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# --------------
# USER INSTRUCTIONS
#
# Now you will put everything together.
#
# First make sure that your sense and move functions
# work as expected for the test cases provided at the
# bottom of the previous two programming assignments.
# Once you are satisfied, copy your sense and move
# definitions into the robot class on this page, BUT
# now include noise.
#
# A good way to include noise in the sense step is to
# add Gaussian noise, centered at zero with variance
# of self.bearing_noise to each bearing. You can do this
# with the command random.gauss(0, self.bearing_noise)
#
# In the move step, you should make sure that your
# actual steering angle is chosen from a Gaussian
# distribution of steering angles. This distribution
# should be centered at the intended steering angle
# with variance of self.steering_noise.
#
# Feel free to use the included set_noise function.
#
# Please do not modify anything except where indicated
# below.
from math import *
import random
# --------
#
# some top level parameters
#
max_steering_angle = pi / 4.0 # You do not need to use this value, but keep in mind the limitations of a real car.
bearing_noise = 0.1 # Noise parameter: should be included in sense function.
steering_noise = 0.1 # Noise parameter: should be included in move function.
distance_noise = 5.0 # Noise parameter: should be included in move function.
tolerance_xy = 15.0 # Tolerance for localization in the x and y directions.
tolerance_orientation = 0.25 # Tolerance for orientation.
# --------
#
# the "world" has 4 landmarks.
# the robot's initial coordinates are somewhere in the square
# represented by the landmarks.
#
# NOTE: Landmark coordinates are given in (y, x) form and NOT
# in the traditional (x, y) format!
landmarks = [[0.0, 100.0], [0.0, 0.0], [100.0, 0.0], [100.0, 100.0]] # position of 4 landmarks in (y, x) format.
world_size = 100.0 # world is NOT cyclic. Robot is allowed to travel "out of bounds"
# ------------------------------------------------
#
# this is the robot class
#
class robot:
# --------
# init:
# creates robot and initializes location/orientation
#
def __init__(self, length = 20.0):
self.x = random.random() * world_size # initial x position
self.y = random.random() * world_size # initial y position
self.orientation = random.random() * 2.0 * pi # initial orientation
self.length = length # length of robot
self.bearing_noise = 0.0 # initialize bearing noise to zero
self.steering_noise = 0.0 # initialize steering noise to zero
self.distance_noise = 0.0 # initialize distance noise to zero
# --------
# set:
# sets a robot coordinate
#
def set(self, new_x, new_y, new_orientation):
if new_orientation < 0 or new_orientation >= 2 * pi:
raise ValueError, 'Orientation must be in [0..2pi]'
self.x = float(new_x)
self.y = float(new_y)
self.orientation = float(new_orientation)
# --------
# set_noise:
# sets the noise parameters
#
def set_noise(self, new_b_noise, new_s_noise, new_d_noise):
# makes it possible to change the noise parameters
# this is often useful in particle filters
self.bearing_noise = float(new_b_noise)
self.steering_noise = float(new_s_noise)
self.distance_noise = float(new_d_noise)
# --------
# measurement_prob
# computes the probability of a measurement
#
def measurement_prob(self, measurements):
# calculate the correct measurement
predicted_measurements = self.sense(0) # Our sense function took 0 as an argument to switch off noise.
# compute errors
error = 1.0
for i in range(len(measurements)):
error_bearing = abs(measurements[i] - predicted_measurements[i])
error_bearing = (error_bearing + pi) % (2.0 * pi) - pi # truncate
# update Gaussian
error *= (exp(- (error_bearing ** 2) / (self.bearing_noise ** 2) / 2.0) /
sqrt(2.0 * pi * (self.bearing_noise ** 2)))
return error
def __repr__(self): #allows us to print robot attributes.
return '[x=%.6s y=%.6s orient=%.6s]' % (str(self.x), str(self.y),
str(self.orientation))
############# ONLY ADD/MODIFY CODE BELOW HERE ###################
# --------
# move:
#
# copy your code from the previous exercise
# and modify it so that it simulates motion noise
# according to the noise parameters
# self.steering_noise
# self.distance_noise
def move(self, motion): # Do not change the name of this function
# ADD CODE HERE
steer = motion[0] + random.gauss(0.0,self.steering_noise)
distance = motion[1] + random.gauss(0.0, self.distance_noise)
#if distance < 0:
# raise ValueError, 'Robot cant move backwards'
theta = self.orientation
beta = distance / self.length * tan(steer)
if abs(beta) >= 0.0001:
radius = distance / beta
Cx = self.x - radius * sin(theta)
Cy = self.y + radius * cos(theta)
x_prime = Cx + radius * sin(beta+theta)
y_prime = Cy - radius * cos(beta+theta)
theta_prime = (theta + beta) % (2 * pi)
result = robot()
result.set(x_prime, y_prime, theta_prime)
else:
x_prime = self.x + distance * cos(theta)
y_prime = self.y + distance * sin(theta)
theta_prime = (theta + beta) % (2 * pi)
result = robot()
result.set(x_prime, y_prime, theta_prime)
result.set_noise(self.bearing_noise, self.steering_noise,self.distance_noise)
return result # make sure your move function returns an instance
# --------
# sense:
#
# copy your code from the previous exercise
# and modify it so that it simulates bearing noise
# according to
# self.bearing_noise
def sense(self, nonoise=None): #do not change the name of this function
Z = []
if nonoise and nonoise == 0:
orientation = self.orientation + random.gauss(0.0, self.bearing_noise)
else:
orientation = self.orientation
bearing1 = atan2(landmarks[0][0]-self.y, landmarks[0][1]-self.x) - orientation + 2*pi
bearing2 = atan2(landmarks[1][0]-self.y, landmarks[1][1]-self.x) - orientation + 2*pi
bearing3 = atan2(landmarks[2][0]-self.y, landmarks[2][1]-self.x) - orientation
bearing4 = atan2(landmarks[3][0]-self.y, landmarks[3][1]-self.x) - orientation
Z = [bearing1, bearing2, bearing3, bearing4]
return Z #Leave this line here. Return vector Z of 4 bearings.
############## ONLY ADD/MODIFY CODE ABOVE HERE ####################
# --------
#
# extract position from a particle set
#
def get_position(p):
x = 0.0
y = 0.0
orientation = 0.0
for i in range(len(p)):
x += p[i].x
y += p[i].y
# orientation is tricky because it is cyclic. By normalizing
# around the first particle we are somewhat more robust to
# the 0=2pi problem
orientation += (((p[i].orientation - p[0].orientation + pi) % (2.0 * pi))
+ p[0].orientation - pi)
return [x / len(p), y / len(p), orientation / len(p)]
# --------
#
# The following code generates the measurements vector
# You can use it to develop your solution.
#
def generate_ground_truth(motions):
myrobot = robot()
myrobot.set_noise(bearing_noise, steering_noise, distance_noise)
Z = []
T = len(motions)
for t in range(T):
myrobot = myrobot.move(motions[t])
Z.append(myrobot.sense())
#print 'Robot: ', myrobot
return [myrobot, Z]
# --------
#
# The following code prints the measurements associated
# with generate_ground_truth
#
def print_measurements(Z):
T = len(Z)
print 'measurements = [[%.8s, %.8s, %.8s, %.8s],' % \
(str(Z[0][0]), str(Z[0][1]), str(Z[0][2]), str(Z[0][3]))
for t in range(1,T-1):
print ' [%.8s, %.8s, %.8s, %.8s],' % \
(str(Z[t][0]), str(Z[t][1]), str(Z[t][2]), str(Z[t][3]))
print ' [%.8s, %.8s, %.8s, %.8s]]' % \
(str(Z[T-1][0]), str(Z[T-1][1]), str(Z[T-1][2]), str(Z[T-1][3]))
# --------
#
# The following code checks to see if your particle filter
# localizes the robot to within the desired tolerances
# of the true position. The tolerances are defined at the top.
#
def check_output(final_robot, estimated_position):
error_x = abs(final_robot.x - estimated_position[0])
error_y = abs(final_robot.y - estimated_position[1])
error_orientation = abs(final_robot.orientation - estimated_position[2])
error_orientation = (error_orientation + pi) % (2.0 * pi) - pi
correct = error_x < tolerance_xy and error_y < tolerance_xy \
and error_orientation < tolerance_orientation
return correct
def particle_filter(motions, measurements, N=500): # I know it's tempting, but don't change N!
# --------
#
# Make particles
#
p = []
for i in range(N):
r = robot()
r.set_noise(bearing_noise, steering_noise, distance_noise)
p.append(r)
# --------
#
# Update particles
#
for t in range(len(motions)):
# motion update (prediction)
p2 = []
for i in range(N):
p2.append(p[i].move(motions[t]))
p = p2
# measurement update
w = []
for i in range(N):
w.append(p[i].measurement_prob(measurements[t]))
# resampling
p3 = []
index = int(random.random() * N)
beta = 0.0
mw = max(w)
for i in range(N):
beta += random.random() * 2.0 * mw
while beta > w[index]:
beta -= w[index]
index = (index + 1) % N
p3.append(p[index])
p = p3
return get_position(p)
## IMPORTANT: You may uncomment the test cases below to test your code.
## But when you submit this code, your test cases MUST be commented
## out.
##
## You can test whether your particle filter works using the
## function check_output (see test case 2). We will be using a similar
## function. Note: Even for a well-implemented particle filter this
## function occasionally returns False. This is because a particle
## filter is a randomized algorithm. We will be testing your code
## multiple times. Make sure check_output returns True at least 80%
## of the time.
## --------
## TEST CASES:
##
##1) Calling the particle_filter function with the following
## motions and measurements should return a [x,y,orientation]
## vector near [x=93.476 y=75.186 orient=5.2664], that is, the
## robot's true location.
##
motions = [[2. * pi / 10, 20.] for row in range(8)]
measurements = [[4.746936, 3.859782, 3.045217, 2.045506],
[3.510067, 2.916300, 2.146394, 1.598332],
[2.972469, 2.407489, 1.588474, 1.611094],
[1.906178, 1.193329, 0.619356, 0.807930],
[1.352825, 0.662233, 0.144927, 0.799090],
[0.856150, 0.214590, 5.651497, 1.062401],
[0.194460, 5.660382, 4.761072, 2.471682],
[5.717342, 4.736780, 3.909599, 2.342536]]
print particle_filter(motions, measurements)
## 2) You can generate your own test cases by generating
## measurements using the generate_ground_truth function.
## It will print the robot's last location when calling it.
##
##
number_of_iterations = 6
motions = [[2. * pi / 20, 12.] for row in range(number_of_iterations)]
x = generate_ground_truth(motions)
final_robot = x[0]
measurements = x[1]
estimated_position = particle_filter(motions, measurements)
print_measurements(measurements)
print 'Ground truth: ', final_robot
print 'Particle filter: ', estimated_position
print 'Code check: ', check_output(final_robot, estimated_position)
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