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import numpy as np
import scipy as scipy
from numpy.random import uniform
import scipy.stats
np.set_printoptions(threshold=3)
np.set_printoptions(suppress=True)
import cv2
def drawLines(img, points, r, g, b):
cv2.polylines(img, [np.int32(points)], isClosed=False, color=(r, g, b))
def drawCross(img, center, r, g, b):
d = 5
t = 2
LINE_AA = cv2.LINE_AA if cv2.__version__[0] == '3' else cv2.CV_AA
color = (r, g, b)
ctrx = center[0,0]
ctry = center[0,1]
cv2.line(img, (ctrx - d, ctry - d), (ctrx + d, ctry + d), color, t, LINE_AA)
cv2.line(img, (ctrx + d, ctry - d), (ctrx - d, ctry + d), color, t, LINE_AA)
def mouseCallback(event, x, y, flags,null):
global center
global trajectory
global previous_x
global previous_y
global zs
center=np.array([[x,y]])
trajectory=np.vstack((trajectory,np.array([x,y])))
if previous_x >0:
heading=np.arctan2(np.array([y-previous_y]), np.array([previous_x-x ]))
if heading>0:
heading=-(heading-np.pi)
else:
heading=-(np.pi+heading)
distance=np.linalg.norm(np.array([[previous_x,previous_y]])-np.array([[x,y]]) ,axis=1)
std=np.array([2,4])
u=np.array([heading,distance])
predict(particles, u, std, dt=1.)
zs = (np.linalg.norm(landmarks - center, axis=1) + (np.random.randn(NL) * sensor_std_err))
update(particles, weights, z=zs, R=50, landmarks=landmarks)
indexes = systematic_resample(weights)
resample_from_index(particles, weights, indexes)
previous_x=x
previous_y=y
WIDTH=800
HEIGHT=600
WINDOW_NAME="Particle Filter"
sensor_std_err=5
def create_uniform_particles(x_range, y_range, N):
particles = np.empty((N, 2))
particles[:, 0] = uniform(x_range[0], x_range[1], size=N)
particles[:, 1] = uniform(y_range[0], y_range[1], size=N)
return particles
def predict(particles, u, std, dt=1.):
N = len(particles)
dist = (u[1] * dt) + (np.random.randn(N) * std[1])
particles[:, 0] += np.cos(u[0]) * dist
particles[:, 1] += np.sin(u[0]) * dist
def update(particles, weights, z, R, landmarks):
weights.fill(1.)
for i, landmark in enumerate(landmarks):
distance=np.power((particles[:,0] - landmark[0])**2 +(particles[:,1] - landmark[1])**2,0.5)
weights *= scipy.stats.norm(distance, R).pdf(z[i])
weights += 1.e-300
weights /= sum(weights)
def neff(weights):
return 1. / np.sum(np.square(weights))
def systematic_resample(weights):
N = len(weights)
positions = (np.arange(N) + np.random.random()) / N
indexes = np.zeros(N, 'i')
cumulative_sum = np.cumsum(weights)
i, j = 0, 0
while i < N and j<N:
if positions[i] < cumulative_sum[j]:
indexes[i] = j
i += 1
else:
j += 1
return indexes
def estimate(particles, weights):
pos = particles[:, 0:1]
mean = np.average(pos, weights=weights, axis=0)
var = np.average((pos - mean)**2, weights=weights, axis=0)
return mean, var
def resample_from_index(particles, weights, indexes):
particles[:] = particles[indexes]
weights[:] = weights[indexes]
weights /= np.sum(weights)
x_range=np.array([0,800])
y_range=np.array([0,600])
N=400
landmarks=np.array([ [144,73], [410,13], [336,175], [718,159], [178,484], [665,464] ])
NL = len(landmarks)
particles=create_uniform_particles(x_range, y_range, N)
weights = np.array([1.0]*N)
img = np.zeros((HEIGHT,WIDTH,3), np.uint8)
cv2.namedWindow(WINDOW_NAME)
cv2.setMouseCallback(WINDOW_NAME,mouseCallback)
center=np.array([[-10,-10]])
trajectory=np.zeros(shape=(0,2))
robot_pos=np.zeros(shape=(0,2))
previous_x=-1
previous_y=-1
DELAY_MSEC=50
while(1):
cv2.imshow(WINDOW_NAME,img)
img = np.zeros((HEIGHT,WIDTH,3), np.uint8)
drawLines(img, trajectory, 0, 255, 0)
drawCross(img, center, r=255, g=0, b=0)
for landmark in landmarks:
cv2.circle(img,tuple(landmark),10,(255,0,0),-1)
for particle in particles:
cv2.circle(img,tuple((int(particle[0]),int(particle[1]))),1,(255,255,255),-1)
if cv2.waitKey(DELAY_MSEC) & 0xFF == 27:
break
cv2.circle(img,(10,10),10,(255,0,0),-1)
cv2.circle(img,(10,30),3,(255,255,255),-1)
cv2.putText(img,"Landmarks",(30,20),1,1.0,(255,0,0))
cv2.putText(img,"Particles",(30,40),1,1.0,(255,255,255))
cv2.putText(img,"Robot Trajectory(Ground truth)",(30,60),1,1.0,(0,255,0))
drawLines(img, np.array([[10,55],[25,55]]), 0, 255, 0)
cv2.destroyAllWindows()
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