mirror of
https://github.com/AtsushiSakai/PythonRobotics.git
synced 2026-01-14 16:57:58 -05:00
435 lines
10 KiB
Python
435 lines
10 KiB
Python
"""
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FastSLAM 2.0 example
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author: Atsushi Sakai (@Atsushi_twi)
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"""
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import numpy as np
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import math
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import matplotlib.pyplot as plt
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# Fast SLAM covariance
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Q = np.diag([3.0, math.radians(10.0)])**2
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R = np.diag([1.0, math.radians(20.0)])**2
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# Simulation parameter
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Qsim = np.diag([0.3, math.radians(2.0)])**2
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Rsim = np.diag([0.5, math.radians(10.0)])**2
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OFFSET_YAWRATE_NOISE = 0.01
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DT = 0.1 # time tick [s]
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SIM_TIME = 50.0 # simulation time [s]
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MAX_RANGE = 20.0 # maximum observation range
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M_DIST_TH = 2.0 # Threshold of Mahalanobis distance for data association.
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STATE_SIZE = 3 # State size [x,y,yaw]
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LM_SIZE = 2 # LM srate size [x,y]
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N_PARTICLE = 100 # number of particle
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NTH = N_PARTICLE / 1.0 # Number of particle for re-sampling
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show_animation = True
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class Particle:
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def __init__(self, N_LM):
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self.w = 1.0 / N_PARTICLE
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self.x = 0.0
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self.y = 0.0
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self.yaw = 0.0
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self.P = np.eye(3)
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# landmark x-y positions
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self.lm = np.matrix(np.zeros((N_LM, LM_SIZE)))
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# landmark position covariance
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self.lmP = np.matrix(np.zeros((N_LM * LM_SIZE, LM_SIZE)))
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def fast_slam2(particles, u, z):
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particles = predict_particles(particles, u)
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particles = update_with_observation(particles, z)
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particles = resampling(particles)
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return particles
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def normalize_weight(particles):
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sumw = sum([p.w for p in particles])
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try:
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for i in range(N_PARTICLE):
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particles[i].w /= sumw
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except ZeroDivisionError:
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for i in range(N_PARTICLE):
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particles[i].w = 1.0 / N_PARTICLE
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return particles
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return particles
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def calc_final_state(particles):
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xEst = np.zeros((STATE_SIZE, 1))
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particles = normalize_weight(particles)
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for i in range(N_PARTICLE):
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xEst[0, 0] += particles[i].w * particles[i].x
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xEst[1, 0] += particles[i].w * particles[i].y
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xEst[2, 0] += particles[i].w * particles[i].yaw
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xEst[2, 0] = pi_2_pi(xEst[2, 0])
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# print(xEst)
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return xEst
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def predict_particles(particles, u):
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for i in range(N_PARTICLE):
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px = np.zeros((STATE_SIZE, 1))
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px[0, 0] = particles[i].x
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px[1, 0] = particles[i].y
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px[2, 0] = particles[i].yaw
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ud = u + (np.matrix(np.random.randn(1, 2)) * R).T # add noise
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px = motion_model(px, ud)
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particles[i].x = px[0, 0]
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particles[i].y = px[1, 0]
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particles[i].yaw = px[2, 0]
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return particles
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def add_new_lm(particle, z, Q):
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r = z[0, 0]
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b = z[0, 1]
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lm_id = int(z[0, 2])
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s = math.sin(pi_2_pi(particle.yaw + b))
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c = math.cos(pi_2_pi(particle.yaw + b))
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particle.lm[lm_id, 0] = particle.x + r * c
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particle.lm[lm_id, 1] = particle.y + r * s
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# covariance
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Gz = np.matrix([[c, -r * s],
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[s, r * c]])
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particle.lmP[2 * lm_id:2 * lm_id + 2] = Gz * Q * Gz.T
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return particle
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def compute_jacobians(particle, xf, Pf, Q):
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dx = xf[0, 0] - particle.x
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dy = xf[1, 0] - particle.y
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d2 = dx**2 + dy**2
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d = math.sqrt(d2)
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zp = np.matrix([[d, pi_2_pi(math.atan2(dy, dx) - particle.yaw)]]).T
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Hv = np.matrix([[-dx / d, -dy / d, 0.0],
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[dy / d2, -dx / d2, -1.0]])
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Hf = np.matrix([[dx / d, dy / d],
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[-dy / d2, dx / d2]])
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Sf = Hf * Pf * Hf.T + Q
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return zp, Hv, Hf, Sf
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def update_KF_with_cholesky(xf, Pf, v, Q, Hf):
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PHt = Pf * Hf.T
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S = Hf * PHt + Q
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S = (S + S.T) * 0.5
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SChol = np.linalg.cholesky(S).T
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SCholInv = np.linalg.inv(SChol)
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W1 = PHt * SCholInv
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W = W1 * SCholInv.T
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x = xf + W * v
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P = Pf - W1 * W1.T
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return x, P
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def update_landmark(particle, z, Q):
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lm_id = int(z[0, 2])
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xf = np.matrix(particle.lm[lm_id, :]).T
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Pf = np.matrix(particle.lmP[2 * lm_id:2 * lm_id + 2, :])
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zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q)
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dz = z[0, 0: 2].T - zp
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dz[1, 0] = pi_2_pi(dz[1, 0])
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xf, Pf = update_KF_with_cholesky(xf, Pf, dz, Q, Hf)
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particle.lm[lm_id, :] = xf.T
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particle.lmP[2 * lm_id:2 * lm_id + 2, :] = Pf
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return particle
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def compute_weight(particle, z, Q):
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lm_id = int(z[0, 2])
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xf = np.matrix(particle.lm[lm_id, :]).T
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Pf = np.matrix(particle.lmP[2 * lm_id:2 * lm_id + 2])
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zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q)
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dz = z[0, 0: 2].T - zp
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dz[1, 0] = pi_2_pi(dz[1, 0])
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S = particle.lmP[2 * lm_id:2 * lm_id + 2]
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try:
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invS = np.linalg.inv(S)
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except np.linalg.linalg.LinAlgError:
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print("singuler")
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return 1.0
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num = math.exp(-0.5 * dz.T * invS * dz)
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den = 2.0 * math.pi * math.sqrt(np.linalg.det(S))
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w = num / den
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return w
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def proposal_sampling(particle, z, Q):
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lm_id = int(z[0, 2])
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xf = np.matrix(particle.lm[lm_id, :]).T
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Pf = np.matrix(particle.lmP[2 * lm_id:2 * lm_id + 2])
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# State
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x = np.matrix([[particle.x, particle.y, particle.yaw]]).T
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P = particle.P
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zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q)
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Sfi = np.linalg.inv(Sf)
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dz = z[0, 0: 2].T - zp
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dz[1, 0] = pi_2_pi(dz[1, 0])
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Pi = np.linalg.inv(P)
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particle.P = np.linalg.inv(Hv.T * Sfi * Hv + Pi) # proposal covariance
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x += particle.P * Hv.T * Sfi * dz # proposal mean
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particle.x = x[0, 0]
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particle.y = x[1, 0]
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particle.yaw = x[2, 0]
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return particle
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def update_with_observation(particles, z):
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for iz in range(len(z[:, 0])):
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lmid = int(z[iz, 2])
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for ip in range(N_PARTICLE):
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# new landmark
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if abs(particles[ip].lm[lmid, 0]) <= 0.01:
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particles[ip] = add_new_lm(particles[ip], z[iz, :], Q)
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# known landmark
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else:
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w = compute_weight(particles[ip], z[iz, :], Q)
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particles[ip].w *= w
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particles[ip] = update_landmark(particles[ip], z[iz, :], Q)
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particles[ip] = proposal_sampling(particles[ip], z[iz, :], Q)
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return particles
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def resampling(particles):
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"""
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low variance re-sampling
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"""
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particles = normalize_weight(particles)
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pw = []
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for i in range(N_PARTICLE):
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pw.append(particles[i].w)
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pw = np.matrix(pw)
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Neff = 1.0 / (pw * pw.T)[0, 0] # Effective particle number
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# print(Neff)
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if Neff < NTH: # resampling
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wcum = np.cumsum(pw)
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base = np.cumsum(pw * 0.0 + 1 / N_PARTICLE) - 1 / N_PARTICLE
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resampleid = base + np.random.rand(base.shape[1]) / N_PARTICLE
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inds = []
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ind = 0
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for ip in range(N_PARTICLE):
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while ((ind < wcum.shape[1] - 1) and (resampleid[0, ip] > wcum[0, ind])):
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ind += 1
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inds.append(ind)
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tparticles = particles[:]
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for i in range(len(inds)):
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particles[i].x = tparticles[inds[i]].x
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particles[i].y = tparticles[inds[i]].y
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particles[i].yaw = tparticles[inds[i]].yaw
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particles[i].lm = tparticles[inds[i]].lm[:, :]
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particles[i].lmP = tparticles[inds[i]].lmP[:, :]
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particles[i].w = 1.0 / N_PARTICLE
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return particles
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def calc_input(time):
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if time <= 3.0:
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v = 0.0
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yawrate = 0.0
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else:
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v = 1.0 # [m/s]
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yawrate = 0.1 # [rad/s]
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u = np.matrix([v, yawrate]).T
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return u
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def observation(xTrue, xd, u, RFID):
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xTrue = motion_model(xTrue, u)
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# add noise to gps x-y
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z = np.matrix(np.zeros((0, 3)))
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for i in range(len(RFID[:, 0])):
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dx = RFID[i, 0] - xTrue[0, 0]
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dy = RFID[i, 1] - xTrue[1, 0]
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d = math.sqrt(dx**2 + dy**2)
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angle = math.atan2(dy, dx) - xTrue[2, 0]
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if d <= MAX_RANGE:
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dn = d + np.random.randn() * Qsim[0, 0] # add noise
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anglen = angle + np.random.randn() * Qsim[1, 1] # add noise
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zi = np.matrix([dn, pi_2_pi(anglen), i])
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z = np.vstack((z, zi))
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# add noise to input
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ud1 = u[0, 0] + np.random.randn() * Rsim[0, 0]
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ud2 = u[1, 0] + np.random.randn() * Rsim[1, 1] + OFFSET_YAWRATE_NOISE
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ud = np.matrix([ud1, ud2]).T
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xd = motion_model(xd, ud)
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return xTrue, z, xd, ud
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def motion_model(x, u):
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F = np.matrix([[1.0, 0, 0],
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[0, 1.0, 0],
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[0, 0, 1.0]])
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B = np.matrix([[DT * math.cos(x[2, 0]), 0],
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[DT * math.sin(x[2, 0]), 0],
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[0.0, DT]])
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x = F * x + B * u
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x[2, 0] = pi_2_pi(x[2, 0])
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return x
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def pi_2_pi(angle):
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return (angle + math.pi) % (2*math.pi) - math.pi
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def main():
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print(__file__ + " start!!")
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time = 0.0
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# RFID positions [x, y]
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RFID = np.array([[10.0, -2.0],
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[15.0, 10.0],
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[15.0, 15.0],
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[10.0, 20.0],
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[3.0, 15.0],
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[-5.0, 20.0],
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[-5.0, 5.0],
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[-10.0, 15.0]
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])
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N_LM = RFID.shape[0]
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# State Vector [x y yaw v]'
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xEst = np.matrix(np.zeros((STATE_SIZE, 1)))
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xTrue = np.matrix(np.zeros((STATE_SIZE, 1)))
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xDR = np.matrix(np.zeros((STATE_SIZE, 1))) # Dead reckoning
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# history
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hxEst = xEst
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hxTrue = xTrue
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hxDR = xTrue
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particles = [Particle(N_LM) for i in range(N_PARTICLE)]
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while SIM_TIME >= time:
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time += DT
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u = calc_input(time)
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xTrue, z, xDR, ud = observation(xTrue, xDR, u, RFID)
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particles = fast_slam2(particles, ud, z)
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xEst = calc_final_state(particles)
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x_state = xEst[0: STATE_SIZE]
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# store data history
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hxEst = np.hstack((hxEst, x_state))
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hxDR = np.hstack((hxDR, xDR))
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hxTrue = np.hstack((hxTrue, xTrue))
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if show_animation:
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plt.cla()
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plt.plot(RFID[:, 0], RFID[:, 1], "*k")
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for iz in range(len(z[:, 0])):
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lmid = int(z[iz, 2])
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plt.plot([xEst[0, 0], RFID[lmid, 0]], [
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xEst[1, 0], RFID[lmid, 1]], "-k")
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for i in range(N_PARTICLE):
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plt.plot(particles[i].x, particles[i].y, ".r")
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plt.plot(particles[i].lm[:, 0], particles[i].lm[:, 1], "xb")
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plt.plot(np.array(hxTrue[0, :]).flatten(),
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np.array(hxTrue[1, :]).flatten(), "-b")
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plt.plot(np.array(hxDR[0, :]).flatten(),
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np.array(hxDR[1, :]).flatten(), "-k")
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plt.plot(np.array(hxEst[0, :]).flatten(),
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np.array(hxEst[1, :]).flatten(), "-r")
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plt.plot(xEst[0], xEst[1], "xk")
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plt.axis("equal")
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plt.grid(True)
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plt.pause(0.001)
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if __name__ == '__main__':
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main()
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