>
+<li><p><span class="math notranslate nohighlight">\(\phi_{s}\)</span>: the orientation of the start pose.</p></li>
+<li><p><span class="math notranslate nohighlight">\(Y\)</span>: <span class="math notranslate nohighlight">\(Y(a, b, c)=\int_{0}^{1} \sin \left(\frac{a}{2} \tau^{2}+b \tau+c\right) d \tau\)</span></p></li>
+</ul>
+</section>
+<section id="step2-calculate-path-parameters">
+<h2>Step2: Calculate path parameters<a class="headerlink" href="#step2-calculate-path-parameters" title="Permalink to this headline"></a></h2>
+<p>We can calculate these path parameters using <span class="math notranslate nohighlight">\(A\)</span>,</p>
+<p><span class="math notranslate nohighlight">\(L\)</span>: path length</p>
+<div class="math notranslate nohighlight">
+\[L=\frac{R}{X\left(2 A, \delta-A, \phi_{s}\right)}\]</div>
+<p>where</p>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(R\)</span>: the distance between start and goal pose</p></li>
+<li><p><span class="math notranslate nohighlight">\(X\)</span>: <span class="math notranslate nohighlight">\(X(a, b, c)=\int_{0}^{1} \cos \left(\frac{a}{2} \tau^{2}+b \tau+c\right) d \tau\)</span></p></li>
+</ul>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(\kappa\)</span>: curvature</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[\kappa=(\delta-A) / L\]</div>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(\kappa'\)</span>: curvature rate</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[\kappa^{\prime}=2 A / L^{2}\]</div>
+</section>
+<section id="step3-construct-a-path-with-fresnel-integral">
+<h2>Step3: Construct a path with Fresnel integral<a class="headerlink" href="#step3-construct-a-path-with-fresnel-integral" title="Permalink to this headline"></a></h2>
+<p>The final clothoid path can be calculated with the path parameters and Fresnel integrals.</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\begin{aligned}
+&x(s)=x_{0}+\int_{0}^{s} \cos \left(\frac{1}{2} \kappa^{\prime} \tau^{2}+\kappa \tau+\vartheta_{0}\right) \mathrm{d} \tau \\
+&y(s)=y_{0}+\int_{0}^{s} \sin \left(\frac{1}{2} \kappa^{\prime} \tau^{2}+\kappa \tau+\vartheta_{0}\right) \mathrm{d} \tau
+\end{aligned}\end{split}\]</div>
+</section>
+<section id="references">
+<h2>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://www.researchgate.net/publication/237062806">Fast and accurate G1 fitting of clothoid curves</a></p></li>
+</ul>
+</section>
+</section>
+
+
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+ <a href="../bspline_path/bspline_path.html" class="btn btn-neutral float-left" title="B-Spline planning" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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+<li class="toctree-l2"><a class="reference internal" href="../prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Coverage path planner</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#grid-based-sweep">Grid based sweep</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#spiral-spanning-tree">Spiral Spanning Tree</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#wavefront-path">Wavefront path</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
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+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+ <div itemprop="articleBody">
+
+ <section id="coverage-path-planner">
+<h1>Coverage path planner<a class="headerlink" href="#coverage-path-planner" title="Permalink to this headline"></a></h1>
+<section id="grid-based-sweep">
+<h2>Grid based sweep<a class="headerlink" href="#grid-based-sweep" title="Permalink to this headline"></a></h2>
+<p>This is a 2D grid based sweep coverage path planner simulation:</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/GridBasedSweepCPP/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/GridBasedSweepCPP/animation.gif" />
+</section>
+<section id="spiral-spanning-tree">
+<h2>Spiral Spanning Tree<a class="headerlink" href="#spiral-spanning-tree" title="Permalink to this headline"></a></h2>
+<p>This is a 2D grid based spiral spanning tree coverage path planner simulation:</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/SpiralSpanningTreeCPP/animation1.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/SpiralSpanningTreeCPP/animation1.gif" />
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/SpiralSpanningTreeCPP/animation2.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/SpiralSpanningTreeCPP/animation2.gif" />
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/SpiralSpanningTreeCPP/animation3.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/SpiralSpanningTreeCPP/animation3.gif" />
+<ul class="simple">
+<li><p><a class="reference external" href="https://ieeexplore.ieee.org/abstract/document/1013479">Spiral-STC: An On-Line Coverage Algorithm of Grid Environments by a Mobile Robot</a></p></li>
+</ul>
+</section>
+<section id="wavefront-path">
+<h2>Wavefront path<a class="headerlink" href="#wavefront-path" title="Permalink to this headline"></a></h2>
+<p>This is a 2D grid based wavefront coverage path planner simulation:</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/WavefrontCPP/animation1.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/WavefrontCPP/animation1.gif" />
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+<li class="toctree-l3"><a class="reference internal" href="#spline-curve-continuity">Spline curve continuity</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#d-cubic-spline">1D cubic spline</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#constraint-1-terminal-constraints">Constraint 1: Terminal constraints</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#constraint-2-point-continuous-constraints">Constraint 2: Point continuous constraints</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#constraint-3-tangent-vector-continuous-constraints">Constraint 3: Tangent vector continuous constraints</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#constraint-4-curvature-continuous-constraints">Constraint 4: Curvature continuous constraints</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#constraint-5-terminal-curvature-constraints">Constraint 5: Terminal curvature constraints</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#how-to-calculate-the-unknown-parameters-a-j-b-j-c-j-d-j">How to calculate the unknown parameters <span class="math notranslate nohighlight">\(a_j, b_j, c_j, d_j\)</span></a></li>
+<li class="toctree-l4"><a class="reference internal" href="#how-to-calculate-the-first-and-second-derivatives-of-the-spline-curve">How to calculate the first and second derivatives of the spline curve</a></li>
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+ <section id="cubic-spline-planning">
+<h1>Cubic spline planning<a class="headerlink" href="#cubic-spline-planning" title="Permalink to this headline"></a></h1>
+<section id="spline-curve-continuity">
+<h2>Spline curve continuity<a class="headerlink" href="#spline-curve-continuity" title="Permalink to this headline"></a></h2>
+<p>Spline curve smoothness is depending on the which kind of spline model is used.</p>
+<p>The smoothness of the spline curve is expressed as <span class="math notranslate nohighlight">\(C_0, C_1\)</span>, and so on.</p>
+<p>This representation represents continuity of the curve.
+For example, for a spline curve in two-dimensional space:</p>
+<ul class="simple">
+<li><p><span class="math notranslate nohighlight">\(C_0\)</span> is position continuous</p></li>
+<li><p><span class="math notranslate nohighlight">\(C_1\)</span> is tangent vector continuous</p></li>
+<li><p><span class="math notranslate nohighlight">\(C_2\)</span> is curvature vector continuous</p></li>
+</ul>
+<p>as shown in the following figure:</p>
+<img alt="../../../_images/spline_continuity.png" src="../../../_images/spline_continuity.png" />
+<p>Cubic spline can generate a curve with <span class="math notranslate nohighlight">\(C_0, C_1, C_2\)</span>.</p>
+</section>
+<section id="d-cubic-spline">
+<h2>1D cubic spline<a class="headerlink" href="#d-cubic-spline" title="Permalink to this headline"></a></h2>
+<p>Cubic spline interpolation is a method of smoothly
+interpolating between multiple data points when given
+multiple data points, as shown in the figure below.</p>
+<img alt="../../../_images/spline.png" src="../../../_images/spline.png" />
+<p>It separates between each interval between data points.</p>
+<p>The each interval part is approximated by each cubic polynomial.</p>
+<p>The cubic spline uses the cubic polynomial equation for interpolation:</p>
+<p><span class="math notranslate nohighlight">\(S_j(x)=a_j+b_j(x-x_j)+c_j(x-x_j)^2+d_j(x-x_j)^3\)</span></p>
+<p>where <span class="math notranslate nohighlight">\(x_j < x < x_{j+1}\)</span>, <span class="math notranslate nohighlight">\(x_j\)</span> is the j-th node of the spline,
+<span class="math notranslate nohighlight">\(a_j\)</span>, <span class="math notranslate nohighlight">\(b_j\)</span>, <span class="math notranslate nohighlight">\(c_j\)</span>, <span class="math notranslate nohighlight">\(d_j\)</span> are the coefficients
+of the spline.</p>
+<p>As the above equation, there are 4 unknown parameters <span class="math notranslate nohighlight">\((a,b,c,d)\)</span> for
+one interval, so if the number of data points is <span class="math notranslate nohighlight">\(N\)</span>, the
+interpolation has <span class="math notranslate nohighlight">\(4N\)</span> unknown parameters.</p>
+<p>The following five conditions are used to determine the <span class="math notranslate nohighlight">\(4N\)</span>
+unknown parameters:</p>
+<section id="constraint-1-terminal-constraints">
+<h3>Constraint 1: Terminal constraints<a class="headerlink" href="#constraint-1-terminal-constraints" title="Permalink to this headline"></a></h3>
+<p><span class="math notranslate nohighlight">\(S_j(x_j)=y_j\)</span></p>
+<p>This constraint is the terminal constraint of each interval.</p>
+<p>The polynomial of each interval will pass through the x,y coordinates of
+the data points.</p>
+</section>
+<section id="constraint-2-point-continuous-constraints">
+<h3>Constraint 2: Point continuous constraints<a class="headerlink" href="#constraint-2-point-continuous-constraints" title="Permalink to this headline"></a></h3>
+<p><span class="math notranslate nohighlight">\(S_j(x_{j+1})=S_{j+1}(x_{j+1})=y_{j+1}\)</span></p>
+<p>This constraint is a continuity condition for the boundary of each interval.</p>
+<p>This constraint ensures that the boundary of each interval is continuous.</p>
+</section>
+<section id="constraint-3-tangent-vector-continuous-constraints">
+<h3>Constraint 3: Tangent vector continuous constraints<a class="headerlink" href="#constraint-3-tangent-vector-continuous-constraints" title="Permalink to this headline"></a></h3>
+<p><span class="math notranslate nohighlight">\(S'_j(x_{j+1})=S'_{j+1}(x_{j+1})\)</span></p>
+<p>This constraint is a continuity condition for the first derivative of
+the boundary of each interval.</p>
+<p>This constraint makes the vectors of the boundaries of each
+interval continuous.</p>
+</section>
+<section id="constraint-4-curvature-continuous-constraints">
+<h3>Constraint 4: Curvature continuous constraints<a class="headerlink" href="#constraint-4-curvature-continuous-constraints" title="Permalink to this headline"></a></h3>
+<p><span class="math notranslate nohighlight">\(S''_j(x_{j+1})=S''_{j+1}(x_{j+1})\)</span></p>
+<p>This constraint is the continuity condition for the second derivative of
+the boundary of each interval.</p>
+<p>This constraint makes the curvature of the boundaries of each
+interval continuous.</p>
+</section>
+<section id="constraint-5-terminal-curvature-constraints">
+<h3>Constraint 5: Terminal curvature constraints<a class="headerlink" href="#constraint-5-terminal-curvature-constraints" title="Permalink to this headline"></a></h3>
+<p><span class="math notranslate nohighlight">\(S''_0(0)=S''_{n+1}(x_{n})=0\)</span>.</p>
+<p>The constraint is a boundary condition for the second derivative of the starting and ending points.</p>
+<p>Our sample code assumes these terminal curvatures are 0, which is well known as Natural Cubic Spline.</p>
+</section>
+<section id="how-to-calculate-the-unknown-parameters-a-j-b-j-c-j-d-j">
+<h3>How to calculate the unknown parameters <span class="math notranslate nohighlight">\(a_j, b_j, c_j, d_j\)</span><a class="headerlink" href="#how-to-calculate-the-unknown-parameters-a-j-b-j-c-j-d-j" title="Permalink to this headline"></a></h3>
+<section id="step1-calculate-a-j">
+<h4>Step1: calculate <span class="math notranslate nohighlight">\(a_j\)</span><a class="headerlink" href="#step1-calculate-a-j" title="Permalink to this headline"></a></h4>
+<p>Spline coefficients <span class="math notranslate nohighlight">\(a_j\)</span> can be calculated by y positions of the data points:</p>
+<p><span class="math notranslate nohighlight">\(a_j = y_i\)</span>.</p>
+</section>
+<section id="step2-calculate-c-j">
+<h4>Step2: calculate <span class="math notranslate nohighlight">\(c_j\)</span><a class="headerlink" href="#step2-calculate-c-j" title="Permalink to this headline"></a></h4>
+<p>Spline coefficients <span class="math notranslate nohighlight">\(c_j\)</span> can be calculated by solving the linear equation:</p>
+<p><span class="math notranslate nohighlight">\(Ac_j = B\)</span>.</p>
+<p>The matrix <span class="math notranslate nohighlight">\(A\)</span> and <span class="math notranslate nohighlight">\(B\)</span> are defined as follows:</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}A=\left[\begin{array}{cccccc}
+1 & 0 & 0 & 0 & \cdots & 0 \\
+h_{0} & 2\left(h_{0}+h_{1}\right) & h_{1} & 0 & \cdots & 0 \\
+0 & h_{1} & 2\left(h_{1}+h_{2}\right) & h_{2} & \cdots & 0 \\
+0 & 0 & h_{2} & 2\left(h_{2}+h_{3}\right) & \cdots & 0 \\
+0 & 0 & 0 & h_{3} & \ddots & \\
+\vdots & \vdots & & & & \\
+0 & 0 & 0 & \cdots & 0 & 1
+\end{array}\right]\end{split}\]</div>
+<div class="math notranslate nohighlight">
+\[\begin{split}B=\left[\begin{array}{c}
+0 \\
+\frac{3}{h_{1}}\left(a_{2}-a_{1}\right)-\frac{3}{h_{0}}\left(a_{1}-a_{0}\right) \\
+\vdots \\
+\frac{3}{h_{n-1}}\left(a_{n}-a_{n-1}\right)-\frac{3}{h_{n-2}}\left(a_{n-1}-a_{n-2}\right) \\
+0
+\end{array}\right]\end{split}\]</div>
+<p>where <span class="math notranslate nohighlight">\(h_{i}\)</span> is the x position distance between the i-th and (i+1)-th data points.</p>
+</section>
+<section id="step3-calculate-d-j">
+<h4>Step3: calculate <span class="math notranslate nohighlight">\(d_j\)</span><a class="headerlink" href="#step3-calculate-d-j" title="Permalink to this headline"></a></h4>
+<p>Spline coefficients <span class="math notranslate nohighlight">\(d_j\)</span> can be calculated by the following equation:</p>
+<p><span class="math notranslate nohighlight">\(d_{j}=\frac{c_{j+1}-c_{j}}{3 h_{j}}\)</span></p>
+</section>
+<section id="step4-calculate-b-j">
+<h4>Step4: calculate <span class="math notranslate nohighlight">\(b_j\)</span><a class="headerlink" href="#step4-calculate-b-j" title="Permalink to this headline"></a></h4>
+<p>Spline coefficients <span class="math notranslate nohighlight">\(b_j\)</span> can be calculated by the following equation:</p>
+<p><span class="math notranslate nohighlight">\(b_{i}=\frac{1}{h_i}(a_{i+1}-a_{i})-\frac{h_i}{3}(2c_{i}+c_{i+1})\)</span></p>
+</section>
+</section>
+<section id="how-to-calculate-the-first-and-second-derivatives-of-the-spline-curve">
+<h3>How to calculate the first and second derivatives of the spline curve<a class="headerlink" href="#how-to-calculate-the-first-and-second-derivatives-of-the-spline-curve" title="Permalink to this headline"></a></h3>
+<p>After we can get the coefficients of the spline curve, we can calculate</p>
+<p>the first derivative by:</p>
+<p><span class="math notranslate nohighlight">\(y^{\prime}(x)=b+2cx+3dx^2\)</span></p>
+<p>the second derivative by:</p>
+<p><span class="math notranslate nohighlight">\(y^{\prime \prime}(x)=2c+6dx\)</span></p>
+<p>These equations can be calculated by differentiating the cubic polynomial.</p>
+</section>
+<section id="api">
+<h3>API<a class="headerlink" href="#api" title="Permalink to this headline"></a></h3>
+<p>This is the 1D cubic spline class API:</p>
+<dl class="py class">
+<dt class="sig sig-object py" id="PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">PathPlanning.CubicSpline.cubic_spline_planner.</span></span><span class="sig-name descname"><span class="pre">CubicSpline1D</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/PathPlanning/CubicSpline/cubic_spline_planner.html#CubicSpline1D"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D" title="Permalink to this definition"></a></dt>
+<dd><p>1D Cubic Spline class</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>x</strong> (<em>list</em>) – x coordinates for data points. This x coordinates must be
+sorted
+in ascending order.</p></li>
+<li><p><strong>y</strong> (<em>list</em>) – y coordinates for data points</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">Examples</p>
+<p>You can interpolate 1D data points.</p>
+<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="gp">>>> </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">5</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mf">1.7</span><span class="p">,</span> <span class="o">-</span><span class="mi">6</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mf">6.5</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]</span>
+<span class="gp">>>> </span><span class="n">sp</span> <span class="o">=</span> <span class="n">CubicSpline1D</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">xi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">yi</span> <span class="o">=</span> <span class="p">[</span><span class="n">sp</span><span class="o">.</span><span class="n">calc_position</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="n">xi</span><span class="p">]</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s2">"xb"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Data points"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xi</span><span class="p">,</span> <span class="n">yi</span> <span class="p">,</span> <span class="s2">"r"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Cubic spline interpolation"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../../_images/cubic_spline_1d.png" src="../../../_images/cubic_spline_1d.png" />
+<dl class="py method">
+<dt class="sig sig-object py" id="PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_first_derivative">
+<span class="sig-name descname"><span class="pre">calc_first_derivative</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/PathPlanning/CubicSpline/cubic_spline_planner.html#CubicSpline1D.calc_first_derivative"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_first_derivative" title="Permalink to this definition"></a></dt>
+<dd><p>Calc first derivative at given x.</p>
+<p>if x is outside the input x, return None</p>
+<dl class="field-list simple">
+<dt class="field-odd">Returns</dt>
+<dd class="field-odd"><p><strong>dy</strong> – first derivative for given x.</p>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p>float</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_position">
+<span class="sig-name descname"><span class="pre">calc_position</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/PathPlanning/CubicSpline/cubic_spline_planner.html#CubicSpline1D.calc_position"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_position" title="Permalink to this definition"></a></dt>
+<dd><p>Calc <cite>y</cite> position for given <cite>x</cite>.</p>
+<p>if <cite>x</cite> is outside the data point’s <cite>x</cite> range, return None.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Returns</dt>
+<dd class="field-odd"><p><strong>y</strong> – y position for given x.</p>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p>float</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_second_derivative">
+<span class="sig-name descname"><span class="pre">calc_second_derivative</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/PathPlanning/CubicSpline/cubic_spline_planner.html#CubicSpline1D.calc_second_derivative"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline1D.calc_second_derivative" title="Permalink to this definition"></a></dt>
+<dd><p>Calc second derivative at given x.</p>
+<p>if x is outside the input x, return None</p>
+<dl class="field-list simple">
+<dt class="field-odd">Returns</dt>
+<dd class="field-odd"><p><strong>ddy</strong> – second derivative for given x.</p>
+</dd>
+<dt class="field-even">Return type</dt>
+<dd class="field-even"><p>float</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+</section>
+<section id="id1">
+<h2>2D cubic spline<a class="headerlink" href="#id1" title="Permalink to this headline"></a></h2>
+<p>Data x positions needs to be mono-increasing for 1D cubic spline.</p>
+<p>So, it cannot be used for 2D path planning.</p>
+<p>2D cubic spline uses two 1D cubic splines based on path distance from
+the start point for each dimension x and y.</p>
+<p>This can generate a curvature continuous path based on x-y waypoints.</p>
+<p>Heading angle of each point can be calculated analytically by:</p>
+<p><span class="math notranslate nohighlight">\(\theta=\tan ^{-1} \frac{y’}{x’}\)</span></p>
+<p>Curvature of each point can be also calculated analytically by:</p>
+<p><span class="math notranslate nohighlight">\(\kappa=\frac{y^{\prime \prime} x^{\prime}-x^{\prime \prime} y^{\prime}}{\left(x^{\prime2}+y^{\prime2}\right)^{\frac{2}{3}}}\)</span></p>
+<section id="id2">
+<h3>API<a class="headerlink" href="#id2" title="Permalink to this headline"></a></h3>
+<dl class="py class">
+<dt class="sig sig-object py" id="PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D">
+<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">PathPlanning.CubicSpline.cubic_spline_planner.</span></span><span class="sig-name descname"><span class="pre">CubicSpline2D</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/PathPlanning/CubicSpline/cubic_spline_planner.html#CubicSpline2D"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D" title="Permalink to this definition"></a></dt>
+<dd><p>Cubic CubicSpline2D class</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>x</strong> (<em>list</em>) – x coordinates for data points.</p></li>
+<li><p><strong>y</strong> (<em>list</em>) – y coordinates for data points.</p></li>
+</ul>
+</dd>
+</dl>
+<p class="rubric">Examples</p>
+<p>You can interpolate a 2D data points.</p>
+<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="p">[</span><span class="o">-</span><span class="mf">2.5</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.5</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">,</span> <span class="mf">7.5</span><span class="p">,</span> <span class="mf">3.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="p">]</span>
+<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.7</span><span class="p">,</span> <span class="o">-</span><span class="mi">6</span><span class="p">,</span> <span class="mi">5</span><span class="p">,</span> <span class="mf">6.5</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">5.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.0</span><span class="p">]</span>
+<span class="gp">>>> </span><span class="n">ds</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="c1"># [m] distance of each interpolated points</span>
+<span class="gp">>>> </span><span class="n">sp</span> <span class="o">=</span> <span class="n">CubicSpline2D</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">sp</span><span class="o">.</span><span class="n">s</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">],</span> <span class="n">ds</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">rx</span><span class="p">,</span> <span class="n">ry</span><span class="p">,</span> <span class="n">ryaw</span><span class="p">,</span> <span class="n">rk</span> <span class="o">=</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[],</span> <span class="p">[]</span>
+<span class="gp">>>> </span><span class="k">for</span> <span class="n">i_s</span> <span class="ow">in</span> <span class="n">s</span><span class="p">:</span>
+<span class="gp">... </span> <span class="n">ix</span><span class="p">,</span> <span class="n">iy</span> <span class="o">=</span> <span class="n">sp</span><span class="o">.</span><span class="n">calc_position</span><span class="p">(</span><span class="n">i_s</span><span class="p">)</span>
+<span class="gp">... </span> <span class="n">rx</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">ix</span><span class="p">)</span>
+<span class="gp">... </span> <span class="n">ry</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">iy</span><span class="p">)</span>
+<span class="gp">... </span> <span class="n">ryaw</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">calc_yaw</span><span class="p">(</span><span class="n">i_s</span><span class="p">))</span>
+<span class="gp">... </span> <span class="n">rk</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">sp</span><span class="o">.</span><span class="n">calc_curvature</span><span class="p">(</span><span class="n">i_s</span><span class="p">))</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s2">"xb"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Data points"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">rx</span><span class="p">,</span> <span class="n">ry</span><span class="p">,</span> <span class="s2">"-r"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"Cubic spline path"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"x[m]"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"y[m]"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../../_images/cubic_spline_2d_path.png" src="../../../_images/cubic_spline_2d_path.png" />
+<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="p">[</span><span class="n">np</span><span class="o">.</span><span class="n">rad2deg</span><span class="p">(</span><span class="n">iyaw</span><span class="p">)</span> <span class="k">for</span> <span class="n">iyaw</span> <span class="ow">in</span> <span class="n">ryaw</span><span class="p">],</span> <span class="s2">"-r"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"yaw"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"line length[m]"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"yaw angle[deg]"</span><span class="p">)</span>
+</pre></div>
+</div>
+<img alt="../../../_images/cubic_spline_2d_yaw.png" src="../../../_images/cubic_spline_2d_yaw.png" />
+<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="mi">1</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="n">rk</span><span class="p">,</span> <span class="s2">"-r"</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"curvature"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"line length[m]"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"curvature [1/m]"</span><span class="p">)</span>
+</pre></div>
+</div>
+<img alt="../../../_images/cubic_spline_2d_curvature.png" src="../../../_images/cubic_spline_2d_curvature.png" />
+<dl class="py method">
+<dt class="sig sig-object py" id="PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_curvature">
+<span class="sig-name descname"><span class="pre">calc_curvature</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/PathPlanning/CubicSpline/cubic_spline_planner.html#CubicSpline2D.calc_curvature"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_curvature" title="Permalink to this definition"></a></dt>
+<dd><p>calc curvature</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><p><strong>s</strong> (<em>float</em>) – distance from the start point. if <cite>s</cite> is outside the data point’s
+range, return None.</p>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>k</strong> – curvature for given s.</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>float</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_position">
+<span class="sig-name descname"><span class="pre">calc_position</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/PathPlanning/CubicSpline/cubic_spline_planner.html#CubicSpline2D.calc_position"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_position" title="Permalink to this definition"></a></dt>
+<dd><p>calc position</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><p><strong>s</strong> (<em>float</em>) – distance from the start point. if <cite>s</cite> is outside the data point’s
+range, return None.</p>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><ul class="simple">
+<li><p><strong>x</strong> (<em>float</em>) – x position for given s.</p></li>
+<li><p><strong>y</strong> (<em>float</em>) – y position for given s.</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+</dd></dl>
+
+<dl class="py method">
+<dt class="sig sig-object py" id="PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_yaw">
+<span class="sig-name descname"><span class="pre">calc_yaw</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/PathPlanning/CubicSpline/cubic_spline_planner.html#CubicSpline2D.calc_yaw"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#PathPlanning.CubicSpline.cubic_spline_planner.CubicSpline2D.calc_yaw" title="Permalink to this definition"></a></dt>
+<dd><p>calc yaw</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><p><strong>s</strong> (<em>float</em>) – distance from the start point. if <cite>s</cite> is outside the data point’s
+range, return None.</p>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><strong>yaw</strong> – yaw angle (tangent vector) for given s.</p>
+</dd>
+<dt class="field-odd">Return type</dt>
+<dd class="field-odd"><p>float</p>
+</dd>
+</dl>
+</dd></dl>
+
+</dd></dl>
+
+</section>
+</section>
+<section id="references">
+<h2>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://people.clas.ufl.edu/kees/files/CubicSplines.pdf">Cubic Splines James Keesling</a></p></li>
+<li><p><a class="reference external" href="http://www.cs.cmu.edu/afs/cs/academic/class/15462-s10/www/lec-slides/lec06.pdf">Curves and Splines</a></p></li>
+</ul>
+</section>
+</section>
+
+
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+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+ <a href="../rrt/rrt.html" class="btn btn-neutral float-left" title="Rapidly-Exploring Random Trees (RRT)" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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+<li class="toctree-l2 current"><a class="current reference internal" href="#">Dubins path planning</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#dubins-path">Dubins path</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#api">API</a></li>
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+
+ <section id="dubins-path-planning">
+<h1>Dubins path planning<a class="headerlink" href="#dubins-path-planning" title="Permalink to this headline"></a></h1>
+<p>A sample code for Dubins path planning.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DubinsPath/animation.gif?raw=True" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DubinsPath/animation.gif?raw=True" />
+<section id="dubins-path">
+<h2>Dubins path<a class="headerlink" href="#dubins-path" title="Permalink to this headline"></a></h2>
+<p>Dubins path is a analytical path planning algorithm for a simple car model.</p>
+<p>It can generates a shortest path between two 2D poses (x, y, yaw) with maximum curvature constraint and tangent(yaw angle) constraint.</p>
+<p>Generated paths consist of 3 segments of maximum curvature curves or a straight line segment.</p>
+<p>Each segment type can is categorized by 3 type: ‘Right turn (R)’ , ‘Left turn (L)’, and ‘Straight (S).’</p>
+<p>Possible path will be at least one of these six types: RSR, RSL, LSR, LSL, RLR, LRL.</p>
+<p>Dubins path planner can output each segment type and distance of each course segment.</p>
+<p>For example, a RSR Dubins path is:</p>
+<a class="reference internal image-reference" href="../../../_images/RSR.jpg"><img alt="../../../_images/RSR.jpg" src="../../../_images/RSR.jpg" style="width: 400px;" /></a>
+<p>Each segment distance can be calculated by:</p>
+<p><span class="math notranslate nohighlight">\(\alpha = mod(-\theta)\)</span></p>
+<p><span class="math notranslate nohighlight">\(\beta = mod(x_{e, yaw} - \theta)\)</span></p>
+<p><span class="math notranslate nohighlight">\(p^2 = 2 + d ^ 2 - 2\cos(\alpha-\beta) + 2d(\sin\alpha - \sin\beta)\)</span></p>
+<p><span class="math notranslate nohighlight">\(t = atan2(\cos\beta - \cos\alpha, d + \sin\alpha - \sin\beta)\)</span></p>
+<p><span class="math notranslate nohighlight">\(d_1 = mod(-\alpha + t)\)</span></p>
+<p><span class="math notranslate nohighlight">\(d_2 = p\)</span></p>
+<p><span class="math notranslate nohighlight">\(d_3 = mod(\beta - t)\)</span></p>
+<p>where <span class="math notranslate nohighlight">\(\theta\)</span> is tangent and d is distance from <span class="math notranslate nohighlight">\(x_s\)</span> to <span class="math notranslate nohighlight">\(x_e\)</span></p>
+<p>A RLR Dubins path is:</p>
+<a class="reference internal image-reference" href="../../../_images/RLR.jpg"><img alt="../../../_images/RLR.jpg" src="../../../_images/RLR.jpg" style="width: 200px;" /></a>
+<p>Each segment distance can be calculated by:</p>
+<p><span class="math notranslate nohighlight">\(t = (6.0 - d^2 + 2\cos(\alpha-\beta) + 2d(\sin\alpha - \sin\beta)) / 8.0\)</span></p>
+<p><span class="math notranslate nohighlight">\(d_2 = mod(2\pi - acos(t))\)</span></p>
+<p><span class="math notranslate nohighlight">\(d_1 = mod(\alpha - atan2(\cos\beta - \cos\alpha, d + \sin\alpha - \sin\beta) + d_2 / 2.0)\)</span></p>
+<p><span class="math notranslate nohighlight">\(d_3 = mod(\alpha - \beta - d_1 + d_2)\)</span></p>
+<p>You can generate a path from these information and the maximum curvature information.</p>
+<p>A path type which has minimum course length among 6 types is selected,
+and then a path is constructed based on the selected type and its distances.</p>
+</section>
+<section id="api">
+<h2>API<a class="headerlink" href="#api" title="Permalink to this headline"></a></h2>
+<dl class="py function">
+<dt class="sig sig-object py" id="PathPlanning.DubinsPath.dubins_path_planner.plan_dubins_path">
+<span class="sig-prename descclassname"><span class="pre">PathPlanning.DubinsPath.dubins_path_planner.</span></span><span class="sig-name descname"><span class="pre">plan_dubins_path</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">s_x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s_y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">s_yaw</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g_x</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g_y</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">g_yaw</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">curvature</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">step_size</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">selected_types</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/PathPlanning/DubinsPath/dubins_path_planner.html#plan_dubins_path"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#PathPlanning.DubinsPath.dubins_path_planner.plan_dubins_path" title="Permalink to this definition"></a></dt>
+<dd><p>Plan dubins path</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>s_x</strong> (<em>float</em>) – x position of the start point [m]</p></li>
+<li><p><strong>s_y</strong> (<em>float</em>) – y position of the start point [m]</p></li>
+<li><p><strong>s_yaw</strong> (<em>float</em>) – yaw angle of the start point [rad]</p></li>
+<li><p><strong>g_x</strong> (<em>float</em>) – x position of the goal point [m]</p></li>
+<li><p><strong>g_y</strong> (<em>float</em>) – y position of the end point [m]</p></li>
+<li><p><strong>g_yaw</strong> (<em>float</em>) – yaw angle of the end point [rad]</p></li>
+<li><p><strong>curvature</strong> (<em>float</em>) – curvature for curve [1/m]</p></li>
+<li><p><strong>step_size</strong> (<em>float</em><em> (</em><em>optional</em><em>)</em>) – step size between two path points [m]. Default is 0.1</p></li>
+<li><p><strong>selected_types</strong> (<em>a list of string</em><em> or </em><em>None</em>) – selected path planning types. If None, all types are used for
+path planning, and minimum path length result is returned.
+You can select used path plannings types by a string list.
+e.g.: [“RSL”, “RSR”]</p></li>
+</ul>
+</dd>
+<dt class="field-even">Returns</dt>
+<dd class="field-even"><p><ul class="simple">
+<li><p><strong>x_list</strong> (<em>array</em>) – x positions of the path</p></li>
+<li><p><strong>y_list</strong> (<em>array</em>) – y positions of the path</p></li>
+<li><p><strong>yaw_list</strong> (<em>array</em>) – yaw angles of the path</p></li>
+<li><p><strong>modes</strong> (<em>array</em>) – mode list of the path</p></li>
+<li><p><strong>lengths</strong> (<em>array</em>) – arrow_length list of the path segments.</p></li>
+</ul>
+</p>
+</dd>
+</dl>
+<p class="rubric">Examples</p>
+<p>You can generate a dubins path.</p>
+<div class="doctest highlight-default notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="n">start_x</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="c1"># [m]</span>
+<span class="gp">>>> </span><span class="n">start_y</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="c1"># [m]</span>
+<span class="gp">>>> </span><span class="n">start_yaw</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">45.0</span><span class="p">)</span> <span class="c1"># [rad]</span>
+<span class="gp">>>> </span><span class="n">end_x</span> <span class="o">=</span> <span class="o">-</span><span class="mf">3.0</span> <span class="c1"># [m]</span>
+<span class="gp">>>> </span><span class="n">end_y</span> <span class="o">=</span> <span class="o">-</span><span class="mf">3.0</span> <span class="c1"># [m]</span>
+<span class="gp">>>> </span><span class="n">end_yaw</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="o">-</span><span class="mf">45.0</span><span class="p">)</span> <span class="c1"># [rad]</span>
+<span class="gp">>>> </span><span class="n">curvature</span> <span class="o">=</span> <span class="mf">1.0</span>
+<span class="gp">>>> </span><span class="n">path_x</span><span class="p">,</span> <span class="n">path_y</span><span class="p">,</span> <span class="n">path_yaw</span><span class="p">,</span> <span class="n">mode</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">plan_dubins_path</span><span class="p">(</span>
+<span class="go"> start_x, start_y, start_yaw, end_x, end_y, end_yaw, curvature)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">path_x</span><span class="p">,</span> <span class="n">path_y</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s2">"final course "</span> <span class="o">+</span> <span class="s2">""</span><span class="o">.</span><span class="n">join</span><span class="p">(</span><span class="n">mode</span><span class="p">))</span>
+<span class="gp">>>> </span><span class="n">plot_arrow</span><span class="p">(</span><span class="n">start_x</span><span class="p">,</span> <span class="n">start_y</span><span class="p">,</span> <span class="n">start_yaw</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plot_arrow</span><span class="p">(</span><span class="n">end_x</span><span class="p">,</span> <span class="n">end_y</span><span class="p">,</span> <span class="n">end_yaw</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+<span class="gp">>>> </span><span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../../_images/dubins_path.jpg" src="../../../_images/dubins_path.jpg" />
+</dd></dl>
+
+</section>
+<section id="reference">
+<h2>Reference<a class="headerlink" href="#reference" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://www.jstor.org/stable/2372560?origin=crossref">On Curves of Minimal Length with a Constraint on Average Curvature, and with Prescribed Initial and Terminal Positions and Tangents</a></p></li>
+<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Dubins_path">Dubins path - Wikipedia</a></p></li>
+<li><p><a class="reference external" href="http://planning.cs.uiuc.edu/node821.html">15.3.1 Dubins Curves</a></p></li>
+<li><p><a class="reference external" href="https://gieseanw.wordpress.com/2012/10/21/a-comprehensive-step-by-step-tutorial-to-computing-dubins-paths/">A Comprehensive, Step-by-Step Tutorial to Computing Dubin’s Paths</a></p></li>
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+ <section id="dynamic-window-approach">
+<span id="id1"></span><h1>Dynamic Window Approach<a class="headerlink" href="#dynamic-window-approach" title="Permalink to this headline"></a></h1>
+<p>This is a 2D navigation sample code with Dynamic Window Approach.</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://www.ri.cmu.edu/pub_files/pub1/fox_dieter_1997_1/fox_dieter_1997_1.pdf">The Dynamic Window Approach to Collision
+Avoidance</a></p></li>
+</ul>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DynamicWindowApproach/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DynamicWindowApproach/animation.gif" />
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+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
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+ <section id="eta-3-spline-path-planning">
+<span id="id1"></span><h1>Eta^3 Spline path planning<a class="headerlink" href="#eta-3-spline-path-planning" title="Permalink to this headline"></a></h1>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/Eta3SplinePath/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/Eta3SplinePath/animation.gif" />
+<p>This is a path planning with Eta^3 spline.</p>
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://ieeexplore.ieee.org/document/4339545/">\eta^3-Splines for the Smooth Path Generation of Wheeled Mobile
+Robots</a></p></li>
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+<li class="toctree-l2"><a class="reference internal" href="../dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Optimal Trajectory in a Frenet Frame</a></li>
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+
+ <section id="optimal-trajectory-in-a-frenet-frame">
+<h1>Optimal Trajectory in a Frenet Frame<a class="headerlink" href="#optimal-trajectory-in-a-frenet-frame" title="Permalink to this headline"></a></h1>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/FrenetOptimalTrajectory/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/FrenetOptimalTrajectory/animation.gif" />
+<p>This is optimal trajectory generation in a Frenet Frame.</p>
+<p>The cyan line is the target course and black crosses are obstacles.</p>
+<p>The red line is predicted path.</p>
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://www.researchgate.net/profile/Moritz_Werling/publication/224156269_Optimal_Trajectory_Generation_for_Dynamic_Street_Scenarios_in_a_Frenet_Frame/links/54f749df0cf210398e9277af.pdf">Optimal Trajectory Generation for Dynamic Street Scenarios in a
+Frenet
+Frame</a></p></li>
+<li><p><a class="reference external" href="https://www.youtube.com/watch?v=Cj6tAQe7UCY">Optimal trajectory generation for dynamic street scenarios in a
+Frenet Frame</a></p></li>
+</ul>
+</section>
+
+
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+<li class="toctree-l2"><a class="reference internal" href="../state_lattice_planner/state_lattice_planner.html">State Lattice Planning</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="../../../how_to_contribute.html">How To Contribute</a></li>
+</ul>
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+ <i data-toggle="wy-nav-top" class="fa fa-bars"></i>
+ <a href="../../../index.html">PythonRobotics</a>
+ </nav>
+
+ <div class="wy-nav-content">
+ <div class="rst-content">
+ <div role="navigation" aria-label="Page navigation">
+ <ul class="wy-breadcrumbs">
+ <li><a href="../../../index.html" class="icon icon-home"></a> »</li>
+ <li><a href="../path_planning.html">Path Planning</a> »</li>
+ <li>Grid based search</li>
+ <li class="wy-breadcrumbs-aside">
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+ </li>
+ </ul>
+ <hr/>
+</div>
+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+ <div itemprop="articleBody">
+
+ <section id="grid-based-search">
+<h1>Grid based search<a class="headerlink" href="#grid-based-search" title="Permalink to this headline"></a></h1>
+<section id="breadth-first-search">
+<h2>Breadth First Search<a class="headerlink" href="#breadth-first-search" title="Permalink to this headline"></a></h2>
+<p>This is a 2D grid based path planning with Breadth first search algorithm.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/BreadthFirstSearch/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/BreadthFirstSearch/animation.gif" />
+<p>In the animation, cyan points are searched nodes.</p>
+</section>
+<section id="depth-first-search">
+<h2>Depth First Search<a class="headerlink" href="#depth-first-search" title="Permalink to this headline"></a></h2>
+<p>This is a 2D grid based path planning with Depth first search algorithm.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DepthFirstSearch/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DepthFirstSearch/animation.gif" />
+<p>In the animation, cyan points are searched nodes.</p>
+</section>
+<section id="dijkstra-algorithm">
+<span id="dijkstra"></span><h2>Dijkstra algorithm<a class="headerlink" href="#dijkstra-algorithm" title="Permalink to this headline"></a></h2>
+<p>This is a 2D grid based shortest path planning with Dijkstra’s algorithm.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/Dijkstra/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/Dijkstra/animation.gif" />
+<p>In the animation, cyan points are searched nodes.</p>
+</section>
+<section id="a-algorithm">
+<span id="id1"></span><h2>A* algorithm<a class="headerlink" href="#a-algorithm" title="Permalink to this headline"></a></h2>
+<p>This is a 2D grid based shortest path planning with A star algorithm.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/AStar/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/AStar/animation.gif" />
+<p>In the animation, cyan points are searched nodes.</p>
+<p>Its heuristic is 2D Euclid distance.</p>
+</section>
+<section id="bidirectional-a-algorithm">
+<h2>Bidirectional A* algorithm<a class="headerlink" href="#bidirectional-a-algorithm" title="Permalink to this headline"></a></h2>
+<p>This is a 2D grid based shortest path planning with bidirectional A star algorithm.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/BidirectionalAStar/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/BidirectionalAStar/animation.gif" />
+<p>In the animation, cyan points are searched nodes.</p>
+</section>
+<section id="d-algorithm">
+<span id="id2"></span><h2>D* algorithm<a class="headerlink" href="#d-algorithm" title="Permalink to this headline"></a></h2>
+<p>This is a 2D grid based shortest path planning with D star algorithm.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DStar/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DStar/animation.gif" />
+<p>The animation shows a robot finding its path avoiding an obstacle using the D* search algorithm.</p>
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/D*">D* search Wikipedia</a></p></li>
+</ul>
+</section>
+<section id="d-lite-algorithm">
+<h2>D* lite algorithm<a class="headerlink" href="#d-lite-algorithm" title="Permalink to this headline"></a></h2>
+<p>This is a 2D grid based path planning and replanning with D star lite algorithm.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DStarLite/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/DStarLite/animation.gif" />
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="http://www.cs.cmu.edu/~maxim/files/dlite_icra02.pdf">Improved Fast Replanning for Robot Navigation in Unknown Terrain</a></p></li>
+</ul>
+</section>
+<section id="potential-field-algorithm">
+<h2>Potential Field algorithm<a class="headerlink" href="#potential-field-algorithm" title="Permalink to this headline"></a></h2>
+<p>This is a 2D grid based path planning with Potential Field algorithm.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/PotentialFieldPlanning/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/PotentialFieldPlanning/animation.gif" />
+<p>In the animation, the blue heat map shows potential value on each grid.</p>
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://www.cs.cmu.edu/~motionplanning/lecture/Chap4-Potential-Field_howie.pdf">Robotic Motion Planning:Potential
+Functions</a></p></li>
+</ul>
+</section>
+</section>
+
+
+ </div>
+ </div>
+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+ <a href="../bugplanner/bugplanner.html" class="btn btn-neutral float-left" title="Bug planner" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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+<li class="toctree-l1"><a class="reference internal" href="../../slam/slam.html">SLAM</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../path_planning.html">Path Planning</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bugplanner/bugplanner.html">Bug planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../grid_base_search/grid_base_search.html">Grid based search</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../model_predictive_trajectory_generator/model_predictive_trajectory_generator.html">Model Predictive Trajectory Generator</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../state_lattice_planner/state_lattice_planner.html">State Lattice Planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../visibility_road_map_planner/visibility_road_map_planner.html">Visibility Road-Map planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../bipedal/bipedal.html">Bipedal</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../control/control.html">Control</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../utils/utils.html">Utilities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../appendix/appendix.html">Appendix</a></li>
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+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
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+
+ <section id="hybrid-a-star">
+<h1>Hybrid a star<a class="headerlink" href="#hybrid-a-star" title="Permalink to this headline"></a></h1>
+<p>This is a simple vehicle model based hybrid A* path planner.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/HybridAStar/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/HybridAStar/animation.gif" />
+</section>
+
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+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+ <a href="../lqr_path/lqr_path.html" class="btn btn-neutral float-left" title="LQR based path planning" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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new file mode 100644
index 00000000000..bfa72d349b3
--- /dev/null
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+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
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+<li class="toctree-l2"><a class="reference internal" href="../model_predictive_trajectory_generator/model_predictive_trajectory_generator.html">Model Predictive Trajectory Generator</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../state_lattice_planner/state_lattice_planner.html">State Lattice Planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../visibility_road_map_planner/visibility_road_map_planner.html">Visibility Road-Map planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
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+<h1>LQR based path planning<a class="headerlink" href="#lqr-based-path-planning" title="Permalink to this headline"></a></h1>
+<p>A sample code using LQR based path planning for double integrator model.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/LQRPlanner/animation.gif?raw=true" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/LQRPlanner/animation.gif?raw=true" />
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+<li class="toctree-l1"><a class="reference internal" href="../../localization/localization.html">Localization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../slam/slam.html">SLAM</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../path_planning.html">Path Planning</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bugplanner/bugplanner.html">Bug planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../grid_base_search/grid_base_search.html">Grid based search</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Model Predictive Trajectory Generator</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#path-optimization-sample">Path optimization sample</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#lookup-table-generation-sample">Lookup table generation sample</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../state_lattice_planner/state_lattice_planner.html">State Lattice Planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../visibility_road_map_planner/visibility_road_map_planner.html">Visibility Road-Map planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
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+ <section id="model-predictive-trajectory-generator">
+<h1>Model Predictive Trajectory Generator<a class="headerlink" href="#model-predictive-trajectory-generator" title="Permalink to this headline"></a></h1>
+<p>This is a path optimization sample on model predictive trajectory
+generator.</p>
+<p>This algorithm is used for state lattice planner.</p>
+<section id="path-optimization-sample">
+<h2>Path optimization sample<a class="headerlink" href="#path-optimization-sample" title="Permalink to this headline"></a></h2>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ModelPredictiveTrajectoryGenerator/kn05animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ModelPredictiveTrajectoryGenerator/kn05animation.gif" />
+</section>
+<section id="lookup-table-generation-sample">
+<h2>Lookup table generation sample<a class="headerlink" href="#lookup-table-generation-sample" title="Permalink to this headline"></a></h2>
+<img alt="../../../_images/lookup_table.png" src="../../../_images/lookup_table.png" />
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="http://journals.sagepub.com/doi/pdf/10.1177/0278364906075328">Optimal rough terrain trajectory generation for wheeled mobile
+robots</a></p></li>
+</ul>
+</section>
+</section>
+
+
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+<li class="toctree-l1 current"><a class="current reference internal" href="#">Path Planning</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="model_predictive_trajectory_generator/model_predictive_trajectory_generator.html">Model Predictive Trajectory Generator</a></li>
+<li class="toctree-l2"><a class="reference internal" href="state_lattice_planner/state_lattice_planner.html">State Lattice Planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="visibility_road_map_planner/visibility_road_map_planner.html">Visibility Road-Map planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
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+<li class="toctree-l1"><a class="reference internal" href="../path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
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+ <section id="path-planning">
+<span id="id1"></span><h1>Path Planning<a class="headerlink" href="#path-planning" title="Permalink to this headline"></a></h1>
+<div class="toctree-wrapper compound">
+<p class="caption" role="heading"><span class="caption-text">Contents</span></p>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
+<li class="toctree-l1"><a class="reference internal" href="bugplanner/bugplanner.html">Bug planner</a></li>
+<li class="toctree-l1"><a class="reference internal" href="grid_base_search/grid_base_search.html">Grid based search</a><ul>
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+<li class="toctree-l2"><a class="reference internal" href="grid_base_search/grid_base_search.html#depth-first-search">Depth First Search</a></li>
+<li class="toctree-l2"><a class="reference internal" href="grid_base_search/grid_base_search.html#dijkstra-algorithm">Dijkstra algorithm</a></li>
+<li class="toctree-l2"><a class="reference internal" href="grid_base_search/grid_base_search.html#a-algorithm">A* algorithm</a></li>
+<li class="toctree-l2"><a class="reference internal" href="grid_base_search/grid_base_search.html#bidirectional-a-algorithm">Bidirectional A* algorithm</a></li>
+<li class="toctree-l2"><a class="reference internal" href="grid_base_search/grid_base_search.html#d-algorithm">D* algorithm</a></li>
+<li class="toctree-l2"><a class="reference internal" href="grid_base_search/grid_base_search.html#d-lite-algorithm">D* lite algorithm</a></li>
+<li class="toctree-l2"><a class="reference internal" href="grid_base_search/grid_base_search.html#potential-field-algorithm">Potential Field algorithm</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="model_predictive_trajectory_generator/model_predictive_trajectory_generator.html">Model Predictive Trajectory Generator</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="model_predictive_trajectory_generator/model_predictive_trajectory_generator.html#path-optimization-sample">Path optimization sample</a></li>
+<li class="toctree-l2"><a class="reference internal" href="model_predictive_trajectory_generator/model_predictive_trajectory_generator.html#lookup-table-generation-sample">Lookup table generation sample</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="state_lattice_planner/state_lattice_planner.html">State Lattice Planning</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="state_lattice_planner/state_lattice_planner.html#uniform-polar-sampling">Uniform polar sampling</a></li>
+<li class="toctree-l2"><a class="reference internal" href="state_lattice_planner/state_lattice_planner.html#biased-polar-sampling">Biased polar sampling</a></li>
+<li class="toctree-l2"><a class="reference internal" href="state_lattice_planner/state_lattice_planner.html#lane-sampling">Lane sampling</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="visibility_road_map_planner/visibility_road_map_planner.html">Visibility Road-Map planner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="visibility_road_map_planner/visibility_road_map_planner.html#algorithms">Algorithms</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="rrt/rrt.html#basic-rrt">Basic RRT</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rrt/rrt.html#rrt">RRT*</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rrt/rrt.html#rrt-with-dubins-path">RRT with dubins path</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rrt/rrt.html#id2">RRT* with dubins path</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rrt/rrt.html#rrt-with-reeds-sheep-path">RRT* with reeds-sheep path</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rrt/rrt.html#informed-rrt">Informed RRT*</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rrt/rrt.html#batch-informed-rrt">Batch Informed RRT*</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rrt/rrt.html#closed-loop-rrt">Closed Loop RRT*</a></li>
+<li class="toctree-l2"><a class="reference internal" href="rrt/rrt.html#lqr-rrt">LQR-RRT*</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="cubic_spline/cubic_spline.html">Cubic spline planning</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="cubic_spline/cubic_spline.html#spline-curve-continuity">Spline curve continuity</a></li>
+<li class="toctree-l2"><a class="reference internal" href="cubic_spline/cubic_spline.html#d-cubic-spline">1D cubic spline</a></li>
+<li class="toctree-l2"><a class="reference internal" href="cubic_spline/cubic_spline.html#id1">2D cubic spline</a></li>
+<li class="toctree-l2"><a class="reference internal" href="cubic_spline/cubic_spline.html#references">References</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="bspline_path/bspline_path.html">B-Spline planning</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="bspline_path/bspline_path.html#bspline-basics">Bspline basics</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bspline_path/bspline_path.html#bspline-interpolation-planning">Bspline interpolation planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bspline_path/bspline_path.html#bspline-approximation-planning">Bspline approximation planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="bspline_path/bspline_path.html#references">References</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="clothoid_path/clothoid_path.html">Clothoid path planning</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="clothoid_path/clothoid_path.html#step1-solve-g-function">Step1: Solve g function</a></li>
+<li class="toctree-l2"><a class="reference internal" href="clothoid_path/clothoid_path.html#step2-calculate-path-parameters">Step2: Calculate path parameters</a></li>
+<li class="toctree-l2"><a class="reference internal" href="clothoid_path/clothoid_path.html#step3-construct-a-path-with-fresnel-integral">Step3: Construct a path with Fresnel integral</a></li>
+<li class="toctree-l2"><a class="reference internal" href="clothoid_path/clothoid_path.html#references">References</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="quintic_polynomials_planner/quintic_polynomials_planner.html#quintic-polynomials-for-one-dimensional-robot-motion">Quintic polynomials for one dimensional robot motion</a></li>
+<li class="toctree-l2"><a class="reference internal" href="quintic_polynomials_planner/quintic_polynomials_planner.html#quintic-polynomials-for-two-dimensional-robot-motion-x-y">Quintic polynomials for two dimensional robot motion (x-y)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="quintic_polynomials_planner/quintic_polynomials_planner.html#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="dubins_path/dubins_path.html">Dubins path planning</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="dubins_path/dubins_path.html#dubins-path">Dubins path</a></li>
+<li class="toctree-l2"><a class="reference internal" href="dubins_path/dubins_path.html#api">API</a></li>
+<li class="toctree-l2"><a class="reference internal" href="dubins_path/dubins_path.html#reference">Reference</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l1"><a class="reference internal" href="frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l1"><a class="reference internal" href="coverage_path/coverage_path.html">Coverage path planner</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="coverage_path/coverage_path.html#grid-based-sweep">Grid based sweep</a></li>
+<li class="toctree-l2"><a class="reference internal" href="coverage_path/coverage_path.html#spiral-spanning-tree">Spiral Spanning Tree</a></li>
+<li class="toctree-l2"><a class="reference internal" href="coverage_path/coverage_path.html#wavefront-path">Wavefront path</a></li>
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+<li class="toctree-l1 current"><a class="reference internal" href="../path_planning.html">Path Planning</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../state_lattice_planner/state_lattice_planner.html">State Lattice Planning</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Probabilistic Road-Map (PRM) planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../visibility_road_map_planner/visibility_road_map_planner.html">Visibility Road-Map planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
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+ <section id="probabilistic-road-map-prm-planning">
+<span id="id1"></span><h1>Probabilistic Road-Map (PRM) planning<a class="headerlink" href="#probabilistic-road-map-prm-planning" title="Permalink to this headline"></a></h1>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ProbabilisticRoadMap/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ProbabilisticRoadMap/animation.gif" />
+<p>This PRM planner uses Dijkstra method for graph search.</p>
+<p>In the animation, blue points are sampled points,</p>
+<p>Cyan crosses means searched points with Dijkstra method,</p>
+<p>The red line is the final path of PRM.</p>
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Probabilistic_roadmap">Probabilistic roadmap -
+Wikipedia</a></p></li>
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+<li class="toctree-l2 current"><a class="current reference internal" href="#">Quintic polynomials planning</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#quintic-polynomials-for-one-dimensional-robot-motion">Quintic polynomials for one dimensional robot motion</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#quintic-polynomials-for-two-dimensional-robot-motion-x-y">Quintic polynomials for two dimensional robot motion (x-y)</a></li>
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+ <section id="quintic-polynomials-planning">
+<h1>Quintic polynomials planning<a class="headerlink" href="#quintic-polynomials-planning" title="Permalink to this headline"></a></h1>
+<p>Motion planning with quintic polynomials.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/QuinticPolynomialsPlanner/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/QuinticPolynomialsPlanner/animation.gif" />
+<p>It can calculate 2D path, velocity, and acceleration profile based on
+quintic polynomials.</p>
+<section id="quintic-polynomials-for-one-dimensional-robot-motion">
+<h2>Quintic polynomials for one dimensional robot motion<a class="headerlink" href="#quintic-polynomials-for-one-dimensional-robot-motion" title="Permalink to this headline"></a></h2>
+<p>We assume a one-dimensional robot motion <span class="math notranslate nohighlight">\(x(t)\)</span> at time <span class="math notranslate nohighlight">\(t\)</span> is
+formulated as a quintic polynomials based on time as follows:</p>
+<div class="math notranslate nohighlight" id="equation-quintic-eq1">
+<span class="eqno">(1)<a class="headerlink" href="#equation-quintic-eq1" title="Permalink to this equation"></a></span>\[x(t) = a_0+a_1t+a_2t^2+a_3t^3+a_4t^4+a_5t^5\]</div>
+<p><span class="math notranslate nohighlight">\(a_0, a_1. a_2, a_3, a_4, a_5\)</span> are parameters of the quintic polynomial.</p>
+<p>It is assumed that terminal states (start and end) are known as boundary conditions.</p>
+<p>Start position, velocity, and acceleration are <span class="math notranslate nohighlight">\(x_s, v_s, a_s\)</span> respectively.</p>
+<p>End position, velocity, and acceleration are <span class="math notranslate nohighlight">\(x_e, v_e, a_e\)</span> respectively.</p>
+<p>So, when time is 0.</p>
+<div class="math notranslate nohighlight" id="equation-quintic-eq2">
+<span class="eqno">(2)<a class="headerlink" href="#equation-quintic-eq2" title="Permalink to this equation"></a></span>\[x(0) = a_0 = x_s\]</div>
+<p>Then, differentiating the equation <a class="reference internal" href="#equation-quintic-eq1">(1)</a> with t,</p>
+<div class="math notranslate nohighlight" id="equation-quintic-eq3">
+<span class="eqno">(3)<a class="headerlink" href="#equation-quintic-eq3" title="Permalink to this equation"></a></span>\[x'(t) = a_1+2a_2t+3a_3t^2+4a_4t^3+5a_5t^4\]</div>
+<p>So, when time is 0,</p>
+<div class="math notranslate nohighlight" id="equation-quintic-eq4">
+<span class="eqno">(4)<a class="headerlink" href="#equation-quintic-eq4" title="Permalink to this equation"></a></span>\[x'(0) = a_1 = v_s\]</div>
+<p>Then, differentiating the equation <a class="reference internal" href="#equation-quintic-eq3">(3)</a> with t again,</p>
+<div class="math notranslate nohighlight" id="equation-quintic-eq5">
+<span class="eqno">(5)<a class="headerlink" href="#equation-quintic-eq5" title="Permalink to this equation"></a></span>\[x''(t) = 2a_2+6a_3t+12a_4t^2\]</div>
+<p>So, when time is 0,</p>
+<div class="math notranslate nohighlight" id="equation-quintic-eq6">
+<span class="eqno">(6)<a class="headerlink" href="#equation-quintic-eq6" title="Permalink to this equation"></a></span>\[x''(0) = 2a_2 = a_s\]</div>
+<p>so, we can calculate <span class="math notranslate nohighlight">\(a_0, a_1, a_2\)</span> with eq. <a class="reference internal" href="#equation-quintic-eq2">(2)</a>, <a class="reference internal" href="#equation-quintic-eq4">(4)</a>, <a class="reference internal" href="#equation-quintic-eq6">(6)</a> and boundary conditions.</p>
+<p><span class="math notranslate nohighlight">\(a_3, a_4, a_5\)</span> are still unknown in eq <a class="reference internal" href="#equation-quintic-eq1">(1)</a>.</p>
+<p>We assume that the end time for a maneuver is <span class="math notranslate nohighlight">\(T\)</span>, we can get these equations from eq <a class="reference internal" href="#equation-quintic-eq1">(1)</a>, <a class="reference internal" href="#equation-quintic-eq3">(3)</a>, <a class="reference internal" href="#equation-quintic-eq5">(5)</a>:</p>
+<div class="math notranslate nohighlight" id="equation-quintic-eq7">
+<span class="eqno">(7)<a class="headerlink" href="#equation-quintic-eq7" title="Permalink to this equation"></a></span>\[x(T)=a_0+a_1T+a_2T^2+a_3T^3+a_4T^4+a_5T^5=x_e\]</div>
+<div class="math notranslate nohighlight" id="equation-quintic-eq8">
+<span class="eqno">(8)<a class="headerlink" href="#equation-quintic-eq8" title="Permalink to this equation"></a></span>\[x'(T)=a_1+2a_2T+3a_3T^2+4a_4T^3+5a_5T^4=v_e\]</div>
+<div class="math notranslate nohighlight" id="equation-quintic-eq9">
+<span class="eqno">(9)<a class="headerlink" href="#equation-quintic-eq9" title="Permalink to this equation"></a></span>\[x''(T)=2a_2+6a_3T+12a_4T^2+20a_5T^3=a_e\]</div>
+<p>From eq <a class="reference internal" href="#equation-quintic-eq7">(7)</a>, <a class="reference internal" href="#equation-quintic-eq8">(8)</a>, <a class="reference internal" href="#equation-quintic-eq9">(9)</a>, we can calculate <span class="math notranslate nohighlight">\(a_3, a_4, a_5\)</span> to solve the linear equations: <span class="math notranslate nohighlight">\(Ax=b\)</span></p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\begin{bmatrix} T^3 & T^4 & T^5 \\ 3T^2 & 4T^3 & 5T^4 \\ 6T & 12T^2 & 20T^3 \end{bmatrix}\begin{bmatrix} a_3\\ a_4\\ a_5\end{bmatrix}=\begin{bmatrix} x_e-x_s-v_sT-0.5a_sT^2\\ v_e-v_s-a_sT\\ a_e-a_s\end{bmatrix}\end{split}\]</div>
+<p>We can get all unknown parameters now.</p>
+</section>
+<section id="quintic-polynomials-for-two-dimensional-robot-motion-x-y">
+<h2>Quintic polynomials for two dimensional robot motion (x-y)<a class="headerlink" href="#quintic-polynomials-for-two-dimensional-robot-motion-x-y" title="Permalink to this headline"></a></h2>
+<p>If you use two quintic polynomials along x axis and y axis, you can plan for two dimensional robot motion in x-y plane.</p>
+<div class="math notranslate nohighlight" id="equation-quintic-eq10">
+<span class="eqno">(10)<a class="headerlink" href="#equation-quintic-eq10" title="Permalink to this equation"></a></span>\[x(t) = a_0+a_1t+a_2t^2+a_3t^3+a_4t^4+a_5t^5\]</div>
+<div class="math notranslate nohighlight" id="equation-quintic-eq11">
+<span class="eqno">(11)<a class="headerlink" href="#equation-quintic-eq11" title="Permalink to this equation"></a></span>\[y(t) = b_0+b_1t+b_2t^2+b_3t^3+b_4t^4+b_5t^5\]</div>
+<p>It is assumed that terminal states (start and end) are known as boundary conditions.</p>
+<p>Start position, orientation, velocity, and acceleration are <span class="math notranslate nohighlight">\(x_s, y_s, \theta_s, v_s, a_s\)</span> respectively.</p>
+<p>End position, orientation, velocity, and acceleration are <span class="math notranslate nohighlight">\(x_e, y_e. \theta_e, v_e, a_e\)</span> respectively.</p>
+<p>Each velocity and acceleration boundary condition can be calculated with each orientation.</p>
+<p><span class="math notranslate nohighlight">\(v_{xs}=v_scos(\theta_s), v_{ys}=v_ssin(\theta_s)\)</span></p>
+<p><span class="math notranslate nohighlight">\(v_{xe}=v_ecos(\theta_e), v_{ye}=v_esin(\theta_e)\)</span></p>
+</section>
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="http://ieeexplore.ieee.org/document/637936/">Local Path Planning And Motion Control For Agv In
+Positioning</a></p></li>
+</ul>
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+<li class="toctree-l2"><a class="reference internal" href="../dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../state_lattice_planner/state_lattice_planner.html">State Lattice Planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../visibility_road_map_planner/visibility_road_map_planner.html">Visibility Road-Map planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Reeds Shepp planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
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+
+ <section id="reeds-shepp-planning">
+<h1>Reeds Shepp planning<a class="headerlink" href="#reeds-shepp-planning" title="Permalink to this headline"></a></h1>
+<p>A sample code with Reeds Shepp path planning.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ReedsSheppPath/animation.gif?raw=true" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ReedsSheppPath/animation.gif?raw=true" />
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="http://planning.cs.uiuc.edu/node822.html">15.3.2 Reeds-Shepp
+Curves</a></p></li>
+<li><p><a class="reference external" href="https://pdfs.semanticscholar.org/932e/c495b1d0018fd59dee12a0bf74434fac7af4.pdf">optimal paths for a car that goes both forwards and
+backwards</a></p></li>
+<li><p><a class="reference external" href="https://github.com/ghliu/pyReedsShepp">ghliu/pyReedsShepp: Implementation of Reeds Shepp
+curve.</a></p></li>
+</ul>
+</section>
+
+
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+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
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+<!DOCTYPE html>
+<html class="writer-html5" lang="en" >
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+<li class="toctree-l1"><a class="reference internal" href="../../mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../slam/slam.html">SLAM</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../path_planning.html">Path Planning</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bugplanner/bugplanner.html">Bug planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../grid_base_search/grid_base_search.html">Grid based search</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../model_predictive_trajectory_generator/model_predictive_trajectory_generator.html">Model Predictive Trajectory Generator</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../state_lattice_planner/state_lattice_planner.html">State Lattice Planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../visibility_road_map_planner/visibility_road_map_planner.html">Visibility Road-Map planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Rapidly-Exploring Random Trees (RRT)</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#basic-rrt">Basic RRT</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#rrt">RRT*</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#simulation">Simulation</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#ref">Ref</a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="#rrt-with-dubins-path">RRT with dubins path</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#id2">RRT* with dubins path</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#rrt-with-reeds-sheep-path">RRT* with reeds-sheep path</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#informed-rrt">Informed RRT*</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#batch-informed-rrt">Batch Informed RRT*</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#closed-loop-rrt">Closed Loop RRT*</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#lqr-rrt">LQR-RRT*</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="../../control/control.html">Control</a></li>
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+ <li><a href="../../../index.html" class="icon icon-home"></a> »</li>
+ <li><a href="../path_planning.html">Path Planning</a> »</li>
+ <li>Rapidly-Exploring Random Trees (RRT)</li>
+ <li class="wy-breadcrumbs-aside">
+ <a href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/docs/modules/path_planning/rrt/rrt_main.rst" class="fa fa-github"> Edit on GitHub</a>
+ </li>
+ </ul>
+ <hr/>
+</div>
+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+ <div itemprop="articleBody">
+
+ <section id="rapidly-exploring-random-trees-rrt">
+<span id="id1"></span><h1>Rapidly-Exploring Random Trees (RRT)<a class="headerlink" href="#rapidly-exploring-random-trees-rrt" title="Permalink to this headline"></a></h1>
+<section id="basic-rrt">
+<h2>Basic RRT<a class="headerlink" href="#basic-rrt" title="Permalink to this headline"></a></h2>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRT/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRT/animation.gif" />
+<p>This is a simple path planning code with Rapidly-Exploring Random Trees
+(RRT)</p>
+<p>Black circles are obstacles, green line is a searched tree, red crosses
+are start and goal positions.</p>
+</section>
+<section id="rrt">
+<h2>RRT*<a class="headerlink" href="#rrt" title="Permalink to this headline"></a></h2>
+<figure class="align-default">
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTstar/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTstar/animation.gif" />
+</figure>
+<p>This is a path planning code with RRT*</p>
+<p>Black circles are obstacles, green line is a searched tree, red crosses are start and goal positions.</p>
+<section id="simulation">
+<h3>Simulation<a class="headerlink" href="#simulation" title="Permalink to this headline"></a></h3>
+<a class="reference internal image-reference" href="../../../_images/rrt_star_1_0.png"><img alt="../../../_images/rrt_star_1_0.png" src="../../../_images/rrt_star_1_0.png" style="width: 600px;" /></a>
+</section>
+<section id="ref">
+<h3>Ref<a class="headerlink" href="#ref" title="Permalink to this headline"></a></h3>
+<ul class="simple">
+<li><p><a class="reference external" href="https://arxiv.org/pdf/1105.1186.pdf">Sampling-based Algorithms for Optimal Motion Planning</a></p></li>
+<li><p><a class="reference external" href="https://arxiv.org/abs/1005.0416">Incremental Sampling-based Algorithms for Optimal Motion Planning</a></p></li>
+</ul>
+</section>
+</section>
+<section id="rrt-with-dubins-path">
+<h2>RRT with dubins path<a class="headerlink" href="#rrt-with-dubins-path" title="Permalink to this headline"></a></h2>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTDubins/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTDubins/animation.gif" />
+<p>Path planning for a car robot with RRT and dubins path planner.</p>
+</section>
+<section id="id2">
+<span id="id3"></span><h2>RRT* with dubins path<a class="headerlink" href="#id2" title="Permalink to this headline"></a></h2>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTStarDubins/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTStarDubins/animation.gif" />
+<p>Path planning for a car robot with RRT* and dubins path planner.</p>
+</section>
+<section id="rrt-with-reeds-sheep-path">
+<span id="id4"></span><h2>RRT* with reeds-sheep path<a class="headerlink" href="#rrt-with-reeds-sheep-path" title="Permalink to this headline"></a></h2>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTStarReedsShepp/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/RRTStarReedsShepp/animation.gif" />
+<p>Path planning for a car robot with RRT* and reeds sheep path planner.</p>
+</section>
+<section id="informed-rrt">
+<span id="id5"></span><h2>Informed RRT*<a class="headerlink" href="#informed-rrt" title="Permalink to this headline"></a></h2>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/InformedRRTStar/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/InformedRRTStar/animation.gif" />
+<p>This is a path planning code with Informed RRT*.</p>
+<p>The cyan ellipse is the heuristic sampling domain of Informed RRT*.</p>
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://arxiv.org/pdf/1404.2334.pdf">Informed RRT*: Optimal Sampling-based Path Planning Focused via
+Direct Sampling of an Admissible Ellipsoidal
+Heuristic</a></p></li>
+</ul>
+</section>
+<section id="batch-informed-rrt">
+<span id="id6"></span><h2>Batch Informed RRT*<a class="headerlink" href="#batch-informed-rrt" title="Permalink to this headline"></a></h2>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/BatchInformedRRTStar/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/BatchInformedRRTStar/animation.gif" />
+<p>This is a path planning code with Batch Informed RRT*.</p>
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://arxiv.org/abs/1405.5848">Batch Informed Trees (BIT*): Sampling-based Optimal Planning via the
+Heuristically Guided Search of Implicit Random Geometric
+Graphs</a></p></li>
+</ul>
+</section>
+<section id="closed-loop-rrt">
+<span id="id7"></span><h2>Closed Loop RRT*<a class="headerlink" href="#closed-loop-rrt" title="Permalink to this headline"></a></h2>
+<p>A vehicle model based path planning with closed loop RRT*.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ClosedLoopRRTStar/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/ClosedLoopRRTStar/animation.gif" />
+<p>In this code, pure-pursuit algorithm is used for steering control,</p>
+<p>PID is used for speed control.</p>
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="http://acl.mit.edu/papers/KuwataGNC08.pdf">Motion Planning in Complex Environments using Closed-loop
+Prediction</a></p></li>
+<li><p><a class="reference external" href="http://acl.mit.edu/papers/KuwataTCST09.pdf">Real-time Motion Planning with Applications to Autonomous Urban
+Driving</a></p></li>
+<li><p><a class="reference external" href="https://arxiv.org/abs/1601.06326">[1601.06326] Sampling-based Algorithms for Optimal Motion Planning
+Using Closed-loop Prediction</a></p></li>
+</ul>
+</section>
+<section id="lqr-rrt">
+<span id="id8"></span><h2>LQR-RRT*<a class="headerlink" href="#lqr-rrt" title="Permalink to this headline"></a></h2>
+<p>This is a path planning simulation with LQR-RRT*.</p>
+<p>A double integrator motion model is used for LQR local planner.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/LQRRRTStar/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/LQRRRTStar/animation.gif" />
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="http://lis.csail.mit.edu/pubs/perez-icra12.pdf">LQR-RRT*: Optimal Sampling-Based Motion Planning with Automatically
+Derived Extension
+Heuristics</a></p></li>
+<li><p><a class="reference external" href="https://github.com/MahanFathi/LQR-RRTstar">MahanFathi/LQR-RRTstar: LQR-RRT* method is used for random motion planning of a simple pendulum in its phase plot</a></p></li>
+</ul>
+</section>
+</section>
+
+
+ </div>
+ </div>
+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
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+<li class="toctree-l1"><a class="reference internal" href="../../mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../slam/slam.html">SLAM</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../path_planning.html">Path Planning</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bugplanner/bugplanner.html">Bug planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../grid_base_search/grid_base_search.html">Grid based search</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../model_predictive_trajectory_generator/model_predictive_trajectory_generator.html">Model Predictive Trajectory Generator</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">State Lattice Planning</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#uniform-polar-sampling">Uniform polar sampling</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#biased-polar-sampling">Biased polar sampling</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#lane-sampling">Lane sampling</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
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+
+ <section id="state-lattice-planning">
+<h1>State Lattice Planning<a class="headerlink" href="#state-lattice-planning" title="Permalink to this headline"></a></h1>
+<p>This script is a path planning code with state lattice planning.</p>
+<p>This code uses the model predictive trajectory generator to solve
+boundary problem.</p>
+<section id="uniform-polar-sampling">
+<h2>Uniform polar sampling<a class="headerlink" href="#uniform-polar-sampling" title="Permalink to this headline"></a></h2>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/StateLatticePlanner/UniformPolarSampling.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/StateLatticePlanner/UniformPolarSampling.gif" />
+</section>
+<section id="biased-polar-sampling">
+<h2>Biased polar sampling<a class="headerlink" href="#biased-polar-sampling" title="Permalink to this headline"></a></h2>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/StateLatticePlanner/BiasedPolarSampling.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/StateLatticePlanner/BiasedPolarSampling.gif" />
+</section>
+<section id="lane-sampling">
+<h2>Lane sampling<a class="headerlink" href="#lane-sampling" title="Permalink to this headline"></a></h2>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/StateLatticePlanner/LaneSampling.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/StateLatticePlanner/LaneSampling.gif" />
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="http://journals.sagepub.com/doi/pdf/10.1177/0278364906075328">Optimal rough terrain trajectory generation for wheeled mobile
+robots</a></p></li>
+<li><p><a class="reference external" href="http://www.frc.ri.cmu.edu/~alonzo/pubs/papers/JFR_08_SS_Sampling.pdf">State Space Sampling of Feasible Motions for High-Performance Mobile
+Robot Navigation in Complex
+Environments</a></p></li>
+</ul>
+</section>
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+<li class="toctree-l2"><a class="reference internal" href="../dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bugplanner/bugplanner.html">Bug planner</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../grid_base_search/grid_base_search.html">Grid based search</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../model_predictive_trajectory_generator/model_predictive_trajectory_generator.html">Model Predictive Trajectory Generator</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../state_lattice_planner/state_lattice_planner.html">State Lattice Planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Visibility Road-Map planner</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#algorithms">Algorithms</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#step1-generate-visibility-nodes-based-on-polygon-obstacles">Step1: Generate visibility nodes based on polygon obstacles</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#step2-generate-visibility-graphs-connecting-the-nodes">Step2: Generate visibility graphs connecting the nodes.</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#step3-search-the-shortest-path-in-the-graphs-using-dijkstra-algorithm">Step3: Search the shortest path in the graphs using Dijkstra algorithm</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#references">References</a></li>
+</ul>
+</li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../vrm_planner/vrm_planner.html">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../clothoid_path/clothoid_path.html">Clothoid path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../eta3_spline/eta3_spline.html">Eta^3 Spline path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_tracking/path_tracking.html">Path Tracking</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
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+ <section id="visibility-road-map-planner">
+<h1>Visibility Road-Map planner<a class="headerlink" href="#visibility-road-map-planner" title="Permalink to this headline"></a></h1>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/VisibilityRoadMap/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/VisibilityRoadMap/animation.gif" />
+<p><a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathPlanning/VisibilityRoadMap/visibility_road_map.py">[Code]</a></p>
+<p>This visibility road-map planner uses Dijkstra method for graph search.</p>
+<p>In the animation, the black lines are polygon obstacles,</p>
+<p>red crosses are visibility nodes, and blue lines area collision free visibility graphs.</p>
+<p>The red line is the final path searched by dijkstra algorithm frm the visibility graphs.</p>
+<section id="algorithms">
+<h2>Algorithms<a class="headerlink" href="#algorithms" title="Permalink to this headline"></a></h2>
+<p>In this chapter, how does the visibility road map planner search a path.</p>
+<p>We assume this planner can be provided these information in the below figure.</p>
+<ul class="simple">
+<li><ol class="arabic simple">
+<li><p>Start point (Red point)</p></li>
+</ol>
+</li>
+<li><ol class="arabic simple" start="2">
+<li><p>Goal point (Blue point)</p></li>
+</ol>
+</li>
+<li><ol class="arabic simple" start="3">
+<li><p>Obstacle polygons (Black lines)</p></li>
+</ol>
+</li>
+</ul>
+<a class="reference internal image-reference" href="../../../_images/step0.png"><img alt="../../../_images/step0.png" src="../../../_images/step0.png" style="width: 400px;" /></a>
+<section id="step1-generate-visibility-nodes-based-on-polygon-obstacles">
+<h3>Step1: Generate visibility nodes based on polygon obstacles<a class="headerlink" href="#step1-generate-visibility-nodes-based-on-polygon-obstacles" title="Permalink to this headline"></a></h3>
+<p>The nodes are generated by expanded these polygons vertexes like the below figure:</p>
+<a class="reference internal image-reference" href="../../../_images/step1.png"><img alt="../../../_images/step1.png" src="../../../_images/step1.png" style="width: 400px;" /></a>
+<p>Each polygon vertex is expanded outward from the vector of adjacent vertices.</p>
+<p>The start and goal point are included as nodes as well.</p>
+</section>
+<section id="step2-generate-visibility-graphs-connecting-the-nodes">
+<h3>Step2: Generate visibility graphs connecting the nodes.<a class="headerlink" href="#step2-generate-visibility-graphs-connecting-the-nodes" title="Permalink to this headline"></a></h3>
+<p>When connecting the nodes, the arc between two nodes is checked to collided or not to each obstacles.</p>
+<p>If the arc is collided, the graph is removed.</p>
+<p>The blue lines are generated visibility graphs in the figure:</p>
+<a class="reference internal image-reference" href="../../../_images/step2.png"><img alt="../../../_images/step2.png" src="../../../_images/step2.png" style="width: 400px;" /></a>
+</section>
+<section id="step3-search-the-shortest-path-in-the-graphs-using-dijkstra-algorithm">
+<h3>Step3: Search the shortest path in the graphs using Dijkstra algorithm<a class="headerlink" href="#step3-search-the-shortest-path-in-the-graphs-using-dijkstra-algorithm" title="Permalink to this headline"></a></h3>
+<p>The red line is searched path in the figure:</p>
+<a class="reference internal image-reference" href="../../../_images/step3.png"><img alt="../../../_images/step3.png" src="../../../_images/step3.png" style="width: 400px;" /></a>
+<p>You can find the details of Dijkstra algorithm in <a class="reference internal" href="../grid_base_search/grid_base_search.html#dijkstra"><span class="std std-ref">Dijkstra algorithm</span></a>.</p>
+</section>
+<section id="references">
+<h3>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h3>
+<ul class="simple">
+<li><p><a class="reference external" href="https://en.wikipedia.org/wiki/Visibility_graph">Visibility graph - Wikipedia</a></p></li>
+</ul>
+</section>
+</section>
+</section>
+
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+<li class="toctree-l2"><a class="reference internal" href="../dynamic_window_approach/dynamic_window_approach.html">Dynamic Window Approach</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../prm_planner/prm_planner.html">Probabilistic Road-Map (PRM) planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../visibility_road_map_planner/visibility_road_map_planner.html">Visibility Road-Map planner</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Voronoi Road-Map planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../rrt/rrt.html">Rapidly-Exploring Random Trees (RRT)</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cubic_spline/cubic_spline.html">Cubic spline planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../bspline_path/bspline_path.html">B-Spline planning</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../bezier_path/bezier_path.html">Bezier path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../quintic_polynomials_planner/quintic_polynomials_planner.html">Quintic polynomials planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../dubins_path/dubins_path.html">Dubins path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../reeds_shepp_path/reeds_shepp_path.html">Reeds Shepp planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_path/lqr_path.html">LQR based path planning</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../hybridastar/hybridastar.html">Hybrid a star</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../frenet_frame_path/frenet_frame_path.html">Optimal Trajectory in a Frenet Frame</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../coverage_path/coverage_path.html">Coverage path planner</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_tracking/path_tracking.html">Path Tracking</a></li>
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+
+ <section id="voronoi-road-map-planning">
+<h1>Voronoi Road-Map planning<a class="headerlink" href="#voronoi-road-map-planning" title="Permalink to this headline"></a></h1>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/VoronoiRoadMap/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathPlanning/VoronoiRoadMap/animation.gif" />
+<p>This Voronoi road-map planner uses Dijkstra method for graph search.</p>
+<p>In the animation, blue points are Voronoi points,</p>
+<p>Cyan crosses mean searched points with Dijkstra method,</p>
+<p>The red line is the final path of Vornoi Road-Map.</p>
+<p>Ref:</p>
+<ul class="simple">
+<li><p><a class="reference external" href="https://www.cs.cmu.edu/~motionplanning/lecture/Chap5-RoadMap-Methods_howie.pdf">Robotic Motion Planning</a></p></li>
+</ul>
+</section>
+
+
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+ </div>
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+ <section id="nonlinear-model-predictive-control-with-c-gmres">
+<h1>Nonlinear Model Predictive Control with C-GMRES<a class="headerlink" href="#nonlinear-model-predictive-control-with-c-gmres" title="Permalink to this headline"></a></h1>
+<a class="reference internal image-reference" href="../../../_images/cgmres_nmpc_1_0.png"><img alt="../../../_images/cgmres_nmpc_1_0.png" src="../../../_images/cgmres_nmpc_1_0.png" style="width: 600px;" /></a>
+<a class="reference internal image-reference" href="../../../_images/cgmres_nmpc_2_0.png"><img alt="../../../_images/cgmres_nmpc_2_0.png" src="../../../_images/cgmres_nmpc_2_0.png" style="width: 600px;" /></a>
+<a class="reference internal image-reference" href="../../../_images/cgmres_nmpc_3_0.png"><img alt="../../../_images/cgmres_nmpc_3_0.png" src="../../../_images/cgmres_nmpc_3_0.png" style="width: 600px;" /></a>
+<a class="reference internal image-reference" href="../../../_images/cgmres_nmpc_4_0.png"><img alt="../../../_images/cgmres_nmpc_4_0.png" src="../../../_images/cgmres_nmpc_4_0.png" style="width: 600px;" /></a>
+<figure class="align-default">
+<img alt="gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/cgmres_nmpc/animation.gif" />
+</figure>
+<section id="mathematical-formulation">
+<h2>Mathematical Formulation<a class="headerlink" href="#mathematical-formulation" title="Permalink to this headline"></a></h2>
+<p>Motion model is</p>
+<div class="math notranslate nohighlight">
+\[\dot{x}=vcos\theta\]</div>
+<div class="math notranslate nohighlight">
+\[\dot{y}=vsin\theta\]</div>
+<div class="math notranslate nohighlight">
+\[\dot{\theta}=\frac{v}{WB}sin(u_{\delta})\]</div>
+<p>(tan is not good for optimization)</p>
+<div class="math notranslate nohighlight">
+\[\dot{v}=u_a\]</div>
+<p>Cost function is</p>
+<div class="math notranslate nohighlight">
+\[J=\frac{1}{2}(u_a^2+u_{\delta}^2)-\phi_a d_a-\phi_\delta d_\delta\]</div>
+<p>Input constraints are</p>
+<div class="math notranslate nohighlight">
+\[|u_a| \leq u_{a,max}\]</div>
+<div class="math notranslate nohighlight">
+\[|u_\delta| \leq u_{\delta,max}\]</div>
+<p>So, Hamiltonian is</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}J=\frac{1}{2}(u_a^2+u_{\delta}^2)-\phi_a d_a-\phi_\delta d_\delta\\ +\lambda_1vcos\theta+\lambda_2vsin\theta+\lambda_3\frac{v}{WB}sin(u_{\delta})+\lambda_4u_a\\
++\rho_1(u_a^2+d_a^2+u_{a,max}^2)+\rho_2(u_\delta^2+d_\delta^2+u_{\delta,max}^2)\end{split}\]</div>
+<p>Partial differential equations of the Hamiltonian are:</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} \frac{\partial H}{\partial \bf{x}}=\\ \begin{bmatrix} \frac{\partial H}{\partial x}= 0&\\ \frac{\partial H}{\partial y}= 0&\\ \frac{\partial H}{\partial \theta}= -\lambda_1vsin\theta+\lambda_2vcos\theta&\\ \frac{\partial H}{\partial v}=-\lambda_1cos\theta+\lambda_2sin\theta+\lambda_3\frac{1}{WB}sin(u_{\delta})&\\ \end{bmatrix} \\ \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} \frac{\partial H}{\partial \bf{u}}=\\ \begin{bmatrix} \frac{\partial H}{\partial u_a}= u_a+\lambda_4+2\rho_1u_a&\\ \frac{\partial H}{\partial u_\delta}= u_\delta+\lambda_3\frac{v}{WB}cos(u_{\delta})+2\rho_2u_\delta&\\ \frac{\partial H}{\partial d_a}= -\phi_a+2\rho_1d_a&\\ \frac{\partial H}{\partial d_\delta}=-\phi_\delta+2\rho_2d_\delta&\\ \end{bmatrix} \\ \end{equation*}\)</span></p>
+</section>
+<section id="ref">
+<h2>Ref<a class="headerlink" href="#ref" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://github.com/Shunichi09/nonlinear_control">Shunichi09/nonlinear_control: Implementing the nonlinear model
+predictive control, sliding mode
+control</a></p></li>
+<li><p><a class="reference external" href="https://qiita.com/MENDY/items/4108190a579395053924">非線形モデル予測制御におけるCGMRES法をpythonで実装する -
+Qiita</a></p></li>
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+<span id="id1"></span><h1>Linear–quadratic regulator (LQR) speed and steering control<a class="headerlink" href="#linearquadratic-regulator-lqr-speed-and-steering-control" title="Permalink to this headline"></a></h1>
+<p>Path tracking simulation with LQR speed and steering control.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/lqr_speed_steer_control/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/lqr_speed_steer_control/animation.gif" />
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="http://ieeexplore.ieee.org/document/5940562/">Towards fully autonomous driving: Systems and algorithms</a></p></li>
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+<li class="toctree-l2"><a class="reference internal" href="../lqr_speed_and_steering_control/lqr_speed_and_steering_control.html">Linear–quadratic regulator (LQR) speed and steering control</a></li>
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+ <section id="linearquadratic-regulator-lqr-steering-control">
+<span id="id1"></span><h1>Linear–quadratic regulator (LQR) steering control<a class="headerlink" href="#linearquadratic-regulator-lqr-steering-control" title="Permalink to this headline"></a></h1>
+<p>Path tracking simulation with LQR steering control and PID speed
+control.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/lqr_steer_control/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/lqr_steer_control/animation.gif" />
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://github.com/ApolloAuto/apollo">ApolloAuto/apollo: An open autonomous driving platform</a></p></li>
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+<li class="toctree-l2 current"><a class="current reference internal" href="#">Model predictive speed and steering control</a><ul>
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+
+ <section id="model-predictive-speed-and-steering-control">
+<h1>Model predictive speed and steering control<a class="headerlink" href="#model-predictive-speed-and-steering-control" title="Permalink to this headline"></a></h1>
+<figure class="align-default" id="id1">
+<img alt="Model predictive speed and steering control" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/model_predictive_speed_and_steer_control/animation.gif?raw=true" />
+<figcaption>
+<p><span class="caption-text">Model predictive speed and steering control</span><a class="headerlink" href="#id1" title="Permalink to this image"></a></p>
+</figcaption>
+</figure>
+<p>code:</p>
+<p><a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py">PythonRobotics/model_predictive_speed_and_steer_control.py at master ·
+AtsushiSakai/PythonRobotics</a></p>
+<p>This is a path tracking simulation using model predictive control (MPC).</p>
+<p>The MPC controller controls vehicle speed and steering base on
+linearized model.</p>
+<p>This code uses cvxpy as an optimization modeling tool.</p>
+<ul class="simple">
+<li><p><a class="reference external" href="http://www.cvxpy.org/">Welcome to CVXPY 1.0 — CVXPY 1.0.6
+documentation</a></p></li>
+</ul>
+<section id="mpc-modeling">
+<h2>MPC modeling<a class="headerlink" href="#mpc-modeling" title="Permalink to this headline"></a></h2>
+<p>State vector is:</p>
+<div class="math notranslate nohighlight">
+\[z = [x, y, v,\phi]\]</div>
+<p>x: x-position, y:y-position, v:velocity, φ: yaw angle</p>
+<p>Input vector is:</p>
+<div class="math notranslate nohighlight">
+\[u = [a, \delta]\]</div>
+<p>a: accellation, δ: steering angle</p>
+<p>The MPC cotroller minimize this cost function for path tracking:</p>
+<div class="math notranslate nohighlight">
+\[min\ Q_f(z_{T,ref}-z_{T})^2+Q\Sigma({z_{t,ref}-z_{t}})^2+R\Sigma{u_t}^2+R_d\Sigma({u_{t+1}-u_{t}})^2\]</div>
+<p>z_ref come from target path and speed.</p>
+<p>subject to:</p>
+<ul class="simple">
+<li><p>Linearlied vehicle model</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[z_{t+1}=Az_t+Bu+C\]</div>
+<ul class="simple">
+<li><p>Maximum steering speed</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[|u_{t+1}-u_{t}|<du_{max}\]</div>
+<ul class="simple">
+<li><p>Maximum steering angle</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[|u_{t}|<u_{max}\]</div>
+<ul class="simple">
+<li><p>Initial state</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[z_0 = z_{0,ob}\]</div>
+<ul class="simple">
+<li><p>Maximum and minimum speed</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[v_{min} < v_t < v_{max}\]</div>
+<ul class="simple">
+<li><p>Maximum and minimum input</p></li>
+</ul>
+<div class="math notranslate nohighlight">
+\[u_{min} < u_t < u_{max}\]</div>
+<p>This is implemented at</p>
+<p><a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/blob/f51a73f47cb922a12659f8ce2d544c347a2a8156/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py#L247-L301">PythonRobotics/model_predictive_speed_and_steer_control.py at
+f51a73f47cb922a12659f8ce2d544c347a2a8156 ·
+AtsushiSakai/PythonRobotics</a></p>
+</section>
+<section id="vehicle-model-linearization">
+<h2>Vehicle model linearization<a class="headerlink" href="#vehicle-model-linearization" title="Permalink to this headline"></a></h2>
+<p>Vehicle model is</p>
+<div class="math notranslate nohighlight">
+\[\dot{x} = vcos(\phi)\]</div>
+<div class="math notranslate nohighlight">
+\[\dot{y} = vsin((\phi)\]</div>
+<div class="math notranslate nohighlight">
+\[\dot{v} = a\]</div>
+<div class="math notranslate nohighlight">
+\[\dot{\phi} = \frac{vtan(\delta)}{L}\]</div>
+<p>ODE is</p>
+<div class="math notranslate nohighlight">
+\[\dot{z} =\frac{\partial }{\partial z} z = f(z, u) = A'z+B'u\]</div>
+<p>where</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} A' = \begin{bmatrix} \frac{\partial }{\partial x}vcos(\phi) & \frac{\partial }{\partial y}vcos(\phi) & \frac{\partial }{\partial v}vcos(\phi) & \frac{\partial }{\partial \phi}vcos(\phi)\\ \frac{\partial }{\partial x}vsin(\phi) & \frac{\partial }{\partial y}vsin(\phi) & \frac{\partial }{\partial v}vsin(\phi) & \frac{\partial }{\partial \phi}vsin(\phi)\\ \frac{\partial }{\partial x}a& \frac{\partial }{\partial y}a& \frac{\partial }{\partial v}a& \frac{\partial }{\partial \phi}a\\ \frac{\partial }{\partial x}\frac{vtan(\delta)}{L}& \frac{\partial }{\partial y}\frac{vtan(\delta)}{L}& \frac{\partial }{\partial v}\frac{vtan(\delta)}{L}& \frac{\partial }{\partial \phi}\frac{vtan(\delta)}{L}\\ \end{bmatrix} \\ = \begin{bmatrix} 0 & 0 & cos(\bar{\phi}) & -\bar{v}sin(\bar{\phi})\\ 0 & 0 & sin(\bar{\phi}) & \bar{v}cos(\bar{\phi}) \\ 0 & 0 & 0 & 0 \\ 0 & 0 &\frac{tan(\bar{\delta})}{L} & 0 \\ \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} B' = \begin{bmatrix} \frac{\partial }{\partial a}vcos(\phi) & \frac{\partial }{\partial \delta}vcos(\phi)\\ \frac{\partial }{\partial a}vsin(\phi) & \frac{\partial }{\partial \delta}vsin(\phi)\\ \frac{\partial }{\partial a}a & \frac{\partial }{\partial \delta}a\\ \frac{\partial }{\partial a}\frac{vtan(\delta)}{L} & \frac{\partial }{\partial \delta}\frac{vtan(\delta)}{L}\\ \end{bmatrix} \\ = \begin{bmatrix} 0 & 0 \\ 0 & 0 \\ 1 & 0 \\ 0 & \frac{\bar{v}}{Lcos^2(\bar{\delta})} \\ \end{bmatrix} \end{equation*}\)</span></p>
+<p>You can get a discrete-time mode with Forward Euler Discretization with
+sampling time dt.</p>
+<div class="math notranslate nohighlight">
+\[z_{k+1}=z_k+f(z_k,u_k)dt\]</div>
+<p>Using first degree Tayer expantion around zbar and ubar</p>
+<div class="math notranslate nohighlight">
+\[z_{k+1}=z_k+(f(\bar{z},\bar{u})+A'z_k+B'u_k-A'\bar{z}-B'\bar{u})dt\]</div>
+<div class="math notranslate nohighlight">
+\[z_{k+1}=(I + dtA')z_k+(dtB')u_k + (f(\bar{z},\bar{u})-A'\bar{z}-B'\bar{u})dt\]</div>
+<p>So,</p>
+<div class="math notranslate nohighlight">
+\[z_{k+1}=Az_k+Bu_k +C\]</div>
+<p>where,</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} A = (I + dtA')\\ = \begin{bmatrix} 1 & 0 & cos(\bar{\phi})dt & -\bar{v}sin(\bar{\phi})dt\\ 0 & 1 & sin(\bar{\phi})dt & \bar{v}cos(\bar{\phi})dt \\ 0 & 0 & 1 & 0 \\ 0 & 0 &\frac{tan(\bar{\delta})}{L}dt & 1 \\ \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} B = dtB'\\ = \begin{bmatrix} 0 & 0 \\ 0 & 0 \\ dt & 0 \\ 0 & \frac{\bar{v}}{Lcos^2(\bar{\delta})}dt \\ \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} C = (f(\bar{z},\bar{u})-A'\bar{z}-B'\bar{u})dt\\ = dt( \begin{bmatrix} \bar{v}cos(\bar{\phi})\\ \bar{v}sin(\bar{\phi}) \\ \bar{a}\\ \frac{\bar{v}tan(\bar{\delta})}{L}\\ \end{bmatrix} - \begin{bmatrix} \bar{v}cos(\bar{\phi})-\bar{v}sin(\bar{\phi})\bar{\phi}\\ \bar{v}sin(\bar{\phi})+\bar{v}cos(\bar{\phi})\bar{\phi}\\ 0\\ \frac{\bar{v}tan(\bar{\delta})}{L}\\ \end{bmatrix} - \begin{bmatrix} 0\\ 0 \\ \bar{a}\\ \frac{\bar{v}\bar{\delta}}{Lcos^2(\bar{\delta})}\\ \end{bmatrix} )\\ = \begin{bmatrix} \bar{v}sin(\bar{\phi})\bar{\phi}dt\\ -\bar{v}cos(\bar{\phi})\bar{\phi}dt\\ 0\\ -\frac{\bar{v}\bar{\delta}}{Lcos^2(\bar{\delta})}dt\\ \end{bmatrix} \end{equation*}\)</span></p>
+<p>This equation is implemented at</p>
+<p><a class="reference external" href="https://github.com/AtsushiSakai/PythonRobotics/blob/eb6d1cbe6fc90c7be9210bf153b3a04f177cc138/PathTracking/model_predictive_speed_and_steer_control/model_predictive_speed_and_steer_control.py#L80-L102">PythonRobotics/model_predictive_speed_and_steer_control.py at
+eb6d1cbe6fc90c7be9210bf153b3a04f177cc138 ·
+AtsushiSakai/PythonRobotics</a></p>
+</section>
+<section id="reference">
+<h2>Reference<a class="headerlink" href="#reference" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="http://www.springer.com/us/book/9781461414322">Vehicle Dynamics and Control | Rajesh Rajamani |
+Springer</a></p></li>
+<li><p><a class="reference external" href="http://www.mpc.berkeley.edu/mpc-course-material">MPC Course Material - MPC Lab @
+UC-Berkeley</a></p></li>
+</ul>
+</section>
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+<li class="toctree-l1"><a class="reference internal" href="../path_planning/path_planning.html">Path Planning</a></li>
+<li class="toctree-l1 current"><a class="current reference internal" href="#">Path Tracking</a><ul>
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+<li class="toctree-l2"><a class="reference internal" href="stanley_control/stanley_control.html">Stanley control</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="lqr_steering_control/lqr_steering_control.html">Linear–quadratic regulator (LQR) steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="lqr_speed_and_steering_control/lqr_speed_and_steering_control.html">Linear–quadratic regulator (LQR) speed and steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control.html">Model predictive speed and steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="cgmres_nmpc/cgmres_nmpc.html">Nonlinear Model Predictive Control with C-GMRES</a></li>
+</ul>
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+<li class="toctree-l1"><a class="reference internal" href="../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="../control/control.html">Control</a></li>
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+<p class="caption" role="heading"><span class="caption-text">Contents</span></p>
+<ul>
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+<li class="toctree-l2"><a class="reference internal" href="pure_pursuit_tracking/pure_pursuit_tracking.html#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="stanley_control/stanley_control.html">Stanley control</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="stanley_control/stanley_control.html#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="rear_wheel_feedback_control/rear_wheel_feedback_control.html">Rear wheel feedback control</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="rear_wheel_feedback_control/rear_wheel_feedback_control.html#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="lqr_steering_control/lqr_steering_control.html">Linear–quadratic regulator (LQR) steering control</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="lqr_steering_control/lqr_steering_control.html#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="lqr_speed_and_steering_control/lqr_speed_and_steering_control.html">Linear–quadratic regulator (LQR) speed and steering control</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="lqr_speed_and_steering_control/lqr_speed_and_steering_control.html#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control.html">Model predictive speed and steering control</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control.html#mpc-modeling">MPC modeling</a></li>
+<li class="toctree-l2"><a class="reference internal" href="model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control.html#vehicle-model-linearization">Vehicle model linearization</a></li>
+<li class="toctree-l2"><a class="reference internal" href="model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control.html#reference">Reference</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="cgmres_nmpc/cgmres_nmpc.html">Nonlinear Model Predictive Control with C-GMRES</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="cgmres_nmpc/cgmres_nmpc.html#mathematical-formulation">Mathematical Formulation</a></li>
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+<li class="toctree-l2"><a class="reference internal" href="../stanley_control/stanley_control.html">Stanley control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../rear_wheel_feedback_control/rear_wheel_feedback_control.html">Rear wheel feedback control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_steering_control/lqr_steering_control.html">Linear–quadratic regulator (LQR) steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_speed_and_steering_control/lqr_speed_and_steering_control.html">Linear–quadratic regulator (LQR) speed and steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control.html">Model predictive speed and steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cgmres_nmpc/cgmres_nmpc.html">Nonlinear Model Predictive Control with C-GMRES</a></li>
+</ul>
+</li>
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+
+ <section id="pure-pursuit-tracking">
+<h1>Pure pursuit tracking<a class="headerlink" href="#pure-pursuit-tracking" title="Permalink to this headline"></a></h1>
+<p>Path tracking simulation with pure pursuit steering control and PID
+speed control.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/pure_pursuit/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/pure_pursuit/animation.gif" />
+<p>The red line is a target course, the green cross means the target point
+for pure pursuit control, the blue line is the tracking.</p>
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://arxiv.org/abs/1604.07446">A Survey of Motion Planning and Control Techniques for Self-driving
+Urban Vehicles</a></p></li>
+</ul>
+</section>
+</section>
+
+
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+<li class="toctree-l1 current"><a class="reference internal" href="../path_tracking.html">Path Tracking</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../pure_pursuit_tracking/pure_pursuit_tracking.html">Pure pursuit tracking</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../stanley_control/stanley_control.html">Stanley control</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Rear wheel feedback control</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_steering_control/lqr_steering_control.html">Linear–quadratic regulator (LQR) steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_speed_and_steering_control/lqr_speed_and_steering_control.html">Linear–quadratic regulator (LQR) speed and steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control.html">Model predictive speed and steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cgmres_nmpc/cgmres_nmpc.html">Nonlinear Model Predictive Control with C-GMRES</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../aerial_navigation/aerial_navigation.html">Aerial Navigation</a></li>
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+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
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+
+ <section id="rear-wheel-feedback-control">
+<h1>Rear wheel feedback control<a class="headerlink" href="#rear-wheel-feedback-control" title="Permalink to this headline"></a></h1>
+<p>Path tracking simulation with rear wheel feedback steering control and
+PID speed control.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/rear_wheel_feedback/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/rear_wheel_feedback/animation.gif" />
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://arxiv.org/abs/1604.07446">A Survey of Motion Planning and Control Techniques for Self-driving
+Urban Vehicles</a></p></li>
+</ul>
+</section>
+</section>
+
+
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+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
+ <a href="../stanley_control/stanley_control.html" class="btn btn-neutral float-left" title="Stanley control" accesskey="p" rel="prev"><span class="fa fa-arrow-circle-left" aria-hidden="true"></span> Previous</a>
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+<li class="toctree-l1"><a class="reference internal" href="../../path_planning/path_planning.html">Path Planning</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../path_tracking.html">Path Tracking</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../pure_pursuit_tracking/pure_pursuit_tracking.html">Pure pursuit tracking</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">Stanley control</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../rear_wheel_feedback_control/rear_wheel_feedback_control.html">Rear wheel feedback control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_steering_control/lqr_steering_control.html">Linear–quadratic regulator (LQR) steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../lqr_speed_and_steering_control/lqr_speed_and_steering_control.html">Linear–quadratic regulator (LQR) speed and steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../model_predictive_speed_and_steering_control/model_predictive_speed_and_steering_control.html">Model predictive speed and steering control</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../cgmres_nmpc/cgmres_nmpc.html">Nonlinear Model Predictive Control with C-GMRES</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../../arm_navigation/arm_navigation.html">Arm Navigation</a></li>
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+ <li><a href="../path_tracking.html">Path Tracking</a> »</li>
+ <li>Stanley control</li>
+ <li class="wy-breadcrumbs-aside">
+ <a href="https://github.com/AtsushiSakai/PythonRobotics/blob/master/docs/modules/path_tracking/stanley_control/stanley_control_main.rst" class="fa fa-github"> Edit on GitHub</a>
+ </li>
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+ <hr/>
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+ <div role="main" class="document" itemscope="itemscope" itemtype="http://schema.org/Article">
+ <div itemprop="articleBody">
+
+ <section id="stanley-control">
+<h1>Stanley control<a class="headerlink" href="#stanley-control" title="Permalink to this headline"></a></h1>
+<p>Path tracking simulation with Stanley steering control and PID speed
+control.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/stanley_controller/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/PathTracking/stanley_controller/animation.gif" />
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="http://robots.stanford.edu/papers/thrun.stanley05.pdf">Stanley: The robot that won the DARPA grand
+challenge</a></p></li>
+<li><p><a class="reference external" href="https://www.ri.cmu.edu/pub_files/2009/2/Automatic_Steering_Methods_for_Autonomous_Automobile_Path_Tracking.pdf">Automatic Steering Methods for Autonomous Automobile Path
+Tracking</a></p></li>
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+<li class="toctree-l1"><a class="reference internal" href="../../../getting_started.html">Getting Started</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../introduction.html">Introduction</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../localization/localization.html">Localization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../slam.html">SLAM</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../iterative_closest_point_matching/iterative_closest_point_matching.html">Iterative Closest Point (ICP) Matching</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../ekf_slam/ekf_slam.html">EKF SLAM</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">FastSLAM1.0</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#simulation">Simulation</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#introduction">Introduction</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#algorithm-walk-through">Algorithm walk through</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#predict">1- Predict</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#update">2- Update</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#resampling">3- Resampling</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#references">References</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../FastSLAM2/FastSLAM2.html">FastSLAM 2.0</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../graph_slam/graph_slam.html">Graph based SLAM</a></li>
+</ul>
+</li>
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+
+ <section id="fastslam1-0">
+<h1>FastSLAM1.0<a class="headerlink" href="#fastslam1-0" title="Permalink to this headline"></a></h1>
+<figure class="align-default">
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/FastSLAM1/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/FastSLAM1/animation.gif" />
+</figure>
+<section id="simulation">
+<h2>Simulation<a class="headerlink" href="#simulation" title="Permalink to this headline"></a></h2>
+<p>This is a feature based SLAM example using FastSLAM 1.0.</p>
+<a class="reference internal image-reference" href="../../../_images/FastSLAM1_1_0.png"><img alt="../../../_images/FastSLAM1_1_0.png" src="../../../_images/FastSLAM1_1_0.png" style="width: 600px;" /></a>
+<p>The blue line is ground truth, the black line is dead reckoning, the red
+line is the estimated trajectory with FastSLAM.</p>
+<p>The red points are particles of FastSLAM.</p>
+<p>Black points are landmarks, blue crosses are estimated landmark
+positions by FastSLAM.</p>
+</section>
+<section id="introduction">
+<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
+<p>FastSLAM algorithm implementation is based on particle filters and
+belongs to the family of probabilistic SLAM approaches. It is used with
+feature-based maps (see gif above) or with occupancy grid maps.</p>
+<p>As it is shown, the particle filter differs from EKF by representing the
+robot’s estimation through a set of particles. Each single particle has
+an independent belief, as it holds the pose <span class="math notranslate nohighlight">\((x, y, \theta)\)</span> and
+an array of landmark locations
+<span class="math notranslate nohighlight">\([(x_1, y_1), (x_2, y_2), ... (x_n, y_n)]\)</span> for n landmarks.</p>
+<ul class="simple">
+<li><p>The blue line is the true trajectory</p></li>
+<li><p>The red line is the estimated trajectory</p></li>
+<li><p>The red dots represent the distribution of particles</p></li>
+<li><p>The black line represent dead reckoning trajectory</p></li>
+<li><p>The blue x is the observed and estimated landmarks</p></li>
+<li><p>The black x is the true landmark</p></li>
+</ul>
+<p>I.e. Each particle maintains a deterministic pose and n-EKFs for each
+landmark and update it with each measurement.</p>
+</section>
+<section id="algorithm-walk-through">
+<h2>Algorithm walk through<a class="headerlink" href="#algorithm-walk-through" title="Permalink to this headline"></a></h2>
+<p>The particles are initially drawn from a uniform distribution the
+represent the initial uncertainty. At each time step we do:</p>
+<ul class="simple">
+<li><p>Predict the pose for each particle by using <span class="math notranslate nohighlight">\(u\)</span> and the motion
+model (the landmarks are not updated).</p></li>
+<li><p>Update the particles with observations <span class="math notranslate nohighlight">\(z\)</span>, where the weights
+are adjusted based on how likely the particle to have the correct
+pose given the sensor measurement</p></li>
+<li><p>Resampling such that the particles with the largest weights survive
+and the unlikely ones with the lowest weights die out.</p></li>
+</ul>
+</section>
+<section id="predict">
+<h2>1- Predict<a class="headerlink" href="#predict" title="Permalink to this headline"></a></h2>
+<p>The following equations and code snippets we can see how the particles
+distribution evolves in case we provide only the control <span class="math notranslate nohighlight">\((v,w)\)</span>,
+which are the linear and angular velocity respectively.</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} F= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} B= \begin{bmatrix} \Delta t cos(\theta) & 0\\ \Delta t sin(\theta) & 0\\ 0 & \Delta t \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} X = FX + BU \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} \begin{bmatrix} x_{t+1} \\ y_{t+1} \\ \theta_{t+1} \end{bmatrix}= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\begin{bmatrix} x_{t} \\ y_{t} \\ \theta_{t} \end{bmatrix}+ \begin{bmatrix} \Delta t cos(\theta) & 0\\ \Delta t sin(\theta) & 0\\ 0 & \Delta t \end{bmatrix} \begin{bmatrix} v_{t} + \sigma_v\\ w_{t} + \sigma_w\\ \end{bmatrix} \end{equation*}\)</span></p>
+<p>The following snippets playback the recorded trajectory of each
+particle.</p>
+<p>To get the insight of the motion model change the value of <span class="math notranslate nohighlight">\(R\)</span> and
+re-run the cells again. As R is the parameters that indicates how much
+we trust that the robot executed the motion commands.</p>
+<p>It is interesting to notice also that only motion will increase the
+uncertainty in the system as the particles start to spread out more. If
+observations are included the uncertainty will decrease and particles
+will converge to the correct estimate.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># CODE SNIPPET #</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">math</span>
+<span class="kn">from</span> <span class="nn">copy</span> <span class="kn">import</span> <span class="n">deepcopy</span>
+<span class="c1"># Fast SLAM covariance</span>
+<span class="n">Q</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="mf">3.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">10.0</span><span class="p">)])</span><span class="o">**</span><span class="mi">2</span>
+<span class="n">R</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">20.0</span><span class="p">)])</span><span class="o">**</span><span class="mi">2</span>
+
+<span class="c1"># Simulation parameter</span>
+<span class="n">Qsim</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="mf">0.3</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">2.0</span><span class="p">)])</span><span class="o">**</span><span class="mi">2</span>
+<span class="n">Rsim</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="mf">0.5</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">10.0</span><span class="p">)])</span><span class="o">**</span><span class="mi">2</span>
+<span class="n">OFFSET_YAWRATE_NOISE</span> <span class="o">=</span> <span class="mf">0.01</span>
+
+<span class="n">DT</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="c1"># time tick [s]</span>
+<span class="n">SIM_TIME</span> <span class="o">=</span> <span class="mf">50.0</span> <span class="c1"># simulation time [s]</span>
+<span class="n">MAX_RANGE</span> <span class="o">=</span> <span class="mf">20.0</span> <span class="c1"># maximum observation range</span>
+<span class="n">M_DIST_TH</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="c1"># Threshold of Mahalanobis distance for data association.</span>
+<span class="n">STATE_SIZE</span> <span class="o">=</span> <span class="mi">3</span> <span class="c1"># State size [x,y,yaw]</span>
+<span class="n">LM_SIZE</span> <span class="o">=</span> <span class="mi">2</span> <span class="c1"># LM srate size [x,y]</span>
+<span class="n">N_PARTICLE</span> <span class="o">=</span> <span class="mi">100</span> <span class="c1"># number of particle</span>
+<span class="n">NTH</span> <span class="o">=</span> <span class="n">N_PARTICLE</span> <span class="o">/</span> <span class="mf">1.5</span> <span class="c1"># Number of particle for re-sampling</span>
+
+<span class="k">class</span> <span class="nc">Particle</span><span class="p">:</span>
+
+ <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">N_LM</span><span class="p">):</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">w</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="n">N_PARTICLE</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">y</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">yaw</span> <span class="o">=</span> <span class="mf">0.0</span>
+ <span class="c1"># landmark x-y positions</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">lm</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N_LM</span><span class="p">,</span> <span class="n">LM_SIZE</span><span class="p">))</span>
+ <span class="c1"># landmark position covariance</span>
+ <span class="bp">self</span><span class="o">.</span><span class="n">lmP</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N_LM</span> <span class="o">*</span> <span class="n">LM_SIZE</span><span class="p">,</span> <span class="n">LM_SIZE</span><span class="p">))</span>
+
+<span class="k">def</span> <span class="nf">motion_model</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">u</span><span class="p">):</span>
+ <span class="n">F</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]])</span>
+
+ <span class="n">B</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">DT</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="p">[</span><span class="n">DT</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">DT</span><span class="p">]])</span>
+ <span class="n">x</span> <span class="o">=</span> <span class="n">F</span> <span class="o">@</span> <span class="n">x</span> <span class="o">+</span> <span class="n">B</span> <span class="o">@</span> <span class="n">u</span>
+
+ <span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+ <span class="k">return</span> <span class="n">x</span>
+
+<span class="k">def</span> <span class="nf">predict_particles</span><span class="p">(</span><span class="n">particles</span><span class="p">,</span> <span class="n">u</span><span class="p">):</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">):</span>
+ <span class="n">px</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">STATE_SIZE</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+ <span class="n">px</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">x</span>
+ <span class="n">px</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">y</span>
+ <span class="n">px</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">yaw</span>
+ <span class="n">ud</span> <span class="o">=</span> <span class="n">u</span> <span class="o">+</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">)</span> <span class="o">@</span> <span class="n">R</span><span class="p">)</span><span class="o">.</span><span class="n">T</span> <span class="c1"># add noise</span>
+ <span class="n">px</span> <span class="o">=</span> <span class="n">motion_model</span><span class="p">(</span><span class="n">px</span><span class="p">,</span> <span class="n">ud</span><span class="p">)</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="n">px</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">y</span> <span class="o">=</span> <span class="n">px</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">yaw</span> <span class="o">=</span> <span class="n">px</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+
+ <span class="k">return</span> <span class="n">particles</span>
+
+<span class="k">def</span> <span class="nf">pi_2_pi</span><span class="p">(</span><span class="n">angle</span><span class="p">):</span>
+ <span class="k">return</span> <span class="p">(</span><span class="n">angle</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="o">%</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="o">-</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span>
+
+<span class="c1"># END OF SNIPPET</span>
+
+<span class="n">N_LM</span> <span class="o">=</span> <span class="mi">0</span>
+<span class="n">particles</span> <span class="o">=</span> <span class="p">[</span><span class="n">Particle</span><span class="p">(</span><span class="n">N_LM</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">)]</span>
+<span class="n">time</span><span class="o">=</span> <span class="mf">0.0</span>
+<span class="n">v</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="c1"># [m/s]</span>
+<span class="n">yawrate</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="c1"># [rad/s]</span>
+<span class="n">u</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">v</span><span class="p">,</span> <span class="n">yawrate</span><span class="p">])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="n">history</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="k">while</span> <span class="n">SIM_TIME</span> <span class="o">>=</span> <span class="n">time</span><span class="p">:</span>
+ <span class="n">time</span> <span class="o">+=</span> <span class="n">DT</span>
+ <span class="n">particles</span> <span class="o">=</span> <span class="n">predict_particles</span><span class="p">(</span><span class="n">particles</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span>
+ <span class="n">history</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">deepcopy</span><span class="p">(</span><span class="n">particles</span><span class="p">))</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># from IPython.html.widgets import *</span>
+<span class="kn">from</span> <span class="nn">ipywidgets</span> <span class="kn">import</span> <span class="o">*</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="o">%</span><span class="k">matplotlib</span> inline
+
+<span class="c1"># playback the recorded motion of the particles</span>
+<span class="k">def</span> <span class="nf">plot_particles</span><span class="p">(</span><span class="n">t</span><span class="o">=</span><span class="mi">0</span><span class="p">):</span>
+ <span class="n">x</span> <span class="o">=</span> <span class="p">[]</span>
+ <span class="n">y</span> <span class="o">=</span> <span class="p">[]</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">history</span><span class="p">[</span><span class="n">t</span><span class="p">])):</span>
+ <span class="n">x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">history</span><span class="p">[</span><span class="n">t</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
+ <span class="n">y</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">history</span><span class="p">[</span><span class="n">t</span><span class="p">][</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">y</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">figtext</span><span class="p">(</span><span class="mf">0.15</span><span class="p">,</span><span class="mf">0.82</span><span class="p">,</span><span class="s1">'t = '</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">t</span><span class="p">))</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">y</span><span class="p">,</span> <span class="s1">'.r'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">([</span><span class="o">-</span><span class="mi">20</span><span class="p">,</span><span class="mi">20</span><span class="p">,</span> <span class="o">-</span><span class="mi">5</span><span class="p">,</span><span class="mi">25</span><span class="p">])</span>
+
+<span class="n">interact</span><span class="p">(</span><span class="n">plot_particles</span><span class="p">,</span> <span class="n">t</span><span class="o">=</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span><span class="nb">len</span><span class="p">(</span><span class="n">history</span><span class="p">)</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">));</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span>interactive(children=(IntSlider(value=0, description='t', max=499), Output()), _dom_classes=('widget-interact'…
+</pre></div>
+</div>
+</section>
+<section id="update">
+<h2>2- Update<a class="headerlink" href="#update" title="Permalink to this headline"></a></h2>
+<p>For the update step it is useful to observe a single particle and the
+effect of getting a new measurements on the weight of the particle.</p>
+<p>As mentioned earlier, each particle maintains <span class="math notranslate nohighlight">\(N\)</span> <span class="math notranslate nohighlight">\(2x2\)</span> EKFs
+to estimate the landmarks, which includes the EKF process described in
+the EKF notebook. The difference is the change in the weight of the
+particle according to how likely the measurement is.</p>
+<p>The weight is updated according to the following equation:</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} w_i = |2\pi Q|^{\frac{-1}{2}} exp\{\frac{-1}{2}(z_t - \hat z_i)^T Q^{-1}(z_t-\hat z_i)\} \end{equation*}\)</span></p>
+<p>Where, <span class="math notranslate nohighlight">\(w_i\)</span> is the computed weight, <span class="math notranslate nohighlight">\(Q\)</span> is the measurement
+covariance, <span class="math notranslate nohighlight">\(z_t\)</span> is the actual measurment and <span class="math notranslate nohighlight">\(\hat z_i\)</span> is
+the predicted measurement of particle <span class="math notranslate nohighlight">\(i\)</span>.</p>
+<p>To experiment this, a single particle is initialized then passed an
+initial measurement, which results in a relatively average weight.
+However, setting the particle coordinate to a wrong value to simulate
+wrong estimation will result in a very low weight. The lower the weight
+the less likely that this particle will be drawn during resampling and
+probably will die out.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># CODE SNIPPET #</span>
+<span class="k">def</span> <span class="nf">observation</span><span class="p">(</span><span class="n">xTrue</span><span class="p">,</span> <span class="n">xd</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">RFID</span><span class="p">):</span>
+
+ <span class="c1"># calc true state</span>
+ <span class="n">xTrue</span> <span class="o">=</span> <span class="n">motion_model</span><span class="p">(</span><span class="n">xTrue</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span>
+
+ <span class="c1"># add noise to range observation</span>
+ <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">))</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">RFID</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">])):</span>
+
+ <span class="n">dx</span> <span class="o">=</span> <span class="n">RFID</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">xTrue</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">dy</span> <span class="o">=</span> <span class="n">RFID</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">xTrue</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">d</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">dx</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">dy</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+ <span class="n">angle</span> <span class="o">=</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">dy</span><span class="p">,</span> <span class="n">dx</span><span class="p">)</span> <span class="o">-</span> <span class="n">xTrue</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+ <span class="k">if</span> <span class="n">d</span> <span class="o"><=</span> <span class="n">MAX_RANGE</span><span class="p">:</span>
+ <span class="n">dn</span> <span class="o">=</span> <span class="n">d</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">()</span> <span class="o">*</span> <span class="n">Qsim</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="c1"># add noise</span>
+ <span class="n">anglen</span> <span class="o">=</span> <span class="n">angle</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">()</span> <span class="o">*</span> <span class="n">Qsim</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="c1"># add noise</span>
+ <span class="n">zi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">dn</span><span class="p">,</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">anglen</span><span class="p">),</span> <span class="n">i</span><span class="p">])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">3</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+ <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">z</span><span class="p">,</span> <span class="n">zi</span><span class="p">))</span>
+
+ <span class="c1"># add noise to input</span>
+ <span class="n">ud1</span> <span class="o">=</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">()</span> <span class="o">*</span> <span class="n">Rsim</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">ud2</span> <span class="o">=</span> <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">()</span> <span class="o">*</span> <span class="n">Rsim</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">+</span> <span class="n">OFFSET_YAWRATE_NOISE</span>
+ <span class="n">ud</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">ud1</span><span class="p">,</span> <span class="n">ud2</span><span class="p">])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+
+ <span class="n">xd</span> <span class="o">=</span> <span class="n">motion_model</span><span class="p">(</span><span class="n">xd</span><span class="p">,</span> <span class="n">ud</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">xTrue</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">xd</span><span class="p">,</span> <span class="n">ud</span>
+
+<span class="k">def</span> <span class="nf">update_with_observation</span><span class="p">(</span><span class="n">particles</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
+ <span class="k">for</span> <span class="n">iz</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">z</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:])):</span>
+
+ <span class="n">lmid</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">z</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="n">iz</span><span class="p">])</span>
+
+ <span class="k">for</span> <span class="n">ip</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">):</span>
+ <span class="c1"># new landmark</span>
+ <span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">particles</span><span class="p">[</span><span class="n">ip</span><span class="p">]</span><span class="o">.</span><span class="n">lm</span><span class="p">[</span><span class="n">lmid</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span> <span class="o"><=</span> <span class="mf">0.01</span><span class="p">:</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">ip</span><span class="p">]</span> <span class="o">=</span> <span class="n">add_new_lm</span><span class="p">(</span><span class="n">particles</span><span class="p">[</span><span class="n">ip</span><span class="p">],</span> <span class="n">z</span><span class="p">[:,</span> <span class="n">iz</span><span class="p">],</span> <span class="n">Q</span><span class="p">)</span>
+ <span class="c1"># known landmark</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">w</span> <span class="o">=</span> <span class="n">compute_weight</span><span class="p">(</span><span class="n">particles</span><span class="p">[</span><span class="n">ip</span><span class="p">],</span> <span class="n">z</span><span class="p">[:,</span> <span class="n">iz</span><span class="p">],</span> <span class="n">Q</span><span class="p">)</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">ip</span><span class="p">]</span><span class="o">.</span><span class="n">w</span> <span class="o">*=</span> <span class="n">w</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">ip</span><span class="p">]</span> <span class="o">=</span> <span class="n">update_landmark</span><span class="p">(</span><span class="n">particles</span><span class="p">[</span><span class="n">ip</span><span class="p">],</span> <span class="n">z</span><span class="p">[:,</span> <span class="n">iz</span><span class="p">],</span> <span class="n">Q</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">particles</span>
+
+<span class="k">def</span> <span class="nf">compute_weight</span><span class="p">(</span><span class="n">particle</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">Q</span><span class="p">):</span>
+ <span class="n">lm_id</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">z</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
+ <span class="n">xf</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">particle</span><span class="o">.</span><span class="n">lm</span><span class="p">[</span><span class="n">lm_id</span><span class="p">,</span> <span class="p">:])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+ <span class="n">Pf</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">particle</span><span class="o">.</span><span class="n">lmP</span><span class="p">[</span><span class="mi">2</span> <span class="o">*</span> <span class="n">lm_id</span><span class="p">:</span><span class="mi">2</span> <span class="o">*</span> <span class="n">lm_id</span> <span class="o">+</span> <span class="mi">2</span><span class="p">])</span>
+ <span class="n">zp</span><span class="p">,</span> <span class="n">Hv</span><span class="p">,</span> <span class="n">Hf</span><span class="p">,</span> <span class="n">Sf</span> <span class="o">=</span> <span class="n">compute_jacobians</span><span class="p">(</span><span class="n">particle</span><span class="p">,</span> <span class="n">xf</span><span class="p">,</span> <span class="n">Pf</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="n">z</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-</span> <span class="n">zp</span>
+ <span class="n">dx</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">dx</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+
+ <span class="k">try</span><span class="p">:</span>
+ <span class="n">invS</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">Sf</span><span class="p">)</span>
+ <span class="k">except</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">LinAlgError</span><span class="p">:</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"singuler"</span><span class="p">)</span>
+ <span class="k">return</span> <span class="mf">1.0</span>
+
+ <span class="n">num</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="mf">0.5</span> <span class="o">*</span> <span class="n">dx</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">invS</span> <span class="o">@</span> <span class="n">dx</span><span class="p">)</span>
+ <span class="n">den</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">det</span><span class="p">(</span><span class="n">Sf</span><span class="p">))</span>
+ <span class="n">w</span> <span class="o">=</span> <span class="n">num</span> <span class="o">/</span> <span class="n">den</span>
+
+ <span class="k">return</span> <span class="n">w</span>
+
+<span class="k">def</span> <span class="nf">compute_jacobians</span><span class="p">(</span><span class="n">particle</span><span class="p">,</span> <span class="n">xf</span><span class="p">,</span> <span class="n">Pf</span><span class="p">,</span> <span class="n">Q</span><span class="p">):</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="n">xf</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">particle</span><span class="o">.</span><span class="n">x</span>
+ <span class="n">dy</span> <span class="o">=</span> <span class="n">xf</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">particle</span><span class="o">.</span><span class="n">y</span>
+ <span class="n">d2</span> <span class="o">=</span> <span class="n">dx</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">dy</span><span class="o">**</span><span class="mi">2</span>
+ <span class="n">d</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">d2</span><span class="p">)</span>
+
+ <span class="n">zp</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span>
+ <span class="p">[</span><span class="n">d</span><span class="p">,</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">dy</span><span class="p">,</span> <span class="n">dx</span><span class="p">)</span> <span class="o">-</span> <span class="n">particle</span><span class="o">.</span><span class="n">yaw</span><span class="p">)])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+
+ <span class="n">Hv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="n">dx</span> <span class="o">/</span> <span class="n">d</span><span class="p">,</span> <span class="o">-</span><span class="n">dy</span> <span class="o">/</span> <span class="n">d</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span>
+ <span class="p">[</span><span class="n">dy</span> <span class="o">/</span> <span class="n">d2</span><span class="p">,</span> <span class="o">-</span><span class="n">dx</span> <span class="o">/</span> <span class="n">d2</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="p">]])</span>
+
+ <span class="n">Hf</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">dx</span> <span class="o">/</span> <span class="n">d</span><span class="p">,</span> <span class="n">dy</span> <span class="o">/</span> <span class="n">d</span><span class="p">],</span>
+ <span class="p">[</span><span class="o">-</span><span class="n">dy</span> <span class="o">/</span> <span class="n">d2</span><span class="p">,</span> <span class="n">dx</span> <span class="o">/</span> <span class="n">d2</span><span class="p">]])</span>
+
+ <span class="n">Sf</span> <span class="o">=</span> <span class="n">Hf</span> <span class="o">@</span> <span class="n">Pf</span> <span class="o">@</span> <span class="n">Hf</span><span class="o">.</span><span class="n">T</span> <span class="o">+</span> <span class="n">Q</span>
+
+ <span class="k">return</span> <span class="n">zp</span><span class="p">,</span> <span class="n">Hv</span><span class="p">,</span> <span class="n">Hf</span><span class="p">,</span> <span class="n">Sf</span>
+
+<span class="k">def</span> <span class="nf">add_new_lm</span><span class="p">(</span><span class="n">particle</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">Q</span><span class="p">):</span>
+
+ <span class="n">r</span> <span class="o">=</span> <span class="n">z</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+ <span class="n">b</span> <span class="o">=</span> <span class="n">z</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+ <span class="n">lm_id</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">z</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
+
+ <span class="n">s</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">pi_2_pi</span><span class="p">(</span><span class="n">particle</span><span class="o">.</span><span class="n">yaw</span> <span class="o">+</span> <span class="n">b</span><span class="p">))</span>
+ <span class="n">c</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">pi_2_pi</span><span class="p">(</span><span class="n">particle</span><span class="o">.</span><span class="n">yaw</span> <span class="o">+</span> <span class="n">b</span><span class="p">))</span>
+
+ <span class="n">particle</span><span class="o">.</span><span class="n">lm</span><span class="p">[</span><span class="n">lm_id</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">particle</span><span class="o">.</span><span class="n">x</span> <span class="o">+</span> <span class="n">r</span> <span class="o">*</span> <span class="n">c</span>
+ <span class="n">particle</span><span class="o">.</span><span class="n">lm</span><span class="p">[</span><span class="n">lm_id</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">particle</span><span class="o">.</span><span class="n">y</span> <span class="o">+</span> <span class="n">r</span> <span class="o">*</span> <span class="n">s</span>
+
+ <span class="c1"># covariance</span>
+ <span class="n">Gz</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">c</span><span class="p">,</span> <span class="o">-</span><span class="n">r</span> <span class="o">*</span> <span class="n">s</span><span class="p">],</span>
+ <span class="p">[</span><span class="n">s</span><span class="p">,</span> <span class="n">r</span> <span class="o">*</span> <span class="n">c</span><span class="p">]])</span>
+
+ <span class="n">particle</span><span class="o">.</span><span class="n">lmP</span><span class="p">[</span><span class="mi">2</span> <span class="o">*</span> <span class="n">lm_id</span><span class="p">:</span><span class="mi">2</span> <span class="o">*</span> <span class="n">lm_id</span> <span class="o">+</span> <span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">Gz</span> <span class="o">@</span> <span class="n">Q</span> <span class="o">@</span> <span class="n">Gz</span><span class="o">.</span><span class="n">T</span>
+
+ <span class="k">return</span> <span class="n">particle</span>
+
+<span class="k">def</span> <span class="nf">update_KF_with_cholesky</span><span class="p">(</span><span class="n">xf</span><span class="p">,</span> <span class="n">Pf</span><span class="p">,</span> <span class="n">v</span><span class="p">,</span> <span class="n">Q</span><span class="p">,</span> <span class="n">Hf</span><span class="p">):</span>
+ <span class="n">PHt</span> <span class="o">=</span> <span class="n">Pf</span> <span class="o">@</span> <span class="n">Hf</span><span class="o">.</span><span class="n">T</span>
+ <span class="n">S</span> <span class="o">=</span> <span class="n">Hf</span> <span class="o">@</span> <span class="n">PHt</span> <span class="o">+</span> <span class="n">Q</span>
+
+ <span class="n">S</span> <span class="o">=</span> <span class="p">(</span><span class="n">S</span> <span class="o">+</span> <span class="n">S</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">*</span> <span class="mf">0.5</span>
+ <span class="n">SChol</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cholesky</span><span class="p">(</span><span class="n">S</span><span class="p">)</span><span class="o">.</span><span class="n">T</span>
+ <span class="n">SCholInv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">SChol</span><span class="p">)</span>
+ <span class="n">W1</span> <span class="o">=</span> <span class="n">PHt</span> <span class="o">@</span> <span class="n">SCholInv</span>
+ <span class="n">W</span> <span class="o">=</span> <span class="n">W1</span> <span class="o">@</span> <span class="n">SCholInv</span><span class="o">.</span><span class="n">T</span>
+
+ <span class="n">x</span> <span class="o">=</span> <span class="n">xf</span> <span class="o">+</span> <span class="n">W</span> <span class="o">@</span> <span class="n">v</span>
+ <span class="n">P</span> <span class="o">=</span> <span class="n">Pf</span> <span class="o">-</span> <span class="n">W1</span> <span class="o">@</span> <span class="n">W1</span><span class="o">.</span><span class="n">T</span>
+
+ <span class="k">return</span> <span class="n">x</span><span class="p">,</span> <span class="n">P</span>
+
+<span class="k">def</span> <span class="nf">update_landmark</span><span class="p">(</span><span class="n">particle</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">Q</span><span class="p">):</span>
+
+ <span class="n">lm_id</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">z</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
+ <span class="n">xf</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">particle</span><span class="o">.</span><span class="n">lm</span><span class="p">[</span><span class="n">lm_id</span><span class="p">,</span> <span class="p">:])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+ <span class="n">Pf</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">particle</span><span class="o">.</span><span class="n">lmP</span><span class="p">[</span><span class="mi">2</span> <span class="o">*</span> <span class="n">lm_id</span><span class="p">:</span><span class="mi">2</span> <span class="o">*</span> <span class="n">lm_id</span> <span class="o">+</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:])</span>
+
+ <span class="n">zp</span><span class="p">,</span> <span class="n">Hv</span><span class="p">,</span> <span class="n">Hf</span><span class="p">,</span> <span class="n">Sf</span> <span class="o">=</span> <span class="n">compute_jacobians</span><span class="p">(</span><span class="n">particle</span><span class="p">,</span> <span class="n">xf</span><span class="p">,</span> <span class="n">Pf</span><span class="p">,</span> <span class="n">Q</span><span class="p">)</span>
+
+ <span class="n">dz</span> <span class="o">=</span> <span class="n">z</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-</span> <span class="n">zp</span>
+ <span class="n">dz</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">dz</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+
+ <span class="n">xf</span><span class="p">,</span> <span class="n">Pf</span> <span class="o">=</span> <span class="n">update_KF_with_cholesky</span><span class="p">(</span><span class="n">xf</span><span class="p">,</span> <span class="n">Pf</span><span class="p">,</span> <span class="n">dz</span><span class="p">,</span> <span class="n">Q</span><span class="p">,</span> <span class="n">Hf</span><span class="p">)</span>
+
+ <span class="n">particle</span><span class="o">.</span><span class="n">lm</span><span class="p">[</span><span class="n">lm_id</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">xf</span><span class="o">.</span><span class="n">T</span>
+ <span class="n">particle</span><span class="o">.</span><span class="n">lmP</span><span class="p">[</span><span class="mi">2</span> <span class="o">*</span> <span class="n">lm_id</span><span class="p">:</span><span class="mi">2</span> <span class="o">*</span> <span class="n">lm_id</span> <span class="o">+</span> <span class="mi">2</span><span class="p">,</span> <span class="p">:]</span> <span class="o">=</span> <span class="n">Pf</span>
+
+ <span class="k">return</span> <span class="n">particle</span>
+
+<span class="c1"># END OF CODE SNIPPET #</span>
+
+
+
+<span class="c1"># Setting up the landmarks</span>
+<span class="n">RFID</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">10.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.0</span><span class="p">],</span>
+ <span class="p">[</span><span class="mf">15.0</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">]])</span>
+<span class="n">N_LM</span> <span class="o">=</span> <span class="n">RFID</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
+
+<span class="c1"># Initialize 1 particle</span>
+<span class="n">N_PARTICLE</span> <span class="o">=</span> <span class="mi">1</span>
+<span class="n">particles</span> <span class="o">=</span> <span class="p">[</span><span class="n">Particle</span><span class="p">(</span><span class="n">N_LM</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">)]</span>
+
+<span class="n">xTrue</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">STATE_SIZE</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+<span class="n">xDR</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">STATE_SIZE</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">"initial weight"</span><span class="p">,</span> <span class="n">particles</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">w</span><span class="p">)</span>
+
+<span class="n">xTrue</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">ud</span> <span class="o">=</span> <span class="n">observation</span><span class="p">(</span><span class="n">xTrue</span><span class="p">,</span> <span class="n">xDR</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">RFID</span><span class="p">)</span>
+<span class="c1"># Initialize landmarks</span>
+<span class="n">particles</span> <span class="o">=</span> <span class="n">update_with_observation</span><span class="p">(</span><span class="n">particles</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"weight after landmark intialization"</span><span class="p">,</span> <span class="n">particles</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">w</span><span class="p">)</span>
+<span class="n">particles</span> <span class="o">=</span> <span class="n">update_with_observation</span><span class="p">(</span><span class="n">particles</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"weight after update "</span><span class="p">,</span> <span class="n">particles</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">w</span><span class="p">)</span>
+
+<span class="n">particles</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="o">-</span><span class="mi">10</span>
+<span class="n">particles</span> <span class="o">=</span> <span class="n">update_with_observation</span><span class="p">(</span><span class="n">particles</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"weight after wrong prediction"</span><span class="p">,</span> <span class="n">particles</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">w</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">initial</span> <span class="n">weight</span> <span class="mf">1.0</span>
+<span class="n">weight</span> <span class="n">after</span> <span class="n">landmark</span> <span class="n">intialization</span> <span class="mf">1.0</span>
+<span class="n">weight</span> <span class="n">after</span> <span class="n">update</span> <span class="mf">0.023098460073039763</span>
+<span class="n">weight</span> <span class="n">after</span> <span class="n">wrong</span> <span class="n">prediction</span> <span class="mf">7.951154575772496e-07</span>
+</pre></div>
+</div>
+</section>
+<section id="resampling">
+<h2>3- Resampling<a class="headerlink" href="#resampling" title="Permalink to this headline"></a></h2>
+<p>In the reseampling steps a new set of particles are chosen from the old
+set. This is done according to the weight of each particle.</p>
+<p>The figure shows 100 particles distributed uniformly between [-0.5, 0.5]
+with the weights of each particle distributed according to a Gaussian
+funciton.</p>
+<p>The resampling picks</p>
+<p><span class="math notranslate nohighlight">\(i \in 1,...,N\)</span> particles with probability to pick particle with
+index <span class="math notranslate nohighlight">\(i ∝ \omega_i\)</span>, where <span class="math notranslate nohighlight">\(\omega_i\)</span> is the weight of that
+particle</p>
+<p>To get the intuition of the resampling step we will look at a set of
+particles which are initialized with a given x location and weight.
+After the resampling the particles are more concetrated in the location
+where they had the highest weights. This is also indicated by the
+indices</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># CODE SNIPPET #</span>
+<span class="k">def</span> <span class="nf">normalize_weight</span><span class="p">(</span><span class="n">particles</span><span class="p">):</span>
+
+ <span class="n">sumw</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">([</span><span class="n">p</span><span class="o">.</span><span class="n">w</span> <span class="k">for</span> <span class="n">p</span> <span class="ow">in</span> <span class="n">particles</span><span class="p">])</span>
+
+ <span class="k">try</span><span class="p">:</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">):</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">w</span> <span class="o">/=</span> <span class="n">sumw</span>
+ <span class="k">except</span> <span class="ne">ZeroDivisionError</span><span class="p">:</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">):</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">w</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="n">N_PARTICLE</span>
+
+ <span class="k">return</span> <span class="n">particles</span>
+
+ <span class="k">return</span> <span class="n">particles</span>
+
+
+<span class="k">def</span> <span class="nf">resampling</span><span class="p">(</span><span class="n">particles</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> low variance re-sampling</span>
+<span class="sd"> """</span>
+
+ <span class="n">particles</span> <span class="o">=</span> <span class="n">normalize_weight</span><span class="p">(</span><span class="n">particles</span><span class="p">)</span>
+
+ <span class="n">pw</span> <span class="o">=</span> <span class="p">[]</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">):</span>
+ <span class="n">pw</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">w</span><span class="p">)</span>
+
+ <span class="n">pw</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">(</span><span class="n">pw</span><span class="p">)</span>
+
+ <span class="n">Neff</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="p">(</span><span class="n">pw</span> <span class="o">@</span> <span class="n">pw</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="c1"># Effective particle number</span>
+ <span class="c1"># print(Neff)</span>
+
+ <span class="k">if</span> <span class="n">Neff</span> <span class="o"><</span> <span class="n">NTH</span><span class="p">:</span> <span class="c1"># resampling</span>
+ <span class="n">wcum</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">pw</span><span class="p">)</span>
+ <span class="n">base</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">pw</span> <span class="o">*</span> <span class="mf">0.0</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">N_PARTICLE</span><span class="p">)</span> <span class="o">-</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">N_PARTICLE</span>
+ <span class="n">resampleid</span> <span class="o">=</span> <span class="n">base</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">rand</span><span class="p">(</span><span class="n">base</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">/</span> <span class="n">N_PARTICLE</span>
+
+ <span class="n">inds</span> <span class="o">=</span> <span class="p">[]</span>
+ <span class="n">ind</span> <span class="o">=</span> <span class="mi">0</span>
+ <span class="k">for</span> <span class="n">ip</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">):</span>
+ <span class="k">while</span> <span class="p">((</span><span class="n">ind</span> <span class="o"><</span> <span class="n">wcum</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="ow">and</span> <span class="p">(</span><span class="n">resampleid</span><span class="p">[</span><span class="n">ip</span><span class="p">]</span> <span class="o">></span> <span class="n">wcum</span><span class="p">[</span><span class="n">ind</span><span class="p">])):</span>
+ <span class="n">ind</span> <span class="o">+=</span> <span class="mi">1</span>
+ <span class="n">inds</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">ind</span><span class="p">)</span>
+
+ <span class="n">tparticles</span> <span class="o">=</span> <span class="n">particles</span><span class="p">[:]</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">inds</span><span class="p">)):</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="n">tparticles</span><span class="p">[</span><span class="n">inds</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">.</span><span class="n">x</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">y</span> <span class="o">=</span> <span class="n">tparticles</span><span class="p">[</span><span class="n">inds</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">.</span><span class="n">y</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">yaw</span> <span class="o">=</span> <span class="n">tparticles</span><span class="p">[</span><span class="n">inds</span><span class="p">[</span><span class="n">i</span><span class="p">]]</span><span class="o">.</span><span class="n">yaw</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">w</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="o">/</span> <span class="n">N_PARTICLE</span>
+
+ <span class="k">return</span> <span class="n">particles</span><span class="p">,</span> <span class="n">inds</span>
+<span class="c1"># END OF SNIPPET #</span>
+
+
+
+<span class="k">def</span> <span class="nf">gaussian</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">mu</span><span class="p">,</span> <span class="n">sig</span><span class="p">):</span>
+ <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">exp</span><span class="p">(</span><span class="o">-</span><span class="n">np</span><span class="o">.</span><span class="n">power</span><span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="n">mu</span><span class="p">,</span> <span class="mf">2.</span><span class="p">)</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">power</span><span class="p">(</span><span class="n">sig</span><span class="p">,</span> <span class="mf">2.</span><span class="p">)))</span>
+<span class="n">N_PARTICLE</span> <span class="o">=</span> <span class="mi">100</span>
+<span class="n">particles</span> <span class="o">=</span> <span class="p">[</span><span class="n">Particle</span><span class="p">(</span><span class="n">N_LM</span><span class="p">)</span> <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">)]</span>
+<span class="n">x_pos</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="n">w</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">):</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">x</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linspace</span><span class="p">(</span><span class="o">-</span><span class="mf">0.5</span><span class="p">,</span><span class="mf">0.5</span><span class="p">,</span><span class="n">N_PARTICLE</span><span class="p">)[</span><span class="n">i</span><span class="p">]</span>
+ <span class="n">x_pos</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
+ <span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">w</span> <span class="o">=</span> <span class="n">gaussian</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">N_PARTICLE</span><span class="o">/</span><span class="mi">2</span><span class="p">,</span> <span class="n">N_PARTICLE</span><span class="o">/</span><span class="mi">20</span><span class="p">)</span>
+ <span class="n">w</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">w</span><span class="p">)</span>
+
+
+<span class="c1"># Normalize weights</span>
+<span class="n">sw</span> <span class="o">=</span> <span class="nb">sum</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">):</span>
+ <span class="n">w</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">/=</span> <span class="n">sw</span>
+
+<span class="n">particles</span><span class="p">,</span> <span class="n">new_indices</span> <span class="o">=</span> <span class="n">resampling</span><span class="p">(</span><span class="n">particles</span><span class="p">)</span>
+<span class="n">x_pos2</span> <span class="o">=</span> <span class="p">[]</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N_PARTICLE</span><span class="p">):</span>
+ <span class="n">x_pos2</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">particles</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">.</span><span class="n">x</span><span class="p">)</span>
+
+<span class="c1"># Plot results</span>
+<span class="n">fig</span><span class="p">,</span> <span class="p">((</span><span class="n">ax1</span><span class="p">,</span><span class="n">ax2</span><span class="p">,</span><span class="n">ax3</span><span class="p">))</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">subplots</span><span class="p">(</span><span class="n">nrows</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">ncols</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">fig</span><span class="o">.</span><span class="n">tight_layout</span><span class="p">()</span>
+<span class="n">ax1</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_pos</span><span class="p">,</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N_PARTICLE</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="s1">'.r'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">2</span><span class="p">)</span>
+<span class="n">ax1</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Particles before resampling"</span><span class="p">)</span>
+<span class="n">ax1</span><span class="o">.</span><span class="n">axis</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
+<span class="n">ax2</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">w</span><span class="p">)</span>
+<span class="n">ax2</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Weights distribution"</span><span class="p">)</span>
+<span class="n">ax3</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_pos2</span><span class="p">,</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">((</span><span class="n">N_PARTICLE</span><span class="p">,</span><span class="mi">1</span><span class="p">)),</span> <span class="s1">'.r'</span><span class="p">)</span>
+<span class="n">ax3</span><span class="o">.</span><span class="n">set_title</span><span class="p">(</span><span class="s2">"Particles after resampling"</span><span class="p">)</span>
+<span class="n">ax3</span><span class="o">.</span><span class="n">axis</span><span class="p">((</span><span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">))</span>
+<span class="n">fig</span><span class="o">.</span><span class="n">subplots_adjust</span><span class="p">(</span><span class="n">hspace</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">hist</span><span class="p">(</span><span class="n">new_indices</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">xlabel</span><span class="p">(</span><span class="s2">"Particles indices to be resampled"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">ylabel</span><span class="p">(</span><span class="s2">"# of time index is used"</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../../_images/FastSLAM1_12_0.png" src="../../../_images/FastSLAM1_12_0.png" />
+<img alt="../../../_images/FastSLAM1_12_1.png" src="../../../_images/FastSLAM1_12_1.png" />
+</section>
+<section id="references">
+<h2>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="http://www.probabilistic-robotics.org/">PROBABILISTIC ROBOTICS</a></p></li>
+<li><p><a class="reference external" href="http://ais.informatik.uni-freiburg.de/teaching/ws12/mapping/pdf/slam10-fastslam.pdf">FastSLAM Lecture</a></p></li>
+</ul>
+</section>
+</section>
+
+
+ </div>
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+<li class="toctree-l1"><a class="reference internal" href="../../mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../slam.html">SLAM</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../iterative_closest_point_matching/iterative_closest_point_matching.html">Iterative Closest Point (ICP) Matching</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../ekf_slam/ekf_slam.html">EKF SLAM</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../FastSLAM1/FastSLAM1.html">FastSLAM1.0</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">FastSLAM 2.0</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#references">References</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../graph_slam/graph_slam.html">Graph based SLAM</a></li>
+</ul>
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+
+ <section id="fastslam-2-0">
+<h1>FastSLAM 2.0<a class="headerlink" href="#fastslam-2-0" title="Permalink to this headline"></a></h1>
+<p>This is a feature based SLAM example using FastSLAM 2.0.</p>
+<p>The animation has the same meanings as one of FastSLAM 1.0.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/FastSLAM2/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/FastSLAM2/animation.gif" />
+<section id="references">
+<h2>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="http://www.probabilistic-robotics.org/">PROBABILISTIC ROBOTICS</a></p></li>
+<li><p><a class="reference external" href="http://www-personal.acfr.usyd.edu.au/tbailey/software/slam_simulations.htm">SLAM simulations by Tim Bailey</a></p></li>
+</ul>
+</section>
+</section>
+
+
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+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
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+<li class="toctree-l1"><a class="reference internal" href="../../introduction.html">Introduction</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../localization/localization.html">Localization</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../slam.html">SLAM</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../iterative_closest_point_matching/iterative_closest_point_matching.html">Iterative Closest Point (ICP) Matching</a></li>
+<li class="toctree-l2 current"><a class="current reference internal" href="#">EKF SLAM</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#simulation">Simulation</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#introduction">Introduction</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#algorithm-walk-through">Algorithm Walk through</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#predict">1- Predict</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#update">2 - Update</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#observation-step">Observation Step</a></li>
+<li class="toctree-l3"><a class="reference internal" href="#references">References:</a></li>
+</ul>
+</li>
+<li class="toctree-l2"><a class="reference internal" href="../FastSLAM1/FastSLAM1.html">FastSLAM1.0</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../FastSLAM2/FastSLAM2.html">FastSLAM 2.0</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../graph_slam/graph_slam.html">Graph based SLAM</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_planning/path_planning.html">Path Planning</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../path_tracking/path_tracking.html">Path Tracking</a></li>
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+<li class="toctree-l1"><a class="reference internal" href="../../utils/utils.html">Utilities</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../appendix/appendix.html">Appendix</a></li>
+<li class="toctree-l1"><a class="reference internal" href="../../../how_to_contribute.html">How To Contribute</a></li>
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+
+ <section id="ekf-slam">
+<h1>EKF SLAM<a class="headerlink" href="#ekf-slam" title="Permalink to this headline"></a></h1>
+<p>This is an Extended Kalman Filter based SLAM example.</p>
+<p>The blue line is ground truth, the black line is dead reckoning, the red
+line is the estimated trajectory with EKF SLAM.</p>
+<p>The green crosses are estimated landmarks.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/EKFSLAM/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/EKFSLAM/animation.gif" />
+<section id="simulation">
+<h2>Simulation<a class="headerlink" href="#simulation" title="Permalink to this headline"></a></h2>
+<p>This is a simulation of EKF SLAM.</p>
+<ul class="simple">
+<li><p>Black stars: landmarks</p></li>
+<li><p>Green crosses: estimates of landmark positions</p></li>
+<li><p>Black line: dead reckoning</p></li>
+<li><p>Blue line: ground truth</p></li>
+<li><p>Red line: EKF SLAM position estimation</p></li>
+</ul>
+</section>
+<section id="introduction">
+<h2>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h2>
+<p>EKF SLAM models the SLAM problem in a single EKF where the modeled state
+is both the pose <span class="math notranslate nohighlight">\((x, y, \theta)\)</span> and an array of landmarks
+<span class="math notranslate nohighlight">\([(x_1, y_1), (x_2, x_y), ... , (x_n, y_n)]\)</span> for <span class="math notranslate nohighlight">\(n\)</span>
+landmarks. The covariance between each of the positions and landmarks
+are also tracked.</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation} X = \begin{bmatrix} x \\ y \\ \theta \\ x_1 \\ y_1 \\ x_2 \\ y_2 \\ \dots \\ x_n \\ y_n \end{bmatrix} \end{equation}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation} P = \begin{bmatrix} \sigma_{xx} & \sigma_{xy} & \sigma_{x\theta} & \sigma_{xx_1} & \sigma_{xy_1} & \sigma_{xx_2} & \sigma_{xy_2} & \dots & \sigma_{xx_n} & \sigma_{xy_n} \\ \sigma_{yx} & \sigma_{yy} & \sigma_{y\theta} & \sigma_{yx_1} & \sigma_{yy_1} & \sigma_{yx_2} & \sigma_{yy_2} & \dots & \sigma_{yx_n} & \sigma_{yy_n} \\ & & & & \vdots & & & & & \\ \sigma_{x_nx} & \sigma_{x_ny} & \sigma_{x_n\theta} & \sigma_{x_nx_1} & \sigma_{x_ny_1} & \sigma_{x_nx_2} & \sigma_{x_ny_2} & \dots & \sigma_{x_nx_n} & \sigma_{x_ny_n} \end{bmatrix} \end{equation}\)</span></p>
+<p>A single estimate of the pose is tracked over time, while the confidence
+in the pose is tracked by the covariance matrix <span class="math notranslate nohighlight">\(P\)</span>. <span class="math notranslate nohighlight">\(P\)</span> is
+a symmetric square matrix which each element in the matrix corresponding
+to the covariance between two parts of the system. For example,
+<span class="math notranslate nohighlight">\(\sigma_{xy}\)</span> represents the covariance between the belief of
+<span class="math notranslate nohighlight">\(x\)</span> and <span class="math notranslate nohighlight">\(y\)</span> and is equal to <span class="math notranslate nohighlight">\(\sigma_{yx}\)</span>.</p>
+<p>The state can be represented more concisely as follows.</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation} X = \begin{bmatrix} x \\ m \end{bmatrix} \end{equation}\)</span>
+<span class="math notranslate nohighlight">\(\begin{equation} P = \begin{bmatrix} \Sigma_{xx} & \Sigma_{xm}\\ \Sigma_{mx} & \Sigma_{mm}\\ \end{bmatrix} \end{equation}\)</span></p>
+<p>Here the state simplifies to a combination of pose (<span class="math notranslate nohighlight">\(x\)</span>) and map
+(<span class="math notranslate nohighlight">\(m\)</span>). The covariance matrix becomes easier to understand and
+simply reads as the uncertainty of the robots pose
+(<span class="math notranslate nohighlight">\(\Sigma_{xx}\)</span>), the uncertainty of the map (<span class="math notranslate nohighlight">\(\Sigma_{mm}\)</span>),
+and the uncertainty of the robots pose with respect to the map and vice
+versa (<span class="math notranslate nohighlight">\(\Sigma_{xm}\)</span>, <span class="math notranslate nohighlight">\(\Sigma_{mx}\)</span>).</p>
+<p>Take care to note the difference between <span class="math notranslate nohighlight">\(X\)</span> (state) and <span class="math notranslate nohighlight">\(x\)</span>
+(pose).</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="sd">"""</span>
+<span class="sd">Extended Kalman Filter SLAM example</span>
+<span class="sd">original author: Atsushi Sakai (@Atsushi_twi)</span>
+<span class="sd">notebook author: Andrew Tu (drewtu2)</span>
+<span class="sd">"""</span>
+
+<span class="kn">import</span> <span class="nn">math</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="o">%</span><span class="k">matplotlib</span> notebook
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+
+
+<span class="c1"># EKF state covariance</span>
+<span class="n">Cx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="mf">0.5</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">30.0</span><span class="p">)])</span><span class="o">**</span><span class="mi">2</span> <span class="c1"># Change in covariance</span>
+
+<span class="c1"># Simulation parameter</span>
+<span class="n">Qsim</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="mf">0.2</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)])</span><span class="o">**</span><span class="mi">2</span> <span class="c1"># Sensor Noise</span>
+<span class="n">Rsim</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="mf">1.0</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">10.0</span><span class="p">)])</span><span class="o">**</span><span class="mi">2</span> <span class="c1"># Process Noise</span>
+
+<span class="n">DT</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="c1"># time tick [s]</span>
+<span class="n">SIM_TIME</span> <span class="o">=</span> <span class="mf">50.0</span> <span class="c1"># simulation time [s]</span>
+<span class="n">MAX_RANGE</span> <span class="o">=</span> <span class="mf">20.0</span> <span class="c1"># maximum observation range</span>
+<span class="n">M_DIST_TH</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="c1"># Threshold of Mahalanobis distance for data association.</span>
+<span class="n">STATE_SIZE</span> <span class="o">=</span> <span class="mi">3</span> <span class="c1"># State size [x,y,yaw]</span>
+<span class="n">LM_SIZE</span> <span class="o">=</span> <span class="mi">2</span> <span class="c1"># LM state size [x,y]</span>
+
+<span class="n">show_animation</span> <span class="o">=</span> <span class="kc">True</span>
+</pre></div>
+</div>
+</section>
+<section id="algorithm-walk-through">
+<h2>Algorithm Walk through<a class="headerlink" href="#algorithm-walk-through" title="Permalink to this headline"></a></h2>
+<p>At each time step, the following is done. - predict the new state using
+the control functions - update the belief in landmark positions based on
+the estimated state and measurements</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">ekf_slam</span><span class="p">(</span><span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Performs an iteration of EKF SLAM from the available information.</span>
+
+<span class="sd"> :param xEst: the belief in last position</span>
+<span class="sd"> :param PEst: the uncertainty in last position</span>
+<span class="sd"> :param u: the control function applied to the last position</span>
+<span class="sd"> :param z: measurements at this step</span>
+<span class="sd"> :returns: the next estimated position and associated covariance</span>
+<span class="sd"> """</span>
+ <span class="n">S</span> <span class="o">=</span> <span class="n">STATE_SIZE</span>
+
+ <span class="c1"># Predict</span>
+ <span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span><span class="p">,</span> <span class="n">G</span><span class="p">,</span> <span class="n">Fx</span> <span class="o">=</span> <span class="n">predict</span><span class="p">(</span><span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span>
+ <span class="n">initP</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="mi">2</span><span class="p">)</span>
+
+ <span class="c1"># Update</span>
+ <span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span> <span class="o">=</span> <span class="n">update</span><span class="p">(</span><span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">initP</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span>
+</pre></div>
+</div>
+</section>
+<section id="predict">
+<h2>1- Predict<a class="headerlink" href="#predict" title="Permalink to this headline"></a></h2>
+<p><strong>Predict State update:</strong> The following equations describe the predicted
+motion model of the robot in case we provide only the control
+<span class="math notranslate nohighlight">\((v,w)\)</span>, which are the linear and angular velocity respectively.</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} F= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} B= \begin{bmatrix} \Delta t cos(\theta) & 0\\ \Delta t sin(\theta) & 0\\ 0 & \Delta t \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} U= \begin{bmatrix} v_t\\ w_t\\ \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} X = FX + BU \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} \begin{bmatrix} x_{t+1} \\ y_{t+1} \\ \theta_{t+1} \end{bmatrix}= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\begin{bmatrix} x_{t} \\ y_{t} \\ \theta_{t} \end{bmatrix}+ \begin{bmatrix} \Delta t cos(\theta) & 0\\ \Delta t sin(\theta) & 0\\ 0 & \Delta t \end{bmatrix} \begin{bmatrix} v_{t} + \sigma_v\\ w_{t} + \sigma_w\\ \end{bmatrix} \end{equation*}\)</span></p>
+<p>Notice that while <span class="math notranslate nohighlight">\(U\)</span> is only defined by <span class="math notranslate nohighlight">\(v_t\)</span> and
+<span class="math notranslate nohighlight">\(w_t\)</span>, in the actual calculations, a <span class="math notranslate nohighlight">\(+\sigma_v\)</span> and
+<span class="math notranslate nohighlight">\(+\sigma_w\)</span> appear. These values represent the error between the
+given control inputs and the actual control inputs.</p>
+<p>As a result, the simulation is set up as the following. <span class="math notranslate nohighlight">\(R\)</span>
+represents the process noise which is added to the control inputs to
+simulate noise experienced in the real world. A set of truth values are
+computed from the raw control values while the values dead reckoning
+values incorporate the error into the estimation.</p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} R= \begin{bmatrix} \sigma_v\\ \sigma_w\\ \end{bmatrix} \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} X_{true} = FX + B(U) \end{equation*}\)</span></p>
+<p><span class="math notranslate nohighlight">\(\begin{equation*} X_{DR} = FX + B(U + R) \end{equation*}\)</span></p>
+<p>The implementation of the motion model prediction code is shown in
+<code class="docutils literal notranslate"><span class="pre">motion_model</span></code>. The <code class="docutils literal notranslate"><span class="pre">observation</span></code> function shows how the simulation
+uses (or doesn’t use) the process noise <code class="docutils literal notranslate"><span class="pre">Rsim</span></code> to the find the ground
+truth and dead reckoning estimates of the pose.</p>
+<p><strong>Predict covariance:</strong> Add the state covariance to the the current
+uncertainty of the EKF. At each time step, the uncertainty in the system
+grows by the covariance of the pose, <span class="math notranslate nohighlight">\(Cx\)</span>.</p>
+<p><span class="math notranslate nohighlight">\(P = G^TPG + Cx\)</span></p>
+<p>Notice this uncertainty is only growing with respect to the pose, not
+the landmarks.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">predict</span><span class="p">(</span><span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span><span class="p">,</span> <span class="n">u</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Performs the prediction step of EKF SLAM</span>
+
+<span class="sd"> :param xEst: nx1 state vector</span>
+<span class="sd"> :param PEst: nxn covariance matrix</span>
+<span class="sd"> :param u: 2x1 control vector</span>
+<span class="sd"> :returns: predicted state vector, predicted covariance, jacobian of control vector, transition fx</span>
+<span class="sd"> """</span>
+ <span class="n">S</span> <span class="o">=</span> <span class="n">STATE_SIZE</span>
+ <span class="n">G</span><span class="p">,</span> <span class="n">Fx</span> <span class="o">=</span> <span class="n">jacob_motion</span><span class="p">(</span><span class="n">xEst</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">S</span><span class="p">],</span> <span class="n">u</span><span class="p">)</span>
+ <span class="n">xEst</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">S</span><span class="p">]</span> <span class="o">=</span> <span class="n">motion_model</span><span class="p">(</span><span class="n">xEst</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">S</span><span class="p">],</span> <span class="n">u</span><span class="p">)</span>
+ <span class="c1"># Fx is an an identity matrix of size (STATE_SIZE)</span>
+ <span class="c1"># sigma = G*sigma*G.T + Noise</span>
+ <span class="n">PEst</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">S</span><span class="p">,</span> <span class="mi">0</span><span class="p">:</span><span class="n">S</span><span class="p">]</span> <span class="o">=</span> <span class="n">G</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">PEst</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">S</span><span class="p">,</span> <span class="mi">0</span><span class="p">:</span><span class="n">S</span><span class="p">]</span> <span class="o">@</span> <span class="n">G</span> <span class="o">+</span> <span class="n">Fx</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">Cx</span> <span class="o">@</span> <span class="n">Fx</span>
+ <span class="k">return</span> <span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span><span class="p">,</span> <span class="n">G</span><span class="p">,</span> <span class="n">Fx</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">motion_model</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">u</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Computes the motion model based on current state and input function.</span>
+
+<span class="sd"> :param x: 3x1 pose estimation</span>
+<span class="sd"> :param u: 2x1 control input [v; w]</span>
+<span class="sd"> :returns: the resulting state after the control function is applied</span>
+<span class="sd"> """</span>
+ <span class="n">F</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]])</span>
+
+ <span class="n">B</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">DT</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="p">[</span><span class="n">DT</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]),</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="n">DT</span><span class="p">]])</span>
+
+ <span class="n">x</span> <span class="o">=</span> <span class="p">(</span><span class="n">F</span> <span class="o">@</span> <span class="n">x</span><span class="p">)</span> <span class="o">+</span> <span class="p">(</span><span class="n">B</span> <span class="o">@</span> <span class="n">u</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">x</span>
+</pre></div>
+</div>
+</section>
+<section id="update">
+<h2>2 - Update<a class="headerlink" href="#update" title="Permalink to this headline"></a></h2>
+<p>In the update phase, the observations of nearby landmarks are used to
+correct the location estimate.</p>
+<p>For every landmark observed, it is associated to a particular landmark
+in the known map. If no landmark exists in the position surrounding the
+landmark, it is taken as a NEW landmark. The distance threshold for how
+far a landmark must be from the next known landmark before its
+considered to be a new landmark is set by <code class="docutils literal notranslate"><span class="pre">M_DIST_TH</span></code>.</p>
+<p>With an observation associated to the appropriate landmark, the
+<strong>innovation</strong> can be calculated. Innovation (<span class="math notranslate nohighlight">\(y\)</span>) is the
+difference between the observation and the observation that <em>should</em>
+have been made if the observation were made from the pose predicted in
+the predict stage.</p>
+<p><span class="math notranslate nohighlight">\(y = z_t - h(X)\)</span></p>
+<p>With the innovation calculated, the question becomes which to trust more
+- the observations or the predictions? To determine this, we calculate
+the Kalman Gain - a percent of how much of the innovation to add to the
+prediction based on the uncertainty in the predict step and the update
+step.</p>
+<p><span class="math notranslate nohighlight">\(K = \bar{P_t}H_t^T(H_t\bar{P_t}H_t^T + Q_t)^{-1}\)</span>
+In these equations, <span class="math notranslate nohighlight">\(H\)</span> is the jacobian of the
+measurement function. The multiplications by <span class="math notranslate nohighlight">\(H^T\)</span> and <span class="math notranslate nohighlight">\(H\)</span>
+represent the application of the delta to the measurement covariance.
+Intuitively, this equation is applying the following from the single
+variate Kalman equation but in the multivariate form, i.e. finding the
+ratio of the uncertainty of the process compared the measurement.</p>
+<p>K = <span class="math notranslate nohighlight">\(\frac{\bar{P_t}}{\bar{P_t} + Q_t}\)</span></p>
+<p>If <span class="math notranslate nohighlight">\(Q_t << \bar{P_t}\)</span>, (i.e. the measurement covariance is low
+relative to the current estimate), then the Kalman gain will be
+<span class="math notranslate nohighlight">\(~1\)</span>. This results in adding all of the innovation to the estimate
+– and therefore completely believing the measurement.</p>
+<p>However, if <span class="math notranslate nohighlight">\(Q_t >> \bar{P_t}\)</span> then the Kalman gain will go to 0,
+signaling a high trust in the process and little trust in the
+measurement.</p>
+<p>The update is captured in the following.</p>
+<p><span class="math notranslate nohighlight">\(xUpdate = xEst + (K * y)\)</span></p>
+<p>Of course, the covariance must also be updated as well to account for
+the changing uncertainty.</p>
+<p><span class="math notranslate nohighlight">\(P_{t} = (I-K_tH_t)\bar{P_t}\)</span></p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">update</span><span class="p">(</span><span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">initP</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Performs the update step of EKF SLAM</span>
+
+<span class="sd"> :param xEst: nx1 the predicted pose of the system and the pose of the landmarks</span>
+<span class="sd"> :param PEst: nxn the predicted covariance</span>
+<span class="sd"> :param u: 2x1 the control function</span>
+<span class="sd"> :param z: the measurements read at new position</span>
+<span class="sd"> :param initP: 2x2 an identity matrix acting as the initial covariance</span>
+<span class="sd"> :returns: the updated state and covariance for the system</span>
+<span class="sd"> """</span>
+ <span class="k">for</span> <span class="n">iz</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">z</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">])):</span> <span class="c1"># for each observation</span>
+ <span class="n">minid</span> <span class="o">=</span> <span class="n">search_correspond_LM_ID</span><span class="p">(</span><span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span><span class="p">,</span> <span class="n">z</span><span class="p">[</span><span class="n">iz</span><span class="p">,</span> <span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">])</span> <span class="c1"># associate to a known landmark</span>
+
+ <span class="n">nLM</span> <span class="o">=</span> <span class="n">calc_n_LM</span><span class="p">(</span><span class="n">xEst</span><span class="p">)</span> <span class="c1"># number of landmarks we currently know about</span>
+
+ <span class="k">if</span> <span class="n">minid</span> <span class="o">==</span> <span class="n">nLM</span><span class="p">:</span> <span class="c1"># Landmark is a NEW landmark</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"New LM"</span><span class="p">)</span>
+ <span class="c1"># Extend state and covariance matrix</span>
+ <span class="n">xAug</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="n">xEst</span><span class="p">,</span> <span class="n">calc_LM_Pos</span><span class="p">(</span><span class="n">xEst</span><span class="p">,</span> <span class="n">z</span><span class="p">[</span><span class="n">iz</span><span class="p">,</span> <span class="p">:])))</span>
+ <span class="n">PAug</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">PEst</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">xEst</span><span class="p">),</span> <span class="n">LM_SIZE</span><span class="p">)))),</span>
+ <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">LM_SIZE</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">xEst</span><span class="p">))),</span> <span class="n">initP</span><span class="p">))))</span>
+ <span class="n">xEst</span> <span class="o">=</span> <span class="n">xAug</span>
+ <span class="n">PEst</span> <span class="o">=</span> <span class="n">PAug</span>
+
+ <span class="n">lm</span> <span class="o">=</span> <span class="n">get_LM_Pos_from_state</span><span class="p">(</span><span class="n">xEst</span><span class="p">,</span> <span class="n">minid</span><span class="p">)</span>
+ <span class="n">y</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">H</span> <span class="o">=</span> <span class="n">calc_innovation</span><span class="p">(</span><span class="n">lm</span><span class="p">,</span> <span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span><span class="p">,</span> <span class="n">z</span><span class="p">[</span><span class="n">iz</span><span class="p">,</span> <span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">],</span> <span class="n">minid</span><span class="p">)</span>
+
+ <span class="n">K</span> <span class="o">=</span> <span class="p">(</span><span class="n">PEst</span> <span class="o">@</span> <span class="n">H</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">S</span><span class="p">)</span> <span class="c1"># Calculate Kalman Gain</span>
+ <span class="n">xEst</span> <span class="o">=</span> <span class="n">xEst</span> <span class="o">+</span> <span class="p">(</span><span class="n">K</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+ <span class="n">PEst</span> <span class="o">=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">xEst</span><span class="p">))</span> <span class="o">-</span> <span class="p">(</span><span class="n">K</span> <span class="o">@</span> <span class="n">H</span><span class="p">))</span> <span class="o">@</span> <span class="n">PEst</span>
+
+ <span class="n">xEst</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">xEst</span><span class="p">[</span><span class="mi">2</span><span class="p">])</span>
+ <span class="k">return</span> <span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">calc_innovation</span><span class="p">(</span><span class="n">lm</span><span class="p">,</span> <span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">LMid</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Calculates the innovation based on expected position and landmark position</span>
+
+<span class="sd"> :param lm: landmark position</span>
+<span class="sd"> :param xEst: estimated position/state</span>
+<span class="sd"> :param PEst: estimated covariance</span>
+<span class="sd"> :param z: read measurements</span>
+<span class="sd"> :param LMid: landmark id</span>
+<span class="sd"> :returns: returns the innovation y, and the jacobian H, and S, used to calculate the Kalman Gain</span>
+<span class="sd"> """</span>
+ <span class="n">delta</span> <span class="o">=</span> <span class="n">lm</span> <span class="o">-</span> <span class="n">xEst</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span>
+ <span class="n">q</span> <span class="o">=</span> <span class="p">(</span><span class="n">delta</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">delta</span><span class="p">)[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">zangle</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">delta</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">delta</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span> <span class="o">-</span> <span class="n">xEst</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">zp</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">q</span><span class="p">),</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">zangle</span><span class="p">)]])</span>
+ <span class="c1"># zp is the expected measurement based on xEst and the expected landmark position</span>
+
+ <span class="n">y</span> <span class="o">=</span> <span class="p">(</span><span class="n">z</span> <span class="o">-</span> <span class="n">zp</span><span class="p">)</span><span class="o">.</span><span class="n">T</span> <span class="c1"># y = innovation</span>
+ <span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">y</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+
+ <span class="n">H</span> <span class="o">=</span> <span class="n">jacobH</span><span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="n">delta</span><span class="p">,</span> <span class="n">xEst</span><span class="p">,</span> <span class="n">LMid</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
+ <span class="n">S</span> <span class="o">=</span> <span class="n">H</span> <span class="o">@</span> <span class="n">PEst</span> <span class="o">@</span> <span class="n">H</span><span class="o">.</span><span class="n">T</span> <span class="o">+</span> <span class="n">Cx</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">:</span><span class="mi">2</span><span class="p">]</span>
+
+ <span class="k">return</span> <span class="n">y</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">H</span>
+
+<span class="k">def</span> <span class="nf">jacobH</span><span class="p">(</span><span class="n">q</span><span class="p">,</span> <span class="n">delta</span><span class="p">,</span> <span class="n">x</span><span class="p">,</span> <span class="n">i</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Calculates the jacobian of the measurement function</span>
+
+<span class="sd"> :param q: the range from the system pose to the landmark</span>
+<span class="sd"> :param delta: the difference between a landmark position and the estimated system position</span>
+<span class="sd"> :param x: the state, including the estimated system position</span>
+<span class="sd"> :param i: landmark id + 1</span>
+<span class="sd"> :returns: the jacobian H</span>
+<span class="sd"> """</span>
+ <span class="n">sq</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">q</span><span class="p">)</span>
+ <span class="n">G</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="n">sq</span> <span class="o">*</span> <span class="n">delta</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="o">-</span> <span class="n">sq</span> <span class="o">*</span> <span class="n">delta</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="mi">0</span><span class="p">,</span> <span class="n">sq</span> <span class="o">*</span> <span class="n">delta</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">sq</span> <span class="o">*</span> <span class="n">delta</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]],</span>
+ <span class="p">[</span><span class="n">delta</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="o">-</span> <span class="n">delta</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="o">-</span> <span class="n">q</span><span class="p">,</span> <span class="o">-</span> <span class="n">delta</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">delta</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]]])</span>
+
+ <span class="n">G</span> <span class="o">=</span> <span class="n">G</span> <span class="o">/</span> <span class="n">q</span>
+ <span class="n">nLM</span> <span class="o">=</span> <span class="n">calc_n_LM</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
+ <span class="n">F1</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="mi">3</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">3</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">nLM</span><span class="p">))))</span>
+ <span class="n">F2</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">3</span><span class="p">)),</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">i</span> <span class="o">-</span> <span class="mi">1</span><span class="p">))),</span>
+ <span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">nLM</span> <span class="o">-</span> <span class="mi">2</span> <span class="o">*</span> <span class="n">i</span><span class="p">))))</span>
+
+ <span class="n">F</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="n">F1</span><span class="p">,</span> <span class="n">F2</span><span class="p">))</span>
+
+ <span class="n">H</span> <span class="o">=</span> <span class="n">G</span> <span class="o">@</span> <span class="n">F</span>
+
+ <span class="k">return</span> <span class="n">H</span>
+</pre></div>
+</div>
+</section>
+<section id="observation-step">
+<h2>Observation Step<a class="headerlink" href="#observation-step" title="Permalink to this headline"></a></h2>
+<p>The observation step described here is outside the main EKF SLAM process
+and is primarily used as a method of driving the simulation. The
+observations function is in charge of calculating how the poses of the
+robots change and accumulate error over time, and the theoretical
+measurements that are expected as a result of each measurement.</p>
+<p>Observations are based on the TRUE position of the robot. Error in dead
+reckoning and control functions are passed along here as well.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">observation</span><span class="p">(</span><span class="n">xTrue</span><span class="p">,</span> <span class="n">xd</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">RFID</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> :param xTrue: the true pose of the system</span>
+<span class="sd"> :param xd: the current noisy estimate of the system</span>
+<span class="sd"> :param u: the current control input</span>
+<span class="sd"> :param RFID: the true position of the landmarks</span>
+
+<span class="sd"> :returns: Computes the true position, observations, dead reckoning (noisy) position,</span>
+<span class="sd"> and noisy control function</span>
+<span class="sd"> """</span>
+ <span class="n">xTrue</span> <span class="o">=</span> <span class="n">motion_model</span><span class="p">(</span><span class="n">xTrue</span><span class="p">,</span> <span class="n">u</span><span class="p">)</span>
+
+ <span class="c1"># add noise to gps x-y</span>
+ <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">))</span>
+
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">RFID</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">])):</span> <span class="c1"># Test all beacons, only add the ones we can see (within MAX_RANGE)</span>
+
+ <span class="n">dx</span> <span class="o">=</span> <span class="n">RFID</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">-</span> <span class="n">xTrue</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">dy</span> <span class="o">=</span> <span class="n">RFID</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">xTrue</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">d</span> <span class="o">=</span> <span class="n">math</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">dx</span><span class="o">**</span><span class="mi">2</span> <span class="o">+</span> <span class="n">dy</span><span class="o">**</span><span class="mi">2</span><span class="p">)</span>
+ <span class="n">angle</span> <span class="o">=</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">atan2</span><span class="p">(</span><span class="n">dy</span><span class="p">,</span> <span class="n">dx</span><span class="p">)</span> <span class="o">-</span> <span class="n">xTrue</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">])</span>
+ <span class="k">if</span> <span class="n">d</span> <span class="o"><=</span> <span class="n">MAX_RANGE</span><span class="p">:</span>
+ <span class="n">dn</span> <span class="o">=</span> <span class="n">d</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">()</span> <span class="o">*</span> <span class="n">Qsim</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="c1"># add noise</span>
+ <span class="n">anglen</span> <span class="o">=</span> <span class="n">angle</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">()</span> <span class="o">*</span> <span class="n">Qsim</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]</span> <span class="c1"># add noise</span>
+ <span class="n">zi</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([</span><span class="n">dn</span><span class="p">,</span> <span class="n">anglen</span><span class="p">,</span> <span class="n">i</span><span class="p">])</span>
+ <span class="n">z</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vstack</span><span class="p">((</span><span class="n">z</span><span class="p">,</span> <span class="n">zi</span><span class="p">))</span>
+
+ <span class="c1"># add noise to input</span>
+ <span class="n">ud</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span>
+ <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">()</span> <span class="o">*</span> <span class="n">Rsim</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
+ <span class="n">u</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">randn</span><span class="p">()</span> <span class="o">*</span> <span class="n">Rsim</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">]]])</span><span class="o">.</span><span class="n">T</span>
+
+ <span class="n">xd</span> <span class="o">=</span> <span class="n">motion_model</span><span class="p">(</span><span class="n">xd</span><span class="p">,</span> <span class="n">ud</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">xTrue</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">xd</span><span class="p">,</span> <span class="n">ud</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">calc_n_LM</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Calculates the number of landmarks currently tracked in the state</span>
+<span class="sd"> :param x: the state</span>
+<span class="sd"> :returns: the number of landmarks n</span>
+<span class="sd"> """</span>
+ <span class="n">n</span> <span class="o">=</span> <span class="nb">int</span><span class="p">((</span><span class="nb">len</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">-</span> <span class="n">STATE_SIZE</span><span class="p">)</span> <span class="o">/</span> <span class="n">LM_SIZE</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">n</span>
+
+
+<span class="k">def</span> <span class="nf">jacob_motion</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">u</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Calculates the jacobian of motion model.</span>
+
+<span class="sd"> :param x: The state, including the estimated position of the system</span>
+<span class="sd"> :param u: The control function</span>
+<span class="sd"> :returns: G: Jacobian</span>
+<span class="sd"> Fx: STATE_SIZE x (STATE_SIZE + 2 * num_landmarks) matrix where the left side is an identity matrix</span>
+<span class="sd"> """</span>
+
+ <span class="c1"># [eye(3) [0 x y; 0 x y; 0 x y]]</span>
+ <span class="n">Fx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">STATE_SIZE</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span>
+ <span class="p">(</span><span class="n">STATE_SIZE</span><span class="p">,</span> <span class="n">LM_SIZE</span> <span class="o">*</span> <span class="n">calc_n_LM</span><span class="p">(</span><span class="n">x</span><span class="p">)))))</span>
+
+ <span class="n">jF</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="o">-</span><span class="n">DT</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">])],</span>
+ <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="n">DT</span> <span class="o">*</span> <span class="n">u</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">])],</span>
+ <span class="p">[</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">]],</span><span class="n">dtype</span><span class="o">=</span><span class="nb">object</span><span class="p">)</span>
+
+ <span class="n">G</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">STATE_SIZE</span><span class="p">)</span> <span class="o">+</span> <span class="n">Fx</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">jF</span> <span class="o">@</span> <span class="n">Fx</span>
+ <span class="k">if</span> <span class="n">calc_n_LM</span><span class="p">(</span><span class="n">x</span><span class="p">)</span> <span class="o">></span> <span class="mi">0</span><span class="p">:</span>
+ <span class="nb">print</span><span class="p">(</span><span class="n">Fx</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
+ <span class="k">return</span> <span class="n">G</span><span class="p">,</span> <span class="n">Fx</span><span class="p">,</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">calc_LM_Pos</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">z</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Calculates the pose in the world coordinate frame of a landmark at the given measurement.</span>
+
+<span class="sd"> :param x: [x; y; theta]</span>
+<span class="sd"> :param z: [range; bearing]</span>
+<span class="sd"> :returns: [x; y] for given measurement</span>
+<span class="sd"> """</span>
+ <span class="n">zp</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+
+ <span class="n">zp</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">z</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">z</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+ <span class="n">zp</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">z</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="n">z</span><span class="p">[</span><span class="mi">1</span><span class="p">])</span>
+ <span class="c1">#zp[0, 0] = x[0, 0] + z[0, 0] * math.cos(x[2, 0] + z[0, 1])</span>
+ <span class="c1">#zp[1, 0] = x[1, 0] + z[0, 0] * math.sin(x[2, 0] + z[0, 1])</span>
+
+ <span class="k">return</span> <span class="n">zp</span>
+
+
+<span class="k">def</span> <span class="nf">get_LM_Pos_from_state</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">ind</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Returns the position of a given landmark</span>
+
+<span class="sd"> :param x: The state containing all landmark positions</span>
+<span class="sd"> :param ind: landmark id</span>
+<span class="sd"> :returns: The position of the landmark</span>
+<span class="sd"> """</span>
+ <span class="n">lm</span> <span class="o">=</span> <span class="n">x</span><span class="p">[</span><span class="n">STATE_SIZE</span> <span class="o">+</span> <span class="n">LM_SIZE</span> <span class="o">*</span> <span class="n">ind</span><span class="p">:</span> <span class="n">STATE_SIZE</span> <span class="o">+</span> <span class="n">LM_SIZE</span> <span class="o">*</span> <span class="p">(</span><span class="n">ind</span> <span class="o">+</span> <span class="mi">1</span><span class="p">),</span> <span class="p">:]</span>
+
+ <span class="k">return</span> <span class="n">lm</span>
+
+
+<span class="k">def</span> <span class="nf">search_correspond_LM_ID</span><span class="p">(</span><span class="n">xAug</span><span class="p">,</span> <span class="n">PAug</span><span class="p">,</span> <span class="n">zi</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Landmark association with Mahalanobis distance.</span>
+
+<span class="sd"> If this landmark is at least M_DIST_TH units away from all known landmarks,</span>
+<span class="sd"> it is a NEW landmark.</span>
+
+<span class="sd"> :param xAug: The estimated state</span>
+<span class="sd"> :param PAug: The estimated covariance</span>
+<span class="sd"> :param zi: the read measurements of specific landmark</span>
+<span class="sd"> :returns: landmark id</span>
+<span class="sd"> """</span>
+
+ <span class="n">nLM</span> <span class="o">=</span> <span class="n">calc_n_LM</span><span class="p">(</span><span class="n">xAug</span><span class="p">)</span>
+
+ <span class="n">mdist</span> <span class="o">=</span> <span class="p">[]</span>
+
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">nLM</span><span class="p">):</span>
+ <span class="n">lm</span> <span class="o">=</span> <span class="n">get_LM_Pos_from_state</span><span class="p">(</span><span class="n">xAug</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
+ <span class="n">y</span><span class="p">,</span> <span class="n">S</span><span class="p">,</span> <span class="n">H</span> <span class="o">=</span> <span class="n">calc_innovation</span><span class="p">(</span><span class="n">lm</span><span class="p">,</span> <span class="n">xAug</span><span class="p">,</span> <span class="n">PAug</span><span class="p">,</span> <span class="n">zi</span><span class="p">,</span> <span class="n">i</span><span class="p">)</span>
+ <span class="n">mdist</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">y</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">S</span><span class="p">)</span> <span class="o">@</span> <span class="n">y</span><span class="p">)</span>
+
+ <span class="n">mdist</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">M_DIST_TH</span><span class="p">)</span> <span class="c1"># new landmark</span>
+
+ <span class="n">minid</span> <span class="o">=</span> <span class="n">mdist</span><span class="o">.</span><span class="n">index</span><span class="p">(</span><span class="nb">min</span><span class="p">(</span><span class="n">mdist</span><span class="p">))</span>
+
+ <span class="k">return</span> <span class="n">minid</span>
+
+<span class="k">def</span> <span class="nf">calc_input</span><span class="p">():</span>
+ <span class="n">v</span> <span class="o">=</span> <span class="mf">1.0</span> <span class="c1"># [m/s]</span>
+ <span class="n">yawrate</span> <span class="o">=</span> <span class="mf">0.1</span> <span class="c1"># [rad/s]</span>
+ <span class="n">u</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="n">v</span><span class="p">,</span> <span class="n">yawrate</span><span class="p">]])</span><span class="o">.</span><span class="n">T</span>
+ <span class="k">return</span> <span class="n">u</span>
+
+<span class="k">def</span> <span class="nf">pi_2_pi</span><span class="p">(</span><span class="n">angle</span><span class="p">):</span>
+ <span class="k">return</span> <span class="p">(</span><span class="n">angle</span> <span class="o">+</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="o">%</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span> <span class="o">-</span> <span class="n">math</span><span class="o">.</span><span class="n">pi</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">main</span><span class="p">():</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s2">" start!!"</span><span class="p">)</span>
+
+ <span class="n">time</span> <span class="o">=</span> <span class="mf">0.0</span>
+
+ <span class="c1"># RFID positions [x, y]</span>
+ <span class="n">RFID</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">10.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.0</span><span class="p">],</span>
+ <span class="p">[</span><span class="mf">15.0</span><span class="p">,</span> <span class="mf">10.0</span><span class="p">],</span>
+ <span class="p">[</span><span class="mf">3.0</span><span class="p">,</span> <span class="mf">15.0</span><span class="p">],</span>
+ <span class="p">[</span><span class="o">-</span><span class="mf">5.0</span><span class="p">,</span> <span class="mf">20.0</span><span class="p">]])</span>
+
+ <span class="c1"># State Vector [x y yaw v]'</span>
+ <span class="n">xEst</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">STATE_SIZE</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+ <span class="n">xTrue</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">STATE_SIZE</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+ <span class="n">PEst</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">eye</span><span class="p">(</span><span class="n">STATE_SIZE</span><span class="p">)</span>
+
+ <span class="n">xDR</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">STATE_SIZE</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span> <span class="c1"># Dead reckoning</span>
+
+ <span class="c1"># history</span>
+ <span class="n">hxEst</span> <span class="o">=</span> <span class="n">xEst</span>
+ <span class="n">hxTrue</span> <span class="o">=</span> <span class="n">xTrue</span>
+ <span class="n">hxDR</span> <span class="o">=</span> <span class="n">xTrue</span>
+
+ <span class="k">while</span> <span class="n">SIM_TIME</span> <span class="o">>=</span> <span class="n">time</span><span class="p">:</span>
+ <span class="n">time</span> <span class="o">+=</span> <span class="n">DT</span>
+ <span class="n">u</span> <span class="o">=</span> <span class="n">calc_input</span><span class="p">()</span>
+
+ <span class="n">xTrue</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">xDR</span><span class="p">,</span> <span class="n">ud</span> <span class="o">=</span> <span class="n">observation</span><span class="p">(</span><span class="n">xTrue</span><span class="p">,</span> <span class="n">xDR</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">RFID</span><span class="p">)</span>
+
+ <span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span> <span class="o">=</span> <span class="n">ekf_slam</span><span class="p">(</span><span class="n">xEst</span><span class="p">,</span> <span class="n">PEst</span><span class="p">,</span> <span class="n">ud</span><span class="p">,</span> <span class="n">z</span><span class="p">)</span>
+
+ <span class="n">x_state</span> <span class="o">=</span> <span class="n">xEst</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">STATE_SIZE</span><span class="p">]</span>
+
+ <span class="c1"># store data history</span>
+ <span class="n">hxEst</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">hxEst</span><span class="p">,</span> <span class="n">x_state</span><span class="p">))</span>
+ <span class="n">hxDR</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">hxDR</span><span class="p">,</span> <span class="n">xDR</span><span class="p">))</span>
+ <span class="n">hxTrue</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">hxTrue</span><span class="p">,</span> <span class="n">xTrue</span><span class="p">))</span>
+
+ <span class="k">if</span> <span class="n">show_animation</span><span class="p">:</span> <span class="c1"># pragma: no cover</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">cla</span><span class="p">()</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">RFID</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">RFID</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"*k"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xEst</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">xEst</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="s2">".r"</span><span class="p">)</span>
+
+ <span class="c1"># plot landmark</span>
+ <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">calc_n_LM</span><span class="p">(</span><span class="n">xEst</span><span class="p">)):</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">xEst</span><span class="p">[</span><span class="n">STATE_SIZE</span> <span class="o">+</span> <span class="n">i</span> <span class="o">*</span> <span class="mi">2</span><span class="p">],</span>
+ <span class="n">xEst</span><span class="p">[</span><span class="n">STATE_SIZE</span> <span class="o">+</span> <span class="n">i</span> <span class="o">*</span> <span class="mi">2</span> <span class="o">+</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"xg"</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">hxTrue</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:],</span>
+ <span class="n">hxTrue</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span> <span class="s2">"-b"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">hxDR</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:],</span>
+ <span class="n">hxDR</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span> <span class="s2">"-k"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">hxEst</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:],</span>
+ <span class="n">hxEst</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span> <span class="s2">"-r"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">axis</span><span class="p">(</span><span class="s2">"equal"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">(</span><span class="kc">True</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">pause</span><span class="p">(</span><span class="mf">0.001</span><span class="p">)</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="o">%</span><span class="k">matplotlib</span> notebook
+<span class="n">main</span><span class="p">()</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span> start!!
+New LM
+New LM
+New LM
+</pre></div>
+</div>
+<img alt="../../../_images/ekf_slam_1_0.png" src="../../../_images/ekf_slam_1_0.png" />
+</section>
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="http://www.probabilistic-robotics.org/">PROBABILISTIC ROBOTICS</a></p></li>
+</ul>
+</section>
+</section>
+
+
+ </div>
+ </div>
+ <footer><div class="rst-footer-buttons" role="navigation" aria-label="Footer">
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+<li class="toctree-l1"><a class="reference internal" href="../../mapping/mapping.html">Mapping</a></li>
+<li class="toctree-l1 current"><a class="reference internal" href="../slam.html">SLAM</a><ul class="current">
+<li class="toctree-l2"><a class="reference internal" href="../iterative_closest_point_matching/iterative_closest_point_matching.html">Iterative Closest Point (ICP) Matching</a></li>
+<li class="toctree-l2"><a class="reference internal" href="../ekf_slam/ekf_slam.html">EKF SLAM</a></li>
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+<li class="toctree-l2 current"><a class="current reference internal" href="#">Graph based SLAM</a><ul>
+<li class="toctree-l3"><a class="reference internal" href="#graph-slam">Graph SLAM</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#introduction">Introduction</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#minimal-example">Minimal Example</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#graph-optimization">Graph Optimization</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#planar-example">Planar Example:</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#the-references">The references:</a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="#graph-slam-formulation">Graph SLAM Formulation</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#problem-formulation">Problem Formulation</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#dimensionality-and-pose-representation">Dimensionality and Pose Representation</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#graph-slam-algorithm">Graph SLAM Algorithm</a></li>
+</ul>
+</li>
+<li class="toctree-l3"><a class="reference internal" href="#graph-slam-for-a-real-world-se-2-dataset">Graph SLAM for a real-world SE(2) dataset</a><ul>
+<li class="toctree-l4"><a class="reference internal" href="#id4">Introduction</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#the-dataset">The Dataset</a></li>
+<li class="toctree-l4"><a class="reference internal" href="#optimization">Optimization</a></li>
+</ul>
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+<li class="toctree-l3"><a class="reference internal" href="#references">References:</a></li>
+</ul>
+</li>
+</ul>
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+
+ <section id="graph-based-slam">
+<h1>Graph based SLAM<a class="headerlink" href="#graph-based-slam" title="Permalink to this headline"></a></h1>
+<p>This is a graph based SLAM example.</p>
+<p>The blue line is ground truth.</p>
+<p>The black line is dead reckoning.</p>
+<p>The red line is the estimated trajectory with Graph based SLAM.</p>
+<p>The black stars are landmarks for graph edge generation.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/GraphBasedSLAM/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/GraphBasedSLAM/animation.gif" />
+<section id="graph-slam">
+<h2>Graph SLAM<a class="headerlink" href="#graph-slam" title="Permalink to this headline"></a></h2>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">copy</span>
+<span class="kn">import</span> <span class="nn">math</span>
+<span class="kn">import</span> <span class="nn">itertools</span>
+<span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
+<span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="k">as</span> <span class="nn">plt</span>
+<span class="kn">from</span> <span class="nn">graph_based_slam</span> <span class="kn">import</span> <span class="n">calc_rotational_matrix</span><span class="p">,</span> <span class="n">calc_jacobian</span><span class="p">,</span> <span class="n">cal_observation_sigma</span><span class="p">,</span> \
+ <span class="n">calc_input</span><span class="p">,</span> <span class="n">observation</span><span class="p">,</span> <span class="n">motion_model</span><span class="p">,</span> <span class="n">Edge</span><span class="p">,</span> <span class="n">pi_2_pi</span>
+
+<span class="o">%</span><span class="k">matplotlib</span> inline
+<span class="n">np</span><span class="o">.</span><span class="n">set_printoptions</span><span class="p">(</span><span class="n">precision</span><span class="o">=</span><span class="mi">3</span><span class="p">,</span> <span class="n">suppress</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+<span class="n">np</span><span class="o">.</span><span class="n">random</span><span class="o">.</span><span class="n">seed</span><span class="p">(</span><span class="mi">0</span><span class="p">)</span>
+</pre></div>
+</div>
+<section id="introduction">
+<h3>Introduction<a class="headerlink" href="#introduction" title="Permalink to this headline"></a></h3>
+<p>In contrast to the probabilistic approaches for solving SLAM, such as
+EKF, UKF, particle filters, and so on, the graph technique formulates
+the SLAM as an optimization problem. It is mostly used to solve the full
+SLAM problem in an offline fashion, i.e. optimize all the poses of the
+robot after the path has been traversed. However, some variants are
+available that uses graph-based approaches to perform online estimation
+or to solve for a subset of the poses.</p>
+<p>GraphSLAM uses the motion information as well as the observations of the
+environment to create least square problem that can be solved using
+standard optimization techniques.</p>
+</section>
+<section id="minimal-example">
+<h3>Minimal Example<a class="headerlink" href="#minimal-example" title="Permalink to this headline"></a></h3>
+<p>The following example illustrates the main idea behind graphSLAM. A
+simple case of a 1D robot is considered that can only move in 1
+direction. The robot is commanded to move forward with a control input
+<span class="math notranslate nohighlight">\(u_t=1\)</span>, however, the motion is not perfect and the measured
+odometry will deviate from the true path. At each time step the robot can
+observe its environment, for this simple case as well, there is only a
+single landmark at coordinates <span class="math notranslate nohighlight">\(x=3\)</span>. The measured observations
+are the range between the robot and landmark. These measurements are
+also subjected to noise. No bearing information is required since this
+is a 1D problem.</p>
+<p>To solve this, graphSLAM creates what is called as the system
+information matrix <span class="math notranslate nohighlight">\(\Omega\)</span> also referred to as <span class="math notranslate nohighlight">\(H\)</span> and the
+information vector <span class="math notranslate nohighlight">\(\xi\)</span> also known as <span class="math notranslate nohighlight">\(b\)</span>. The entries are
+created based on the information of the motion and the observation.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">R</span> <span class="o">=</span> <span class="mf">0.2</span>
+<span class="n">Q</span> <span class="o">=</span> <span class="mf">0.2</span>
+<span class="n">N</span> <span class="o">=</span> <span class="mi">3</span>
+<span class="n">graphics_radius</span> <span class="o">=</span> <span class="mf">0.1</span>
+
+<span class="n">odom</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="mi">1</span><span class="p">))</span>
+<span class="n">obs</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="mi">1</span><span class="p">))</span>
+<span class="n">x_true</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="mi">1</span><span class="p">))</span>
+
+<span class="n">landmark</span> <span class="o">=</span> <span class="mi">3</span>
+<span class="c1"># Simulated readings of odometry and observations</span>
+<span class="n">x_true</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">odom</span><span class="p">[</span><span class="mi">0</span><span class="p">],</span> <span class="n">obs</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.9</span>
+<span class="n">x_true</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">odom</span><span class="p">[</span><span class="mi">1</span><span class="p">],</span> <span class="n">obs</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">=</span> <span class="mf">1.0</span><span class="p">,</span> <span class="mf">1.5</span><span class="p">,</span> <span class="mf">2.0</span>
+<span class="n">x_true</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">odom</span><span class="p">[</span><span class="mi">2</span><span class="p">],</span> <span class="n">obs</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">2.4</span><span class="p">,</span> <span class="mf">1.0</span>
+
+<span class="n">hxDR</span> <span class="o">=</span> <span class="n">copy</span><span class="o">.</span><span class="n">deepcopy</span><span class="p">(</span><span class="n">odom</span><span class="p">)</span>
+<span class="c1"># Visualization</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">landmark</span><span class="p">,</span><span class="mi">0</span><span class="p">,</span> <span class="s1">'*k'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">30</span><span class="p">)</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">):</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">odom</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="mi">0</span><span class="p">,</span> <span class="s1">'.'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'steelblue'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">odom</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">odom</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">+</span> <span class="n">graphics_radius</span><span class="p">],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">],</span> <span class="s1">'r'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">text</span><span class="p">(</span><span class="n">odom</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="mf">0.02</span><span class="p">,</span> <span class="s2">"X_</span><span class="si">{}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">i</span><span class="p">),</span> <span class="n">fontsize</span><span class="o">=</span><span class="mi">12</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">obs</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">+</span><span class="n">odom</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="mi">0</span><span class="p">,</span><span class="s1">'.'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">25</span><span class="p">,</span> <span class="n">color</span><span class="o">=</span><span class="s1">'brown'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_true</span><span class="p">[</span><span class="n">i</span><span class="p">],</span><span class="mi">0</span><span class="p">,</span><span class="s1">'.g'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+
+<span class="c1"># Defined as a function to facilitate iteration</span>
+<span class="k">def</span> <span class="nf">get_H_b</span><span class="p">(</span><span class="n">odom</span><span class="p">,</span> <span class="n">obs</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""</span>
+<span class="sd"> Create the information matrix and information vector. This implementation is</span>
+<span class="sd"> based on the concept of virtual measurement i.e. the observations of the</span>
+<span class="sd"> landmarks are converted into constraints (edges) between the nodes that</span>
+<span class="sd"> have observed this landmark.</span>
+<span class="sd"> """</span>
+ <span class="n">measure_constraints</span> <span class="o">=</span> <span class="p">{}</span>
+ <span class="n">omegas</span> <span class="o">=</span> <span class="p">{}</span>
+ <span class="n">zids</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">itertools</span><span class="o">.</span><span class="n">combinations</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="n">N</span><span class="p">),</span><span class="mi">2</span><span class="p">))</span>
+ <span class="n">H</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="n">N</span><span class="p">))</span>
+ <span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">N</span><span class="p">,</span><span class="mi">1</span><span class="p">))</span>
+ <span class="k">for</span> <span class="p">(</span><span class="n">t1</span><span class="p">,</span> <span class="n">t2</span><span class="p">)</span> <span class="ow">in</span> <span class="n">zids</span><span class="p">:</span>
+ <span class="n">x1</span> <span class="o">=</span> <span class="n">odom</span><span class="p">[</span><span class="n">t1</span><span class="p">]</span>
+ <span class="n">x2</span> <span class="o">=</span> <span class="n">odom</span><span class="p">[</span><span class="n">t2</span><span class="p">]</span>
+ <span class="n">z1</span> <span class="o">=</span> <span class="n">obs</span><span class="p">[</span><span class="n">t1</span><span class="p">]</span>
+ <span class="n">z2</span> <span class="o">=</span> <span class="n">obs</span><span class="p">[</span><span class="n">t2</span><span class="p">]</span>
+
+ <span class="c1"># Adding virtual measurement constraint</span>
+ <span class="n">measure_constraints</span><span class="p">[(</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">)]</span> <span class="o">=</span> <span class="p">(</span><span class="n">x2</span><span class="o">-</span><span class="n">x1</span><span class="o">-</span><span class="n">z1</span><span class="o">+</span><span class="n">z2</span><span class="p">)</span>
+ <span class="n">omegas</span><span class="p">[(</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">)]</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">Q</span><span class="p">))</span>
+
+ <span class="c1"># populate system's information matrix and vector</span>
+ <span class="n">H</span><span class="p">[</span><span class="n">t1</span><span class="p">,</span><span class="n">t1</span><span class="p">]</span> <span class="o">+=</span> <span class="n">omegas</span><span class="p">[(</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">)]</span>
+ <span class="n">H</span><span class="p">[</span><span class="n">t2</span><span class="p">,</span><span class="n">t2</span><span class="p">]</span> <span class="o">+=</span> <span class="n">omegas</span><span class="p">[(</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">)]</span>
+ <span class="n">H</span><span class="p">[</span><span class="n">t2</span><span class="p">,</span><span class="n">t1</span><span class="p">]</span> <span class="o">-=</span> <span class="n">omegas</span><span class="p">[(</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">)]</span>
+ <span class="n">H</span><span class="p">[</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">]</span> <span class="o">-=</span> <span class="n">omegas</span><span class="p">[(</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">)]</span>
+
+ <span class="n">b</span><span class="p">[</span><span class="n">t1</span><span class="p">]</span> <span class="o">+=</span> <span class="n">omegas</span><span class="p">[(</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">)]</span> <span class="o">*</span> <span class="n">measure_constraints</span><span class="p">[(</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">)]</span>
+ <span class="n">b</span><span class="p">[</span><span class="n">t2</span><span class="p">]</span> <span class="o">-=</span> <span class="n">omegas</span><span class="p">[(</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">)]</span> <span class="o">*</span> <span class="n">measure_constraints</span><span class="p">[(</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">)]</span>
+
+ <span class="k">return</span> <span class="n">H</span><span class="p">,</span> <span class="n">b</span>
+
+
+<span class="n">H</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">get_H_b</span><span class="p">(</span><span class="n">odom</span><span class="p">,</span> <span class="n">obs</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"The determinant of H: "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">det</span><span class="p">(</span><span class="n">H</span><span class="p">))</span>
+<span class="n">H</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]</span> <span class="o">+=</span> <span class="mi">1</span> <span class="c1"># np.inf ?</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"The determinant of H after anchoring constraint: "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">det</span><span class="p">(</span><span class="n">H</span><span class="p">))</span>
+
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="mi">5</span><span class="p">):</span>
+ <span class="n">H</span><span class="p">,</span> <span class="n">b</span> <span class="o">=</span> <span class="n">get_H_b</span><span class="p">(</span><span class="n">odom</span><span class="p">,</span> <span class="n">obs</span><span class="p">)</span>
+ <span class="n">H</span><span class="p">[(</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">)]</span> <span class="o">+=</span> <span class="mi">1</span>
+
+ <span class="c1"># Recover the posterior over the path</span>
+ <span class="n">dx</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">H</span><span class="p">)</span> <span class="o">@</span> <span class="n">b</span>
+ <span class="n">odom</span> <span class="o">+=</span> <span class="n">dx</span>
+ <span class="c1"># repeat till convergence</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"Running graphSLAM ..."</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"Odometry values after optimzation: </span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span> <span class="n">odom</span><span class="p">)</span>
+
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x_true</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">x_true</span><span class="o">.</span><span class="n">shape</span><span class="p">),</span> <span class="s1">'.'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Ground truth'</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">odom</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">x_true</span><span class="o">.</span><span class="n">shape</span><span class="p">),</span> <span class="s1">'.'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Estimation'</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">hxDR</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">x_true</span><span class="o">.</span><span class="n">shape</span><span class="p">),</span> <span class="s1">'.'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Odom'</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../../_images/graphSLAM_doc_2_0.png" src="../../../_images/graphSLAM_doc_2_0.png" />
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">The</span> <span class="n">determinant</span> <span class="n">of</span> <span class="n">H</span><span class="p">:</span> <span class="mf">0.0</span>
+<span class="n">The</span> <span class="n">determinant</span> <span class="n">of</span> <span class="n">H</span> <span class="n">after</span> <span class="n">anchoring</span> <span class="n">constraint</span><span class="p">:</span> <span class="mf">18.750000000000007</span>
+<span class="n">Running</span> <span class="n">graphSLAM</span> <span class="o">...</span>
+<span class="n">Odometry</span> <span class="n">values</span> <span class="n">after</span> <span class="n">optimzation</span><span class="p">:</span>
+ <span class="p">[[</span><span class="o">-</span><span class="mf">0.</span> <span class="p">]</span>
+ <span class="p">[</span> <span class="mf">0.9</span><span class="p">]</span>
+ <span class="p">[</span> <span class="mf">1.9</span><span class="p">]]</span>
+</pre></div>
+</div>
+<img alt="../../../_images/graphSLAM_doc_2_2.png" src="../../../_images/graphSLAM_doc_2_2.png" />
+<p>In particular, the tasks are split into 2 parts, graph construction, and
+graph optimization. ### Graph Construction</p>
+<p>Firstly the nodes are defined
+<span class="math notranslate nohighlight">\(\boldsymbol{x} = \boldsymbol{x}_{1:n}\)</span> such that each node is the
+pose of the robot at time <span class="math notranslate nohighlight">\(t_i\)</span> Secondly, the edges i.e. the
+constraints, are constructed according to the following conditions:</p>
+<ul class="simple">
+<li><p>robot moves from <span class="math notranslate nohighlight">\(\boldsymbol{x}_i\)</span> to
+<span class="math notranslate nohighlight">\(\boldsymbol{x}_j\)</span>. This edge corresponds to the odometry
+measurement. Relative motion constraints (Not included in the
+previous minimal example).</p></li>
+<li><p>Measurement constraints, this can be done in two ways:</p>
+<ul>
+<li><p>The information matrix is set in such a way that it includes the
+landmarks in the map as well. Then the constraints can be entered
+in a straightforward fashion between a node
+<span class="math notranslate nohighlight">\(\boldsymbol{x}_i\)</span> and some landmark <span class="math notranslate nohighlight">\(m_k\)</span></p></li>
+<li><p>Through creating a virtual measurement among all the node that
+have observed the same landmark. More concretely, robot observes
+the same landmark from <span class="math notranslate nohighlight">\(\boldsymbol{x}_i\)</span> and
+<span class="math notranslate nohighlight">\(\boldsymbol{x}_j\)</span>. Relative measurement constraint. The
+“virtual measurement” <span class="math notranslate nohighlight">\(\boldsymbol{z}_{ij}\)</span>, which is the
+estimated pose of <span class="math notranslate nohighlight">\(\boldsymbol{x}_j\)</span> as seen from the node
+<span class="math notranslate nohighlight">\(\boldsymbol{x}_i\)</span>. The virtual measurement can then be
+entered in the information matrix and vector in a similar fashion
+to the motion constraints.</p></li>
+</ul>
+</li>
+</ul>
+<p>An edge is fully characterized by the values of the error (entry to
+information vector) and the local information matrix (entry to the
+system’s information vector). The larger the local information matrix
+(lower <span class="math notranslate nohighlight">\(Q\)</span> or <span class="math notranslate nohighlight">\(R\)</span>) the values that this edge will contribute
+with.</p>
+<p>Important Notes:</p>
+<ul class="simple">
+<li><p>The addition to the information matrix and vector are added to the
+earlier values.</p></li>
+<li><p>In the case of 2D robot, the constraints will be non-linear,
+therefore, a Jacobian of the error w.r.t the states is needed when
+updated <span class="math notranslate nohighlight">\(H\)</span> and <span class="math notranslate nohighlight">\(b\)</span>.</p></li>
+<li><p>The anchoring constraint is needed in order to avoid having a
+singular information matri.</p></li>
+</ul>
+</section>
+<section id="graph-optimization">
+<h3>Graph Optimization<a class="headerlink" href="#graph-optimization" title="Permalink to this headline"></a></h3>
+<p>The result from this formulation yields an overdetermined system of
+equations. The goal after constructing the graph is to find:
+<span class="math notranslate nohighlight">\(x^*=\underset{x}{\mathrm{argmin}}~\underset{ij}\Sigma~f(e_{ij})\)</span>,
+where <span class="math notranslate nohighlight">\(f\)</span> is some error function that depends on the edges between
+to related nodes <span class="math notranslate nohighlight">\(i\)</span> and <span class="math notranslate nohighlight">\(j\)</span>. The derivation in the references
+arrive at the solution for <span class="math notranslate nohighlight">\(x^* = H^{-1}b\)</span></p>
+</section>
+<section id="planar-example">
+<h3>Planar Example:<a class="headerlink" href="#planar-example" title="Permalink to this headline"></a></h3>
+<p>Now we will go through an example with a more realistic case of a 2D
+robot with 3DoF, namely, <span class="math notranslate nohighlight">\([x, y, \theta]^T\)</span></p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Simulation parameter</span>
+<span class="n">Qsim</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="mf">0.01</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">0.010</span><span class="p">)])</span><span class="o">**</span><span class="mi">2</span> <span class="c1"># error added to range and bearing</span>
+<span class="n">Rsim</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="mf">0.1</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)])</span><span class="o">**</span><span class="mi">2</span> <span class="c1"># error added to [v, w]</span>
+
+<span class="n">DT</span> <span class="o">=</span> <span class="mf">2.0</span> <span class="c1"># time tick [s]</span>
+<span class="n">SIM_TIME</span> <span class="o">=</span> <span class="mf">100.0</span> <span class="c1"># simulation time [s]</span>
+<span class="n">MAX_RANGE</span> <span class="o">=</span> <span class="mf">30.0</span> <span class="c1"># maximum observation range</span>
+<span class="n">STATE_SIZE</span> <span class="o">=</span> <span class="mi">3</span> <span class="c1"># State size [x,y,yaw]</span>
+
+<span class="c1"># TODO: Why not use Qsim ?</span>
+<span class="c1"># Covariance parameter of Graph Based SLAM</span>
+<span class="n">C_SIGMA1</span> <span class="o">=</span> <span class="mf">0.1</span>
+<span class="n">C_SIGMA2</span> <span class="o">=</span> <span class="mf">0.1</span>
+<span class="n">C_SIGMA3</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mf">1.0</span><span class="p">)</span>
+
+<span class="n">MAX_ITR</span> <span class="o">=</span> <span class="mi">20</span> <span class="c1"># Maximum iteration during optimization</span>
+<span class="n">timesteps</span> <span class="o">=</span> <span class="mi">1</span>
+
+<span class="c1"># consider only 2 landmarks for simplicity</span>
+<span class="c1"># RFID positions [x, y, yaw]</span>
+<span class="n">RFID</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">10.0</span><span class="p">,</span> <span class="o">-</span><span class="mf">2.0</span><span class="p">,</span> <span class="mf">0.0</span><span class="p">],</span>
+<span class="c1"># [15.0, 10.0, 0.0],</span>
+<span class="c1"># [3.0, 15.0, 0.0],</span>
+<span class="c1"># [-5.0, 20.0, 0.0],</span>
+<span class="c1"># [-5.0, 5.0, 0.0]</span>
+ <span class="p">])</span>
+
+<span class="c1"># State Vector [x y yaw v]'</span>
+<span class="n">xTrue</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">STATE_SIZE</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+<span class="n">xDR</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">STATE_SIZE</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span> <span class="c1"># Dead reckoning</span>
+<span class="n">xTrue</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mi">45</span><span class="p">)</span>
+<span class="n">xDR</span><span class="p">[</span><span class="mi">2</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">deg2rad</span><span class="p">(</span><span class="mi">45</span><span class="p">)</span>
+<span class="c1"># history initial values</span>
+<span class="n">hxTrue</span> <span class="o">=</span> <span class="n">xTrue</span>
+<span class="n">hxDR</span> <span class="o">=</span> <span class="n">xTrue</span>
+<span class="n">_</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">_</span><span class="p">,</span> <span class="n">_</span> <span class="o">=</span> <span class="n">observation</span><span class="p">(</span><span class="n">xTrue</span><span class="p">,</span> <span class="n">xDR</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mi">0</span><span class="p">,</span><span class="mi">0</span><span class="p">]])</span><span class="o">.</span><span class="n">T</span><span class="p">,</span> <span class="n">RFID</span><span class="p">)</span>
+<span class="n">hz</span> <span class="o">=</span> <span class="p">[</span><span class="n">z</span><span class="p">]</span>
+
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">timesteps</span><span class="p">):</span>
+ <span class="n">u</span> <span class="o">=</span> <span class="n">calc_input</span><span class="p">()</span>
+ <span class="n">xTrue</span><span class="p">,</span> <span class="n">z</span><span class="p">,</span> <span class="n">xDR</span><span class="p">,</span> <span class="n">ud</span> <span class="o">=</span> <span class="n">observation</span><span class="p">(</span><span class="n">xTrue</span><span class="p">,</span> <span class="n">xDR</span><span class="p">,</span> <span class="n">u</span><span class="p">,</span> <span class="n">RFID</span><span class="p">)</span>
+ <span class="n">hxDR</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">hxDR</span><span class="p">,</span> <span class="n">xDR</span><span class="p">))</span>
+ <span class="n">hxTrue</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">hstack</span><span class="p">((</span><span class="n">hxTrue</span><span class="p">,</span> <span class="n">xTrue</span><span class="p">))</span>
+ <span class="n">hz</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">z</span><span class="p">)</span>
+
+<span class="c1"># visualize</span>
+<span class="n">graphics_radius</span> <span class="o">=</span> <span class="mf">0.3</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">RFID</span><span class="p">[:,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">RFID</span><span class="p">[:,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"*k"</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">hxDR</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:],</span> <span class="n">hxDR</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span> <span class="s1">'.'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'Odom'</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">hxTrue</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="p">:],</span> <span class="n">hxTrue</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="p">:],</span> <span class="s1">'.'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.6</span><span class="p">,</span> <span class="n">label</span><span class="o">=</span><span class="s1">'X_true'</span><span class="p">)</span>
+
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">hxDR</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]):</span>
+ <span class="n">x</span> <span class="o">=</span> <span class="n">hxDR</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span>
+ <span class="n">y</span> <span class="o">=</span> <span class="n">hxDR</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span>
+ <span class="n">yaw</span> <span class="o">=</span> <span class="n">hxDR</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span> <span class="o">+</span> <span class="n">graphics_radius</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">yaw</span><span class="p">)],</span>
+ <span class="p">[</span><span class="n">y</span><span class="p">,</span> <span class="n">y</span> <span class="o">+</span> <span class="n">graphics_radius</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">yaw</span><span class="p">)],</span> <span class="s1">'r'</span><span class="p">)</span>
+ <span class="n">d</span> <span class="o">=</span> <span class="n">hz</span><span class="p">[</span><span class="n">i</span><span class="p">][:,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">angle</span> <span class="o">=</span> <span class="n">hz</span><span class="p">[</span><span class="n">i</span><span class="p">][:,</span> <span class="mi">1</span><span class="p">]</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">x</span> <span class="o">+</span> <span class="n">d</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">angle</span> <span class="o">+</span> <span class="n">yaw</span><span class="p">)],</span> <span class="p">[</span><span class="n">y</span> <span class="o">+</span> <span class="n">d</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">angle</span> <span class="o">+</span> <span class="n">yaw</span><span class="p">)],</span> <span class="s1">'.'</span><span class="p">,</span>
+ <span class="n">markersize</span><span class="o">=</span><span class="mi">20</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.7</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<img alt="../../../_images/graphSLAM_doc_4_0.png" src="../../../_images/graphSLAM_doc_4_0.png" />
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Copy the data to have a consistent naming with the .py file</span>
+<span class="n">zlist</span> <span class="o">=</span> <span class="n">copy</span><span class="o">.</span><span class="n">deepcopy</span><span class="p">(</span><span class="n">hz</span><span class="p">)</span>
+<span class="n">x_opt</span> <span class="o">=</span> <span class="n">copy</span><span class="o">.</span><span class="n">deepcopy</span><span class="p">(</span><span class="n">hxDR</span><span class="p">)</span>
+<span class="n">xlist</span> <span class="o">=</span> <span class="n">copy</span><span class="o">.</span><span class="n">deepcopy</span><span class="p">(</span><span class="n">hxDR</span><span class="p">)</span>
+<span class="n">number_of_nodes</span> <span class="o">=</span> <span class="n">x_opt</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span>
+<span class="n">n</span> <span class="o">=</span> <span class="n">number_of_nodes</span> <span class="o">*</span> <span class="n">STATE_SIZE</span>
+</pre></div>
+</div>
+<p>After the data has been saved, the graph will be constructed by looking
+at each pair for nodes. The virtual measurement is only created if two
+nodes have observed the same landmark at different points in time. The
+next cells are a walk through for a single iteration of graph
+construction -> optimization -> estimate update.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># get all the possible combination of the different node</span>
+<span class="n">zids</span> <span class="o">=</span> <span class="nb">list</span><span class="p">(</span><span class="n">itertools</span><span class="o">.</span><span class="n">combinations</span><span class="p">(</span><span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">zlist</span><span class="p">)),</span> <span class="mi">2</span><span class="p">))</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"Node combinations: </span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span> <span class="n">zids</span><span class="p">)</span>
+
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">xlist</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">1</span><span class="p">]):</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"Node </span><span class="si">{}</span><span class="s2"> observed landmark with ID </span><span class="si">{}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">zlist</span><span class="p">[</span><span class="n">i</span><span class="p">][</span><span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">]))</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Node</span> <span class="n">combinations</span><span class="p">:</span>
+ <span class="p">[(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)]</span>
+<span class="n">Node</span> <span class="mi">0</span> <span class="n">observed</span> <span class="n">landmark</span> <span class="k">with</span> <span class="n">ID</span> <span class="mf">0.0</span>
+<span class="n">Node</span> <span class="mi">1</span> <span class="n">observed</span> <span class="n">landmark</span> <span class="k">with</span> <span class="n">ID</span> <span class="mf">0.0</span>
+</pre></div>
+</div>
+<p>In the following code snippet the error based on the virtual measurement
+between node 0 and 1 will be created. The equations for the error is as follows:
+<span class="math notranslate nohighlight">\(e_{ij}^x = x_j + d_j cos(\psi_j +\theta_j) - x_i - d_i cos(\psi_i + \theta_i)\)</span></p>
+<p><span class="math notranslate nohighlight">\(e_{ij}^y = y_j + d_j sin(\psi_j + \theta_j) - y_i - d_i sin(\psi_i + \theta_i)\)</span></p>
+<p><span class="math notranslate nohighlight">\(e_{ij}^x = \psi_j + \theta_j - \psi_i - \theta_i\)</span></p>
+<p>Where <span class="math notranslate nohighlight">\([x_i, y_i, \psi_i]\)</span> is the pose for node <span class="math notranslate nohighlight">\(i\)</span> and
+similarly for node <span class="math notranslate nohighlight">\(j\)</span>, <span class="math notranslate nohighlight">\(d\)</span> is the measured distance at
+nodes <span class="math notranslate nohighlight">\(i\)</span> and <span class="math notranslate nohighlight">\(j\)</span>, and <span class="math notranslate nohighlight">\(\theta\)</span> is the measured
+bearing to the landmark. The difference is visualized with the figure in
+the next cell.</p>
+<p>In case of perfect motion and perfect measurement the error shall be
+zero since <span class="math notranslate nohighlight">\(x_j + d_j cos(\psi_j + \theta_j)\)</span> should equal
+<span class="math notranslate nohighlight">\(x_i + d_i cos(\psi_i + \theta_i)\)</span></p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Initialize edges list</span>
+<span class="n">edges</span> <span class="o">=</span> <span class="p">[]</span>
+
+<span class="c1"># Go through all the different combinations</span>
+<span class="k">for</span> <span class="p">(</span><span class="n">t1</span><span class="p">,</span> <span class="n">t2</span><span class="p">)</span> <span class="ow">in</span> <span class="n">zids</span><span class="p">:</span>
+ <span class="n">x1</span><span class="p">,</span> <span class="n">y1</span><span class="p">,</span> <span class="n">yaw1</span> <span class="o">=</span> <span class="n">xlist</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">t1</span><span class="p">],</span> <span class="n">xlist</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">t1</span><span class="p">],</span> <span class="n">xlist</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="n">t1</span><span class="p">]</span>
+ <span class="n">x2</span><span class="p">,</span> <span class="n">y2</span><span class="p">,</span> <span class="n">yaw2</span> <span class="o">=</span> <span class="n">xlist</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">t2</span><span class="p">],</span> <span class="n">xlist</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="n">t2</span><span class="p">],</span> <span class="n">xlist</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="n">t2</span><span class="p">]</span>
+
+ <span class="c1"># All nodes have valid observation with ID=0, therefore, no data association condition</span>
+ <span class="n">iz1</span> <span class="o">=</span> <span class="mi">0</span>
+ <span class="n">iz2</span> <span class="o">=</span> <span class="mi">0</span>
+
+ <span class="n">d1</span> <span class="o">=</span> <span class="n">zlist</span><span class="p">[</span><span class="n">t1</span><span class="p">][</span><span class="n">iz1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">angle1</span><span class="p">,</span> <span class="n">phi1</span> <span class="o">=</span> <span class="n">zlist</span><span class="p">[</span><span class="n">t1</span><span class="p">][</span><span class="n">iz1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">zlist</span><span class="p">[</span><span class="n">t1</span><span class="p">][</span><span class="n">iz1</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>
+ <span class="n">d2</span> <span class="o">=</span> <span class="n">zlist</span><span class="p">[</span><span class="n">t2</span><span class="p">][</span><span class="n">iz2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+ <span class="n">angle2</span><span class="p">,</span> <span class="n">phi2</span> <span class="o">=</span> <span class="n">zlist</span><span class="p">[</span><span class="n">t2</span><span class="p">][</span><span class="n">iz2</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="n">zlist</span><span class="p">[</span><span class="n">t2</span><span class="p">][</span><span class="n">iz2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]</span>
+
+ <span class="c1"># find angle between observation and horizontal</span>
+ <span class="n">tangle1</span> <span class="o">=</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">yaw1</span> <span class="o">+</span> <span class="n">angle1</span><span class="p">)</span>
+ <span class="n">tangle2</span> <span class="o">=</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">yaw2</span> <span class="o">+</span> <span class="n">angle2</span><span class="p">)</span>
+
+ <span class="c1"># project the observations</span>
+ <span class="n">tmp1</span> <span class="o">=</span> <span class="n">d1</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">tangle1</span><span class="p">)</span>
+ <span class="n">tmp2</span> <span class="o">=</span> <span class="n">d2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">tangle2</span><span class="p">)</span>
+ <span class="n">tmp3</span> <span class="o">=</span> <span class="n">d1</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">tangle1</span><span class="p">)</span>
+ <span class="n">tmp4</span> <span class="o">=</span> <span class="n">d2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">tangle2</span><span class="p">)</span>
+
+ <span class="n">edge</span> <span class="o">=</span> <span class="n">Edge</span><span class="p">()</span>
+ <span class="nb">print</span><span class="p">(</span><span class="n">y1</span><span class="p">,</span><span class="n">y2</span><span class="p">,</span> <span class="n">tmp3</span><span class="p">,</span> <span class="n">tmp4</span><span class="p">)</span>
+ <span class="c1"># calculate the error of the virtual measurement</span>
+ <span class="c1"># node 1 as seen from node 2 throught the observations 1,2</span>
+ <span class="n">edge</span><span class="o">.</span><span class="n">e</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">x2</span> <span class="o">-</span> <span class="n">x1</span> <span class="o">-</span> <span class="n">tmp1</span> <span class="o">+</span> <span class="n">tmp2</span>
+ <span class="n">edge</span><span class="o">.</span><span class="n">e</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">y2</span> <span class="o">-</span> <span class="n">y1</span> <span class="o">-</span> <span class="n">tmp3</span> <span class="o">+</span> <span class="n">tmp4</span>
+ <span class="n">edge</span><span class="o">.</span><span class="n">e</span><span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span> <span class="o">=</span> <span class="n">pi_2_pi</span><span class="p">(</span><span class="n">yaw2</span> <span class="o">-</span> <span class="n">yaw1</span> <span class="o">-</span> <span class="n">tangle1</span> <span class="o">+</span> <span class="n">tangle2</span><span class="p">)</span>
+
+ <span class="n">edge</span><span class="o">.</span><span class="n">d1</span><span class="p">,</span> <span class="n">edge</span><span class="o">.</span><span class="n">d2</span> <span class="o">=</span> <span class="n">d1</span><span class="p">,</span> <span class="n">d2</span>
+ <span class="n">edge</span><span class="o">.</span><span class="n">yaw1</span><span class="p">,</span> <span class="n">edge</span><span class="o">.</span><span class="n">yaw2</span> <span class="o">=</span> <span class="n">yaw1</span><span class="p">,</span> <span class="n">yaw2</span>
+ <span class="n">edge</span><span class="o">.</span><span class="n">angle1</span><span class="p">,</span> <span class="n">edge</span><span class="o">.</span><span class="n">angle2</span> <span class="o">=</span> <span class="n">angle1</span><span class="p">,</span> <span class="n">angle2</span>
+ <span class="n">edge</span><span class="o">.</span><span class="n">id1</span><span class="p">,</span> <span class="n">edge</span><span class="o">.</span><span class="n">id2</span> <span class="o">=</span> <span class="n">t1</span><span class="p">,</span> <span class="n">t2</span>
+
+ <span class="n">edges</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">edge</span><span class="p">)</span>
+
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"For nodes"</span><span class="p">,(</span><span class="n">t1</span><span class="p">,</span><span class="n">t2</span><span class="p">))</span>
+ <span class="nb">print</span><span class="p">(</span><span class="s2">"Added edge with errors: </span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span> <span class="n">edge</span><span class="o">.</span><span class="n">e</span><span class="p">)</span>
+
+ <span class="c1"># Visualize measurement projections</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">RFID</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">RFID</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="s2">"*k"</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">20</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">x1</span><span class="p">,</span><span class="n">x2</span><span class="p">],[</span><span class="n">y1</span><span class="p">,</span><span class="n">y2</span><span class="p">],</span> <span class="s1">'.'</span><span class="p">,</span> <span class="n">markersize</span><span class="o">=</span><span class="mi">50</span><span class="p">,</span> <span class="n">alpha</span><span class="o">=</span><span class="mf">0.8</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">x1</span><span class="p">,</span> <span class="n">x1</span> <span class="o">+</span> <span class="n">graphics_radius</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">yaw1</span><span class="p">)],</span>
+ <span class="p">[</span><span class="n">y1</span><span class="p">,</span> <span class="n">y1</span> <span class="o">+</span> <span class="n">graphics_radius</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">yaw1</span><span class="p">)],</span> <span class="s1">'r'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">x2</span><span class="p">,</span> <span class="n">x2</span> <span class="o">+</span> <span class="n">graphics_radius</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">yaw2</span><span class="p">)],</span>
+ <span class="p">[</span><span class="n">y2</span><span class="p">,</span> <span class="n">y2</span> <span class="o">+</span> <span class="n">graphics_radius</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">yaw2</span><span class="p">)],</span> <span class="s1">'r'</span><span class="p">)</span>
+
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">x1</span><span class="p">,</span><span class="n">x1</span><span class="o">+</span><span class="n">tmp1</span><span class="p">],</span> <span class="p">[</span><span class="n">y1</span><span class="p">,</span><span class="n">y1</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"obs 1 x"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">x2</span><span class="p">,</span><span class="n">x2</span><span class="o">+</span><span class="n">tmp2</span><span class="p">],</span> <span class="p">[</span><span class="n">y2</span><span class="p">,</span><span class="n">y2</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"obs 2 x"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">x1</span><span class="p">,</span><span class="n">x1</span><span class="p">],</span> <span class="p">[</span><span class="n">y1</span><span class="p">,</span><span class="n">y1</span><span class="o">+</span><span class="n">tmp3</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"obs 1 y"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">([</span><span class="n">x2</span><span class="p">,</span><span class="n">x2</span><span class="p">],</span> <span class="p">[</span><span class="n">y2</span><span class="p">,</span><span class="n">y2</span><span class="o">+</span><span class="n">tmp4</span><span class="p">],</span> <span class="n">label</span><span class="o">=</span><span class="s2">"obs 2 y"</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x1</span><span class="o">+</span><span class="n">tmp1</span><span class="p">,</span> <span class="n">y1</span><span class="o">+</span><span class="n">tmp3</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">)</span>
+ <span class="n">plt</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">x2</span><span class="o">+</span><span class="n">tmp2</span><span class="p">,</span> <span class="n">y2</span><span class="o">+</span><span class="n">tmp4</span><span class="p">,</span> <span class="s1">'o'</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">legend</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">grid</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="mf">0.0</span> <span class="mf">1.427649841628278</span> <span class="o">-</span><span class="mf">2.0126109674819155</span> <span class="o">-</span><span class="mf">3.524048014922737</span>
+<span class="n">For</span> <span class="n">nodes</span> <span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
+<span class="n">Added</span> <span class="n">edge</span> <span class="k">with</span> <span class="n">errors</span><span class="p">:</span>
+ <span class="p">[[</span><span class="o">-</span><span class="mf">0.02</span> <span class="p">]</span>
+ <span class="p">[</span><span class="o">-</span><span class="mf">0.084</span><span class="p">]</span>
+ <span class="p">[</span> <span class="mf">0.</span> <span class="p">]]</span>
+</pre></div>
+</div>
+<img alt="../../../_images/graphSLAM_doc_9_1.png" src="../../../_images/graphSLAM_doc_9_1.png" />
+<p>Since the constraints equations derived before are non-linear,
+linearization is needed before we can insert them into the information
+matrix and information vector. Two jacobians</p>
+<p><span class="math notranslate nohighlight">\(A = \frac{\partial e_{ij}}{\partial \boldsymbol{x}_i}\)</span> as
+<span class="math notranslate nohighlight">\(\boldsymbol{x}_i\)</span> holds the three variabls x, y, and theta.
+Similarly, <span class="math notranslate nohighlight">\(B = \frac{\partial e_{ij}}{\partial \boldsymbol{x}_j}\)</span></p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Initialize the system information matrix and information vector</span>
+<span class="n">H</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="n">n</span><span class="p">))</span>
+<span class="n">b</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">n</span><span class="p">,</span> <span class="mi">1</span><span class="p">))</span>
+<span class="n">x_opt</span> <span class="o">=</span> <span class="n">copy</span><span class="o">.</span><span class="n">deepcopy</span><span class="p">(</span><span class="n">hxDR</span><span class="p">)</span>
+
+<span class="k">for</span> <span class="n">edge</span> <span class="ow">in</span> <span class="n">edges</span><span class="p">:</span>
+ <span class="n">id1</span> <span class="o">=</span> <span class="n">edge</span><span class="o">.</span><span class="n">id1</span> <span class="o">*</span> <span class="n">STATE_SIZE</span>
+ <span class="n">id2</span> <span class="o">=</span> <span class="n">edge</span><span class="o">.</span><span class="n">id2</span> <span class="o">*</span> <span class="n">STATE_SIZE</span>
+
+ <span class="n">t1</span> <span class="o">=</span> <span class="n">edge</span><span class="o">.</span><span class="n">yaw1</span> <span class="o">+</span> <span class="n">edge</span><span class="o">.</span><span class="n">angle1</span>
+ <span class="n">A</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">edge</span><span class="o">.</span><span class="n">d1</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">t1</span><span class="p">)],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="p">,</span> <span class="o">-</span><span class="n">edge</span><span class="o">.</span><span class="n">d1</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">t1</span><span class="p">)],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="mf">1.0</span><span class="p">]])</span>
+
+ <span class="n">t2</span> <span class="o">=</span> <span class="n">edge</span><span class="o">.</span><span class="n">yaw2</span> <span class="o">+</span> <span class="n">edge</span><span class="o">.</span><span class="n">angle2</span>
+ <span class="n">B</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">array</span><span class="p">([[</span><span class="mf">1.0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="o">-</span><span class="n">edge</span><span class="o">.</span><span class="n">d2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="n">t2</span><span class="p">)],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">,</span> <span class="n">edge</span><span class="o">.</span><span class="n">d2</span> <span class="o">*</span> <span class="n">math</span><span class="o">.</span><span class="n">cos</span><span class="p">(</span><span class="n">t2</span><span class="p">)],</span>
+ <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mf">1.0</span><span class="p">]])</span>
+
+ <span class="c1"># TODO: use Qsim instead of sigma</span>
+ <span class="n">sigma</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">([</span><span class="n">C_SIGMA1</span><span class="p">,</span> <span class="n">C_SIGMA2</span><span class="p">,</span> <span class="n">C_SIGMA3</span><span class="p">])</span>
+ <span class="n">Rt1</span> <span class="o">=</span> <span class="n">calc_rotational_matrix</span><span class="p">(</span><span class="n">tangle1</span><span class="p">)</span>
+ <span class="n">Rt2</span> <span class="o">=</span> <span class="n">calc_rotational_matrix</span><span class="p">(</span><span class="n">tangle2</span><span class="p">)</span>
+ <span class="n">edge</span><span class="o">.</span><span class="n">omega</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">Rt1</span> <span class="o">@</span> <span class="n">sigma</span> <span class="o">@</span> <span class="n">Rt1</span><span class="o">.</span><span class="n">T</span> <span class="o">+</span> <span class="n">Rt2</span> <span class="o">@</span> <span class="n">sigma</span> <span class="o">@</span> <span class="n">Rt2</span><span class="o">.</span><span class="n">T</span><span class="p">)</span>
+
+ <span class="c1"># Fill in entries in H and b</span>
+ <span class="n">H</span><span class="p">[</span><span class="n">id1</span><span class="p">:</span><span class="n">id1</span> <span class="o">+</span> <span class="n">STATE_SIZE</span><span class="p">,</span> <span class="n">id1</span><span class="p">:</span><span class="n">id1</span> <span class="o">+</span> <span class="n">STATE_SIZE</span><span class="p">]</span> <span class="o">+=</span> <span class="n">A</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">edge</span><span class="o">.</span><span class="n">omega</span> <span class="o">@</span> <span class="n">A</span>
+ <span class="n">H</span><span class="p">[</span><span class="n">id1</span><span class="p">:</span><span class="n">id1</span> <span class="o">+</span> <span class="n">STATE_SIZE</span><span class="p">,</span> <span class="n">id2</span><span class="p">:</span><span class="n">id2</span> <span class="o">+</span> <span class="n">STATE_SIZE</span><span class="p">]</span> <span class="o">+=</span> <span class="n">A</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">edge</span><span class="o">.</span><span class="n">omega</span> <span class="o">@</span> <span class="n">B</span>
+ <span class="n">H</span><span class="p">[</span><span class="n">id2</span><span class="p">:</span><span class="n">id2</span> <span class="o">+</span> <span class="n">STATE_SIZE</span><span class="p">,</span> <span class="n">id1</span><span class="p">:</span><span class="n">id1</span> <span class="o">+</span> <span class="n">STATE_SIZE</span><span class="p">]</span> <span class="o">+=</span> <span class="n">B</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">edge</span><span class="o">.</span><span class="n">omega</span> <span class="o">@</span> <span class="n">A</span>
+ <span class="n">H</span><span class="p">[</span><span class="n">id2</span><span class="p">:</span><span class="n">id2</span> <span class="o">+</span> <span class="n">STATE_SIZE</span><span class="p">,</span> <span class="n">id2</span><span class="p">:</span><span class="n">id2</span> <span class="o">+</span> <span class="n">STATE_SIZE</span><span class="p">]</span> <span class="o">+=</span> <span class="n">B</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">edge</span><span class="o">.</span><span class="n">omega</span> <span class="o">@</span> <span class="n">B</span>
+
+ <span class="n">b</span><span class="p">[</span><span class="n">id1</span><span class="p">:</span><span class="n">id1</span> <span class="o">+</span> <span class="n">STATE_SIZE</span><span class="p">]</span> <span class="o">+=</span> <span class="p">(</span><span class="n">A</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">edge</span><span class="o">.</span><span class="n">omega</span> <span class="o">@</span> <span class="n">edge</span><span class="o">.</span><span class="n">e</span><span class="p">)</span>
+ <span class="n">b</span><span class="p">[</span><span class="n">id2</span><span class="p">:</span><span class="n">id2</span> <span class="o">+</span> <span class="n">STATE_SIZE</span><span class="p">]</span> <span class="o">+=</span> <span class="p">(</span><span class="n">B</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">edge</span><span class="o">.</span><span class="n">omega</span> <span class="o">@</span> <span class="n">edge</span><span class="o">.</span><span class="n">e</span><span class="p">)</span>
+
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">"The determinant of H: "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">det</span><span class="p">(</span><span class="n">H</span><span class="p">))</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="n">extent</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">n</span><span class="p">])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">extent</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">n</span><span class="p">])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+
+<span class="c1"># Fix the origin, multiply by large number gives same results but better visualization</span>
+<span class="n">H</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="n">STATE_SIZE</span><span class="p">,</span> <span class="mi">0</span><span class="p">:</span><span class="n">STATE_SIZE</span><span class="p">]</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">STATE_SIZE</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"The determinant of H after origin constraint: "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">det</span><span class="p">(</span><span class="n">H</span><span class="p">))</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">H</span><span class="p">,</span> <span class="n">extent</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="n">n</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">n</span><span class="p">])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">subplot</span><span class="p">(</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">)</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">imshow</span><span class="p">(</span><span class="n">b</span><span class="p">,</span> <span class="n">extent</span><span class="o">=</span><span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="n">n</span><span class="p">])</span>
+<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">The</span> <span class="n">determinant</span> <span class="n">of</span> <span class="n">H</span><span class="p">:</span> <span class="mf">0.0</span>
+<span class="n">The</span> <span class="n">determinant</span> <span class="n">of</span> <span class="n">H</span> <span class="n">after</span> <span class="n">origin</span> <span class="n">constraint</span><span class="p">:</span> <span class="mf">716.1972439134893</span>
+</pre></div>
+</div>
+<img alt="../../../_images/graphSLAM_doc_11_1.png" src="../../../_images/graphSLAM_doc_11_1.png" />
+<img alt="../../../_images/graphSLAM_doc_11_2.png" src="../../../_images/graphSLAM_doc_11_2.png" />
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="c1"># Find the solution (first iteration)</span>
+<span class="n">dx</span> <span class="o">=</span> <span class="o">-</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">H</span><span class="p">)</span> <span class="o">@</span> <span class="n">b</span>
+<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">number_of_nodes</span><span class="p">):</span>
+ <span class="n">x_opt</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span><span class="mi">3</span><span class="p">,</span> <span class="n">i</span><span class="p">]</span> <span class="o">+=</span> <span class="n">dx</span><span class="p">[</span><span class="n">i</span> <span class="o">*</span> <span class="mi">3</span><span class="p">:</span><span class="n">i</span> <span class="o">*</span> <span class="mi">3</span> <span class="o">+</span> <span class="mi">3</span><span class="p">,</span> <span class="mi">0</span><span class="p">]</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"dx: </span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span><span class="n">dx</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"ground truth: </span><span class="se">\n</span><span class="s2"> "</span><span class="p">,</span><span class="n">hxTrue</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"Odom: </span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span> <span class="n">hxDR</span><span class="p">)</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"SLAM: </span><span class="se">\n</span><span class="s2">"</span><span class="p">,</span> <span class="n">x_opt</span><span class="p">)</span>
+
+<span class="c1"># performance will improve with more iterations, nodes and landmarks.</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2">graphSLAM localization error: "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">x_opt</span> <span class="o">-</span> <span class="n">hxTrue</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">))</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"Odom localization error: "</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">((</span><span class="n">hxDR</span> <span class="o">-</span> <span class="n">hxTrue</span><span class="p">)</span> <span class="o">**</span> <span class="mi">2</span><span class="p">))</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">dx</span><span class="p">:</span>
+ <span class="p">[[</span><span class="o">-</span><span class="mf">0.</span> <span class="p">]</span>
+ <span class="p">[</span><span class="o">-</span><span class="mf">0.</span> <span class="p">]</span>
+ <span class="p">[</span> <span class="mf">0.</span> <span class="p">]</span>
+ <span class="p">[</span> <span class="mf">0.02</span> <span class="p">]</span>
+ <span class="p">[</span> <span class="mf">0.084</span><span class="p">]</span>
+ <span class="p">[</span><span class="o">-</span><span class="mf">0.</span> <span class="p">]]</span>
+<span class="n">ground</span> <span class="n">truth</span><span class="p">:</span>
+ <span class="p">[[</span><span class="mf">0.</span> <span class="mf">1.414</span><span class="p">]</span>
+ <span class="p">[</span><span class="mf">0.</span> <span class="mf">1.414</span><span class="p">]</span>
+ <span class="p">[</span><span class="mf">0.785</span> <span class="mf">0.985</span><span class="p">]]</span>
+<span class="n">Odom</span><span class="p">:</span>
+ <span class="p">[[</span><span class="mf">0.</span> <span class="mf">1.428</span><span class="p">]</span>
+ <span class="p">[</span><span class="mf">0.</span> <span class="mf">1.428</span><span class="p">]</span>
+ <span class="p">[</span><span class="mf">0.785</span> <span class="mf">0.976</span><span class="p">]]</span>
+<span class="n">SLAM</span><span class="p">:</span>
+ <span class="p">[[</span><span class="o">-</span><span class="mf">0.</span> <span class="mf">1.448</span><span class="p">]</span>
+ <span class="p">[</span><span class="o">-</span><span class="mf">0.</span> <span class="mf">1.512</span><span class="p">]</span>
+ <span class="p">[</span> <span class="mf">0.785</span> <span class="mf">0.976</span><span class="p">]]</span>
+
+<span class="n">graphSLAM</span> <span class="n">localization</span> <span class="n">error</span><span class="p">:</span> <span class="mf">0.010729072751057656</span>
+<span class="n">Odom</span> <span class="n">localization</span> <span class="n">error</span><span class="p">:</span> <span class="mf">0.0004460978857535104</span>
+</pre></div>
+</div>
+</section>
+<section id="the-references">
+<h3>The references:<a class="headerlink" href="#the-references" title="Permalink to this headline"></a></h3>
+<ul class="simple">
+<li><p><a class="reference external" href="http://robots.stanford.edu/papers/thrun.graphslam.pdf">The GraphSLAM Algorithm with Applications to Large-Scale Mapping of Urban Structures</a></p></li>
+<li><p><a class="reference external" href="http://ais.informatik.uni-freiburg.de/teaching/ss13/robotics/slides/16-graph-slam.pdf">Introduction to Mobile Robotics Graph-Based SLAM</a></p></li>
+<li><p><a class="reference external" href="http://www2.informatik.uni-freiburg.de/~stachnis/pdf/grisetti10titsmag.pdf">A Tutorial on Graph-Based SLAM</a></p></li>
+</ul>
+<p>N.B. An additional step is required that uses the estimated path to
+update the belief regarding the map.</p>
+</section>
+</section>
+<section id="graph-slam-formulation">
+<span id="id1"></span><h2>Graph SLAM Formulation<a class="headerlink" href="#graph-slam-formulation" title="Permalink to this headline"></a></h2>
+<p>Author Jeff Irion</p>
+<section id="problem-formulation">
+<h3>Problem Formulation<a class="headerlink" href="#problem-formulation" title="Permalink to this headline"></a></h3>
+<p>Let a robot’s trajectory through its environment be represented by a
+sequence of <span class="math notranslate nohighlight">\(N\)</span> poses:
+<span class="math notranslate nohighlight">\(\mathbf{p}_1, \mathbf{p}_2, \ldots, \mathbf{p}_N\)</span>. Each pose lies
+on a manifold: <span class="math notranslate nohighlight">\(\mathbf{p}_i \in \mathcal{M}\)</span>. Simple examples of
+manifolds used in Graph SLAM include 1-D, 2-D, and 3-D space, i.e.,
+<span class="math notranslate nohighlight">\(\mathbb{R}\)</span>, <span class="math notranslate nohighlight">\(\mathbb{R}^2\)</span>, and <span class="math notranslate nohighlight">\(\mathbb{R}^3\)</span>.
+These environments are <em>rectilinear</em>, meaning that there is no concept
+of orientation. By contrast, in <span class="math notranslate nohighlight">\(SE(2)\)</span> problem settings a robot’s
+pose consists of its location in <span class="math notranslate nohighlight">\(\mathbb{R}^2\)</span> and its
+orientation <span class="math notranslate nohighlight">\(\theta\)</span>. Similarly, in <span class="math notranslate nohighlight">\(SE(3)\)</span> a robot’s pose
+consists of its location in <span class="math notranslate nohighlight">\(\mathbb{R}^3\)</span> and its orientation,
+which can be represented via Euler angles, quaternions, or <span class="math notranslate nohighlight">\(SO(3)\)</span>
+rotation matrices.</p>
+<p>As the robot explores its environment, it collects a set of <span class="math notranslate nohighlight">\(M\)</span>
+measurements <span class="math notranslate nohighlight">\(\mathcal{Z} = \{\mathbf{z}_j\}\)</span>. Examples of such
+measurements include odometry, GPS, and IMU data. Given a set of poses
+<span class="math notranslate nohighlight">\(\mathbf{p}_1, \ldots, \mathbf{p}_N\)</span>, we can compute the estimated
+measurement
+<span class="math notranslate nohighlight">\(\hat{\mathbf{z}}_j(\mathbf{p}_1, \ldots, \mathbf{p}_N)\)</span>. We can
+then compute the <em>residual</em>
+<span class="math notranslate nohighlight">\(\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j)\)</span> for measurement
+<span class="math notranslate nohighlight">\(j\)</span>. The formula for the residual depends on the type of
+measurement. As an example, let <span class="math notranslate nohighlight">\(\mathbf{z}_1\)</span> be an odometry
+measurement that was collected when the robot traveled from
+<span class="math notranslate nohighlight">\(\mathbf{p}_1\)</span> to <span class="math notranslate nohighlight">\(\mathbf{p}_2\)</span>. The expected measurement
+and the residual are computed as</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\begin{aligned}
+ \hat{\mathbf{z}}_1(\mathbf{p}_1, \mathbf{p}_2) &= \mathbf{p}_2 \ominus \mathbf{p}_1 \\
+ \mathbf{e}_1(\mathbf{z}_1, \hat{\mathbf{z}}_1) &= \mathbf{z}_1 \ominus \hat{\mathbf{z}}_1 = \mathbf{z}_1 \ominus (\mathbf{p}_2 \ominus \mathbf{p}_1),\end{aligned}\end{split}\]</div>
+<p>where the <span class="math notranslate nohighlight">\(\ominus\)</span> operator indicates inverse pose composition.
+We model measurement <span class="math notranslate nohighlight">\(\mathbf{z}_j\)</span> as having independent Gaussian
+noise with zero mean and covariance matrix <span class="math notranslate nohighlight">\(\Omega_j^{-1}\)</span>; we
+refer to <span class="math notranslate nohighlight">\(\Omega_j\)</span> as the <em>information matrix</em> for measurement
+<span class="math notranslate nohighlight">\(j\)</span>. That is,</p>
+<div class="math notranslate nohighlight" id="equation-infomat">
+<span class="eqno">(1)<a class="headerlink" href="#equation-infomat" title="Permalink to this equation"></a></span>\[p(\mathbf{z}_j \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) = \eta_j \exp (-\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\mathsf{T}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j)\]</div>
+<p>where <span class="math notranslate nohighlight">\(\eta_j\)</span> is the normalization constant.</p>
+<p>The objective of Graph SLAM is to find the maximum likelihood set of
+poses given the measurements <span class="math notranslate nohighlight">\(\mathcal{Z} = \{\mathbf{z}_j\}\)</span>; in
+other words, we want to find</p>
+<div class="math notranslate nohighlight">
+\[\mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z})\]</div>
+<p>Using Bayes’ rule, we can write this probability as</p>
+<div class="math notranslate nohighlight" id="equation-bayes">
+<span class="eqno">(2)<a class="headerlink" href="#equation-bayes" title="Permalink to this equation"></a></span>\[\begin{split}\begin{aligned}
+ p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z}) &= \frac{p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) p(\mathbf{p}_1, \ldots, \mathbf{p}_N) }{ p(\mathcal{Z}) } \notag \\
+ &\propto p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N)
+\end{aligned}\end{split}\]</div>
+<p>since <span class="math notranslate nohighlight">\(p(\mathcal{Z})\)</span> is a constant (albeit, an unknown constant)
+and we assume that <span class="math notranslate nohighlight">\(p(\mathbf{p}_1, \ldots, \mathbf{p}_N)\)</span> is
+uniformly distributed. Therefore, we
+can use Eq. <a class="reference internal" href="#equation-infomat">(1)</a> and and Eq. <a class="reference internal" href="#equation-bayes">(2)</a> to simplify the Graph SLAM
+optimization as follows:</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\begin{aligned}
+ \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p(\mathbf{p}_1, \ldots, \mathbf{p}_N \ | \ \mathcal{Z}) &= \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \ p( \mathcal{Z} \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) \\
+ &= \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \prod_{j=1}^M p(\mathbf{z}_j \ | \ \mathbf{p}_1, \ldots, \mathbf{p}_N) \\
+ &= \mathop{\mathrm{arg\,max}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \prod_{j=1}^M \exp \left( -(\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j) \right) \\
+ &= \mathop{\mathrm{arg\,min}}_{\mathbf{p}_1, \ldots, \mathbf{p}_N} \sum_{j=1}^M (\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j).\end{aligned}\end{split}\]</div>
+<p>We define</p>
+<div class="math notranslate nohighlight">
+\[\chi^2 := \sum_{j=1}^M (\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j))^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j),\]</div>
+<p>and this is what we seek to minimize.</p>
+</section>
+<section id="dimensionality-and-pose-representation">
+<h3>Dimensionality and Pose Representation<a class="headerlink" href="#dimensionality-and-pose-representation" title="Permalink to this headline"></a></h3>
+<p>Before proceeding further, it is helpful to discuss the dimensionality
+of the problem. We have:</p>
+<ul class="simple">
+<li><p>A set of <span class="math notranslate nohighlight">\(N\)</span> poses
+<span class="math notranslate nohighlight">\(\mathbf{p}_1, \mathbf{p}_2, \ldots, \mathbf{p}_N\)</span>, where each
+pose lies on the manifold <span class="math notranslate nohighlight">\(\mathcal{M}\)</span></p>
+<ul>
+<li><p>Each pose <span class="math notranslate nohighlight">\(\mathbf{p}_i\)</span> is represented as a vector in (a
+subset of) <span class="math notranslate nohighlight">\(\mathbb{R}^d\)</span>. For example:</p>
+<ul>
+<li><p>An <span class="math notranslate nohighlight">\(SE(2)\)</span> pose is typically represented as
+<span class="math notranslate nohighlight">\((x, y, \theta)\)</span>, and thus <span class="math notranslate nohighlight">\(d = 3\)</span>.</p></li>
+<li><p>An <span class="math notranslate nohighlight">\(SE(3)\)</span> pose is typically represented as
+<span class="math notranslate nohighlight">\((x, y, z, q_x, q_y, q_z, q_w)\)</span>, where <span class="math notranslate nohighlight">\((x, y, z)\)</span>
+is a point in <span class="math notranslate nohighlight">\(\mathbb{R}^3\)</span> and
+<span class="math notranslate nohighlight">\((q_x, q_y, q_z, q_w)\)</span> is a <em>quaternion</em>, and so
+<span class="math notranslate nohighlight">\(d = 7\)</span>. For more information about <span class="math notranslate nohighlight">\(SE(3)\)</span>
+parameterization and pose transformations, see
+<a class="reference internal" href="#blanco2010tutorial" id="id2"><span>[blanco2010tutorial]</span></a>.</p></li>
+</ul>
+</li>
+<li><p>We also need to be able to represent each pose compactly as a
+vector in (a subset of) <span class="math notranslate nohighlight">\(\mathbb{R}^c\)</span>.</p>
+<ul>
+<li><p>Since an <span class="math notranslate nohighlight">\(SE(2)\)</span> pose has three degrees of freedom, the
+<span class="math notranslate nohighlight">\((x, y, \theta)\)</span> representation is again sufficient and
+<span class="math notranslate nohighlight">\(c=3\)</span>.</p></li>
+<li><p>An <span class="math notranslate nohighlight">\(SE(3)\)</span> pose only has six degrees of freedom, and we
+can represent it compactly as <span class="math notranslate nohighlight">\((x, y, z, q_x, q_y, q_z)\)</span>,
+and thus <span class="math notranslate nohighlight">\(c=6\)</span>.</p></li>
+</ul>
+</li>
+<li><p>We use the <span class="math notranslate nohighlight">\(\boxplus\)</span> operator to indicate pose composition
+when one or both of the poses are represented compactly. The
+output can be a pose in <span class="math notranslate nohighlight">\(\mathcal{M}\)</span> or a vector in
+<span class="math notranslate nohighlight">\(\mathbb{R}^c\)</span>, as required by context.</p></li>
+</ul>
+</li>
+<li><p>A set of <span class="math notranslate nohighlight">\(M\)</span> measurements
+<span class="math notranslate nohighlight">\(\mathcal{Z} = \{\mathbf{z}_1, \mathbf{z}_2, \ldots, \mathbf{z}_M\}\)</span></p>
+<ul>
+<li><p>Each measurement’s dimensionality can be unique, and we will use
+<span class="math notranslate nohighlight">\(\bullet\)</span> to denote a “wildcard” variable.</p></li>
+<li><p>Measurement <span class="math notranslate nohighlight">\(\mathbf{z}_j \in \mathbb{R}^\bullet\)</span> has an
+associated information matrix
+<span class="math notranslate nohighlight">\(\Omega_j \in \mathbb{R}^{\bullet \times \bullet}\)</span> and
+residual function
+<span class="math notranslate nohighlight">\(\mathbf{e}_j(\mathbf{z}_j, \hat{\mathbf{z}}_j) = \mathbf{e}_j(\mathbf{z}_j, \mathbf{p}_1, \ldots, \mathbf{p}_N) \in \mathbb{R}^\bullet\)</span>.</p></li>
+<li><p>A measurement could, in theory, constrain anywhere from 1 pose to
+all <span class="math notranslate nohighlight">\(N\)</span> poses. In practice, each measurement usually
+constrains only 1 or 2 poses.</p></li>
+</ul>
+</li>
+</ul>
+</section>
+<section id="graph-slam-algorithm">
+<h3>Graph SLAM Algorithm<a class="headerlink" href="#graph-slam-algorithm" title="Permalink to this headline"></a></h3>
+<p>The “Graph” in Graph SLAM refers to the fact that we view the problem as
+a graph. The graph has a set <span class="math notranslate nohighlight">\(\mathcal{V}\)</span> of <span class="math notranslate nohighlight">\(N\)</span> vertices,
+where each vertex <span class="math notranslate nohighlight">\(v_i\)</span> has an associated pose
+<span class="math notranslate nohighlight">\(\mathbf{p}_i\)</span>. Similarly, the graph has a set <span class="math notranslate nohighlight">\(\mathcal{E}\)</span>
+of <span class="math notranslate nohighlight">\(M\)</span> edges, where each edge <span class="math notranslate nohighlight">\(e_j\)</span> has an associated
+measurement <span class="math notranslate nohighlight">\(\mathbf{z}_j\)</span>. In practice, the edges in this graph
+are either unary (i.e., a loop) or binary. (Note: <span class="math notranslate nohighlight">\(e_j\)</span> refers to
+the edge in the graph associated with measurement <span class="math notranslate nohighlight">\(\mathbf{z}_j\)</span>,
+whereas <span class="math notranslate nohighlight">\(\mathbf{e}_j\)</span> refers to the residual function associated
+with <span class="math notranslate nohighlight">\(\mathbf{z}_j\)</span>.) For more information about the Graph SLAM
+algorithm, see <a class="reference internal" href="#grisetti2010tutorial" id="id3"><span>[grisetti2010tutorial]</span></a>.</p>
+<p>We want to optimize</p>
+<div class="math notranslate nohighlight">
+\[\chi^2 = \sum_{e_j \in \mathcal{E}} \mathbf{e}_j^{\scriptstyle{\mathsf{T}}}\Omega_j \mathbf{e}_j.\]</div>
+<p>Let <span class="math notranslate nohighlight">\(\mathbf{x}_i \in \mathbb{R}^c\)</span> be the compact representation
+of pose <span class="math notranslate nohighlight">\(\mathbf{p}_i \in \mathcal{M}\)</span>, and let</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\mathbf{x} := \begin{bmatrix} \mathbf{x}_1 \\ \mathbf{x}_2 \\ \vdots \\ \mathbf{x}_N \end{bmatrix} \in \mathbb{R}^{cN}\end{split}\]</div>
+<p>We will solve this optimization problem iteratively. Let</p>
+<div class="math notranslate nohighlight" id="equation-update">
+<span class="eqno">(3)<a class="headerlink" href="#equation-update" title="Permalink to this equation"></a></span>\[\begin{split}\mathbf{x}^{k+1} := \mathbf{x}^k \boxplus \Delta \mathbf{x}^k = \begin{bmatrix} \mathbf{x}_1 \boxplus \Delta \mathbf{x}_1 \\ \mathbf{x}_2 \boxplus \Delta \mathbf{x}_2 \\ \vdots \\ \mathbf{x}_N \boxplus \Delta \mathbf{x}_2 \end{bmatrix}\end{split}\]</div>
+<p>The <span class="math notranslate nohighlight">\(\chi^2\)</span> error at iteration <span class="math notranslate nohighlight">\(k+1\)</span> is</p>
+<div class="math notranslate nohighlight" id="equation-chisq-at-kplusone">
+<span class="eqno">(4)<a class="headerlink" href="#equation-chisq-at-kplusone" title="Permalink to this equation"></a></span>\[\chi_{k+1}^2 = \sum_{e_j \in \mathcal{E}} \underbrace{\left[ \mathbf{e}_j(\mathbf{x}^{k+1}) \right]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\mathbf{e}_j(\mathbf{x}^{k+1})}_{\bullet \times 1}.\]</div>
+<p>We will linearize the residuals as:</p>
+<div class="math notranslate nohighlight" id="equation-linearization">
+<span class="eqno">(5)<a class="headerlink" href="#equation-linearization" title="Permalink to this equation"></a></span>\[\begin{split}\begin{aligned}
+ \mathbf{e}_j(\mathbf{x}^{k+1}) &= \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k) \\
+ &\approx \mathbf{e}_j(\mathbf{x}^{k}) + \frac{\partial}{\partial \Delta \mathbf{x}^k} \left[ \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k) \right] \Delta \mathbf{x}^k \\
+ &= \mathbf{e}_j(\mathbf{x}^{k}) + \left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right) \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \Delta \mathbf{x}^k.
+\end{aligned}\end{split}\]</div>
+<p>Plugging <a class="reference internal" href="#equation-linearization">(5)</a> into <a class="reference internal" href="#equation-chisq-at-kplusone">(4)</a>, we get:</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\begin{aligned}
+ \chi_{k+1}^2 &\approx \ \ \ \ \ \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x}^k)]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\mathbf{e}_j(\mathbf{x}^k)}_{\bullet \times 1} \notag \\
+ &\hphantom{\approx} \ \ \ + \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x^k}) ]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \underbrace{\Delta \mathbf{x}^k}_{cN \times 1} \notag \\
+ &\hphantom{\approx} \ \ \ + \sum_{e_j \in \mathcal{E}} \underbrace{(\Delta \mathbf{x}^k)^{\scriptstyle{\mathsf{T}}}}_{1 \times cN} \underbrace{ \left( \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \right)^{\scriptstyle{\mathsf{T}}}}_{cN \times dN} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)^{\scriptstyle{\mathsf{T}}}}_{dN \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \underbrace{\Delta \mathbf{x}^k}_{cN \times 1} \notag \\
+ &= \chi_k^2 + 2 \mathbf{b}^{\scriptstyle{\mathsf{T}}}\Delta \mathbf{x}^k + (\Delta \mathbf{x}^k)^{\scriptstyle{\mathsf{T}}}H \Delta \mathbf{x}^k, \notag\end{aligned}\end{split}\]</div>
+<p>where</p>
+<div class="math notranslate nohighlight">
+\[\begin{split}\begin{aligned}
+ \mathbf{b}^{\scriptstyle{\mathsf{T}}}&= \sum_{e_j \in \mathcal{E}} \underbrace{[ \mathbf{e}_j(\mathbf{x^k}) ]^{\scriptstyle{\mathsf{T}}}}_{1 \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN} \\
+ H &= \sum_{e_j \in \mathcal{E}} \underbrace{ \left( \frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k} \right)^{\scriptstyle{\mathsf{T}}}}_{cN \times dN} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)^{\scriptstyle{\mathsf{T}}}}_{dN \times \bullet} \underbrace{\Omega_j}_{\bullet \times \bullet} \underbrace{\left( \left. \frac{\partial \mathbf{e}_j(\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)} \right|_{\Delta \mathbf{x}^k = \mathbf{0}} \right)}_{\bullet \times dN} \underbrace{\frac{\partial (\mathbf{x}^k \boxplus \Delta \mathbf{x}^k)}{\partial \Delta \mathbf{x}^k}}_{dN \times cN}.\end{aligned}\end{split}\]</div>
+<p>Using this notation, we obtain the optimal update as</p>
+<div class="math notranslate nohighlight">
+\[\Delta \mathbf{x}^k = -H^{-1} \mathbf{b}. \label{eq:deltax}\]</div>
+<p>We apply this update to the poses via <a class="reference internal" href="#equation-update">(3)</a> and repeat until convergence.</p>
+<dl class="citation">
+<dt class="label" id="blanco2010tutorial"><span class="brackets"><a class="fn-backref" href="#id2">blanco2010tutorial</a></span></dt>
+<dd><p>Blanco, J.-L.A tutorial onSE(3) transformation parameterization and on-manifold optimization.University of Malaga, Tech. Rep 3(2010)</p>
+</dd>
+<dt class="label" id="grisetti2010tutorial"><span class="brackets"><a class="fn-backref" href="#id3">grisetti2010tutorial</a></span></dt>
+<dd><p>Grisetti, G., Kummerle, R., Stachniss, C., and Burgard, W.A tutorial on graph-based SLAM.IEEE Intelligent Transportation Systems Magazine 2, 4 (2010), 31–43.</p>
+</dd>
+</dl>
+</section>
+</section>
+<section id="graph-slam-for-a-real-world-se-2-dataset">
+<h2>Graph SLAM for a real-world SE(2) dataset<a class="headerlink" href="#graph-slam-for-a-real-world-se-2-dataset" title="Permalink to this headline"></a></h2>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="kn">from</span> <span class="nn">graphslam.graph</span> <span class="kn">import</span> <span class="n">Graph</span>
+<span class="kn">from</span> <span class="nn">graphslam.load</span> <span class="kn">import</span> <span class="n">load_g2o_se2</span>
+</pre></div>
+</div>
+<section id="id4">
+<h3>Introduction<a class="headerlink" href="#id4" title="Permalink to this headline"></a></h3>
+<p>For a complete derivation of the Graph SLAM algorithm, please see
+<a class="reference internal" href="#graph-slam-formulation">Graph SLAM Formulation</a>.</p>
+<p>This notebook illustrates the iterative optimization of a real-world
+<span class="math notranslate nohighlight">\(SE(2)\)</span> dataset. The code can be found in the <code class="docutils literal notranslate"><span class="pre">graphslam</span></code>
+folder. For simplicity, numerical differentiation is used in lieu of
+analytic Jacobians. This code originated from the
+<a class="reference external" href="https://github.com/JeffLIrion/python-graphslam">python-graphslam</a>
+repo, which is a full-featured Graph SLAM solver. The dataset in this
+example is used with permission from Luca Carlone and was downloaded
+from his <a class="reference external" href="https://lucacarlone.mit.edu/datasets/">website</a>.</p>
+</section>
+<section id="the-dataset">
+<h3>The Dataset<a class="headerlink" href="#the-dataset" title="Permalink to this headline"></a></h3>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span> <span class="o">=</span> <span class="n">load_g2o_se2</span><span class="p">(</span><span class="s2">"data/input_INTEL.g2o"</span><span class="p">)</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">"Number of edges: </span><span class="si">{}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">g</span><span class="o">.</span><span class="n">_edges</span><span class="p">)))</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"Number of vertices: </span><span class="si">{}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">g</span><span class="o">.</span><span class="n">_vertices</span><span class="p">)))</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Number</span> <span class="n">of</span> <span class="n">edges</span><span class="p">:</span> <span class="mi">1483</span>
+<span class="n">Number</span> <span class="n">of</span> <span class="n">vertices</span><span class="p">:</span> <span class="mi">1228</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="sa">r</span><span class="s2">"Original ($\chi^2 = </span><span class="si">{:.0f}</span><span class="s2">$)"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">g</span><span class="o">.</span><span class="n">calc_chi2</span><span class="p">()))</span>
+</pre></div>
+</div>
+<img alt="../../../_images/graphSLAM_SE2_example_4_0.png" src="../../../_images/graphSLAM_SE2_example_4_0.png" />
+<p>Each edge in this dataset is a constraint that compares the measured
+<span class="math notranslate nohighlight">\(SE(2)\)</span> transformation between two poses to the expected
+<span class="math notranslate nohighlight">\(SE(2)\)</span> transformation between them, as computed using the current
+pose estimates. These edges can be classified into two categories:</p>
+<ol class="arabic simple">
+<li><p>Odometry edges constrain two consecutive vertices, and the
+measurement for the <span class="math notranslate nohighlight">\(SE(2)\)</span> transformation comes directly from
+odometry data.</p></li>
+<li><p>Scan-matching edges constrain two non-consecutive vertices. These
+scan matches can be computed using, for example, 2-D LiDAR data or
+landmarks; the details of how these constraints are determined is
+beyond the scope of this example. This is often referred to as <em>loop
+closure</em> in the Graph SLAM literature.</p></li>
+</ol>
+<p>We can easily parse out the two different types of edges present in this
+dataset and plot them.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="k">def</span> <span class="nf">parse_edges</span><span class="p">(</span><span class="n">g</span><span class="p">):</span>
+<span class="w"> </span><span class="sd">"""Split the graph `g` into two graphs, one with only odometry edges and the other with only scan-matching edges.</span>
+
+<span class="sd"> Parameters</span>
+<span class="sd"> ----------</span>
+<span class="sd"> g : graphslam.graph.Graph</span>
+<span class="sd"> The input graph</span>
+
+<span class="sd"> Returns</span>
+<span class="sd"> -------</span>
+<span class="sd"> g_odom : graphslam.graph.Graph</span>
+<span class="sd"> A graph consisting of the vertices and odometry edges from `g`</span>
+<span class="sd"> g_scan : graphslam.graph.Graph</span>
+<span class="sd"> A graph consisting of the vertices and scan-matching edges from `g`</span>
+
+<span class="sd"> """</span>
+ <span class="n">edges_odom</span> <span class="o">=</span> <span class="p">[]</span>
+ <span class="n">edges_scan</span> <span class="o">=</span> <span class="p">[]</span>
+
+ <span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">g</span><span class="o">.</span><span class="n">_edges</span><span class="p">:</span>
+ <span class="k">if</span> <span class="nb">abs</span><span class="p">(</span><span class="n">e</span><span class="o">.</span><span class="n">vertex_ids</span><span class="p">[</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">e</span><span class="o">.</span><span class="n">vertex_ids</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
+ <span class="n">edges_odom</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+ <span class="k">else</span><span class="p">:</span>
+ <span class="n">edges_scan</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+
+ <span class="n">g_odom</span> <span class="o">=</span> <span class="n">Graph</span><span class="p">(</span><span class="n">edges_odom</span><span class="p">,</span> <span class="n">g</span><span class="o">.</span><span class="n">_vertices</span><span class="p">)</span>
+ <span class="n">g_scan</span> <span class="o">=</span> <span class="n">Graph</span><span class="p">(</span><span class="n">edges_scan</span><span class="p">,</span> <span class="n">g</span><span class="o">.</span><span class="n">_vertices</span><span class="p">)</span>
+
+ <span class="k">return</span> <span class="n">g_odom</span><span class="p">,</span> <span class="n">g_scan</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">g_odom</span><span class="p">,</span> <span class="n">g_scan</span> <span class="o">=</span> <span class="n">parse_edges</span><span class="p">(</span><span class="n">g</span><span class="p">)</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">"Number of odometry edges: </span><span class="si">{:4d}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">g_odom</span><span class="o">.</span><span class="n">_edges</span><span class="p">)))</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"Number of scan-matching edges: </span><span class="si">{:4d}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">g_scan</span><span class="o">.</span><span class="n">_edges</span><span class="p">)))</span>
+
+<span class="nb">print</span><span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2">χ^2 error from odometry edges: </span><span class="si">{:11.3f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">g_odom</span><span class="o">.</span><span class="n">calc_chi2</span><span class="p">()))</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"χ^2 error from scan-matching edges: </span><span class="si">{:11.3f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">g_scan</span><span class="o">.</span><span class="n">calc_chi2</span><span class="p">()))</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Number</span> <span class="n">of</span> <span class="n">odometry</span> <span class="n">edges</span><span class="p">:</span> <span class="mi">1227</span>
+<span class="n">Number</span> <span class="n">of</span> <span class="n">scan</span><span class="o">-</span><span class="n">matching</span> <span class="n">edges</span><span class="p">:</span> <span class="mi">256</span>
+
+<span class="n">χ</span><span class="o">^</span><span class="mi">2</span> <span class="n">error</span> <span class="kn">from</span> <span class="nn">odometry</span> <span class="n">edges</span><span class="p">:</span> <span class="mf">0.232</span>
+<span class="n">χ</span><span class="o">^</span><span class="mi">2</span> <span class="n">error</span> <span class="kn">from</span> <span class="nn">scan</span><span class="o">-</span><span class="n">matching</span> <span class="n">edges</span><span class="p">:</span> <span class="mf">7191686.151</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">g_odom</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s2">"Odometry edges"</span><span class="p">)</span>
+</pre></div>
+</div>
+<img alt="../../../_images/graphSLAM_SE2_example_8_0.png" src="../../../_images/graphSLAM_SE2_example_8_0.png" />
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">g_scan</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s2">"Scan-matching edges"</span><span class="p">)</span>
+</pre></div>
+</div>
+<img alt="../../../_images/graphSLAM_SE2_example_9_0.png" src="../../../_images/graphSLAM_SE2_example_9_0.png" />
+</section>
+<section id="optimization">
+<h3>Optimization<a class="headerlink" href="#optimization" title="Permalink to this headline"></a></h3>
+<p>Initially, the pose estimates are consistent with the collected odometry
+measurements, and the odometry edges contribute almost zero towards the
+<span class="math notranslate nohighlight">\(\chi^2\)</span> error. However, there are large discrepancies between the
+scan-matching constraints and the initial pose estimates. This is not
+surprising, since small errors in odometry readings that are propagated
+over time can lead to large errors in the robot’s trajectory. What makes
+Graph SLAM effective is that it allows incorporation of multiple
+different data sources into a single optimization problem.</p>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span><span class="o">.</span><span class="n">optimize</span><span class="p">()</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">Iteration</span> <span class="n">chi</span><span class="o">^</span><span class="mi">2</span> <span class="n">rel</span><span class="o">.</span> <span class="n">change</span>
+<span class="o">---------</span> <span class="o">-----</span> <span class="o">-----------</span>
+ <span class="mi">0</span> <span class="mf">7191686.3825</span>
+ <span class="mi">1</span> <span class="mf">320031728.8624</span> <span class="mf">43.500234</span>
+ <span class="mi">2</span> <span class="mf">125083004.3299</span> <span class="o">-</span><span class="mf">0.609154</span>
+ <span class="mi">3</span> <span class="mf">338155.9074</span> <span class="o">-</span><span class="mf">0.997297</span>
+ <span class="mi">4</span> <span class="mf">735.1344</span> <span class="o">-</span><span class="mf">0.997826</span>
+ <span class="mi">5</span> <span class="mf">215.8405</span> <span class="o">-</span><span class="mf">0.706393</span>
+ <span class="mi">6</span> <span class="mf">215.8405</span> <span class="o">-</span><span class="mf">0.000000</span>
+</pre></div>
+</div>
+<figure class="align-default">
+<img alt="../../../_images/Graph_SLAM_optimization.gif" src="../../../_images/Graph_SLAM_optimization.gif" />
+</figure>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">g</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s2">"Optimized"</span><span class="p">)</span>
+</pre></div>
+</div>
+<img alt="../../../_images/graphSLAM_SE2_example_13_0.png" src="../../../_images/graphSLAM_SE2_example_13_0.png" />
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="nb">print</span><span class="p">(</span><span class="s2">"</span><span class="se">\n</span><span class="s2">χ^2 error from odometry edges: </span><span class="si">{:7.3f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">g_odom</span><span class="o">.</span><span class="n">calc_chi2</span><span class="p">()))</span>
+<span class="nb">print</span><span class="p">(</span><span class="s2">"χ^2 error from scan-matching edges: </span><span class="si">{:7.3f}</span><span class="s2">"</span><span class="o">.</span><span class="n">format</span><span class="p">(</span><span class="n">g_scan</span><span class="o">.</span><span class="n">calc_chi2</span><span class="p">()))</span>
+</pre></div>
+</div>
+<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">χ</span><span class="o">^</span><span class="mi">2</span> <span class="n">error</span> <span class="kn">from</span> <span class="nn">odometry</span> <span class="n">edges</span><span class="p">:</span> <span class="mf">142.189</span>
+<span class="n">χ</span><span class="o">^</span><span class="mi">2</span> <span class="n">error</span> <span class="kn">from</span> <span class="nn">scan</span><span class="o">-</span><span class="n">matching</span> <span class="n">edges</span><span class="p">:</span> <span class="mf">73.652</span>
+</pre></div>
+</div>
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">g_odom</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s2">"Odometry edges"</span><span class="p">)</span>
+</pre></div>
+</div>
+<img alt="../../../_images/graphSLAM_SE2_example_15_0.png" src="../../../_images/graphSLAM_SE2_example_15_0.png" />
+<div class="highlight-ipython3 notranslate"><div class="highlight"><pre><span></span><span class="n">g_scan</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">title</span><span class="o">=</span><span class="s2">"Scan-matching edges"</span><span class="p">)</span>
+</pre></div>
+</div>
+<img alt="../../../_images/graphSLAM_SE2_example_16_0.png" src="../../../_images/graphSLAM_SE2_example_16_0.png" />
+</section>
+</section>
+<section id="references">
+<h2>References:<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="http://www2.informatik.uni-freiburg.de/~stachnis/pdf/grisetti10titsmag.pdf">A Tutorial on Graph-Based SLAM</a></p></li>
+</ul>
+</section>
+</section>
+
+
+ </div>
+ </div>
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+ <section id="iterative-closest-point-icp-matching">
+<span id="id1"></span><h1>Iterative Closest Point (ICP) Matching<a class="headerlink" href="#iterative-closest-point-icp-matching" title="Permalink to this headline"></a></h1>
+<p>This is a 2D ICP matching example with singular value decomposition.</p>
+<p>It can calculate a rotation matrix and a translation vector between
+points to points.</p>
+<img alt="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/iterative_closest_point/animation.gif" src="https://github.com/AtsushiSakai/PythonRoboticsGifs/raw/master/SLAM/iterative_closest_point/animation.gif" />
+<section id="references">
+<h2>References<a class="headerlink" href="#references" title="Permalink to this headline"></a></h2>
+<ul class="simple">
+<li><p><a class="reference external" href="https://cs.gmu.edu/~kosecka/cs685/cs685-icp.pdf">Introduction to Mobile Robotics: Iterative Closest Point Algorithm</a></p></li>
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+<li class="toctree-l1"><a class="reference internal" href="iterative_closest_point_matching/iterative_closest_point_matching.html">Iterative Closest Point (ICP) Matching</a><ul>
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+</li>
+<li class="toctree-l1"><a class="reference internal" href="FastSLAM2/FastSLAM2.html">FastSLAM 2.0</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="FastSLAM2/FastSLAM2.html#references">References</a></li>
+</ul>
+</li>
+<li class="toctree-l1"><a class="reference internal" href="graph_slam/graph_slam.html">Graph based SLAM</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="graph_slam/graph_slam.html#graph-slam">Graph SLAM</a></li>
+<li class="toctree-l2"><a class="reference internal" href="graph_slam/graph_slam.html#graph-slam-formulation">Graph SLAM Formulation</a></li>
+<li class="toctree-l2"><a class="reference internal" href="graph_slam/graph_slam.html#graph-slam-for-a-real-world-se-2-dataset">Graph SLAM for a real-world SE(2) dataset</a></li>
+<li class="toctree-l2"><a class="reference internal" href="graph_slam/graph_slam.html#references">References:</a></li>
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+ <section id="plotting-utilities">
+<span id="plot-utils"></span><h1>Plotting Utilities<a class="headerlink" href="#plotting-utilities" title="Permalink to this headline"></a></h1>
+<p>This module contains a number of utility functions for plotting data.</p>
+<section id="plot-curvature">
+<span id="id1"></span><h2>plot_curvature<a class="headerlink" href="#plot-curvature" title="Permalink to this headline"></a></h2>
+<dl class="py function">
+<dt class="sig sig-object py" id="utils.plot.plot_curvature">
+<span class="sig-prename descclassname"><span class="pre">utils.plot.</span></span><span class="sig-name descname"><span class="pre">plot_curvature</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x_list</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">y_list</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">heading_list</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">curvature</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">k</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">0.01</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">c</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'-c'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">label</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'Curvature'</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="../../../_modules/utils/plot.html#plot_curvature"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#utils.plot.plot_curvature" title="Permalink to this definition"></a></dt>
+<dd><p>Plot curvature on 2D path. This plot is a line from the original path,
+the lateral distance from the original path shows curvature magnitude.
+Left turning shows right side plot, right turning shows left side plot.
+For straight path, the curvature plot will be on the path, because
+curvature is 0 on the straight path.</p>
+<dl class="field-list simple">
+<dt class="field-odd">Parameters</dt>
+<dd class="field-odd"><ul class="simple">
+<li><p><strong>x_list</strong> (<em>array_like</em>) – x position list of the path</p></li>
+<li><p><strong>y_list</strong> (<em>array_like</em>) – y position list of the path</p></li>
+<li><p><strong>heading_list</strong> (<em>array_like</em>) – heading list of the path</p></li>
+<li><p><strong>curvature</strong> (<em>array_like</em>) – curvature list of the path</p></li>
+<li><p><strong>k</strong> (<em>float</em>) – curvature scale factor to calculate distance from the original path</p></li>
+<li><p><strong>c</strong> (<em>string</em>) – color of the plot</p></li>
+<li><p><strong>label</strong> (<em>string</em>) – label of the plot</p></li>
+</ul>
+</dd>
+</dl>
+</dd></dl>
+
+<img alt="../../../_images/curvature_plot.png" src="../../../_images/curvature_plot.png" />
+</section>
+</section>
+
+
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+
+ <section id="utilities">
+<span id="utils"></span><h1>Utilities<a class="headerlink" href="#utilities" title="Permalink to this headline"></a></h1>
+<p>Common utilities for PythonRobotics.</p>
+<div class="toctree-wrapper compound">
+<p class="caption" role="heading"><span class="caption-text">Contents</span></p>
+<ul>
+<li class="toctree-l1"><a class="reference internal" href="plot/plot.html">Plotting Utilities</a><ul>
+<li class="toctree-l2"><a class="reference internal" href="plot/plot.html#plot-curvature">plot_curvature</a></li>
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deleted file mode 100644
index 1215375ed9b..00000000000
--- a/mypy.ini
+++ /dev/null
@@ -1,2 +0,0 @@
-[mypy]
-ignore_missing_imports = True
\ No newline at end of file
diff --git a/objects.inv b/objects.inv
new file mode 100644
index 00000000000..aa6e436ffc6
Binary files /dev/null and b/objects.inv differ
diff --git a/requirements/environment.yml b/requirements/environment.yml
deleted file mode 100644
index afbb3fb8cec..00000000000
--- a/requirements/environment.yml
+++ /dev/null
@@ -1,10 +0,0 @@
-name: python_robotics
-channels:
- - conda-forge
-dependencies:
- - python=3.12
- - pip
- - scipy
- - numpy
- - cvxpy
- - matplotlib
diff --git a/requirements/requirements.txt b/requirements/requirements.txt
deleted file mode 100644
index 5438678f87d..00000000000
--- a/requirements/requirements.txt
+++ /dev/null
@@ -1,8 +0,0 @@
-numpy == 2.2.4
-scipy == 1.15.2
-matplotlib == 3.10.1
-cvxpy == 1.5.3
-pytest == 8.3.5 # For unit test
-pytest-xdist == 3.6.1 # For unit test
-mypy == 1.15.0 # For unit test
-ruff == 0.11.0 # For unit test
diff --git a/ruff.toml b/ruff.toml
deleted file mode 100644
index 5823ca3db75..00000000000
--- a/ruff.toml
+++ /dev/null
@@ -1,18 +0,0 @@
-line-length = 88
-
-select = ["F", "E", "W", "UP"]
-ignore = ["E501", "E741", "E402"]
-exclude = [
-]
-
-# Assume Python 3.11
-target-version = "py312"
-
-[per-file-ignores]
-
-[mccabe]
-# Unlike Flake8, default to a complexity level of 10.
-max-complexity = 10
-
-[pydocstyle]
-convention = "numpy"
diff --git a/runtests.sh b/runtests.sh
deleted file mode 100755
index 12d1b804534..00000000000
--- a/runtests.sh
+++ /dev/null
@@ -1,8 +0,0 @@
-#!/usr/bin/env bash
-echo "Run test suites! "
-
-# === pytest based test runner ===
-# -Werror: warning as error
-# --durations=0: show ranking of test durations
-# -l (--showlocals); show local variables when test failed
-pytest tests -l -Werror --durations=0
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Started","How To Contribute","Welcome to PythonRobotics\u2019s documentation!","Aerial Navigation","Drone 3d trajectory following","Rocket powered landing","KF Basics - Part I","KF Basics - Part 2","Appendix","Arm Navigation","N joint arm to point control","Arm navigation with obstacle avoidance","Two joint arm to point control","Bipedal","Bipedal Planner","Control","Inverted Pendulum Control","Move to a Pose Control","Introduction","Ensamble Kalman Filter Localization","Extended Kalman Filter Localization","Histogram filter localization","Localization","Particle filter localization","Unscented Kalman Filter localization","Object shape recognition using circle fitting","Gaussian grid map","k-means object clustering","Lidar to grid map","Mapping","Normal Distance Transform (NDT) map","Normal vector estimation","Point cloud Sampling","Ray casting grid map","Object shape recognition using rectangle fitting","Bezier path planning","B-Spline planning","Bug planner","Clothoid path planning","Coverage path planner","Cubic spline planning","Dubins path planning","Dynamic Window Approach","Eta^3 Spline path planning","Optimal Trajectory in a Frenet Frame","Grid based search","Hybrid a star","LQR based path planning","Model Predictive Trajectory Generator","Path Planning","Probabilistic Road-Map (PRM) planning","Quintic polynomials planning","Reeds Shepp planning","Rapidly-Exploring Random Trees (RRT)","State Lattice Planning","Visibility Road-Map planner","Voronoi Road-Map planning","Nonlinear Model Predictive Control with C-GMRES","Linear\u2013quadratic regulator (LQR) speed and steering control","Linear\u2013quadratic regulator (LQR) steering control","Model predictive speed and steering control","Path Tracking","Pure pursuit tracking","Rear wheel feedback control","Stanley control","FastSLAM1.0","FastSLAM 2.0","EKF SLAM","Graph based SLAM","Iterative Closest Point (ICP) Matching","SLAM","Plotting Utilities","Utilities"],titleterms:{"0":[65,66],"1":[1,34,40,65,67],"1d":40,"1st":7,"2":[1,7,34,40,65,66,67,68],"2d":40,"2nd":7,"3":[1,34,40,43,65],"3d":[4,31],"4":[1,40],"5":[1,40],"class":17,"do":6,"function":[17,38],"new":1,A:45,Of:18,The:68,To:1,a_j:40,about:1,ad:1,adapt:34,add:1,advantag:6,aerial:3,algorithm:[1,7,17,18,21,45,55,65,67,68],an:1,anim:1,api:[30,31,32,34,36,40,41],appendix:8,applic:18,approach:42,approxim:36,area:34,arm:[9,10,11,12],avoid:11,b:36,b_j:40,base:[1,39,45,47,55,68],basic:[6,7,36,53],batch:53,bay:7,belief:6,bezier:35,bias:54,bidirect:45,biped:[13,14],breadth:45,bspline:36,bug:37,c:57,c_j:40,calcul:[23,31,38,40],cast:33,central:6,choos:1,circl:25,close:[34,53],closest:69,clothoid:38,cloud:32,cluster:27,code:1,condit:7,connect:55,consensu:31,constraint:40,construct:38,constructor:17,content:[2,3,8,9,13,15,22,29,49,61,70,72],continu:40,contribut:1,control:[10,12,15,16,17,57,58,59,60,63,64],correl:6,covari:[6,23],coverag:39,criteria:34,cubic:40,curv:40,curvatur:40,d:45,d_j:40,dataset:68,defect:1,definit:18,depend:7,depth:45,deriv:40,describ:6,design:20,dijkstra:[45,55],dimension:[51,68],disk:32,distanc:30,distribut:[6,30],document:[1,2],doe:17,drone:4,dubin:[41,53],dynam:42,ekf:67,ensambl:19,equat:5,estim:[21,31],eta:43,exampl:[1,7,68],exist:1,expect:6,explor:53,extend:20,farthest:32,fastslam1:65,fastslam:66,feedback:63,field:45,filter:[7,19,20,21,23,24],first:[40,45],fit:[25,34],fix:1,follow:4,formul:[57,68],frame:44,frenet:44,fresnel:38,from:[21,23],g:38,gain:7,gaussian:[6,26],gener:[5,7,48,55],get:0,gmre:57,graph:[55,68],grid:[26,28,33,39,45],histogram:21,histori:18,holonom:17,how:[0,1,17,23,40],hybrid:46,i:6,icp:69,implement:1,independ:7,indic:2,inform:53,initi:21,integr:38,interpol:36,introduct:[6,18,65,67,68],invers:12,invert:16,iter:69,joint:[10,12],k:27,kalman:[7,19,20,24],kf:[6,7],kinemat:12,land:5,lane:54,lattic:54,law:7,learn:18,lidar:28,limit:6,linear:[58,59,60],link:12,lite:45,local:[7,19,20,21,22,23,24],lookup:48,loop:53,lqr:[16,47,53,58,59],map:[26,28,29,30,33,50,55,56],match:69,mathemat:57,matplotlib:1,matrix:23,mean:27,member:17,minim:[34,68],miss:1,model:[16,20,48,57,60],motion:[20,21,51],move:17,mpc:[16,60],multimod:6,multivari:7,n:10,navig:[3,9,11],ndt:30,need:6,node:55,non:17,nonlinear:57,normal:[30,31],object:[25,27,34],observ:[20,21,67],obstacl:[11,55],one:51,oppos:6,optim:[44,48,68],paramet:[38,40],part:[6,7],particl:23,path:[35,38,39,41,43,47,48,49,53,55,61],pathfindercontrol:17,pdf:6,pendulum:16,plan:[35,36,38,40,41,43,47,49,50,51,52,54,56],planar:[12,68],planner:[14,37,39,55],plot:71,plot_curvatur:71,point:[10,12,32,40,69],poisson:32,polar:54,polygon:55,polynomi:51,pose:[17,68],posit:[17,21],potenti:45,power:5,predict:[21,48,57,60,65,67],prm:50,probabilist:[7,50],probabl:21,problem:68,project:1,properti:6,pull:1,pure:62,pursuit:62,python:18,pythonrobot:2,quadrat:[58,59],quintic:51,rai:33,randam:31,random:[6,53],rang:34,ransac:31,rapidli:53,real:68,rear:63,recognit:[25,34],rectangl:34,reed:[52,53],ref:[20,53,57],refer:[5,6,7,17,21,23,24,34,36,38,40,41,51,55,58,59,60,62,63,64,65,66,67,68,69],regul:[58,59],report:1,repres:6,represent:68,request:1,requir:0,resampl:65,review:1,road:[50,55,56],robot:[12,17,18,51],rocket:5,rrt:53,rule:7,s:[2,6,17],sampl:[31,32,48,54],se:68,search:[34,45,55],second:40,segment:34,shape:[25,34],sheep:53,shepp:52,shortest:55,simul:[5,53,65,67],slam:[67,68,70],softwar:18,solv:38,span:39,speed:[58,60],spiral:39,spline:[36,40,43],sponsor:1,stanlei:64,star:46,start:0,state:54,steer:[58,59,60],step1:[21,34,38,40,55],step2:[21,34,38,40,55],step3:[21,38,40,55],step4:[21,40],step:[1,30,67],structur:7,submit:1,support:1,sweep:39,system:17,tabl:[2,48],tangent:40,term:6,termin:40,theorem:6,thi:[0,1],through:[65,67],track:[61,62],trajectori:[4,44,48],transform:30,tree:[39,53],triangl:31,two:[12,51],uniform:54,unimod:6,unittest:1,univari:7,unknown:40,unscent:24,updat:[21,65,67],us:[0,25,34,55],util:[71,72],variabl:6,varianc:[6,34],vector:[31,40],vehicl:60,visibl:55,voronoi:56,voxel:32,walk:[65,67],wavefront:39,we:6,welcom:2,what:[0,6],wheel:63,why:6,window:42,work:17,world:68,write:1,x:51,y:51}})
\ No newline at end of file
diff --git a/tests/__init__.py b/tests/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/tests/conftest.py b/tests/conftest.py
deleted file mode 100644
index 3485fe81502..00000000000
--- a/tests/conftest.py
+++ /dev/null
@@ -1,13 +0,0 @@
-"""Path hack to make tests work."""
-import sys
-import os
-import pytest
-
-TEST_DIR = os.path.dirname(os.path.abspath(__file__))
-sys.path.append(TEST_DIR) # to import this file from test code.
-ROOT_DIR = os.path.dirname(TEST_DIR)
-sys.path.append(ROOT_DIR)
-
-
-def run_this_test(file):
- pytest.main([os.path.abspath(file)])
diff --git a/tests/test_LQR_planner.py b/tests/test_LQR_planner.py
deleted file mode 100644
index be12195eac2..00000000000
--- a/tests/test_LQR_planner.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.LQRPlanner import lqr_planner as m
-
-
-def test_1():
- m.SHOW_ANIMATION = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_a_star.py b/tests/test_a_star.py
deleted file mode 100644
index 82f76401ad2..00000000000
--- a/tests/test_a_star.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.AStar import a_star as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_a_star_searching_two_side.py b/tests/test_a_star_searching_two_side.py
deleted file mode 100644
index ad90ebc509a..00000000000
--- a/tests/test_a_star_searching_two_side.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import conftest
-from PathPlanning.AStar import a_star_searching_from_two_side as m
-
-
-def test1():
- m.show_animation = False
- m.main(800)
-
-
-def test2():
- m.show_animation = False
- m.main(5000) # increase obstacle number, block path
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_a_star_variants.py b/tests/test_a_star_variants.py
deleted file mode 100644
index b9ef7914026..00000000000
--- a/tests/test_a_star_variants.py
+++ /dev/null
@@ -1,44 +0,0 @@
-import PathPlanning.AStar.a_star_variants as a_star
-import conftest
-
-
-def test_1():
- # A* with beam search
- a_star.show_animation = False
-
- a_star.use_beam_search = True
- a_star.main()
- reset_all()
-
- # A* with iterative deepening
- a_star.use_iterative_deepening = True
- a_star.main()
- reset_all()
-
- # A* with dynamic weighting
- a_star.use_dynamic_weighting = True
- a_star.main()
- reset_all()
-
- # theta*
- a_star.use_theta_star = True
- a_star.main()
- reset_all()
-
- # A* with jump point
- a_star.use_jump_point = True
- a_star.main()
- reset_all()
-
-
-def reset_all():
- a_star.show_animation = False
- a_star.use_beam_search = False
- a_star.use_iterative_deepening = False
- a_star.use_dynamic_weighting = False
- a_star.use_theta_star = False
- a_star.use_jump_point = False
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_batch_informed_rrt_star.py b/tests/test_batch_informed_rrt_star.py
deleted file mode 100644
index 3ad78bdb231..00000000000
--- a/tests/test_batch_informed_rrt_star.py
+++ /dev/null
@@ -1,14 +0,0 @@
-import random
-
-import conftest
-from PathPlanning.BatchInformedRRTStar import batch_informed_rrtstar as m
-
-
-def test_1():
- m.show_animation = False
- random.seed(12345)
- m.main(maxIter=10)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_behavior_tree.py b/tests/test_behavior_tree.py
deleted file mode 100644
index 0898690448f..00000000000
--- a/tests/test_behavior_tree.py
+++ /dev/null
@@ -1,207 +0,0 @@
-import pytest
-import conftest
-
-from MissionPlanning.BehaviorTree.behavior_tree import (
- BehaviorTreeFactory,
- Status,
- ActionNode,
-)
-
-
-def test_sequence_node1():
- xml_string = """
- <Sequence>
- <Echo name="Echo 1" message="Hello, World1!" />
- <Echo name="Echo 2" message="Hello, World2!" />
- <ForceFailure name="Force Failure">
- <Echo name="Echo 3" message="Hello, World3!" />
- </ForceFailure>
- </Sequence>
- """
- bt_factory = BehaviorTreeFactory()
- bt = bt_factory.build_tree(xml_string)
- bt.tick()
- assert bt.root.status == Status.RUNNING
- assert bt.root.children[0].status == Status.SUCCESS
- assert bt.root.children[1].status is None
- assert bt.root.children[2].status is None
- bt.tick()
- bt.tick()
- assert bt.root.status == Status.FAILURE
- assert bt.root.children[0].status is None
- assert bt.root.children[1].status is None
- assert bt.root.children[2].status is None
-
-
-def test_sequence_node2():
- xml_string = """
- <Sequence>
- <Echo name="Echo 1" message="Hello, World1!" />
- <Echo name="Echo 2" message="Hello, World2!" />
- <ForceSuccess name="Force Success">
- <Echo name="Echo 3" message="Hello, World3!" />
- </ForceSuccess>
- </Sequence>
- """
- bt_factory = BehaviorTreeFactory()
- bt = bt_factory.build_tree(xml_string)
- bt.tick_while_running()
- assert bt.root.status == Status.SUCCESS
- assert bt.root.children[0].status is None
- assert bt.root.children[1].status is None
- assert bt.root.children[2].status is None
-
-
-def test_selector_node1():
- xml_string = """
- <Selector>
- <ForceFailure name="Force Failure">
- <Echo name="Echo 1" message="Hello, World1!" />
- </ForceFailure>
- <Echo name="Echo 2" message="Hello, World2!" />
- <Echo name="Echo 3" message="Hello, World3!" />
- </Selector>
- """
- bt_factory = BehaviorTreeFactory()
- bt = bt_factory.build_tree(xml_string)
- bt.tick()
- assert bt.root.status == Status.RUNNING
- assert bt.root.children[0].status == Status.FAILURE
- assert bt.root.children[1].status is None
- assert bt.root.children[2].status is None
- bt.tick()
- assert bt.root.status == Status.SUCCESS
- assert bt.root.children[0].status is None
- assert bt.root.children[1].status is None
- assert bt.root.children[2].status is None
-
-
-def test_selector_node2():
- xml_string = """
- <Selector>
- <ForceFailure name="Force Success">
- <Echo name="Echo 1" message="Hello, World1!" />
- </ForceFailure>
- <ForceFailure name="Force Failure">
- <Echo name="Echo 2" message="Hello, World2!" />
- </ForceFailure>
- </Selector>
- """
- bt_factory = BehaviorTreeFactory()
- bt = bt_factory.build_tree(xml_string)
- bt.tick_while_running()
- assert bt.root.status == Status.FAILURE
- assert bt.root.children[0].status is None
- assert bt.root.children[1].status is None
-
-
-def test_while_do_else_node():
- xml_string = """
- <WhileDoElse>
- <Count name="Count" count_threshold="3" />
- <Echo name="Echo 1" message="Hello, World1!" />
- <Echo name="Echo 2" message="Hello, World2!" />
- </WhileDoElse>
- """
-
- class CountNode(ActionNode):
- def __init__(self, name, count_threshold):
- super().__init__(name)
- self.count = 0
- self.count_threshold = count_threshold
-
- def tick(self):
- self.count += 1
- if self.count >= self.count_threshold:
- return Status.FAILURE
- else:
- return Status.SUCCESS
-
- bt_factory = BehaviorTreeFactory()
- bt_factory.register_node_builder(
- "Count",
- lambda node: CountNode(
- node.attrib.get("name", CountNode.__name__),
- int(node.attrib["count_threshold"]),
- ),
- )
- bt = bt_factory.build_tree(xml_string)
- bt.tick()
- assert bt.root.status == Status.RUNNING
- assert bt.root.children[0].status == Status.SUCCESS
- assert bt.root.children[1].status is Status.SUCCESS
- assert bt.root.children[2].status is None
- bt.tick()
- assert bt.root.status == Status.RUNNING
- assert bt.root.children[0].status == Status.SUCCESS
- assert bt.root.children[1].status is Status.SUCCESS
- assert bt.root.children[2].status is None
- bt.tick()
- assert bt.root.status == Status.SUCCESS
- assert bt.root.children[0].status is None
- assert bt.root.children[1].status is None
- assert bt.root.children[2].status is None
-
-
-def test_node_children():
- # ControlNode Must have children
- xml_string = """
- <Sequence>
- </Sequence>
- """
- bt_factory = BehaviorTreeFactory()
- with pytest.raises(ValueError):
- bt_factory.build_tree(xml_string)
-
- # DecoratorNode Must have child
- xml_string = """
- <Inverter>
- </Inverter>
- """
- with pytest.raises(ValueError):
- bt_factory.build_tree(xml_string)
-
- # DecoratorNode Must have only one child
- xml_string = """
- <Inverter>
- <Echo name="Echo 1" message="Hello, World1!" />
- <Echo name="Echo 2" message="Hello, World2!" />
- </Inverter>
- """
- with pytest.raises(ValueError):
- bt_factory.build_tree(xml_string)
-
- # ActionNode Must have no children
- xml_string = """
- <Echo name="Echo 1" message="Hello, World1!">
- <Echo name="Echo 2" message="Hello, World2!" />
- </Echo>
- """
- with pytest.raises(ValueError):
- bt_factory.build_tree(xml_string)
-
- # WhileDoElse Must have exactly 2 or 3 children
- xml_string = """
- <WhileDoElse>
- <Echo name="Echo 1" message="Hello, World1!" />
- </WhileDoElse>
- """
- with pytest.raises(ValueError):
- bt = bt_factory.build_tree(xml_string)
- bt.tick()
-
- xml_string = """
- <WhileDoElse>
- <Echo name="Echo 1" message="Hello, World1!" />
- <Echo name="Echo 2" message="Hello, World2!" />
- <Echo name="Echo 3" message="Hello, World3!" />
- <Echo name="Echo 4" message="Hello, World4!" />
- </WhileDoElse>
- """
- with pytest.raises(ValueError):
- bt = bt_factory.build_tree(xml_string)
- bt.tick()
-
-
-if __name__ == "__main__":
- conftest.run_this_test(__file__)
diff --git a/tests/test_bezier_path.py b/tests/test_bezier_path.py
deleted file mode 100644
index 67a5d520de8..00000000000
--- a/tests/test_bezier_path.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import conftest
-from PathPlanning.BezierPath import bezier_path as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-def test_2():
- m.show_animation = False
- m.main2()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_bipedal_planner.py b/tests/test_bipedal_planner.py
deleted file mode 100644
index 818957bcdcb..00000000000
--- a/tests/test_bipedal_planner.py
+++ /dev/null
@@ -1,18 +0,0 @@
-import conftest
-from Bipedal.bipedal_planner import bipedal_planner as m
-
-
-def test_1():
- bipedal_planner = m.BipedalPlanner()
-
- footsteps = [[0.0, 0.2, 0.0],
- [0.3, 0.2, 0.0],
- [0.3, 0.2, 0.2],
- [0.3, 0.2, 0.2],
- [0.0, 0.2, 0.2]]
- bipedal_planner.set_ref_footsteps(footsteps)
- bipedal_planner.walk(plot=False)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_breadth_first_search.py b/tests/test_breadth_first_search.py
deleted file mode 100644
index bfc63e39d6b..00000000000
--- a/tests/test_breadth_first_search.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.BreadthFirstSearch import breadth_first_search as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_bspline_path.py b/tests/test_bspline_path.py
deleted file mode 100644
index 4918c9810f5..00000000000
--- a/tests/test_bspline_path.py
+++ /dev/null
@@ -1,74 +0,0 @@
-import conftest
-import numpy as np
-import pytest
-from PathPlanning.BSplinePath import bspline_path
-
-
-def test_list_input():
- way_point_x = [-1.0, 3.0, 4.0, 2.0, 1.0]
- way_point_y = [0.0, -3.0, 1.0, 1.0, 3.0]
- n_course_point = 50 # sampling number
-
- rax, ray, heading, curvature = bspline_path.approximate_b_spline_path(
- way_point_x, way_point_y, n_course_point, s=0.5)
-
- assert len(rax) == len(ray) == len(heading) == len(curvature)
-
- rix, riy, heading, curvature = bspline_path.interpolate_b_spline_path(
- way_point_x, way_point_y, n_course_point)
-
- assert len(rix) == len(riy) == len(heading) == len(curvature)
-
-
-def test_array_input():
- way_point_x = np.array([-1.0, 3.0, 4.0, 2.0, 1.0])
- way_point_y = np.array([0.0, -3.0, 1.0, 1.0, 3.0])
- n_course_point = 50 # sampling number
-
- rax, ray, heading, curvature = bspline_path.approximate_b_spline_path(
- way_point_x, way_point_y, n_course_point, s=0.5)
-
- assert len(rax) == len(ray) == len(heading) == len(curvature)
-
- rix, riy, heading, curvature = bspline_path.interpolate_b_spline_path(
- way_point_x, way_point_y, n_course_point)
-
- assert len(rix) == len(riy) == len(heading) == len(curvature)
-
-
-def test_degree_change():
- way_point_x = np.array([-1.0, 3.0, 4.0, 2.0, 1.0])
- way_point_y = np.array([0.0, -3.0, 1.0, 1.0, 3.0])
- n_course_point = 50 # sampling number
-
- rax, ray, heading, curvature = bspline_path.approximate_b_spline_path(
- way_point_x, way_point_y, n_course_point, s=0.5, degree=4)
-
- assert len(rax) == len(ray) == len(heading) == len(curvature)
-
- rix, riy, heading, curvature = bspline_path.interpolate_b_spline_path(
- way_point_x, way_point_y, n_course_point, degree=4)
-
- assert len(rix) == len(riy) == len(heading) == len(curvature)
-
- rax, ray, heading, curvature = bspline_path.approximate_b_spline_path(
- way_point_x, way_point_y, n_course_point, s=0.5, degree=2)
-
- assert len(rax) == len(ray) == len(heading) == len(curvature)
-
- rix, riy, heading, curvature = bspline_path.interpolate_b_spline_path(
- way_point_x, way_point_y, n_course_point, degree=2)
-
- assert len(rix) == len(riy) == len(heading) == len(curvature)
-
- with pytest.raises(ValueError):
- bspline_path.approximate_b_spline_path(
- way_point_x, way_point_y, n_course_point, s=0.5, degree=1)
-
- with pytest.raises(ValueError):
- bspline_path.interpolate_b_spline_path(
- way_point_x, way_point_y, n_course_point, degree=1)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_bug.py b/tests/test_bug.py
deleted file mode 100644
index f94794a45e4..00000000000
--- a/tests/test_bug.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.BugPlanning import bug as m
-
-
-def test_1():
- m.show_animation = False
- m.main(bug_0=True, bug_1=True, bug_2=True)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_catmull_rom_spline.py b/tests/test_catmull_rom_spline.py
deleted file mode 100644
index 41a73588c3f..00000000000
--- a/tests/test_catmull_rom_spline.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import conftest
-from PathPlanning.Catmull_RomSplinePath.catmull_rom_spline_path import catmull_rom_spline
-
-def test_catmull_rom_spline():
- way_points = [[0, 0], [1, 2], [2, 0], [3, 3]]
- num_points = 100
-
- spline_x, spline_y = catmull_rom_spline(way_points, num_points)
-
- assert spline_x.size > 0, "Spline X coordinates should not be empty"
- assert spline_y.size > 0, "Spline Y coordinates should not be empty"
-
- assert spline_x.shape == spline_y.shape, "Spline X and Y coordinates should have the same shape"
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_cgmres_nmpc.py b/tests/test_cgmres_nmpc.py
deleted file mode 100644
index db3ada5065c..00000000000
--- a/tests/test_cgmres_nmpc.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathTracking.cgmres_nmpc import cgmres_nmpc as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_circle_fitting.py b/tests/test_circle_fitting.py
deleted file mode 100644
index b3888d7cc31..00000000000
--- a/tests/test_circle_fitting.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from Mapping.circle_fitting import circle_fitting as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_closed_loop_rrt_star_car.py b/tests/test_closed_loop_rrt_star_car.py
deleted file mode 100644
index c33e413e926..00000000000
--- a/tests/test_closed_loop_rrt_star_car.py
+++ /dev/null
@@ -1,13 +0,0 @@
-import conftest
-from PathPlanning.ClosedLoopRRTStar import closed_loop_rrt_star_car as m
-import random
-
-
-def test_1():
- random.seed(12345)
- m.show_animation = False
- m.main(gx=1.0, gy=0.0, gyaw=0.0, max_iter=5)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_clothoidal_paths.py b/tests/test_clothoidal_paths.py
deleted file mode 100644
index 0b038c03381..00000000000
--- a/tests/test_clothoidal_paths.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.ClothoidPath import clothoid_path_planner as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_codestyle.py b/tests/test_codestyle.py
deleted file mode 100644
index 55e558c184e..00000000000
--- a/tests/test_codestyle.py
+++ /dev/null
@@ -1,138 +0,0 @@
-"""
-Diff code style checker with ruff
-
-This code come from:
-https://github.com/scipy/scipy/blob/main/tools/lint.py
-
-Scipy's licence: https://github.com/scipy/scipy/blob/main/LICENSE.txt
-Copyright (c) 2001-2002 Enthought, Inc. 2003-2022, SciPy Developers.
-All rights reserved.
-
-Redistribution and use in source and binary forms, with or without
-modification, are permitted provided that the following conditions
-are met:
-
-1. Redistributions of source code must retain the above copyright
- notice, this list of conditions and the following disclaimer.
-
-2. Redistributions in binary form must reproduce the above
- copyright notice, this list of conditions and the following
- disclaimer in the documentation and/or other materials provided
- with the distribution.
-
-3. Neither the name of the copyright holder nor the names of its
- contributors may be used to endorse or promote products derived
- from this software without specific prior written permission.
-
-THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
-"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
-LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
-A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
-OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
-SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
-LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
-DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
-THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
-(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
-OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
-"""
-import conftest
-import os
-import subprocess
-
-
-CONFIG = os.path.join(
- os.path.abspath(os.path.dirname(os.path.dirname(__file__))),
- 'ruff.toml',
-)
-
-ROOT_DIR = os.path.abspath(os.path.dirname(os.path.dirname(__file__)))
-
-
-def run_ruff(files, fix):
- if not files:
- return 0, ""
- args = ['--fix'] if fix else []
- res = subprocess.run(
- ['ruff', 'check', f'--config={CONFIG}'] + args + files,
- stdout=subprocess.PIPE,
- encoding='utf-8'
- )
- return res.returncode, res.stdout
-
-
-def rev_list(branch, num_commits):
- """List commits in reverse chronological order.
- Only the first `num_commits` are shown.
- """
- res = subprocess.run(
- [
- 'git',
- 'rev-list',
- '--max-count',
- f'{num_commits}',
- '--first-parent',
- branch
- ],
- stdout=subprocess.PIPE,
- encoding='utf-8',
- )
- res.check_returncode()
- return res.stdout.rstrip('\n').split('\n')
-
-
-def find_branch_point(branch):
- """Find when the current branch split off from the given branch.
- It is based off of this Stackoverflow post:
- https://stackoverflow.com/questions/1527234/finding-a-branch-point-with-git#4991675
- """
- branch_commits = rev_list('HEAD', 1000)
- main_commits = set(rev_list(branch, 1000))
- for branch_commit in branch_commits:
- if branch_commit in main_commits:
- return branch_commit
-
- # If a branch split off over 1000 commits ago we will fail to find
- # the ancestor.
- raise RuntimeError(
- 'Failed to find a common ancestor in the last 1000 commits')
-
-
-def find_diff(sha):
- """Find the diff since the given sha."""
- files = ['*.py']
- res = subprocess.run(
- ['git', 'diff', '--unified=0', sha, '--'] + files,
- stdout=subprocess.PIPE,
- encoding='utf-8'
- )
- res.check_returncode()
- return res.stdout
-
-
-def diff_files(sha):
- """Find the diff since the given SHA."""
- res = subprocess.run(
- ['git', 'diff', '--name-only', '--diff-filter=ACMR', '-z', sha, '--',
- '*.py', '*.pyx', '*.pxd', '*.pxi'],
- stdout=subprocess.PIPE,
- encoding='utf-8'
- )
- res.check_returncode()
- return [os.path.join(ROOT_DIR, f) for f in res.stdout.split('\0') if f]
-
-
-def test():
- branch_commit = find_branch_point("origin/master")
- files = diff_files(branch_commit)
- print(files)
- rc, errors = run_ruff(files, fix=True)
- if errors:
- print(errors)
- else:
- print("No lint errors found.")
- assert rc == 0
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_cubature_kalman_filter.py b/tests/test_cubature_kalman_filter.py
deleted file mode 100644
index 00f9d8bc5ff..00000000000
--- a/tests/test_cubature_kalman_filter.py
+++ /dev/null
@@ -1,13 +0,0 @@
-import conftest
-from Localization.cubature_kalman_filter import cubature_kalman_filter as m
-
-
-def test1():
- m.show_final = False
- m.show_animation = False
- m.show_ellipse = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_d_star_lite.py b/tests/test_d_star_lite.py
deleted file mode 100644
index b60a140a89b..00000000000
--- a/tests/test_d_star_lite.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.DStarLite import d_star_lite as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_depth_first_search.py b/tests/test_depth_first_search.py
deleted file mode 100644
index 8dd009278f1..00000000000
--- a/tests/test_depth_first_search.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.DepthFirstSearch import depth_first_search as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_dijkstra.py b/tests/test_dijkstra.py
deleted file mode 100644
index 40404153d8b..00000000000
--- a/tests/test_dijkstra.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.Dijkstra import dijkstra as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_distance_map.py b/tests/test_distance_map.py
deleted file mode 100644
index df6e394e2ce..00000000000
--- a/tests/test_distance_map.py
+++ /dev/null
@@ -1,118 +0,0 @@
-import conftest # noqa
-import numpy as np
-from Mapping.DistanceMap import distance_map as m
-
-
-def test_compute_sdf():
- """Test the computation of Signed Distance Field (SDF)"""
- # Create a simple obstacle map for testing
- obstacles = np.array([[0, 0, 0], [0, 1, 0], [0, 0, 0]])
-
- sdf = m.compute_sdf(obstacles)
-
- # Verify basic properties of SDF
- assert sdf.shape == obstacles.shape, "SDF should have the same shape as input map"
- assert np.all(np.isfinite(sdf)), "SDF should not contain infinite values"
-
- # Verify SDF value is negative at obstacle position
- assert sdf[1, 1] < 0, "SDF value should be negative at obstacle position"
-
- # Verify SDF value is positive in free space
- assert sdf[0, 0] > 0, "SDF value should be positive in free space"
-
-
-def test_compute_udf():
- """Test the computation of Unsigned Distance Field (UDF)"""
- # Create obstacle map for testing
- obstacles = np.array([[0, 0, 0], [0, 1, 0], [0, 0, 0]])
-
- udf = m.compute_udf(obstacles)
-
- # Verify basic properties of UDF
- assert udf.shape == obstacles.shape, "UDF should have the same shape as input map"
- assert np.all(np.isfinite(udf)), "UDF should not contain infinite values"
- assert np.all(udf >= 0), "All UDF values should be non-negative"
-
- # Verify UDF value is 0 at obstacle position
- assert np.abs(udf[1, 1]) < 1e-10, "UDF value should be 0 at obstacle position"
-
- # Verify UDF value is 1 for adjacent cells
- assert np.abs(udf[0, 1] - 1.0) < 1e-10, (
- "UDF value should be 1 for cells adjacent to obstacle"
- )
- assert np.abs(udf[1, 0] - 1.0) < 1e-10, (
- "UDF value should be 1 for cells adjacent to obstacle"
- )
- assert np.abs(udf[1, 2] - 1.0) < 1e-10, (
- "UDF value should be 1 for cells adjacent to obstacle"
- )
- assert np.abs(udf[2, 1] - 1.0) < 1e-10, (
- "UDF value should be 1 for cells adjacent to obstacle"
- )
-
-
-def test_dt():
- """Test the computation of 1D distance transform"""
- # Create test data
- d = np.array([m.INF, 0, m.INF])
- m.dt(d)
-
- # Verify distance transform results
- assert np.all(np.isfinite(d)), (
- "Distance transform result should not contain infinite values"
- )
- assert d[1] == 0, "Distance at obstacle position should be 0"
- assert d[0] == 1, "Distance at adjacent position should be 1"
- assert d[2] == 1, "Distance at adjacent position should be 1"
-
-
-def test_compute_sdf_empty():
- """Test SDF computation with empty map"""
- # Test with empty map (no obstacles)
- empty_map = np.zeros((5, 5))
- sdf = m.compute_sdf(empty_map)
-
- assert np.all(sdf > 0), "All SDF values should be positive for empty map"
- assert sdf.shape == empty_map.shape, "Output shape should match input shape"
-
-
-def test_compute_sdf_full():
- """Test SDF computation with fully occupied map"""
- # Test with fully occupied map
- full_map = np.ones((5, 5))
- sdf = m.compute_sdf(full_map)
-
- assert np.all(sdf < 0), "All SDF values should be negative for fully occupied map"
- assert sdf.shape == full_map.shape, "Output shape should match input shape"
-
-
-def test_compute_udf_invalid_input():
- """Test UDF computation with invalid input values"""
- # Test with invalid values (not 0 or 1)
- invalid_map = np.array([[0, 2, 0], [0, -1, 0], [0, 0.5, 0]])
-
- try:
- m.compute_udf(invalid_map)
- assert False, "Should raise ValueError for invalid input values"
- except ValueError:
- pass
-
-
-def test_compute_udf_empty():
- """Test UDF computation with empty map"""
- # Test with empty map
- empty_map = np.zeros((5, 5))
- udf = m.compute_udf(empty_map)
-
- assert np.all(udf > 0), "All UDF values should be positive for empty map"
- assert np.all(np.isfinite(udf)), "UDF should not contain infinite values"
-
-
-def test_main():
- """Test the execution of main function"""
- m.ENABLE_PLOT = False
- m.main()
-
-
-if __name__ == "__main__":
- conftest.run_this_test(__file__)
diff --git a/tests/test_drone_3d_trajectory_following.py b/tests/test_drone_3d_trajectory_following.py
deleted file mode 100644
index e3fd4170247..00000000000
--- a/tests/test_drone_3d_trajectory_following.py
+++ /dev/null
@@ -1,12 +0,0 @@
-import conftest
-from AerialNavigation.drone_3d_trajectory_following \
- import drone_3d_trajectory_following as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_dstar.py b/tests/test_dstar.py
deleted file mode 100644
index f8f40fecefc..00000000000
--- a/tests/test_dstar.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.DStar import dstar as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_dubins_path_planning.py b/tests/test_dubins_path_planning.py
deleted file mode 100644
index aceb0b752a2..00000000000
--- a/tests/test_dubins_path_planning.py
+++ /dev/null
@@ -1,92 +0,0 @@
-import numpy as np
-
-import conftest
-from PathPlanning.DubinsPath import dubins_path_planner
-
-np.random.seed(12345)
-
-
-def check_edge_condition(px, py, pyaw, start_x, start_y, start_yaw, end_x,
- end_y, end_yaw):
- assert (abs(px[0] - start_x) <= 0.01)
- assert (abs(py[0] - start_y) <= 0.01)
- assert (abs(pyaw[0] - start_yaw) <= 0.01)
- assert (abs(px[-1] - end_x) <= 0.01)
- assert (abs(py[-1] - end_y) <= 0.01)
- assert (abs(pyaw[-1] - end_yaw) <= 0.01)
-
-
-def check_path_length(px, py, lengths):
- path_len = sum(
- [np.hypot(dx, dy) for (dx, dy) in zip(np.diff(px), np.diff(py))])
- assert (abs(path_len - sum(lengths)) <= 0.1)
-
-
-def test_1():
- start_x = 1.0 # [m]
- start_y = 1.0 # [m]
- start_yaw = np.deg2rad(45.0) # [rad]
-
- end_x = -3.0 # [m]
- end_y = -3.0 # [m]
- end_yaw = np.deg2rad(-45.0) # [rad]
-
- curvature = 1.0
-
- px, py, pyaw, mode, lengths = dubins_path_planner.plan_dubins_path(
- start_x, start_y, start_yaw, end_x, end_y, end_yaw, curvature)
-
- check_edge_condition(px, py, pyaw, start_x, start_y, start_yaw, end_x,
- end_y, end_yaw)
- check_path_length(px, py, lengths)
-
-
-def test_2():
- dubins_path_planner.show_animation = False
- dubins_path_planner.main()
-
-
-def test_3():
- N_TEST = 10
-
- for i in range(N_TEST):
- start_x = (np.random.rand() - 0.5) * 10.0 # [m]
- start_y = (np.random.rand() - 0.5) * 10.0 # [m]
- start_yaw = np.deg2rad((np.random.rand() - 0.5) * 180.0) # [rad]
-
- end_x = (np.random.rand() - 0.5) * 10.0 # [m]
- end_y = (np.random.rand() - 0.5) * 10.0 # [m]
- end_yaw = np.deg2rad((np.random.rand() - 0.5) * 180.0) # [rad]
-
- curvature = 1.0 / (np.random.rand() * 5.0)
-
- px, py, pyaw, mode, lengths = \
- dubins_path_planner.plan_dubins_path(
- start_x, start_y, start_yaw, end_x, end_y, end_yaw, curvature)
-
- check_edge_condition(px, py, pyaw, start_x, start_y, start_yaw, end_x,
- end_y, end_yaw)
- check_path_length(px, py, lengths)
-
-
-def test_path_plannings_types():
- dubins_path_planner.show_animation = False
- start_x = 1.0 # [m]
- start_y = 1.0 # [m]
- start_yaw = np.deg2rad(45.0) # [rad]
-
- end_x = -3.0 # [m]
- end_y = -3.0 # [m]
- end_yaw = np.deg2rad(-45.0) # [rad]
-
- curvature = 1.0
-
- _, _, _, mode, _ = dubins_path_planner.plan_dubins_path(
- start_x, start_y, start_yaw, end_x, end_y, end_yaw, curvature,
- selected_types=["RSL"])
-
- assert mode == ["R", "S", "L"]
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_dynamic_movement_primitives.py b/tests/test_dynamic_movement_primitives.py
deleted file mode 100644
index 3ab1c8a32c5..00000000000
--- a/tests/test_dynamic_movement_primitives.py
+++ /dev/null
@@ -1,49 +0,0 @@
-import conftest
-import numpy as np
-from PathPlanning.DynamicMovementPrimitives import \
- dynamic_movement_primitives
-
-
-def test_1():
- # test that trajectory can be learned from user-passed data
- T = 5
- t = np.arange(0, T, 0.01)
- sin_t = np.sin(t)
- train_data = np.array([t, sin_t]).T
-
- DMP_controller = dynamic_movement_primitives.DMP(train_data, T)
- DMP_controller.recreate_trajectory(train_data[0], train_data[-1], 4)
-
-
-def test_2():
- # test that length of trajectory is equal to desired number of timesteps
- T = 5
- t = np.arange(0, T, 0.01)
- sin_t = np.sin(t)
- train_data = np.array([t, sin_t]).T
-
- DMP_controller = dynamic_movement_primitives.DMP(train_data, T)
- t, path = DMP_controller.recreate_trajectory(train_data[0],
- train_data[-1], 4)
-
- assert(path.shape[0] == DMP_controller.timesteps)
-
-
-def test_3():
- # check that learned trajectory is close to initial
- T = 3*np.pi/2
- A_noise = 0.02
- t = np.arange(0, T, 0.01)
- noisy_sin_t = np.sin(t) + A_noise*np.random.rand(len(t))
- train_data = np.array([t, noisy_sin_t]).T
-
- DMP_controller = dynamic_movement_primitives.DMP(train_data, T)
- t, pos = DMP_controller.recreate_trajectory(train_data[0],
- train_data[-1], T)
-
- diff = abs(pos[:, 1] - noisy_sin_t)
- assert(max(diff) < 5*A_noise)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_dynamic_window_approach.py b/tests/test_dynamic_window_approach.py
deleted file mode 100644
index fdb452b4a7a..00000000000
--- a/tests/test_dynamic_window_approach.py
+++ /dev/null
@@ -1,48 +0,0 @@
-import conftest
-import numpy as np
-
-from PathPlanning.DynamicWindowApproach import dynamic_window_approach as m
-
-
-def test_main1():
- m.show_animation = False
- m.main(gx=1.0, gy=1.0)
-
-
-def test_main2():
- m.show_animation = False
- m.main(gx=1.0, gy=1.0, robot_type=m.RobotType.rectangle)
-
-
-def test_stuck_main():
- m.show_animation = False
- # adjust cost
- m.config.to_goal_cost_gain = 0.2
- m.config.obstacle_cost_gain = 2.0
- # obstacles and goals for stuck condition
- m.config.ob = -1 * np.array([[-1.0, -1.0],
- [0.0, 2.0],
- [2.0, 6.0],
- [2.0, 8.0],
- [3.0, 9.27],
- [3.79, 9.39],
- [7.25, 8.97],
- [7.0, 2.0],
- [3.0, 4.0],
- [6.0, 5.0],
- [3.5, 5.8],
- [6.0, 9.0],
- [8.8, 9.0],
- [5.0, 9.0],
- [7.5, 3.0],
- [9.0, 8.0],
- [5.8, 4.4],
- [12.0, 12.0],
- [3.0, 2.0],
- [13.0, 13.0]
- ])
- m.main(gx=-5.0, gy=-7.0)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_ekf_slam.py b/tests/test_ekf_slam.py
deleted file mode 100644
index 4181bb64bae..00000000000
--- a/tests/test_ekf_slam.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from SLAM.EKFSLAM import ekf_slam as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_elastic_bands.py b/tests/test_elastic_bands.py
deleted file mode 100644
index ad4e13af1af..00000000000
--- a/tests/test_elastic_bands.py
+++ /dev/null
@@ -1,23 +0,0 @@
-import conftest
-import numpy as np
-from PathPlanning.ElasticBands.elastic_bands import ElasticBands
-
-
-def test_1():
- path = np.load("PathPlanning/ElasticBands/path.npy")
- obstacles_points = np.load("PathPlanning/ElasticBands/obstacles.npy")
- obstacles = np.zeros((500, 500))
- for x, y in obstacles_points:
- size = 30 # Side length of the square
- half_size = size // 2
- x_start = max(0, x - half_size)
- x_end = min(obstacles.shape[0], x + half_size)
- y_start = max(0, y - half_size)
- y_end = min(obstacles.shape[1], y + half_size)
- obstacles[x_start:x_end, y_start:y_end] = 1
- elastic_bands = ElasticBands(path, obstacles)
- elastic_bands.update_bubbles()
-
-
-if __name__ == "__main__":
- conftest.run_this_test(__file__)
diff --git a/tests/test_eta3_spline_path.py b/tests/test_eta3_spline_path.py
deleted file mode 100644
index 7fa3883ea59..00000000000
--- a/tests/test_eta3_spline_path.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.Eta3SplinePath import eta3_spline_path as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_extended_kalman_filter.py b/tests/test_extended_kalman_filter.py
deleted file mode 100644
index d9ad6437a8e..00000000000
--- a/tests/test_extended_kalman_filter.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from Localization.extended_kalman_filter import extended_kalman_filter as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_fast_slam1.py b/tests/test_fast_slam1.py
deleted file mode 100644
index b72ab6b9efa..00000000000
--- a/tests/test_fast_slam1.py
+++ /dev/null
@@ -1,12 +0,0 @@
-import conftest
-from SLAM.FastSLAM1 import fast_slam1 as m
-
-
-def test1():
- m.show_animation = False
- m.SIM_TIME = 3.0
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_fast_slam2.py b/tests/test_fast_slam2.py
deleted file mode 100644
index 95cdc69d424..00000000000
--- a/tests/test_fast_slam2.py
+++ /dev/null
@@ -1,12 +0,0 @@
-import conftest
-from SLAM.FastSLAM2 import fast_slam2 as m
-
-
-def test1():
- m.show_animation = False
- m.SIM_TIME = 3.0
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_flow_field.py b/tests/test_flow_field.py
deleted file mode 100644
index d049731fe59..00000000000
--- a/tests/test_flow_field.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-import PathPlanning.FlowField.flowfield as flow_field
-
-
-def test():
- flow_field.show_animation = False
- flow_field.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_frenet_optimal_trajectory.py b/tests/test_frenet_optimal_trajectory.py
deleted file mode 100644
index b8761ff4a6c..00000000000
--- a/tests/test_frenet_optimal_trajectory.py
+++ /dev/null
@@ -1,48 +0,0 @@
-import conftest
-from PathPlanning.FrenetOptimalTrajectory import frenet_optimal_trajectory as m
-from PathPlanning.FrenetOptimalTrajectory.frenet_optimal_trajectory import (
- LateralMovement,
- LongitudinalMovement,
-)
-
-
-def default_scenario_test():
- m.show_animation = False
- m.SIM_LOOP = 5
- m.main()
-
-
-def high_speed_and_merging_and_stopping_scenario_test():
- m.show_animation = False
- m.LATERAL_MOVEMENT = LateralMovement.HIGH_SPEED
- m.LONGITUDINAL_MOVEMENT = LongitudinalMovement.MERGING_AND_STOPPING
- m.SIM_LOOP = 5
- m.main()
-
-
-def high_speed_and_velocity_keeping_scenario_test():
- m.show_animation = False
- m.LATERAL_MOVEMENT = LateralMovement.HIGH_SPEED
- m.LONGITUDINAL_MOVEMENT = LongitudinalMovement.VELOCITY_KEEPING
- m.SIM_LOOP = 5
- m.main()
-
-
-def low_speed_and_velocity_keeping_scenario_test():
- m.show_animation = False
- m.LATERAL_MOVEMENT = LateralMovement.LOW_SPEED
- m.LONGITUDINAL_MOVEMENT = LongitudinalMovement.VELOCITY_KEEPING
- m.SIM_LOOP = 5
- m.main()
-
-
-def low_speed_and_merging_and_stopping_scenario_test():
- m.show_animation = False
- m.LATERAL_MOVEMENT = LateralMovement.LOW_SPEED
- m.LONGITUDINAL_MOVEMENT = LongitudinalMovement.MERGING_AND_STOPPING
- m.SIM_LOOP = 5
- m.main()
-
-
-if __name__ == "__main__":
- conftest.run_this_test(__file__)
diff --git a/tests/test_gaussian_grid_map.py b/tests/test_gaussian_grid_map.py
deleted file mode 100644
index af1e138721b..00000000000
--- a/tests/test_gaussian_grid_map.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from Mapping.gaussian_grid_map import gaussian_grid_map as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_graph_based_slam.py b/tests/test_graph_based_slam.py
deleted file mode 100644
index 67d75f0f858..00000000000
--- a/tests/test_graph_based_slam.py
+++ /dev/null
@@ -1,12 +0,0 @@
-import conftest
-from SLAM.GraphBasedSLAM import graph_based_slam as m
-
-
-def test_1():
- m.show_animation = False
- m.SIM_TIME = 20.0
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_greedy_best_first_search.py b/tests/test_greedy_best_first_search.py
deleted file mode 100644
index e573ecf6255..00000000000
--- a/tests/test_greedy_best_first_search.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.GreedyBestFirstSearch import greedy_best_first_search as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_grid_based_sweep_coverage_path_planner.py b/tests/test_grid_based_sweep_coverage_path_planner.py
deleted file mode 100644
index 8cbe36eb497..00000000000
--- a/tests/test_grid_based_sweep_coverage_path_planner.py
+++ /dev/null
@@ -1,118 +0,0 @@
-import conftest
-from PathPlanning.GridBasedSweepCPP \
- import grid_based_sweep_coverage_path_planner
-
-grid_based_sweep_coverage_path_planner.do_animation = False
-RIGHT = grid_based_sweep_coverage_path_planner. \
- SweepSearcher.MovingDirection.RIGHT
-LEFT = grid_based_sweep_coverage_path_planner. \
- SweepSearcher.MovingDirection.LEFT
-UP = grid_based_sweep_coverage_path_planner. \
- SweepSearcher.SweepDirection.UP
-DOWN = grid_based_sweep_coverage_path_planner. \
- SweepSearcher.SweepDirection.DOWN
-
-
-def test_planning1():
- ox = [0.0, 20.0, 50.0, 100.0, 130.0, 40.0, 0.0]
- oy = [0.0, -20.0, 0.0, 30.0, 60.0, 80.0, 0.0]
- resolution = 5.0
-
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=RIGHT,
- sweeping_direction=DOWN,
- )
- assert len(px) >= 5
-
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=LEFT,
- sweeping_direction=DOWN,
- )
- assert len(px) >= 5
-
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=RIGHT,
- sweeping_direction=UP,
- )
- assert len(px) >= 5
-
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=RIGHT,
- sweeping_direction=UP,
- )
- assert len(px) >= 5
-
-
-def test_planning2():
- ox = [0.0, 50.0, 50.0, 0.0, 0.0]
- oy = [0.0, 0.0, 30.0, 30.0, 0.0]
- resolution = 1.3
-
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=RIGHT,
- sweeping_direction=DOWN,
- )
- assert len(px) >= 5
-
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=LEFT,
- sweeping_direction=DOWN,
- )
- assert len(px) >= 5
-
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=RIGHT,
- sweeping_direction=UP,
- )
- assert len(px) >= 5
-
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=RIGHT,
- sweeping_direction=DOWN,
- )
- assert len(px) >= 5
-
-
-def test_planning3():
- ox = [0.0, 20.0, 50.0, 200.0, 130.0, 40.0, 0.0]
- oy = [0.0, -80.0, 0.0, 30.0, 60.0, 80.0, 0.0]
- resolution = 5.1
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=RIGHT,
- sweeping_direction=DOWN,
- )
- assert len(px) >= 5
-
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=LEFT,
- sweeping_direction=DOWN,
- )
- assert len(px) >= 5
-
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=RIGHT,
- sweeping_direction=UP,
- )
- assert len(px) >= 5
-
- px, py = grid_based_sweep_coverage_path_planner.planning(
- ox, oy, resolution,
- moving_direction=RIGHT,
- sweeping_direction=DOWN,
- )
- assert len(px) >= 5
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_grid_map_lib.py b/tests/test_grid_map_lib.py
deleted file mode 100644
index 670b357ad3f..00000000000
--- a/tests/test_grid_map_lib.py
+++ /dev/null
@@ -1,40 +0,0 @@
-from Mapping.grid_map_lib.grid_map_lib import GridMap
-import conftest
-import numpy as np
-
-
-def test_position_set():
- grid_map = GridMap(100, 120, 0.5, 10.0, -0.5)
-
- grid_map.set_value_from_xy_pos(10.1, -1.1, 1.0)
- grid_map.set_value_from_xy_pos(10.1, -0.1, 1.0)
- grid_map.set_value_from_xy_pos(10.1, 1.1, 1.0)
- grid_map.set_value_from_xy_pos(11.1, 0.1, 1.0)
- grid_map.set_value_from_xy_pos(10.1, 0.1, 1.0)
- grid_map.set_value_from_xy_pos(9.1, 0.1, 1.0)
-
-
-def test_polygon_set():
- ox = [0.0, 4.35, 20.0, 50.0, 100.0, 130.0, 40.0]
- oy = [0.0, -4.15, -20.0, 0.0, 30.0, 60.0, 80.0]
-
- grid_map = GridMap(600, 290, 0.7, 60.0, 30.5)
-
- grid_map.set_value_from_polygon(ox, oy, 1.0, inside=False)
- grid_map.set_value_from_polygon(np.array(ox), np.array(oy),
- 1.0, inside=False)
-
-
-def test_xy_and_grid_index_conversion():
- grid_map = GridMap(100, 120, 0.5, 10.0, -0.5)
-
- for x_ind in range(grid_map.width):
- for y_ind in range(grid_map.height):
- grid_ind = grid_map.calc_grid_index_from_xy_index(x_ind, y_ind)
- x_ind_2, y_ind_2 = grid_map.calc_xy_index_from_grid_index(grid_ind)
- assert x_ind == x_ind_2
- assert y_ind == y_ind_2
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_histogram_filter.py b/tests/test_histogram_filter.py
deleted file mode 100644
index 4474ead0979..00000000000
--- a/tests/test_histogram_filter.py
+++ /dev/null
@@ -1,12 +0,0 @@
-import conftest
-from Localization.histogram_filter import histogram_filter as m
-
-
-def test1():
- m.show_animation = False
- m.SIM_TIME = 1.0
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_hybrid_a_star.py b/tests/test_hybrid_a_star.py
deleted file mode 100644
index dbcf3ba9f43..00000000000
--- a/tests/test_hybrid_a_star.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.HybridAStar import hybrid_a_star as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_informed_rrt_star.py b/tests/test_informed_rrt_star.py
deleted file mode 100644
index 10974ecfcb5..00000000000
--- a/tests/test_informed_rrt_star.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from PathPlanning.InformedRRTStar import informed_rrt_star as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_inverted_pendulum_lqr_control.py b/tests/test_inverted_pendulum_lqr_control.py
deleted file mode 100644
index 62afda71c38..00000000000
--- a/tests/test_inverted_pendulum_lqr_control.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from InvertedPendulum import inverted_pendulum_lqr_control as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_inverted_pendulum_mpc_control.py b/tests/test_inverted_pendulum_mpc_control.py
deleted file mode 100644
index 94859c2e0af..00000000000
--- a/tests/test_inverted_pendulum_mpc_control.py
+++ /dev/null
@@ -1,12 +0,0 @@
-import conftest
-
-from InvertedPendulum import inverted_pendulum_mpc_control as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_iterative_closest_point.py b/tests/test_iterative_closest_point.py
deleted file mode 100644
index 3e726b5649a..00000000000
--- a/tests/test_iterative_closest_point.py
+++ /dev/null
@@ -1,16 +0,0 @@
-import conftest
-from SLAM.iterative_closest_point import iterative_closest_point as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-def test_2():
- m.show_animation = False
- m.main_3d_points()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_kmeans_clustering.py b/tests/test_kmeans_clustering.py
deleted file mode 100644
index 5e39d64ae6e..00000000000
--- a/tests/test_kmeans_clustering.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest
-from Mapping.kmeans_clustering import kmeans_clustering as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_lqr_rrt_star.py b/tests/test_lqr_rrt_star.py
deleted file mode 100644
index 444b4616b85..00000000000
--- a/tests/test_lqr_rrt_star.py
+++ /dev/null
@@ -1,14 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.LQRRRTStar import lqr_rrt_star as m
-import random
-
-random.seed(12345)
-
-
-def test1():
- m.show_animation = False
- m.main(maxIter=5)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_lqr_speed_steer_control.py b/tests/test_lqr_speed_steer_control.py
deleted file mode 100644
index cee9759a26b..00000000000
--- a/tests/test_lqr_speed_steer_control.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathTracking.lqr_speed_steer_control import lqr_speed_steer_control as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_lqr_steer_control.py b/tests/test_lqr_steer_control.py
deleted file mode 100644
index 24427a8ffdd..00000000000
--- a/tests/test_lqr_steer_control.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathTracking.lqr_steer_control import lqr_steer_control as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_model_predictive_speed_and_steer_control.py b/tests/test_model_predictive_speed_and_steer_control.py
deleted file mode 100644
index 9bc8ccf31ce..00000000000
--- a/tests/test_model_predictive_speed_and_steer_control.py
+++ /dev/null
@@ -1,18 +0,0 @@
-import conftest # Add root path to sys.path
-
-from PathTracking.model_predictive_speed_and_steer_control \
- import model_predictive_speed_and_steer_control as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-def test_2():
- m.show_animation = False
- m.main2()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_move_to_pose.py b/tests/test_move_to_pose.py
deleted file mode 100644
index e06d801555b..00000000000
--- a/tests/test_move_to_pose.py
+++ /dev/null
@@ -1,90 +0,0 @@
-import itertools
-import numpy as np
-import conftest # Add root path to sys.path
-from PathTracking.move_to_pose import move_to_pose as m
-
-
-def test_random():
- m.show_animation = False
- m.main()
-
-
-def test_stability():
- """
- This unit test tests the move_to_pose.py program for stability
- """
- m.show_animation = False
- x_start = 5
- y_start = 5
- theta_start = 0
- x_goal = 1
- y_goal = 4
- theta_goal = 0
- _, _, v_traj, w_traj = m.move_to_pose(
- x_start, y_start, theta_start, x_goal, y_goal, theta_goal
- )
-
- def v_is_change(current, previous):
- return abs(current - previous) > m.MAX_LINEAR_SPEED
-
- def w_is_change(current, previous):
- return abs(current - previous) > m.MAX_ANGULAR_SPEED
-
- # Check if the speed is changing too much
- window_size = 10
- count_threshold = 4
- v_change = [v_is_change(v_traj[i], v_traj[i - 1]) for i in range(1, len(v_traj))]
- w_change = [w_is_change(w_traj[i], w_traj[i - 1]) for i in range(1, len(w_traj))]
- for i in range(len(v_change) - window_size + 1):
- v_window = v_change[i : i + window_size]
- w_window = w_change[i : i + window_size]
-
- v_unstable = sum(v_window) > count_threshold
- w_unstable = sum(w_window) > count_threshold
-
- assert not v_unstable, (
- f"v_unstable in window [{i}, {i + window_size}], unstable count: {sum(v_window)}"
- )
- assert not w_unstable, (
- f"w_unstable in window [{i}, {i + window_size}], unstable count: {sum(w_window)}"
- )
-
-
-def test_reach_goal():
- """
- This unit test tests the move_to_pose.py program for reaching the goal
- """
- m.show_animation = False
- x_start = 5
- y_start = 5
- theta_start_list = [0, np.pi / 2, np.pi, 3 * np.pi / 2]
- x_goal_list = [0, 5, 10]
- y_goal_list = [0, 5, 10]
- theta_goal = 0
- for theta_start, x_goal, y_goal in itertools.product(
- theta_start_list, x_goal_list, y_goal_list
- ):
- x_traj, y_traj, _, _ = m.move_to_pose(
- x_start, y_start, theta_start, x_goal, y_goal, theta_goal
- )
- x_diff = x_goal - x_traj[-1]
- y_diff = y_goal - y_traj[-1]
- rho = np.hypot(x_diff, y_diff)
- assert rho < 0.001, (
- f"start:[{x_start}, {y_start}, {theta_start}], goal:[{x_goal}, {y_goal}, {theta_goal}], rho: {rho} is too large"
- )
-
-
-def test_max_speed():
- """
- This unit test tests the move_to_pose.py program for a MAX_LINEAR_SPEED and
- MAX_ANGULAR_SPEED
- """
- m.show_animation = False
- m.MAX_LINEAR_SPEED = 11
- m.MAX_ANGULAR_SPEED = 5
- m.main()
-
-
-if __name__ == "__main__":
- conftest.run_this_test(__file__)
diff --git a/tests/test_move_to_pose_robot.py b/tests/test_move_to_pose_robot.py
deleted file mode 100644
index 7a82f985561..00000000000
--- a/tests/test_move_to_pose_robot.py
+++ /dev/null
@@ -1,14 +0,0 @@
-import conftest # Add root path to sys.path
-from PathTracking.move_to_pose import move_to_pose as m
-
-
-def test_1():
- """
- This unit test tests the move_to_pose_robot.py program
- """
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_mypy_type_check.py b/tests/test_mypy_type_check.py
deleted file mode 100644
index 6b933c1011a..00000000000
--- a/tests/test_mypy_type_check.py
+++ /dev/null
@@ -1,50 +0,0 @@
-import os
-import subprocess
-
-import conftest
-
-SUBPACKAGE_LIST = [
- "AerialNavigation",
- "ArmNavigation",
- "Bipedal",
- "Localization",
- "Mapping",
- "PathPlanning",
- "PathTracking",
- "SLAM",
- "InvertedPendulum"
-]
-
-
-def run_mypy(dir_name, project_path, config_path):
- res = subprocess.run(
- ['mypy',
- '--config-file',
- config_path,
- '-p',
- dir_name],
- cwd=project_path,
- stdout=subprocess.PIPE,
- encoding='utf-8')
- return res.returncode, res.stdout
-
-
-def test():
- project_dir_path = os.path.dirname(
- os.path.dirname(os.path.abspath(__file__)))
- print(f"{project_dir_path=}")
-
- config_path = os.path.join(project_dir_path, "mypy.ini")
- print(f"{config_path=}")
-
- for sub_package_name in SUBPACKAGE_LIST:
- rc, errors = run_mypy(sub_package_name, project_dir_path, config_path)
- if errors:
- print(errors)
- else:
- print("No lint errors found.")
- assert rc == 0
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_n_joint_arm_to_point_control.py b/tests/test_n_joint_arm_to_point_control.py
deleted file mode 100644
index 1d886d36705..00000000000
--- a/tests/test_n_joint_arm_to_point_control.py
+++ /dev/null
@@ -1,15 +0,0 @@
-import conftest # Add root path to sys.path
-from ArmNavigation.n_joint_arm_to_point_control\
- import n_joint_arm_to_point_control as m
-import random
-
-random.seed(12345)
-
-
-def test1():
- m.show_animation = False
- m.animation()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_normal_vector_estimation.py b/tests/test_normal_vector_estimation.py
deleted file mode 100644
index 7612f22aa73..00000000000
--- a/tests/test_normal_vector_estimation.py
+++ /dev/null
@@ -1,19 +0,0 @@
-import conftest # Add root path to sys.path
-from Mapping.normal_vector_estimation import normal_vector_estimation as m
-import random
-
-random.seed(12345)
-
-
-def test_1():
- m.show_animation = False
- m.main1()
-
-
-def test_2():
- m.show_animation = False
- m.main2()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_particle_filter.py b/tests/test_particle_filter.py
deleted file mode 100644
index 13a20f602af..00000000000
--- a/tests/test_particle_filter.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from Localization.particle_filter import particle_filter as m
-
-
-def test_1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_point_cloud_sampling.py b/tests/test_point_cloud_sampling.py
deleted file mode 100644
index 8f6447c69c4..00000000000
--- a/tests/test_point_cloud_sampling.py
+++ /dev/null
@@ -1,15 +0,0 @@
-import conftest # Add root path to sys.path
-from Mapping.point_cloud_sampling import point_cloud_sampling as m
-
-
-def test_1(capsys):
- m.do_plot = False
- m.main()
- captured = capsys.readouterr()
- assert "voxel_sampling_points.shape=(27, 3)" in captured.out
- assert "farthest_sampling_points.shape=(20, 3)" in captured.out
- assert "poisson_disk_points.shape=(20, 3)" in captured.out
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_potential_field_planning.py b/tests/test_potential_field_planning.py
deleted file mode 100644
index ce178d793d2..00000000000
--- a/tests/test_potential_field_planning.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.PotentialFieldPlanning import potential_field_planning as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_probabilistic_road_map.py b/tests/test_probabilistic_road_map.py
deleted file mode 100644
index 6c5eb540b1c..00000000000
--- a/tests/test_probabilistic_road_map.py
+++ /dev/null
@@ -1,12 +0,0 @@
-import conftest # Add root path to sys.path
-import numpy as np
-from PathPlanning.ProbabilisticRoadMap import probabilistic_road_map
-
-
-def test1():
- probabilistic_road_map.show_animation = False
- probabilistic_road_map.main(rng=np.random.default_rng(1233))
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_pure_pursuit.py b/tests/test_pure_pursuit.py
deleted file mode 100644
index 0e0b83bf6ce..00000000000
--- a/tests/test_pure_pursuit.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathTracking.pure_pursuit import pure_pursuit as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_quintic_polynomials_planner.py b/tests/test_quintic_polynomials_planner.py
deleted file mode 100644
index 43f3c6bada2..00000000000
--- a/tests/test_quintic_polynomials_planner.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.QuinticPolynomialsPlanner import quintic_polynomials_planner as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_raycasting_grid_map.py b/tests/test_raycasting_grid_map.py
deleted file mode 100644
index f08ae9277e3..00000000000
--- a/tests/test_raycasting_grid_map.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from Mapping.raycasting_grid_map import raycasting_grid_map as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_rear_wheel_feedback.py b/tests/test_rear_wheel_feedback.py
deleted file mode 100644
index 895eb188b32..00000000000
--- a/tests/test_rear_wheel_feedback.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathTracking.rear_wheel_feedback import rear_wheel_feedback as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_rectangle_fitting.py b/tests/test_rectangle_fitting.py
deleted file mode 100644
index cb28b6035ec..00000000000
--- a/tests/test_rectangle_fitting.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from Mapping.rectangle_fitting import rectangle_fitting as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_reeds_shepp_path_planning.py b/tests/test_reeds_shepp_path_planning.py
deleted file mode 100644
index 34ccfe7730c..00000000000
--- a/tests/test_reeds_shepp_path_planning.py
+++ /dev/null
@@ -1,57 +0,0 @@
-import numpy as np
-
-import conftest # Add root path to sys.path
-from PathPlanning.ReedsSheppPath import reeds_shepp_path_planning as m
-
-
-def check_edge_condition(px, py, pyaw, start_x, start_y, start_yaw, end_x,
- end_y, end_yaw):
- assert (abs(px[0] - start_x) <= 0.01)
- assert (abs(py[0] - start_y) <= 0.01)
- assert (abs(pyaw[0] - start_yaw) <= 0.01)
- assert (abs(px[-1] - end_x) <= 0.01)
- assert (abs(py[-1] - end_y) <= 0.01)
- assert (abs(pyaw[-1] - end_yaw) <= 0.01)
-
-
-def check_path_length(px, py, lengths):
- sum_len = sum(abs(length) for length in lengths)
- dpx = np.diff(px)
- dpy = np.diff(py)
- actual_len = sum(
- np.hypot(dx, dy) for (dx, dy) in zip(dpx, dpy))
- diff_len = sum_len - actual_len
- assert (diff_len <= 0.01)
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-def test2():
- N_TEST = 10
- np.random.seed(1234)
-
- for i in range(N_TEST):
- start_x = (np.random.rand() - 0.5) * 10.0 # [m]
- start_y = (np.random.rand() - 0.5) * 10.0 # [m]
- start_yaw = np.deg2rad((np.random.rand() - 0.5) * 180.0) # [rad]
-
- end_x = (np.random.rand() - 0.5) * 10.0 # [m]
- end_y = (np.random.rand() - 0.5) * 10.0 # [m]
- end_yaw = np.deg2rad((np.random.rand() - 0.5) * 180.0) # [rad]
-
- curvature = 1.0 / (np.random.rand() * 5.0)
-
- px, py, pyaw, mode, lengths = m.reeds_shepp_path_planning(
- start_x, start_y, start_yaw,
- end_x, end_y, end_yaw, curvature)
-
- check_edge_condition(px, py, pyaw, start_x, start_y, start_yaw, end_x,
- end_y, end_yaw)
- check_path_length(px, py, lengths)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_rocket_powered_landing.py b/tests/test_rocket_powered_landing.py
deleted file mode 100644
index 2f294c74cff..00000000000
--- a/tests/test_rocket_powered_landing.py
+++ /dev/null
@@ -1,20 +0,0 @@
-import conftest # Add root path to sys.path
-import numpy as np
-from numpy.testing import suppress_warnings
-
-from AerialNavigation.rocket_powered_landing import rocket_powered_landing as m
-
-
-def test1():
- m.show_animation = False
- with suppress_warnings() as sup:
- sup.filter(UserWarning,
- "You are solving a parameterized problem that is not DPP"
- )
- sup.filter(UserWarning,
- "Solution may be inaccurate")
- m.main(rng=np.random.default_rng(1234))
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_rrt.py b/tests/test_rrt.py
deleted file mode 100644
index 14a81759315..00000000000
--- a/tests/test_rrt.py
+++ /dev/null
@@ -1,21 +0,0 @@
-import conftest
-import random
-
-from PathPlanning.RRT import rrt as m
-from PathPlanning.RRT import rrt_with_pathsmoothing as m1
-
-random.seed(12345)
-
-
-def test1():
- m.show_animation = False
- m.main(gx=1.0, gy=1.0)
-
-
-def test2():
- m1.show_animation = False
- m1.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_rrt_dubins.py b/tests/test_rrt_dubins.py
deleted file mode 100644
index 66130484bc1..00000000000
--- a/tests/test_rrt_dubins.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.RRTDubins import rrt_dubins as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_rrt_star.py b/tests/test_rrt_star.py
deleted file mode 100644
index 232995ecb42..00000000000
--- a/tests/test_rrt_star.py
+++ /dev/null
@@ -1,36 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.RRTStar import rrt_star as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-def test_no_obstacle():
- obstacle_list = []
-
- # Set Initial parameters
- rrt_star = m.RRTStar(start=[0, 0],
- goal=[6, 10],
- rand_area=[-2, 15],
- obstacle_list=obstacle_list)
- path = rrt_star.planning(animation=False)
- assert path is not None
-
-
-def test_no_obstacle_and_robot_radius():
- obstacle_list = []
-
- # Set Initial parameters
- rrt_star = m.RRTStar(start=[0, 0],
- goal=[6, 10],
- rand_area=[-2, 15],
- obstacle_list=obstacle_list,
- robot_radius=0.8)
- path = rrt_star.planning(animation=False)
- assert path is not None
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_rrt_star_dubins.py b/tests/test_rrt_star_dubins.py
deleted file mode 100644
index c55ca23e43d..00000000000
--- a/tests/test_rrt_star_dubins.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.RRTStarDubins import rrt_star_dubins as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_rrt_star_reeds_shepp.py b/tests/test_rrt_star_reeds_shepp.py
deleted file mode 100644
index 11157aa57ae..00000000000
--- a/tests/test_rrt_star_reeds_shepp.py
+++ /dev/null
@@ -1,46 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.RRTStarReedsShepp import rrt_star_reeds_shepp as m
-
-
-def test1():
- m.show_animation = False
- m.main(max_iter=5)
-
-obstacleList = [
- (5, 5, 1),
- (4, 6, 1),
- (4, 8, 1),
- (4, 10, 1),
- (6, 5, 1),
- (7, 5, 1),
- (8, 6, 1),
- (8, 8, 1),
- (8, 10, 1)
-] # [x,y,size(radius)]
-
-start = [0.0, 0.0, m.np.deg2rad(0.0)]
-goal = [6.0, 7.0, m.np.deg2rad(90.0)]
-
-def test2():
- step_size = 0.2
- rrt_star_reeds_shepp = m.RRTStarReedsShepp(start, goal,
- obstacleList, [-2.0, 15.0],
- max_iter=100, step_size=step_size)
- rrt_star_reeds_shepp.set_random_seed(seed=8)
- path = rrt_star_reeds_shepp.planning(animation=False)
- for i in range(len(path)-1):
- # + 0.00000000000001 for acceptable errors arising from the planning process
- assert m.math.dist(path[i][0:2], path[i+1][0:2]) < step_size + 0.00000000000001
-
-def test_too_big_step_size():
- step_size = 20
- rrt_star_reeds_shepp = m.RRTStarReedsShepp(start, goal,
- obstacleList, [-2.0, 15.0],
- max_iter=100, step_size=step_size)
- rrt_star_reeds_shepp.set_random_seed(seed=8)
- path = rrt_star_reeds_shepp.planning(animation=False)
- assert path is None
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_rrt_star_seven_joint_arm.py b/tests/test_rrt_star_seven_joint_arm.py
deleted file mode 100644
index 2f6622cf6cf..00000000000
--- a/tests/test_rrt_star_seven_joint_arm.py
+++ /dev/null
@@ -1,12 +0,0 @@
-import conftest # Add root path to sys.path
-from ArmNavigation.rrt_star_seven_joint_arm_control \
- import rrt_star_seven_joint_arm_control as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_rrt_with_sobol_sampler.py b/tests/test_rrt_with_sobol_sampler.py
deleted file mode 100644
index affe2b165a6..00000000000
--- a/tests/test_rrt_with_sobol_sampler.py
+++ /dev/null
@@ -1,14 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.RRT import rrt_with_sobol_sampler as m
-import random
-
-random.seed(12345)
-
-
-def test1():
- m.show_animation = False
- m.main(gx=1.0, gy=1.0)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_safe_interval_path_planner.py b/tests/test_safe_interval_path_planner.py
deleted file mode 100644
index f1fbf90d2a8..00000000000
--- a/tests/test_safe_interval_path_planner.py
+++ /dev/null
@@ -1,33 +0,0 @@
-from PathPlanning.TimeBasedPathPlanning.GridWithDynamicObstacles import (
- Grid,
- ObstacleArrangement,
- Position,
-)
-from PathPlanning.TimeBasedPathPlanning import SafeInterval as m
-import numpy as np
-import conftest
-
-
-def test_1():
- start = Position(1, 11)
- goal = Position(19, 19)
- grid_side_length = 21
- grid = Grid(
- np.array([grid_side_length, grid_side_length]),
- obstacle_arrangement=ObstacleArrangement.ARRANGEMENT1,
- )
-
- m.show_animation = False
- planner = m.SafeIntervalPathPlanner(grid, start, goal)
-
- path = planner.plan(False)
-
- # path should have 31 entries
- assert len(path.path) == 31
-
- # path should end at the goal
- assert path.path[-1].position == goal
-
-
-if __name__ == "__main__":
- conftest.run_this_test(__file__)
diff --git a/tests/test_space_time_astar.py b/tests/test_space_time_astar.py
deleted file mode 100644
index 390c7732dcd..00000000000
--- a/tests/test_space_time_astar.py
+++ /dev/null
@@ -1,34 +0,0 @@
-from PathPlanning.TimeBasedPathPlanning.GridWithDynamicObstacles import (
- Grid,
- ObstacleArrangement,
- Position,
-)
-from PathPlanning.TimeBasedPathPlanning import SpaceTimeAStar as m
-import numpy as np
-import conftest
-
-
-def test_1():
- start = Position(1, 11)
- goal = Position(19, 19)
- grid_side_length = 21
- grid = Grid(
- np.array([grid_side_length, grid_side_length]),
- obstacle_arrangement=ObstacleArrangement.ARRANGEMENT1,
- )
-
- m.show_animation = False
- planner = m.SpaceTimeAStar(grid, start, goal)
-
- path = planner.plan(False)
-
- # path should have 28 entries
- assert len(path.path) == 31
-
- # path should end at the goal
- assert path.path[-1].position == goal
-
- assert planner.expanded_node_count < 1000
-
-if __name__ == "__main__":
- conftest.run_this_test(__file__)
diff --git a/tests/test_spiral_spanning_tree_coverage_path_planner.py b/tests/test_spiral_spanning_tree_coverage_path_planner.py
deleted file mode 100644
index 44170fa4cc3..00000000000
--- a/tests/test_spiral_spanning_tree_coverage_path_planner.py
+++ /dev/null
@@ -1,58 +0,0 @@
-import conftest # Add root path to sys.path
-import os
-import matplotlib.pyplot as plt
-from PathPlanning.SpiralSpanningTreeCPP \
- import spiral_spanning_tree_coverage_path_planner
-
-spiral_spanning_tree_coverage_path_planner.do_animation = True
-
-
-def spiral_stc_cpp(img, start):
- num_free = 0
- for i in range(img.shape[0]):
- for j in range(img.shape[1]):
- num_free += img[i][j]
-
- STC_planner = spiral_spanning_tree_coverage_path_planner.\
- SpiralSpanningTreeCoveragePlanner(img)
-
- edge, route, path = STC_planner.plan(start)
-
- covered_nodes = set()
- for p, q in edge:
- covered_nodes.add(p)
- covered_nodes.add(q)
-
- # assert complete coverage
- assert len(covered_nodes) == num_free / 4
-
-
-def test_spiral_stc_cpp_1():
- img_dir = os.path.dirname(
- os.path.abspath(__file__)) + \
- "/../PathPlanning/SpiralSpanningTreeCPP"
- img = plt.imread(os.path.join(img_dir, 'map', 'test.png'))
- start = (0, 0)
- spiral_stc_cpp(img, start)
-
-
-def test_spiral_stc_cpp_2():
- img_dir = os.path.dirname(
- os.path.abspath(__file__)) + \
- "/../PathPlanning/SpiralSpanningTreeCPP"
- img = plt.imread(os.path.join(img_dir, 'map', 'test_2.png'))
- start = (10, 0)
- spiral_stc_cpp(img, start)
-
-
-def test_spiral_stc_cpp_3():
- img_dir = os.path.dirname(
- os.path.abspath(__file__)) + \
- "/../PathPlanning/SpiralSpanningTreeCPP"
- img = plt.imread(os.path.join(img_dir, 'map', 'test_3.png'))
- start = (0, 0)
- spiral_stc_cpp(img, start)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_stanley_controller.py b/tests/test_stanley_controller.py
deleted file mode 100644
index a1d8073764e..00000000000
--- a/tests/test_stanley_controller.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathTracking.stanley_controller import stanley_controller as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_state_lattice_planner.py b/tests/test_state_lattice_planner.py
deleted file mode 100644
index 0c14222e815..00000000000
--- a/tests/test_state_lattice_planner.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.StateLatticePlanner import state_lattice_planner as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_state_machine.py b/tests/test_state_machine.py
deleted file mode 100644
index e36a8120fd5..00000000000
--- a/tests/test_state_machine.py
+++ /dev/null
@@ -1,51 +0,0 @@
-import conftest
-
-from MissionPlanning.StateMachine.state_machine import StateMachine
-
-
-def test_transition():
- sm = StateMachine("state_machine")
- sm.add_transition(src_state="idle", event="start", dst_state="running")
- sm.set_current_state("idle")
- sm.process("start")
- assert sm.get_current_state().name == "running"
-
-
-def test_guard():
- class Model:
- def can_start(self):
- return False
-
- sm = StateMachine("state_machine", Model())
- sm.add_transition(
- src_state="idle", event="start", dst_state="running", guard="can_start"
- )
- sm.set_current_state("idle")
- sm.process("start")
- assert sm.get_current_state().name == "idle"
-
-
-def test_action():
- class Model:
- def on_start(self):
- self.start_called = True
-
- model = Model()
- sm = StateMachine("state_machine", model)
- sm.add_transition(
- src_state="idle", event="start", dst_state="running", action="on_start"
- )
- sm.set_current_state("idle")
- sm.process("start")
- assert model.start_called
-
-
-def test_plantuml():
- sm = StateMachine("state_machine")
- sm.add_transition(src_state="idle", event="start", dst_state="running")
- sm.set_current_state("idle")
- assert sm.generate_plantuml()
-
-
-if __name__ == "__main__":
- conftest.run_this_test(__file__)
diff --git a/tests/test_two_joint_arm_to_point_control.py b/tests/test_two_joint_arm_to_point_control.py
deleted file mode 100644
index 1de4fcd8057..00000000000
--- a/tests/test_two_joint_arm_to_point_control.py
+++ /dev/null
@@ -1,12 +0,0 @@
-import conftest # Add root path to sys.path
-from ArmNavigation.two_joint_arm_to_point_control \
- import two_joint_arm_to_point_control as m
-
-
-def test1():
- m.show_animation = False
- m.animation()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_unscented_kalman_filter.py b/tests/test_unscented_kalman_filter.py
deleted file mode 100644
index b7dda6e2761..00000000000
--- a/tests/test_unscented_kalman_filter.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from Localization.unscented_kalman_filter import unscented_kalman_filter as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_utils.py b/tests/test_utils.py
deleted file mode 100644
index 36861c52b45..00000000000
--- a/tests/test_utils.py
+++ /dev/null
@@ -1,27 +0,0 @@
-import conftest # Add root path to sys.path
-from utils import angle
-from numpy.testing import assert_allclose
-import numpy as np
-
-
-def test_rot_mat_2d():
- assert_allclose(angle.rot_mat_2d(0.0),
- np.array([[1., 0.],
- [0., 1.]]))
-
-
-def test_angle_mod():
- assert_allclose(angle.angle_mod(-4.0), 2.28318531)
- assert(isinstance(angle.angle_mod(-4.0), float))
- assert_allclose(angle.angle_mod([-4.0]), [2.28318531])
- assert(isinstance(angle.angle_mod([-4.0]), np.ndarray))
-
- assert_allclose(angle.angle_mod([-150.0, 190.0, 350], degree=True),
- [-150., -170., -10.])
-
- assert_allclose(angle.angle_mod(-60.0, zero_2_2pi=True, degree=True),
- [300.])
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_visibility_road_map_planner.py b/tests/test_visibility_road_map_planner.py
deleted file mode 100644
index 5a663d289d2..00000000000
--- a/tests/test_visibility_road_map_planner.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.VoronoiRoadMap import voronoi_road_map as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_voronoi_road_map_planner.py b/tests/test_voronoi_road_map_planner.py
deleted file mode 100644
index b0b7550fb2f..00000000000
--- a/tests/test_voronoi_road_map_planner.py
+++ /dev/null
@@ -1,11 +0,0 @@
-import conftest # Add root path to sys.path
-from PathPlanning.VisibilityRoadMap import visibility_road_map as m
-
-
-def test1():
- m.show_animation = False
- m.main()
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/tests/test_wavefront_coverage_path_planner.py b/tests/test_wavefront_coverage_path_planner.py
deleted file mode 100644
index 28bb5987e7f..00000000000
--- a/tests/test_wavefront_coverage_path_planner.py
+++ /dev/null
@@ -1,63 +0,0 @@
-import conftest # Add root path to sys.path
-import os
-import matplotlib.pyplot as plt
-from PathPlanning.WavefrontCPP import wavefront_coverage_path_planner
-
-wavefront_coverage_path_planner.do_animation = False
-
-
-def wavefront_cpp(img, start, goal):
- num_free = 0
- for i in range(img.shape[0]):
- for j in range(img.shape[1]):
- num_free += 1 - img[i][j]
-
- DT = wavefront_coverage_path_planner.transform(
- img, goal, transform_type='distance')
- DT_path = wavefront_coverage_path_planner.wavefront(DT, start, goal)
- assert len(DT_path) == num_free # assert complete coverage
-
- PT = wavefront_coverage_path_planner.transform(
- img, goal, transform_type='path', alpha=0.01)
- PT_path = wavefront_coverage_path_planner.wavefront(PT, start, goal)
- assert len(PT_path) == num_free # assert complete coverage
-
-
-def test_wavefront_CPP_1():
- img_dir = os.path.dirname(
- os.path.abspath(__file__)) + "/../PathPlanning/WavefrontCPP"
- img = plt.imread(os.path.join(img_dir, 'map', 'test.png'))
- img = 1 - img
-
- start = (43, 0)
- goal = (0, 0)
-
- wavefront_cpp(img, start, goal)
-
-
-def test_wavefront_CPP_2():
- img_dir = os.path.dirname(
- os.path.abspath(__file__)) + "/../PathPlanning/WavefrontCPP"
- img = plt.imread(os.path.join(img_dir, 'map', 'test_2.png'))
- img = 1 - img
-
- start = (10, 0)
- goal = (10, 40)
-
- wavefront_cpp(img, start, goal)
-
-
-def test_wavefront_CPP_3():
- img_dir = os.path.dirname(
- os.path.abspath(__file__)) + "/../PathPlanning/WavefrontCPP"
- img = plt.imread(os.path.join(img_dir, 'map', 'test_3.png'))
- img = 1 - img
-
- start = (0, 0)
- goal = (30, 30)
-
- wavefront_cpp(img, start, goal)
-
-
-if __name__ == '__main__':
- conftest.run_this_test(__file__)
diff --git a/users_comments.md b/users_comments.md
deleted file mode 100644
index a2f798eac46..00000000000
--- a/users_comments.md
+++ /dev/null
@@ -1,415 +0,0 @@
-# User's demos
-
-## WHILL MODEL CR with move to a pose control
-
-This is an electric wheelchair control demo by [Katsushun89](https://github.com/Katsushun89).
-
-[WHILL Model CR](https://whill.jp/model-cr) is the control target, [M5Stack](https://m5stack.com/) is used for the controller, and [toio](https://toio.io/) is used for the control input device.
-
-[Move to a Pose Control — PythonRobotics documentation](https://atsushisakai.github.io/PythonRobotics/modules/control/move_to_a_pose_control/move_to_a_pose_control.html) is used for its control algorithm ([code link](https://github.com/AtsushiSakai/PythonRobotics/blob/master/PathTracking/move_to_pose/move_to_pose.py)).
-
-
-
-Ref:
-
-- [toioと同じように動くWHILL Model CR (in Japanese)](https://qiita.com/KatsuShun89/items/68fde7544ecfe36096d2)
-
-
-# Educational users
-
-If you found users who are using PythonRobotics for education, please make an issue to let me know.
-
-# Stargazers location map
-
-You can check stargazer's locations of this project from:
-
-- [Stargazers location map](https://drive.google.com/open?id=1bBXS9IQmZ3Tfe1wNGvJbObRt9Htt4PGC&usp=sharing)
-
-
-# Related projects
-
-This is a list of related projects.
-
-- [onlytailei/CppRobotics: cpp implementation of robotics algorithms including localization, mapping, SLAM, path planning and control](https://github.com/onlytailei/CppRobotics)
-
-# Individual users comments
-
----
-
-Dear AtsushiSakai, <br>thank you for building this cool repo for robotics. <br>I am still learning robotics and this will give me a good starting point. <br>I hope this note gets to you. <br> <br>
-
---David Senicic
-
----
-
-Dear AtsushiSakai, <br>WE found your project from google when first searching for a rosbag to csv converter. We are a small team in MCity working on Connected (and Automated) vehicles. We are working with an opensource platform that serve as the AI to control the vehicle. Your code and documentation helped us a lot! <br> <br>Thank you! Have a nice day!
-
---Hanlin(Julia) Chen, MCity Apollo team
-
----
-
-Dear Atsushi Sakai, <br> <br>With your simplistic descriptions in text and as gifs, i was able to help my students understand easily and effectively, I would be honored to help, in anyway towards this, As a hobbyist have been developing lidar based slam navigation systems from 2011 and its only right to acknowledge and thank you for your contributions.
-
---Shiva
-
----
-
-Dear Atsushi Sakai <br>I first came across your Matlab repository on ICP and SLAM. The repository for both python and Matlab helped me in understanding the essential concepts of robotics.I am really grateful to you for helping me develop my understanding of the concepts of robotics.
-
---Sparsh Garg
-
----
-
-Dear AtsushiSakai, <br>Thank you very much for all the example programs related to Robotics
-
---Kalyan
-
----
-Dear AtsushiSakai, <br> <br>Thanks for Python Robotics
-
---Rebecca Li
-
----
-
-Thanks alot.
-
---Zain
-
----
-
-Dear AtsushiSakai,<br> <br>thank you for you code!
-
-—- Anonymous
-
----
-
-Thanks!
-
---a friend
-
----
-
-Thanks for the awesome collection of codes!
-
---Qi
-
----
-
-Thank you!
-
---huang pingzhong
-
----
-
-Dear AtsushiSakai, <br>Thanks a lot for the wonderful collection of projects.It was really useful. I really appreciate your time in maintaing and building this repository.It will be really great if I get a chance to meet you in person sometime.I got really inspired looking at your work. <br>All the very best for all your future endeavors! <br> Thanks once again, <br>
-
----Ezhil Bharathi
-
----
-
-Dear Atsushi Sakai, <br>Thank you so much for gathering all the useful stuff and good examples of robotics things ! :) <br>I am very new in this area and want to know more about robotics and SLAM things. <br>and again, thank you so much :) <br>
-
---Tutorgaming
-
----
-
-Dear AtsushiSakai, <br>Very excellent work. Thank you for your share.
-
---Thomas Yang
-
----
-
-Dear Atsushi Saka Arigato 🤗🤗
-
---Badal Kumar
-
----
-
-Dear AtsushiSakai, <br>Thanks for teaching how to implement path planning algorithms in robotics. <br>
-
----
-
-Your Github page is very useful. I will apply it with cooperative robot.
-
---Soloist
-
----
-
-help me very much thankyou
-
---sanchuan
-
----
-
-Dear AtsushiSakai, <br>U R so niubility!
-
---FangKD
-
----
-
-thankyou AtsushiSakai!
-
---ou minghua
-
----
-
-Dear AtsushiSakai <br>Thank You
-
---Dogukan Altay
-
----
-
-so kind of you can you make videos of it.
-
----
-
-Dear AtshshiSakai, <br>You are very wise and smart that you created this library for students wanting to learn Probabilistic Robotics and actually perform robot control. <br>Hats off to you and your work. <br>I am also reading your book titled : Python Robotics
-
---Himanshu
-
----
-
-Dear AtsushiSakai, <br>Hello! YOUR CODE IS SUPER SUPER HELPFUL AND GIVES ME CLEAR INSTRUCTIONs as well as STRONG SUPPORT!! <br>Thank you so much !
-
---Lee
-
----
-
-Hi AtsushiSakai, <br> <br>Thanks for creating the pythonrobotics repo! It's an awesome repo that has been of great help to me. I've referenced your extended kalman filter algorithm while creating my own for localization using a 2D lidar, camera, and IMU. Our robot is destined to compete soon, so fingers crossed that all works out! Thanks again.
-
----
-
-You rock!
-
---Matt
-
----
-
-Dear AtsushiSakai, <br>You are the best. This is by far the best tutorial for learning and implementing robotics. <br>Thanks a lot for your time and efforts to do this!
-
---Adi B
-
----
-
-Dear Atushi, thank you for this amazing repository. It is a pleasure to have access to python algorithms without the burden of ROS. While I'm no longer working on such robotics projects, it's wonderful to know its available when I need it and it was amazing to see all the beautiful animations for each algorithm.
-
---Shreeyak Sajjan
-
----
-
-Dear AtsushiSakai <br>Thank you for your contributions!
-
---Luo
-
----
-
-Dear AtsushiSakai, Your visualizations are awesome, and I am going to have this link bookmarked for future references. Thank you!
-
---Srinivasa Varadhan Agaram Chakravarthy
-
----
-
-Dear AtsushiSakai, <br>Thank you for this great resource! I very much appreciate all your hard work and effort.
-
---Mridul Aanjaneya
-
----
-
-Thank you for the python robotics sample code and visualizations!! This is my new favorite thing on the internet.
-
---selamg@mit.edu
-
----
-
-Mr AtsushiSakai .. <br>Your work and teaching is light for me <br>thank you very much for giving time and effort to make it public for us
-
---Karim Anass
-
----
-
-Thank You
-
---Anonymous
-
----
-
-I've learned the robotics from the traditional way of solving problem through finding packages and reading papers. This amazing project is unbelievably helpful for new-comers to learn and get familiar with the algorithms. Gods know how many hours you've taken to sort all the materials and written everything into one single coherent project. I'm truly amazed and deepest appreciation.
-
---Ewing Kang
-
----
-
-Hey, I'm a student and I just recently got into robotics, and visited your repository multiple times. Today I was super happy to find the link to Patreon! I am impressed by didactic quality of the repo, keep up the good work!
-
---Carolina Bianchi
-
----
-
-Dear AtsushiSakai, thanks a lot for the PythonRobotics git repository. I'm a college student who is trying to make a mini autonomous robot for my final project submission, I still haven't started using your code but by the look of it I'm sure it will be of greater use. Will let you know how my project is coming up.
-
---Pragdheesh
-
----
-
-Hello AtsushiSakai, <br> <br>Thank you very much for sharing your work!
-
---Uma K
-
----
-
-Hey Atsushi <br>We are working on a multiagent simulation game and this project gave us really good insights. <br>In future, I would like to contribute to this project with our multiagent task allocation among robots and multi robot map merging( Which is a big hurdle as we found). <br>Thanks for what you are doing for open source. <br>
-
---Mayank
-
----
-
-Thanks a lot for this amazing set of very useful librarires!
-
---Razvan Viorel Mihai
-
----
-
-Dear Atsushi Sakai, <br> <br>This is probably one of the best open-source robotics based Algorithms I have seen so far. Thank you for posting this knowledge with other engineers. It will definitely help soon to become engineers like myself.
-
---Don
-
----
-
-hanks frnd, for ur contibusion
-
-—--
-
-Thank you for python robotics!!
-
---Manuel Miguez
-
----
-
-Great job
-
---Anonymous
-
----
-
-Dear Atsushi Sakai <br>Thank you for the Python Robotics
-
---Alex Liberzon
-
----
-
-Thanks for your robotics repo!
-
---Mithi
-
----
-
-You made such a nice work. Congratulations :)
-
---ATroya
-
----
-
-thank you for python path finding repo
-
---fengzongbao
-
----
-
-Dear AtsushiSakai, <br> <br>Thank you so much for making the concept of robotics approachable for the general mass. Keep up the good work :)
-
---Harsh Munshi
-
----
-
-Benefit a lot for your GitHub repository of PythonRobotics. Thanks so much.
-
---Haoran
-
----
-
-Thanks!
-
---Reinzor
-
----
-
-Thanks for writing these algorithms. They are very helpful for learning robotics.
-
---Arihant Lunawat
-
----
-
-Dear AtsushiSakai, <br>Thank you for providing us this great repository for playing and look around:)!
-
---Hsin-Wen
-
----
-
-Thanks for PythonRobotics!
-
---Nick V
-
----
-
-Dear AtsushiSakai, thank you so much for this material, it's so useful to me, i'm really glad with it =D
-
---Juanda
-
----
-
-Dear Atsushi Thanks for compiling such a vast resource for robotics motion planning.
-
---Kartik Prakash
-
----
-
-Thanks for your job! <br>I have learned a lot from it!
-
---ZhongyiShen
-
----
-
-Dear Atsushi Sakai, <br>Thank you so much for creating PythonRobotics and documenting it so well. I am a senior in high school trying to learn and better myself in these concepts.
-
---Rohan Mathur
-
-
-
-# Citations
-
-1. B. Blaga, M. Deac, R. W. Y. Al-doori, M. Negru and R. Dǎnescu, "Miniature Autonomous Vehicle Development on Raspberry Pi," 2018 IEEE 14th International Conference on Intelligent Computer Communication and Processing (ICCP), Cluj-Napoca, Romania, 2018, pp. 229-236.
-doi: 10.1109/ICCP.2018.8516589
-keywords: {Automobiles;Task analysis;Autonomous vehicles;Path planning;Global Positioning System;Cameras;miniature autonomous vehicle;path planning;navigation;parking assist;lane detection and tracking;traffic sign recognition},
-URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8516589&isnumber=8516425
-
-2. Peggy (Yuchun) Wang and Caitlin Hogan, "Path Planning with Dynamic Obstacle Avoidance for a Jumping-Enabled Robot", AA228/CS238 class report, Department of Computer Science, Stanford University, URL: https://web.stanford.edu/class/aa228/reports/2018/final113.pdf
-
-3. Welburn, E, Hakim Khalili, H, Gupta, A, Watson, S & Carrasco, J 2019, A Navigational System for Quadcopter Remote Inspection of Offshore Substations. in The Fifteenth International Conference on Autonomic and Autonomous Systems 2019. URL:https://research.manchester.ac.uk/portal/files/107169964/ICAS19_A_Navigational_System_for_Quadcopter_Remote_Inspection_of_Offshore_Substations.pdf
-
-4. E. Horváth, C. Hajdu, C. Radu and Á. Ballagi, "Range Sensor-based Occupancy Grid Mapping with Signatures," 2019 20th International Carpathian Control Conference (ICCC), Krakow-Wieliczka, Poland, 2019, pp. 1-5.
-URL: https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=8765684&isnumber=8765679
-
-5. Josie Hughes, Masaru Shimizu, and Arnoud Visser, "A Review of Robot Rescue Simulation Platforms for Robotics Education"
-URL: https://2019.robocup.org/downloads/program/HughesEtAl2019.pdf
-
-6. Hughes, Josie, Masaru Shimizu, and Arnoud Visser. "A review of robot rescue simulation platforms for robotics education." (2019).
-URL: https://www.semanticscholar.org/paper/A-Review-of-Robot-Rescue-Simulation-Platforms-for-Hughes-Shimizu/318a4bcb97a44661422ae1430d950efc408097da
-
-7. Ghosh, Ritwika, et al. "CyPhyHouse: A Programming, Simulation, and Deployment Toolchain for Heterogeneous Distributed Coordination." arXiv preprint arXiv:1910.01557 (2019).
-URL: https://arxiv.org/abs/1910.01557
-
-8. Hahn, Carsten, et al. "Dynamic Path Planning with Stable Growing Neural Gas." (2019).
-URL: https://pdfs.semanticscholar.org/5c06/f3cb9542a51e1bf1a32523c1bc7fea6cecc5.pdf
-
-9. Brijen Thananjeyan, et al. "ABC-LMPC: Safe Sample-Based Learning MPC for Stochastic Nonlinear Dynamical Systems with Adjustable Boundary Conditions"
-URL: https://arxiv.org/pdf/2003.01410
-
-# Others
-
-- Autonomous Vehicle Readings https://richardkelley.io/readings
-
-- 36 Amazing Python Open Source Projects (v.2019) – Mybridge for Professionals https://medium.mybridge.co/36-amazing-python-open-source-projects-v-2019-2fe058d79450
-
-- Real-time Model Predictive Control (MPC), ACADO, Python | Work-is-Playing http://grauonline.de/wordpress/?page_id=3244
-
-- 💡 Greatest of GitHub - Python Robotics (Amazing!) - YouTube https://www.youtube.com/watch?v=f_pPaYx6Gu0&feature=emb_logo
diff --git a/utils/__init__.py b/utils/__init__.py
deleted file mode 100644
index e69de29bb2d..00000000000
diff --git a/utils/angle.py b/utils/angle.py
deleted file mode 100644
index c9e02c5f2e7..00000000000
--- a/utils/angle.py
+++ /dev/null
@@ -1,83 +0,0 @@
-import numpy as np
-from scipy.spatial.transform import Rotation as Rot
-
-
-def rot_mat_2d(angle):
- """
- Create 2D rotation matrix from an angle
-
- Parameters
- ----------
- angle :
-
- Returns
- -------
- A 2D rotation matrix
-
- Examples
- --------
- >>> angle_mod(-4.0)
-
-
- """
- return Rot.from_euler('z', angle).as_matrix()[0:2, 0:2]
-
-
-def angle_mod(x, zero_2_2pi=False, degree=False):
- """
- Angle modulo operation
- Default angle modulo range is [-pi, pi)
-
- Parameters
- ----------
- x : float or array_like
- A angle or an array of angles. This array is flattened for
- the calculation. When an angle is provided, a float angle is returned.
- zero_2_2pi : bool, optional
- Change angle modulo range to [0, 2pi)
- Default is False.
- degree : bool, optional
- If True, then the given angles are assumed to be in degrees.
- Default is False.
-
- Returns
- -------
- ret : float or ndarray
- an angle or an array of modulated angle.
-
- Examples
- --------
- >>> angle_mod(-4.0)
- 2.28318531
-
- >>> angle_mod([-4.0])
- np.array(2.28318531)
-
- >>> angle_mod([-150.0, 190.0, 350], degree=True)
- array([-150., -170., -10.])
-
- >>> angle_mod(-60.0, zero_2_2pi=True, degree=True)
- array([300.])
-
- """
- if isinstance(x, float):
- is_float = True
- else:
- is_float = False
-
- x = np.asarray(x).flatten()
- if degree:
- x = np.deg2rad(x)
-
- if zero_2_2pi:
- mod_angle = x % (2 * np.pi)
- else:
- mod_angle = (x + np.pi) % (2 * np.pi) - np.pi
-
- if degree:
- mod_angle = np.rad2deg(mod_angle)
-
- if is_float:
- return mod_angle.item()
- else:
- return mod_angle
diff --git a/utils/plot.py b/utils/plot.py
deleted file mode 100644
index eb5aa7ad048..00000000000
--- a/utils/plot.py
+++ /dev/null
@@ -1,234 +0,0 @@
-"""
-Matplotlib based plotting utilities
-"""
-import math
-import matplotlib.pyplot as plt
-import numpy as np
-from mpl_toolkits.mplot3d import art3d
-from matplotlib.patches import FancyArrowPatch
-from mpl_toolkits.mplot3d.proj3d import proj_transform
-from mpl_toolkits.mplot3d import Axes3D
-
-from utils.angle import rot_mat_2d
-
-
-def plot_covariance_ellipse(x, y, cov, chi2=3.0, color="-r", ax=None):
- """
- This function plots an ellipse that represents a covariance matrix. The ellipse is centered at (x, y) and its shape, size and rotation are determined by the covariance matrix.
-
- Parameters:
- x : (float) The x-coordinate of the center of the ellipse.
- y : (float) The y-coordinate of the center of the ellipse.
- cov : (numpy.ndarray) A 2x2 covariance matrix that determines the shape, size, and rotation of the ellipse.
- chi2 : (float, optional) A scalar value that scales the ellipse size. This value is typically set based on chi-squared distribution quantiles to achieve certain confidence levels (e.g., 3.0 corresponds to ~95% confidence for a 2D Gaussian). Defaults to 3.0.
- color : (str, optional) The color and line style of the ellipse plot, following matplotlib conventions. Defaults to "-r" (a red solid line).
- ax : (matplotlib.axes.Axes, optional) The Axes object to draw the ellipse on. If None (default), a new figure and axes are created.
-
- Returns:
- None. This function plots the covariance ellipse on the specified axes.
- """
- eig_val, eig_vec = np.linalg.eig(cov)
-
- if eig_val[0] >= eig_val[1]:
- big_ind = 0
- small_ind = 1
- else:
- big_ind = 1
- small_ind = 0
- a = math.sqrt(chi2 * eig_val[big_ind])
- b = math.sqrt(chi2 * eig_val[small_ind])
- angle = math.atan2(eig_vec[1, big_ind], eig_vec[0, big_ind])
- plot_ellipse(x, y, a, b, angle, color=color, ax=ax)
-
-
-def plot_ellipse(x, y, a, b, angle, color="-r", ax=None, **kwargs):
- """
- This function plots an ellipse based on the given parameters.
-
- Parameters
- ----------
- x : (float) The x-coordinate of the center of the ellipse.
- y : (float) The y-coordinate of the center of the ellipse.
- a : (float) The length of the semi-major axis of the ellipse.
- b : (float) The length of the semi-minor axis of the ellipse.
- angle : (float) The rotation angle of the ellipse, in radians.
- color : (str, optional) The color and line style of the ellipse plot, following matplotlib conventions. Defaults to "-r" (a red solid line).
- ax : (matplotlib.axes.Axes, optional) The Axes object to draw the ellipse on. If None (default), a new figure and axes are created.
- **kwargs: Additional keyword arguments to pass to plt.plot or ax.plot.
-
- Returns
- ---------
- None. This function plots the ellipse based on the specified parameters.
- """
-
- t = np.arange(0, 2 * math.pi + 0.1, 0.1)
- px = [a * math.cos(it) for it in t]
- py = [b * math.sin(it) for it in t]
- fx = rot_mat_2d(angle) @ (np.array([px, py]))
- px = np.array(fx[0, :] + x).flatten()
- py = np.array(fx[1, :] + y).flatten()
- if ax is None:
- plt.plot(px, py, color, **kwargs)
- else:
- ax.plot(px, py, color, **kwargs)
-
-
-def plot_arrow(x, y, yaw, arrow_length=1.0,
- origin_point_plot_style="xr",
- head_width=0.1, fc="r", ec="k", **kwargs):
- """
- Plot an arrow or arrows based on 2D state (x, y, yaw)
-
- All optional settings of matplotlib.pyplot.arrow can be used.
- - matplotlib.pyplot.arrow:
- https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.arrow.html
-
- Parameters
- ----------
- x : a float or array_like
- a value or a list of arrow origin x position.
- y : a float or array_like
- a value or a list of arrow origin y position.
- yaw : a float or array_like
- a value or a list of arrow yaw angle (orientation).
- arrow_length : a float (optional)
- arrow length. default is 1.0
- origin_point_plot_style : str (optional)
- origin point plot style. If None, not plotting.
- head_width : a float (optional)
- arrow head width. default is 0.1
- fc : string (optional)
- face color
- ec : string (optional)
- edge color
- """
- if not isinstance(x, float):
- for (i_x, i_y, i_yaw) in zip(x, y, yaw):
- plot_arrow(i_x, i_y, i_yaw, head_width=head_width,
- fc=fc, ec=ec, **kwargs)
- else:
- plt.arrow(x, y,
- arrow_length * math.cos(yaw),
- arrow_length * math.sin(yaw),
- head_width=head_width,
- fc=fc, ec=ec,
- **kwargs)
- if origin_point_plot_style is not None:
- plt.plot(x, y, origin_point_plot_style)
-
-
-def plot_curvature(x_list, y_list, heading_list, curvature,
- k=0.01, c="-c", label="Curvature"):
- """
- Plot curvature on 2D path. This plot is a line from the original path,
- the lateral distance from the original path shows curvature magnitude.
- Left turning shows right side plot, right turning shows left side plot.
- For straight path, the curvature plot will be on the path, because
- curvature is 0 on the straight path.
-
- Parameters
- ----------
- x_list : array_like
- x position list of the path
- y_list : array_like
- y position list of the path
- heading_list : array_like
- heading list of the path
- curvature : array_like
- curvature list of the path
- k : float
- curvature scale factor to calculate distance from the original path
- c : string
- color of the plot
- label : string
- label of the plot
- """
- cx = [x + d * k * np.cos(yaw - np.pi / 2.0) for x, y, yaw, d in
- zip(x_list, y_list, heading_list, curvature)]
- cy = [y + d * k * np.sin(yaw - np.pi / 2.0) for x, y, yaw, d in
- zip(x_list, y_list, heading_list, curvature)]
-
- plt.plot(cx, cy, c, label=label)
- for ix, iy, icx, icy in zip(x_list, y_list, cx, cy):
- plt.plot([ix, icx], [iy, icy], c)
-
-
-class Arrow3D(FancyArrowPatch):
-
- def __init__(self, x, y, z, dx, dy, dz, *args, **kwargs):
- super().__init__((0, 0), (0, 0), *args, **kwargs)
- self._xyz = (x, y, z)
- self._dxdydz = (dx, dy, dz)
-
- def draw(self, renderer):
- x1, y1, z1 = self._xyz
- dx, dy, dz = self._dxdydz
- x2, y2, z2 = (x1 + dx, y1 + dy, z1 + dz)
-
- xs, ys, zs = proj_transform((x1, x2), (y1, y2), (z1, z2), self.axes.M)
- self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
- super().draw(renderer)
-
- def do_3d_projection(self, renderer=None):
- x1, y1, z1 = self._xyz
- dx, dy, dz = self._dxdydz
- x2, y2, z2 = (x1 + dx, y1 + dy, z1 + dz)
-
- xs, ys, zs = proj_transform((x1, x2), (y1, y2), (z1, z2), self.axes.M)
- self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
-
- return np.min(zs)
-
-
-def _arrow3D(ax, x, y, z, dx, dy, dz, *args, **kwargs):
- '''Add an 3d arrow to an `Axes3D` instance.'''
- arrow = Arrow3D(x, y, z, dx, dy, dz, *args, **kwargs)
- ax.add_artist(arrow)
-
-
-def plot_3d_vector_arrow(ax, p1, p2):
- setattr(Axes3D, 'arrow3D', _arrow3D)
- ax.arrow3D(p1[0], p1[1], p1[2],
- p2[0]-p1[0], p2[1]-p1[1], p2[2]-p1[2],
- mutation_scale=20,
- arrowstyle="-|>",
- )
-
-
-def plot_triangle(p1, p2, p3, ax):
- ax.add_collection3d(art3d.Poly3DCollection([[p1, p2, p3]], color='b'))
-
-
-def set_equal_3d_axis(ax, x_lims, y_lims, z_lims):
- """Helper function to set equal axis
-
- Args:
- ax (Axes3DSubplot): matplotlib 3D axis, created by
- `ax = fig.add_subplot(projection='3d')`
- x_lims (np.array): array containing min and max value of x
- y_lims (np.array): array containing min and max value of y
- z_lims (np.array): array containing min and max value of z
- """
- x_lims = np.asarray(x_lims)
- y_lims = np.asarray(y_lims)
- z_lims = np.asarray(z_lims)
- # compute max required range
- max_range = np.array([x_lims.max() - x_lims.min(),
- y_lims.max() - y_lims.min(),
- z_lims.max() - z_lims.min()]).max() / 2.0
- # compute mid-point along each axis
- mid_x = (x_lims.max() + x_lims.min()) * 0.5
- mid_y = (y_lims.max() + y_lims.min()) * 0.5
- mid_z = (z_lims.max() + z_lims.min()) * 0.5
-
- # set limits to axis
- ax.set_xlim(mid_x - max_range, mid_x + max_range)
- ax.set_ylim(mid_y - max_range, mid_y + max_range)
- ax.set_zlim(mid_z - max_range, mid_z + max_range)
-
-
-if __name__ == '__main__':
- plot_ellipse(0, 0, 1, 2, np.deg2rad(15))
- plt.axis('equal')
- plt.show()
-