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README.md

PythonRobotics

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Python codes for robotics algorithm.

Table of Contents

What is this?

This is a Python code collection of robotics algorithms, especially for autonomous navigation.

Features:

  1. Widely used and practical algorithms are selected.

  2. Minimum dependency.

  3. Easy to read for understanding each algorithm's basic idea.

Requirements

  • Python 3.6.x

  • numpy

  • scipy

  • matplotlib

  • pandas

  • cvxpy

How to use

  1. Install the required libraries. You can use environment.yml with conda command.

  2. Clone this repo.

  3. Execute python script in each directory.

  4. Add star to this repo if you like it 😃.

Localization

Extended Kalman Filter localization

This is a sensor fusion localization with Extended Kalman Filter(EKF).

The blue line is true trajectory, the black line is dead reckoning trajectory,

the green point is positioning observation (ex. GPS), and the red line is estimated trajectory with EKF.

The red ellipse is estimated covariance ellipse with EKF.

Ref:

Unscented Kalman Filter localization

2

This is a sensor fusion localization with Unscented Kalman Filter(UKF).

The lines and points are same meaning of the EKF simulation.

Ref:

Particle filter localization

2

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 estimated trajectory with PF.

It is assumed that the robot can measure a distance from landmarks (RFID).

This measurements are used for PF localization.

Ref:

Histogram filter localization

3

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:

Mapping

Gaussian grid map

This is a 2D Gaussian grid mapping example.

2

Ray casting grid map

This is a 2D ray casting grid mapping example.

2

k-means object clustering

This is a 2D object clustering with k-means algorithm.

2

Object shape recognition using circle fitting

This is an object shape recognition using circle fitting.

2

The blue circle is the true object shape.

The red crosses are observations from a ranging sensor.

The red circle is the estimated object shape using circle fitting.

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 to points.

3

Ref:

EKF SLAM

This is an Extended Kalman Filter based SLAM example.

The blue line is ground truth, the black line is dead reckoning, the red line is the estimated trajectory with EKF SLAM.

The green crosses are estimated landmarks.

3

Ref:

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.

3

Ref:

FastSLAM 2.0

This is a feature based SLAM example using FastSLAM 2.0.

The animation has the same meanings as one of FastSLAM 1.0.

3

Ref:

Graph based SLAM

This is a graph based SLAM example.

The blue line is ground truth.

The black line is dead reckoning.

The red line is the estimated trajectory with Graph based SLAM.

The black stars are landmarks for graph edge generation.

3

Ref:

Path Planning

Dynamic Window Approach

This is a 2D navigation sample code with Dynamic Window Approach.

2

Grid based search

Dijkstra algorithm

This is a 2D grid based shortest path planning with Dijkstra's algorithm.

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

In the animation, cyan points are searched nodes.

A* algorithm

This is a 2D grid based shortest path planning with A star algorithm.

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

In the animation, cyan points are searched nodes.

Its heuristic is 2D Euclid distance.

Potential Field algorithm

This is a 2D grid based path planning with Potential Field algorithm.

PotentialField

In the animation, the blue heat map shows potential value on each grid.

Ref:

Model Predictive Trajectory Generator

This is a path optimization sample on model predictive trajectory generator.

This algorithm is used for state lattice planner.

Path optimization sample

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

Lookup table generation sample

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

Ref:

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:

Uniform polar sampling

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

Biased polar sampling

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

Lane sampling

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

Probabilistic Road-Map (PRM) planning

PRM

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:

  

Voronoi Road-Map planning

VRM

This Voronoi road-map planner uses Dijkstra method for graph search.

In the animation, blue points are Voronoi points,

Cyan crosses mean searched points with Dijkstra method,

The red line is the final path of Vornoi Road-Map.

Ref:

Rapidly-Exploring Random Trees (RRT)

Basic RRT

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

This is a simple path planning code with Rapidly-Exploring Random Trees (RRT)

Black circles are obstacles, green line is a searched tree, red crosses are start and goal positions.

RRT*

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

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:

RRT with dubins path

PythonRobotics

Path planning for a car robot with RRT and dubins path planner.

RRT* with dubins path

AtsushiSakai/PythonRobotics

Path planning for a car robot with RRT* and dubins path planner.

RRT* with reeds-sheep path

Robotics/animation.gif at master · AtsushiSakai/PythonRobotics)

Path planning for a car robot with RRT* and reeds sheep path planner.

Informed RRT*

irrt)

This is a path planning code with Informed RRT*.

The cyan ellipse is the heuristic sampling domain of Informed RRT*.

Ref:

Batch Informed RRT*

irrt)

This is a path planning code with Batch Informed RRT*.

Ref:

Closed Loop RRT*

A vehicle model based path planning with closed loop RRT*.

CLRRT

In this code, pure-pursuit algorithm is used for steering control,

PID is used for speed control.

Ref:

LQR-RRT*

This is a path planning simulation with LQR-RRT*.

A double integrator motion model is used for LQR local planner.

LQRRRT

Ref:

Cubic spline planning

A sample code for cubic path planning.

This code generates a curvature continuous path based on x-y waypoints with cubic spline.

Heading angle of each point can be also calculated analytically.

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

B-Spline planning

B-Spline

This is a path planning with B-Spline curse.

If you input waypoints, it generates a smooth path with B-Spline curve.

The final course should be on the first and last waypoints.

Ref:

Eta^3 Spline path planning

eta3

This is a path planning with Eta^3 spline.

Ref:

Bezier path planning

A sample code of Bezier path planning.

It is based on 4 control points Beier path.

Bezier1

If you change the offset distance from start and end point,

You can get different Beizer course:

Bezier2

Ref:

Quintic polynomials planning

Motion planning with quintic polynomials.

2

It can calculate 2D path, velocity, and acceleration profile based on quintic polynomials.

Ref:

Dubins path planning

A sample code for Dubins path planning.

dubins

Ref:

Reeds Shepp planning

A sample code with Reeds Shepp path planning.

RSPlanning

Ref:

LQR based path planning

A sample code using LQR based path planning for double integrator model.

RSPlanning

Optimal Trajectory in a Frenet Frame

3

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:

Path tracking

move to a pose control

This is a simulation of moving to a pose control

2

Ref:

Pure pursuit tracking

Path tracking simulation with pure pursuit steering control and PID speed control.

2

The red line is a target course, the green cross means the target point for pure pursuit control, the blue line is the tracking.

Ref:

Stanley control

Path tracking simulation with Stanley steering control and PID speed control.

2

Ref:

Rear wheel feedback control

Path tracking simulation with rear wheel feedback steering control and PID speed control.

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

Ref:

Linear–quadratic regulator (LQR) steering control

Path tracking simulation with LQR steering control and PID speed control.

PythonRobotics/figure_1.png at master · AtsushiSakai/PythonRobotics

Ref:

Linear–quadratic regulator (LQR) speed and steering control

Path tracking simulation with LQR speed and steering control.

3

Ref:

Model predictive speed and steering control

Path tracking simulation with iterative linear model predictive speed and steering control.

Ref:

Arm Navigation

Two joint arm to point control

Two joint arm to a point control simulation.

3

License

MIT

Contribution

A small PR like bug fix is welcome.

If your PR is merged multiple times, I will add your account to the author list.

Support

You can support this project financially via Patreon.

You can get e-mail technical supports about the codes if you are being a patron.

PayPal donation is also welcome.

Support via PayPal

Authors