``````

In [1]:

import numpy as np
import copy
import math, random
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse
from scipy.stats import norm

def draw_landmarks(landmarks):
xs = [ e[0] for e in landmarks ]
ys = [ e[1] for e in landmarks ]
plt.scatter(xs,ys, s=300, marker="*", label ="landmarks", color="orange")

def draw_robot(pose):
plt.quiver([pose[0]],[pose[1]],[math.cos(pose[2])],[math.sin(pose[2])],color="red",label="actual robot motion")

def relative_landmark_pos(pose,landmark):
x,y,th =pose
lx,ly = landmark
distance  = math.sqrt((x-lx)**2 + (y-ly)**2)
direction = math.atan2(ly-y, lx-x) - th

return (distance, direction, lx, ly)

def draw_observation(pose, measurment):
x,y,th =pose
distance, direction,lx,ly = measurment
lx = distance * math.cos(th + direction) + x
ly = distance * math.sin(th + direction) + y
plt.plot([x, lx],[y, ly],color="pink")

def draw_observations(pose,  measurements):
for m in measurements:
draw_observation(pose, m)

def observation(pose, landmark):
actual_distance, actual_direction,lx,ly = relative_landmark_pos(pose,landmark)

if(math.cos(actual_direction) < 0.0 ):
return None

measured_distance = random.gauss(actual_distance, actual_distance*0.1) #10% error
measured_direction = random.gauss(actual_direction,5.0/180.0*math.pi) #5deg error
return (measured_distance, measured_direction,lx,ly)

def observations(pose,landmarks):
return filter(lambda x: x != None, [ observation(pose,e) for e in landmarks])

def likelihood(pose, measurement):
x,y,th = pose
distance, direction,lx,ly = measurement

rel_distance, rel_direction, tmp_x, tmp_y = relative_landmark_pos(pose,(lx,ly))

return norm.pdf(x = distance - rel_distance, loc = 0.0, scale = rel_distance / 10.0)  \
* norm.pdf(x = direction - rel_direction, loc = 0.0, scale = 5.0/180.0 * math.pi)

def change_weights(particles, measurement):
for p in particles:
p.weight *= likelihood(p.pose, measurement)

ws = [ p.weight for p in particles ]
s = sum(ws)
for p in particles:
p.weight = p.weight / s

class Particles:
def __init__(self,pose, w ):
self.pose = np.array(pose)
self.weight = w

def __repr__(self):
return "pose: " + str(self.pose) + "weight: " + str(self.weight)

def motion(pose,u):
p_x, p_y, p_th = pose
fw, rot = u

actual_fw = random.gauss(fw, fw/10)
dir_error = random.gauss(0.0, math.pi/ 180.0 * 3.0)
actual_rot     = random.gauss(rot,rot/10)

p_x += actual_fw * math.cos(p_th + dir_error)
p_y += actual_fw * math.sin(p_th + dir_error)
p_th += actual_rot + dir_error

return np.array([p_x, p_y, p_th])

def draw(pose,particles):
fig = plt.figure(i, figsize= (8, 8))
sp.set_xlim(-1.0,1.0)
sp.set_ylim(-0.5,1.5)

xs = [e.pose[0] for e in particles]
ys = [e.pose[1] for e in particles]
vxs = [math.cos(e.pose[2])*e.weight for e in particles]
vys = [math.sin(e.pose[2])*e.weight for e in particles]
plt.quiver(xs,ys,vxs,vys,color="blue",label="particles")

plt.quiver([pose[0]],[pose[1]],[math.cos(pose[2])],[math.sin(pose[2])],color="red",label="actual robot motion")

if __name__ == '__main__':
actual_x = np.array([0.0,0.0,0.0])
u = np.array([0.2,math.pi / 180.0 * 20])
actual_landmarks =[np.array([-0.5,0.0]),np.array([0.5,0.0]),np.array([0.0,0.5])]
particles = [Particles([0.0,0.0,0.0],1.0/100) for i in range(100)] ## 100 ##

path = [actual_x]
particle_path = [copy.deepcopy(particles)]
measurements = [observations(actual_x, actual_landmarks)]

for i in range(15):
actual_x = motion(actual_x,u)
path.append(actual_x)

ms = observations(actual_x, actual_landmarks)
measurements.append(ms)

for p in particles:
p.pose = motion(p.pose,u)

for m in ms:
change_weights(particles, m)

pointer = random.uniform(0.0,1.0/len(particles))
new_particles = []
particles_num = len(particles)

accum =[]
sm = 0.0
for p in particles:
accum.append(p.weight + sm)
sm += p.weight

while pointer < 1.0:
if accum[0] >= pointer:
new_particles.append(
Particles(copy.deepcopy(particles[0].pose),1.0/particles_num)
)
pointer += 1.0/particles_num
else:
accum.pop(0)
particles.pop(0)

particles = new_particles

particle_path.append(copy.deepcopy(particles))

for i,p in enumerate(path):
draw(path[i],particle_path[i])
draw_landmarks(actual_landmarks)
draw_observations(path[i], measurements[i])
plt.show()

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