Parcticle Filter Explained With Python Code From Scratch
In the following code I have implemented a localization algorithm based on particle filter. I have used conda to run my code, you can run the following for installation of dependencies:
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conda create -n Filters python=3 conda activate Filters conda install -c menpo opencv3 conda install numpy scipy matplotlib sympy |
and the code:
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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]))) #noise=sensorSigma * np.random.randn(1,2) + sensorMu 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" #sensorMu=0 #sensorSigma=3 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 # avoid round-off to zero 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]) #Number of partciles 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) # Create a black image, a window and bind the function to window 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) #landmarks for landmark in landmarks: cv2.circle(img,tuple(landmark),10,(255,0,0),-1) #draw_particles: 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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