github/PythonRobotics
1
1
Fork 0
mirror of https://github.com/AtsushiSakai/PythonRobotics.git synced 2026-01-12 23:58:04 -05:00
Code Issues Packages Projects Releases Wiki Activity

remove np.matrix

Browse Source
This commit is contained in:
Atsushi Sakai
2018-12-02 21:58:26 +09:00
parent 91d6f0e1f6
commit c9a9e48f72
2 changed files with 77 additions and 81 deletions
Download Patch File Download Diff File Expand all files Collapse all files

3
SLAM/FastSLAM1/fast_slam1.py
View File

@@ -132,7 +132,8 @@ def compute_jacobians(particle, xf, Pf, Q):
d2 = dx**2 + dy**2
d = math.sqrt(d2)
zp = np.array([[d, pi_2_pi(math.atan2(dy, dx) - particle.yaw)]]).T
zp = np.array(
[d, pi_2_pi(math.atan2(dy, dx) - particle.yaw)]).reshape(2, 1)
Hv = np.array([[-dx / d, -dy / d, 0.0],
[dy / d2, -dx / d2, -1.0]])

155
SLAM/FastSLAM2/fast_slam2.py
View File

@@ -27,7 +27,7 @@ M_DIST_TH = 2.0 # Threshold of Mahalanobis distance for data association.
STATE_SIZE = 3 # State size [x,y,yaw]
LM_SIZE = 2 # LM srate size [x,y]
N_PARTICLE = 100 # number of particle
NTH = N_PARTICLE / 1.0 # Number of particle for re-sampling
NTH = N_PARTICLE / 1.5 # Number of particle for re-sampling
show_animation = True
@@ -41,9 +41,9 @@ class Particle:
self.yaw = 0.0
self.P = np.eye(3)
# landmark x-y positions
self.lm = np.matrix(np.zeros((N_LM, LM_SIZE)))
self.lm = np.zeros((N_LM, LM_SIZE))
# landmark position covariance
self.lmP = np.matrix(np.zeros((N_LM * LM_SIZE, LM_SIZE)))
self.lmP = np.zeros((N_LM * LM_SIZE, LM_SIZE))
def fast_slam2(particles, u, z):
@@ -97,7 +97,7 @@ def predict_particles(particles, u):
px[0, 0] = particles[i].x
px[1, 0] = particles[i].y
px[2, 0] = particles[i].yaw
ud = u + (np.matrix(np.random.randn(1, 2)) * R).T # add noise
ud = u + (np.random.randn(1, 2) @ R).T # add noise
px = motion_model(px, ud)
particles[i].x = px[0, 0]
particles[i].y = px[1, 0]
@@ -108,9 +108,9 @@ def predict_particles(particles, u):
def add_new_lm(particle, z, Q):
r = z[0, 0]
b = z[0, 1]
lm_id = int(z[0, 2])
r = z[0]
b = z[1]
lm_id = int(z[2])
s = math.sin(pi_2_pi(particle.yaw + b))
c = math.cos(pi_2_pi(particle.yaw + b))
@@ -119,10 +119,10 @@ def add_new_lm(particle, z, Q):
particle.lm[lm_id, 1] = particle.y + r * s
# covariance
Gz = np.matrix([[c, -r * s],
[s, r * c]])
Gz = np.array([[c, -r * s],
[s, r * c]])
particle.lmP[2 * lm_id:2 * lm_id + 2] = Gz * Q * Gz.T
particle.lmP[2 * lm_id:2 * lm_id + 2] = Gz @ Q @ Gz.T
return particle
@@ -133,44 +133,45 @@ def compute_jacobians(particle, xf, Pf, Q):
d2 = dx**2 + dy**2
d = math.sqrt(d2)
zp = np.matrix([[d, pi_2_pi(math.atan2(dy, dx) - particle.yaw)]]).T
zp = np.array(
[d, pi_2_pi(math.atan2(dy, dx) - particle.yaw)]).reshape(2, 1)
Hv = np.matrix([[-dx / d, -dy / d, 0.0],
[dy / d2, -dx / d2, -1.0]])
Hv = np.array([[-dx / d, -dy / d, 0.0],
[dy / d2, -dx / d2, -1.0]])
Hf = np.matrix([[dx / d, dy / d],
[-dy / d2, dx / d2]])
Hf = np.array([[dx / d, dy / d],
[-dy / d2, dx / d2]])
Sf = Hf * Pf * Hf.T + Q
Sf = Hf @ Pf @ Hf.T + Q
return zp, Hv, Hf, Sf
def update_KF_with_cholesky(xf, Pf, v, Q, Hf):
PHt = Pf * Hf.T
S = Hf * PHt + Q
PHt = Pf @ Hf.T
S = Hf @ PHt + Q
S = (S + S.T) * 0.5
SChol = np.linalg.cholesky(S).T
SCholInv = np.linalg.inv(SChol)
W1 = PHt * SCholInv
W = W1 * SCholInv.T
W1 = PHt @ SCholInv
W = W1 @ SCholInv.T
x = xf + W * v
P = Pf - W1 * W1.T
x = xf + W @ v
P = Pf - W1 @ W1.T
return x, P
def update_landmark(particle, z, Q):
lm_id = int(z[0, 2])
xf = np.matrix(particle.lm[lm_id, :]).T
Pf = np.matrix(particle.lmP[2 * lm_id:2 * lm_id + 2, :])
lm_id = int(z[2])
xf = np.array(particle.lm[lm_id, :]).reshape(2, 1)
Pf = np.array(particle.lmP[2 * lm_id:2 * lm_id + 2])
zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q)
dz = z[0, 0: 2].T - zp
dz = z[0:2].reshape(2, 1) - zp
dz[1, 0] = pi_2_pi(dz[1, 0])
xf, Pf = update_KF_with_cholesky(xf, Pf, dz, Q, Hf)
@@ -183,21 +184,20 @@ def update_landmark(particle, z, Q):
def compute_weight(particle, z, Q):
lm_id = int(z[0, 2])
xf = np.matrix(particle.lm[lm_id, :]).T
Pf = np.matrix(particle.lmP[2 * lm_id:2 * lm_id + 2])
lm_id = int(z[2])
xf = np.array(particle.lm[lm_id, :]).reshape(2, 1)
Pf = np.array(particle.lmP[2 * lm_id:2 * lm_id + 2])
zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q)
dz = z[0, 0: 2].T - zp
dz = z[0:2].reshape(2, 1) - zp
dz[1, 0] = pi_2_pi(dz[1, 0])
try:
invS = np.linalg.inv(Sf)
except np.linalg.linalg.LinAlgError:
print("singuler")
return 1.0
num = math.exp(-0.5 * dz.T * invS * dz)
num = math.exp(-0.5 * dz.T @ invS @ dz)
den = 2.0 * math.pi * math.sqrt(np.linalg.det(Sf))
w = num / den
@@ -207,22 +207,22 @@ def compute_weight(particle, z, Q):
def proposal_sampling(particle, z, Q):
lm_id = int(z[0, 2])
xf = np.matrix(particle.lm[lm_id, :]).T
Pf = np.matrix(particle.lmP[2 * lm_id:2 * lm_id + 2])
lm_id = int(z[2])
xf = particle.lm[lm_id, :].reshape(2, 1)
Pf = particle.lmP[2 * lm_id:2 * lm_id + 2]
# State
x = np.matrix([[particle.x, particle.y, particle.yaw]]).T
x = np.array([particle.x, particle.y, particle.yaw]).reshape(3, 1)
P = particle.P
zp, Hv, Hf, Sf = compute_jacobians(particle, xf, Pf, Q)
Sfi = np.linalg.inv(Sf)
dz = z[0, 0: 2].T - zp
dz[1, 0] = pi_2_pi(dz[1, 0])
dz = z[0:2].reshape(2, 1) - zp
dz[1] = pi_2_pi(dz[1])
Pi = np.linalg.inv(P)
particle.P = np.linalg.inv(Hv.T * Sfi * Hv + Pi) # proposal covariance
x += particle.P * Hv.T * Sfi * dz # proposal mean
particle.P = np.linalg.inv(Hv.T @ Sfi @ Hv + Pi) # proposal covariance
x += particle.P @ Hv.T @ Sfi @ dz # proposal mean
particle.x = x[0, 0]
particle.y = x[1, 0]
@@ -233,21 +233,20 @@ def proposal_sampling(particle, z, Q):
def update_with_observation(particles, z):
for iz in range(len(z[:, 0])):
lmid = int(z[iz, 2])
for iz in range(len(z[0, :])):
lmid = int(z[2, iz])
for ip in range(N_PARTICLE):
# new landmark
if abs(particles[ip].lm[lmid, 0]) <= 0.01:
particles[ip] = add_new_lm(particles[ip], z[iz, :], Q)
particles[ip] = add_new_lm(particles[ip], z[:, iz], Q)
# known landmark
else:
w = compute_weight(particles[ip], z[iz, :], Q)
w = compute_weight(particles[ip], z[:, iz], Q)
particles[ip].w *= w
particles[ip] = update_landmark(particles[ip], z[iz, :], Q)
particles[ip] = proposal_sampling(particles[ip], z[iz, :], Q)
particles[ip] = update_landmark(particles[ip], z[:, iz], Q)
particles[ip] = proposal_sampling(particles[ip], z[:, iz], Q)
return particles
@@ -263,20 +262,20 @@ def resampling(particles):
for i in range(N_PARTICLE):
pw.append(particles[i].w)
pw = np.matrix(pw)
pw = np.array(pw)
Neff = 1.0 / (pw * pw.T)[0, 0] # Effective particle number
Neff = 1.0 / (pw @ pw.T) # Effective particle number
# print(Neff)
if Neff < NTH: # resampling
wcum = np.cumsum(pw)
base = np.cumsum(pw * 0.0 + 1 / N_PARTICLE) - 1 / N_PARTICLE
resampleid = base + np.random.rand(base.shape[1]) / N_PARTICLE
resampleid = base + np.random.rand(base.shape[0]) / N_PARTICLE
inds = []
ind = 0
for ip in range(N_PARTICLE):
while ((ind < wcum.shape[1] - 1) and (resampleid[0, ip] > wcum[0, ind])):
while ((ind < wcum.shape[0] - 1) and (resampleid[ip] > wcum[ind])):
ind += 1
inds.append(ind)
@@ -294,41 +293,42 @@ def resampling(particles):
def calc_input(time):
if time <= 3.0:
if time <= 3.0: # wait at first
v = 0.0
yawrate = 0.0
else:
v = 1.0 # [m/s]
yawrate = 0.1 # [rad/s]
u = np.matrix([v, yawrate]).T
u = np.array([v, yawrate]).reshape(2, 1)
return u
def observation(xTrue, xd, u, RFID):
# calc true state
xTrue = motion_model(xTrue, u)
# add noise to gps x-y
z = np.matrix(np.zeros((0, 3)))
# add noise to range observation
z = np.zeros((3, 0))
for i in range(len(RFID[:, 0])):
dx = RFID[i, 0] - xTrue[0, 0]
dy = RFID[i, 1] - xTrue[1, 0]
d = math.sqrt(dx**2 + dy**2)
angle = math.atan2(dy, dx) - xTrue[2, 0]
angle = pi_2_pi(math.atan2(dy, dx) - xTrue[2, 0])
if d <= MAX_RANGE:
dn = d + np.random.randn() * Qsim[0, 0] # add noise
anglen = angle + np.random.randn() * Qsim[1, 1] # add noise
zi = np.matrix([dn, pi_2_pi(anglen), i])
z = np.vstack((z, zi))
zi = np.array([dn, pi_2_pi(anglen), i]).reshape(3, 1)
z = np.hstack((z, zi))
# add noise to input
ud1 = u[0, 0] + np.random.randn() * Rsim[0, 0]
ud2 = u[1, 0] + np.random.randn() * Rsim[1, 1] + OFFSET_YAWRATE_NOISE
ud = np.matrix([ud1, ud2]).T
ud = np.array([ud1, ud2]).reshape(2, 1)
xd = motion_model(xd, ud)
@@ -337,15 +337,15 @@ def observation(xTrue, xd, u, RFID):
def motion_model(x, u):
F = np.matrix([[1.0, 0, 0],
[0, 1.0, 0],
[0, 0, 1.0]])
F = np.array([[1.0, 0, 0],
[0, 1.0, 0],
[0, 0, 1.0]])
B = np.matrix([[DT * math.cos(x[2, 0]), 0],
[DT * math.sin(x[2, 0]), 0],
[0.0, DT]])
B = np.array([[DT * math.cos(x[2, 0]), 0],
[DT * math.sin(x[2, 0]), 0],
[0.0, DT]])
x = F * x + B * u
x = F @ x + B @ u
x[2, 0] = pi_2_pi(x[2, 0])
@@ -374,10 +374,9 @@ def main():
N_LM = RFID.shape[0]
# State Vector [x y yaw v]'
xEst = np.matrix(np.zeros((STATE_SIZE, 1)))
xTrue = np.matrix(np.zeros((STATE_SIZE, 1)))
xDR = np.matrix(np.zeros((STATE_SIZE, 1))) # Dead reckoning
xEst = np.zeros((STATE_SIZE, 1)) # SLAM estimation
xTrue = np.zeros((STATE_SIZE, 1)) # True state
xDR = np.zeros((STATE_SIZE, 1)) # Dead reckoning
# history
hxEst = xEst
@@ -408,21 +407,17 @@ def main():
plt.plot(RFID[:, 0], RFID[:, 1], "*k")
for iz in range(len(z[:, 0])):
lmid = int(z[iz, 2])
plt.plot([xEst[0, 0], RFID[lmid, 0]], [
xEst[1, 0], RFID[lmid, 1]], "-k")
lmid = int(z[2, iz])
plt.plot([xEst[0], RFID[lmid, 0]], [
xEst[1], RFID[lmid, 1]], "-k")
for i in range(N_PARTICLE):
plt.plot(particles[i].x, particles[i].y, ".r")
plt.plot(particles[i].lm[:, 0], particles[i].lm[:, 1], "xb")
plt.plot(np.array(hxTrue[0, :]).flatten(),
np.array(hxTrue[1, :]).flatten(), "-b")
plt.plot(np.array(hxDR[0, :]).flatten(),
np.array(hxDR[1, :]).flatten(), "-k")
plt.plot(np.array(hxEst[0, :]).flatten(),
np.array(hxEst[1, :]).flatten(), "-r")
plt.plot(hxTrue[0, :], hxTrue[1, :], "-b")
plt.plot(hxDR[0, :], hxDR[1, :], "-k")
plt.plot(hxEst[0, :], hxEst[1, :], "-r")
plt.plot(xEst[0], xEst[1], "xk")
plt.axis("equal")
plt.grid(True)