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|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/histogram_filter/histogram_filter.py
|
map_shift
|
(grid_map, x_shift, y_shift)
|
return grid_map
| 174 | 186 |
def map_shift(grid_map, x_shift, y_shift):
tmp_grid_map = copy.deepcopy(grid_map.data)
for ix in range(grid_map.x_w):
for iy in range(grid_map.y_w):
nix = ix + x_shift
niy = iy + y_shift
if 0 <= nix < grid_map.x_w and 0 <= niy < grid_map.y_w:
grid_map.data[ix + x_shift][iy + y_shift] =\
tmp_grid_map[ix][iy]
return grid_map
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/histogram_filter/histogram_filter.py#L174-L186
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
11,
12
] | 92.307692 |
[] | 0 | false | 90.410959 | 13 | 5 | 100 | 0 |
def map_shift(grid_map, x_shift, y_shift):
tmp_grid_map = copy.deepcopy(grid_map.data)
for ix in range(grid_map.x_w):
for iy in range(grid_map.y_w):
nix = ix + x_shift
niy = iy + y_shift
if 0 <= nix < grid_map.x_w and 0 <= niy < grid_map.y_w:
grid_map.data[ix + x_shift][iy + y_shift] =\
tmp_grid_map[ix][iy]
return grid_map
| 544 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/histogram_filter/histogram_filter.py
|
motion_update
|
(grid_map, u, yaw)
|
return grid_map
| 189 | 204 |
def motion_update(grid_map, u, yaw):
grid_map.dx += DT * math.cos(yaw) * u[0]
grid_map.dy += DT * math.sin(yaw) * u[0]
x_shift = grid_map.dx // grid_map.xy_resolution
y_shift = grid_map.dy // grid_map.xy_resolution
if abs(x_shift) >= 1.0 or abs(y_shift) >= 1.0: # map should be shifted
grid_map = map_shift(grid_map, int(x_shift), int(y_shift))
grid_map.dx -= x_shift * grid_map.xy_resolution
grid_map.dy -= y_shift * grid_map.xy_resolution
# Add motion noise
grid_map.data = gaussian_filter(grid_map.data, sigma=MOTION_STD)
return grid_map
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/histogram_filter/histogram_filter.py#L189-L204
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15
] | 100 |
[] | 0 | true | 90.410959 | 16 | 3 | 100 | 0 |
def motion_update(grid_map, u, yaw):
grid_map.dx += DT * math.cos(yaw) * u[0]
grid_map.dy += DT * math.sin(yaw) * u[0]
x_shift = grid_map.dx // grid_map.xy_resolution
y_shift = grid_map.dy // grid_map.xy_resolution
if abs(x_shift) >= 1.0 or abs(y_shift) >= 1.0: # map should be shifted
grid_map = map_shift(grid_map, int(x_shift), int(y_shift))
grid_map.dx -= x_shift * grid_map.xy_resolution
grid_map.dy -= y_shift * grid_map.xy_resolution
# Add motion noise
grid_map.data = gaussian_filter(grid_map.data, sigma=MOTION_STD)
return grid_map
| 545 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/histogram_filter/histogram_filter.py
|
calc_grid_index
|
(grid_map)
|
return mx, my
| 207 | 215 |
def calc_grid_index(grid_map):
mx, my = np.mgrid[slice(grid_map.min_x - grid_map.xy_resolution / 2.0,
grid_map.max_x + grid_map.xy_resolution / 2.0,
grid_map.xy_resolution),
slice(grid_map.min_y - grid_map.xy_resolution / 2.0,
grid_map.max_y + grid_map.xy_resolution / 2.0,
grid_map.xy_resolution)]
return mx, my
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/histogram_filter/histogram_filter.py#L207-L215
| 2 |
[
0,
1,
7,
8
] | 44.444444 |
[] | 0 | false | 90.410959 | 9 | 1 | 100 | 0 |
def calc_grid_index(grid_map):
mx, my = np.mgrid[slice(grid_map.min_x - grid_map.xy_resolution / 2.0,
grid_map.max_x + grid_map.xy_resolution / 2.0,
grid_map.xy_resolution),
slice(grid_map.min_y - grid_map.xy_resolution / 2.0,
grid_map.max_y + grid_map.xy_resolution / 2.0,
grid_map.xy_resolution)]
return mx, my
| 546 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/histogram_filter/histogram_filter.py
|
GridMap.__init__
|
(self)
| 46 | 56 |
def __init__(self):
self.data = None
self.xy_resolution = None
self.min_x = None
self.min_y = None
self.max_x = None
self.max_y = None
self.x_w = None
self.y_w = None
self.dx = 0.0 # movement distance
self.dy = 0.0
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/histogram_filter/histogram_filter.py#L46-L56
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10
] | 100 |
[] | 0 | true | 90.410959 | 11 | 1 | 100 | 0 |
def __init__(self):
self.data = None
self.xy_resolution = None
self.min_x = None
self.min_y = None
self.max_x = None
self.max_y = None
self.x_w = None
self.y_w = None
self.dx = 0.0 # movement distance
self.dy = 0.0
| 547 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
calc_input
|
()
|
return u
| 45 | 49 |
def calc_input():
v = 1.0 # [m/s]
yawRate = 0.1 # [rad/s]
u = np.array([[v, yawRate]]).T
return u
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L45-L49
| 2 |
[
0,
1,
2,
3,
4
] | 100 |
[] | 0 | true | 91.729323 | 5 | 1 | 100 | 0 |
def calc_input():
v = 1.0 # [m/s]
yawRate = 0.1 # [rad/s]
u = np.array([[v, yawRate]]).T
return u
| 548 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
observation
|
(xTrue, xd, u)
|
return xTrue, z, xd, ud
| 52 | 63 |
def observation(xTrue, xd, u):
xTrue = motion_model(xTrue, u)
# add noise to gps x-y
z = observation_model(xTrue) + GPS_NOISE @ np.random.randn(2, 1)
# add noise to input
ud = u + INPUT_NOISE @ np.random.randn(2, 1)
xd = motion_model(xd, ud)
return xTrue, z, xd, ud
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L52-L63
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11
] | 100 |
[] | 0 | true | 91.729323 | 12 | 1 | 100 | 0 |
def observation(xTrue, xd, u):
xTrue = motion_model(xTrue, u)
# add noise to gps x-y
z = observation_model(xTrue) + GPS_NOISE @ np.random.randn(2, 1)
# add noise to input
ud = u + INPUT_NOISE @ np.random.randn(2, 1)
xd = motion_model(xd, ud)
return xTrue, z, xd, ud
| 549 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
motion_model
|
(x, u)
|
return x
| 66 | 79 |
def motion_model(x, u):
F = np.array([[1.0, 0, 0, 0],
[0, 1.0, 0, 0],
[0, 0, 1.0, 0],
[0, 0, 0, 0]])
B = np.array([[DT * math.cos(x[2]), 0],
[DT * math.sin(x[2]), 0],
[0.0, DT],
[1.0, 0.0]])
x = F @ x + B @ u
return x
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L66-L79
| 2 |
[
0,
1,
5,
6,
10,
11,
12,
13
] | 57.142857 |
[] | 0 | false | 91.729323 | 14 | 1 | 100 | 0 |
def motion_model(x, u):
F = np.array([[1.0, 0, 0, 0],
[0, 1.0, 0, 0],
[0, 0, 1.0, 0],
[0, 0, 0, 0]])
B = np.array([[DT * math.cos(x[2]), 0],
[DT * math.sin(x[2]), 0],
[0.0, DT],
[1.0, 0.0]])
x = F @ x + B @ u
return x
| 550 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
observation_model
|
(x)
|
return z
| 82 | 90 |
def observation_model(x):
H = np.array([
[1, 0, 0, 0],
[0, 1, 0, 0]
])
z = H @ x
return z
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L82-L90
| 2 |
[
0,
1,
5,
6,
7,
8
] | 66.666667 |
[] | 0 | false | 91.729323 | 9 | 1 | 100 | 0 |
def observation_model(x):
H = np.array([
[1, 0, 0, 0],
[0, 1, 0, 0]
])
z = H @ x
return z
| 551 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
generate_sigma_points
|
(xEst, PEst, gamma)
|
return sigma
| 93 | 105 |
def generate_sigma_points(xEst, PEst, gamma):
sigma = xEst
Psqrt = scipy.linalg.sqrtm(PEst)
n = len(xEst[:, 0])
# Positive direction
for i in range(n):
sigma = np.hstack((sigma, xEst + gamma * Psqrt[:, i:i + 1]))
# Negative direction
for i in range(n):
sigma = np.hstack((sigma, xEst - gamma * Psqrt[:, i:i + 1]))
return sigma
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L93-L105
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12
] | 100 |
[] | 0 | true | 91.729323 | 13 | 3 | 100 | 0 |
def generate_sigma_points(xEst, PEst, gamma):
sigma = xEst
Psqrt = scipy.linalg.sqrtm(PEst)
n = len(xEst[:, 0])
# Positive direction
for i in range(n):
sigma = np.hstack((sigma, xEst + gamma * Psqrt[:, i:i + 1]))
# Negative direction
for i in range(n):
sigma = np.hstack((sigma, xEst - gamma * Psqrt[:, i:i + 1]))
return sigma
| 552 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
predict_sigma_motion
|
(sigma, u)
|
return sigma
|
Sigma Points prediction with motion model
|
Sigma Points prediction with motion model
| 108 | 115 |
def predict_sigma_motion(sigma, u):
"""
Sigma Points prediction with motion model
"""
for i in range(sigma.shape[1]):
sigma[:, i:i + 1] = motion_model(sigma[:, i:i + 1], u)
return sigma
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L108-L115
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7
] | 100 |
[] | 0 | true | 91.729323 | 8 | 2 | 100 | 1 |
def predict_sigma_motion(sigma, u):
for i in range(sigma.shape[1]):
sigma[:, i:i + 1] = motion_model(sigma[:, i:i + 1], u)
return sigma
| 553 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
predict_sigma_observation
|
(sigma)
|
return sigma
|
Sigma Points prediction with observation model
|
Sigma Points prediction with observation model
| 118 | 127 |
def predict_sigma_observation(sigma):
"""
Sigma Points prediction with observation model
"""
for i in range(sigma.shape[1]):
sigma[0:2, i] = observation_model(sigma[:, i])
sigma = sigma[0:2, :]
return sigma
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L118-L127
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9
] | 100 |
[] | 0 | true | 91.729323 | 10 | 2 | 100 | 1 |
def predict_sigma_observation(sigma):
for i in range(sigma.shape[1]):
sigma[0:2, i] = observation_model(sigma[:, i])
sigma = sigma[0:2, :]
return sigma
| 554 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
calc_sigma_covariance
|
(x, sigma, wc, Pi)
|
return P
| 130 | 136 |
def calc_sigma_covariance(x, sigma, wc, Pi):
nSigma = sigma.shape[1]
d = sigma - x[0:sigma.shape[0]]
P = Pi
for i in range(nSigma):
P = P + wc[0, i] * d[:, i:i + 1] @ d[:, i:i + 1].T
return P
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L130-L136
| 2 |
[
0,
1,
2,
3,
4,
5,
6
] | 100 |
[] | 0 | true | 91.729323 | 7 | 2 | 100 | 0 |
def calc_sigma_covariance(x, sigma, wc, Pi):
nSigma = sigma.shape[1]
d = sigma - x[0:sigma.shape[0]]
P = Pi
for i in range(nSigma):
P = P + wc[0, i] * d[:, i:i + 1] @ d[:, i:i + 1].T
return P
| 555 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
calc_pxz
|
(sigma, x, z_sigma, zb, wc)
|
return P
| 139 | 148 |
def calc_pxz(sigma, x, z_sigma, zb, wc):
nSigma = sigma.shape[1]
dx = sigma - x
dz = z_sigma - zb[0:2]
P = np.zeros((dx.shape[0], dz.shape[0]))
for i in range(nSigma):
P = P + wc[0, i] * dx[:, i:i + 1] @ dz[:, i:i + 1].T
return P
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L139-L148
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9
] | 100 |
[] | 0 | true | 91.729323 | 10 | 2 | 100 | 0 |
def calc_pxz(sigma, x, z_sigma, zb, wc):
nSigma = sigma.shape[1]
dx = sigma - x
dz = z_sigma - zb[0:2]
P = np.zeros((dx.shape[0], dz.shape[0]))
for i in range(nSigma):
P = P + wc[0, i] * dx[:, i:i + 1] @ dz[:, i:i + 1].T
return P
| 556 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
ukf_estimation
|
(xEst, PEst, z, u, wm, wc, gamma)
|
return xEst, PEst
| 151 | 170 |
def ukf_estimation(xEst, PEst, z, u, wm, wc, gamma):
# Predict
sigma = generate_sigma_points(xEst, PEst, gamma)
sigma = predict_sigma_motion(sigma, u)
xPred = (wm @ sigma.T).T
PPred = calc_sigma_covariance(xPred, sigma, wc, Q)
# Update
zPred = observation_model(xPred)
y = z - zPred
sigma = generate_sigma_points(xPred, PPred, gamma)
zb = (wm @ sigma.T).T
z_sigma = predict_sigma_observation(sigma)
st = calc_sigma_covariance(zb, z_sigma, wc, R)
Pxz = calc_pxz(sigma, xPred, z_sigma, zb, wc)
K = Pxz @ np.linalg.inv(st)
xEst = xPred + K @ y
PEst = PPred - K @ st @ K.T
return xEst, PEst
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L151-L170
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19
] | 100 |
[] | 0 | true | 91.729323 | 20 | 1 | 100 | 0 |
def ukf_estimation(xEst, PEst, z, u, wm, wc, gamma):
# Predict
sigma = generate_sigma_points(xEst, PEst, gamma)
sigma = predict_sigma_motion(sigma, u)
xPred = (wm @ sigma.T).T
PPred = calc_sigma_covariance(xPred, sigma, wc, Q)
# Update
zPred = observation_model(xPred)
y = z - zPred
sigma = generate_sigma_points(xPred, PPred, gamma)
zb = (wm @ sigma.T).T
z_sigma = predict_sigma_observation(sigma)
st = calc_sigma_covariance(zb, z_sigma, wc, R)
Pxz = calc_pxz(sigma, xPred, z_sigma, zb, wc)
K = Pxz @ np.linalg.inv(st)
xEst = xPred + K @ y
PEst = PPred - K @ st @ K.T
return xEst, PEst
| 557 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
plot_covariance_ellipse
|
(xEst, PEst)
| 173 | 193 |
def plot_covariance_ellipse(xEst, PEst): # pragma: no cover
Pxy = PEst[0:2, 0:2]
eigval, eigvec = np.linalg.eig(Pxy)
if eigval[0] >= eigval[1]:
bigind = 0
smallind = 1
else:
bigind = 1
smallind = 0
t = np.arange(0, 2 * math.pi + 0.1, 0.1)
a = math.sqrt(eigval[bigind])
b = math.sqrt(eigval[smallind])
x = [a * math.cos(it) for it in t]
y = [b * math.sin(it) for it in t]
angle = math.atan2(eigvec[1, bigind], eigvec[0, bigind])
fx = rot_mat_2d(angle) @ np.array([x, y])
px = np.array(fx[0, :] + xEst[0, 0]).flatten()
py = np.array(fx[1, :] + xEst[1, 0]).flatten()
plt.plot(px, py, "--r")
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L173-L193
| 2 |
[] | 0 |
[] | 0 | false | 91.729323 | 21 | 4 | 100 | 0 |
def plot_covariance_ellipse(xEst, PEst): # pragma: no cover
Pxy = PEst[0:2, 0:2]
eigval, eigvec = np.linalg.eig(Pxy)
if eigval[0] >= eigval[1]:
bigind = 0
smallind = 1
else:
bigind = 1
smallind = 0
t = np.arange(0, 2 * math.pi + 0.1, 0.1)
a = math.sqrt(eigval[bigind])
b = math.sqrt(eigval[smallind])
x = [a * math.cos(it) for it in t]
y = [b * math.sin(it) for it in t]
angle = math.atan2(eigvec[1, bigind], eigvec[0, bigind])
fx = rot_mat_2d(angle) @ np.array([x, y])
px = np.array(fx[0, :] + xEst[0, 0]).flatten()
py = np.array(fx[1, :] + xEst[1, 0]).flatten()
plt.plot(px, py, "--r")
| 558 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
setup_ukf
|
(nx)
|
return wm, wc, gamma
| 196 | 209 |
def setup_ukf(nx):
lamb = ALPHA ** 2 * (nx + KAPPA) - nx
# calculate weights
wm = [lamb / (lamb + nx)]
wc = [(lamb / (lamb + nx)) + (1 - ALPHA ** 2 + BETA)]
for i in range(2 * nx):
wm.append(1.0 / (2 * (nx + lamb)))
wc.append(1.0 / (2 * (nx + lamb)))
gamma = math.sqrt(nx + lamb)
wm = np.array([wm])
wc = np.array([wc])
return wm, wc, gamma
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L196-L209
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13
] | 100 |
[] | 0 | true | 91.729323 | 14 | 2 | 100 | 0 |
def setup_ukf(nx):
lamb = ALPHA ** 2 * (nx + KAPPA) - nx
# calculate weights
wm = [lamb / (lamb + nx)]
wc = [(lamb / (lamb + nx)) + (1 - ALPHA ** 2 + BETA)]
for i in range(2 * nx):
wm.append(1.0 / (2 * (nx + lamb)))
wc.append(1.0 / (2 * (nx + lamb)))
gamma = math.sqrt(nx + lamb)
wm = np.array([wm])
wc = np.array([wc])
return wm, wc, gamma
| 559 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/unscented_kalman_filter/unscented_kalman_filter.py
|
main
|
()
| 212 | 260 |
def main():
print(__file__ + " start!!")
nx = 4 # State Vector [x y yaw v]'
xEst = np.zeros((nx, 1))
xTrue = np.zeros((nx, 1))
PEst = np.eye(nx)
xDR = np.zeros((nx, 1)) # Dead reckoning
wm, wc, gamma = setup_ukf(nx)
# history
hxEst = xEst
hxTrue = xTrue
hxDR = xTrue
hz = np.zeros((2, 1))
time = 0.0
while SIM_TIME >= time:
time += DT
u = calc_input()
xTrue, z, xDR, ud = observation(xTrue, xDR, u)
xEst, PEst = ukf_estimation(xEst, PEst, z, ud, wm, wc, gamma)
# store data history
hxEst = np.hstack((hxEst, xEst))
hxDR = np.hstack((hxDR, xDR))
hxTrue = np.hstack((hxTrue, xTrue))
hz = np.hstack((hz, z))
if show_animation:
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect('key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.plot(hz[0, :], hz[1, :], ".g")
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")
plot_covariance_ellipse(xEst, PEst)
plt.axis("equal")
plt.grid(True)
plt.pause(0.001)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/unscented_kalman_filter/unscented_kalman_filter.py#L212-L260
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33
] | 69.387755 |
[
34,
36,
38,
39,
41,
43,
45,
46,
47,
48
] | 20.408163 | false | 91.729323 | 49 | 3 | 79.591837 | 0 |
def main():
print(__file__ + " start!!")
nx = 4 # State Vector [x y yaw v]'
xEst = np.zeros((nx, 1))
xTrue = np.zeros((nx, 1))
PEst = np.eye(nx)
xDR = np.zeros((nx, 1)) # Dead reckoning
wm, wc, gamma = setup_ukf(nx)
# history
hxEst = xEst
hxTrue = xTrue
hxDR = xTrue
hz = np.zeros((2, 1))
time = 0.0
while SIM_TIME >= time:
time += DT
u = calc_input()
xTrue, z, xDR, ud = observation(xTrue, xDR, u)
xEst, PEst = ukf_estimation(xEst, PEst, z, ud, wm, wc, gamma)
# store data history
hxEst = np.hstack((hxEst, xEst))
hxDR = np.hstack((hxDR, xDR))
hxTrue = np.hstack((hxTrue, xTrue))
hz = np.hstack((hz, z))
if show_animation:
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect('key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.plot(hz[0, :], hz[1, :], ".g")
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")
plot_covariance_ellipse(xEst, PEst)
plt.axis("equal")
plt.grid(True)
plt.pause(0.001)
| 560 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/particle_filter/particle_filter.py
|
calc_input
|
()
|
return u
| 38 | 42 |
def calc_input():
v = 1.0 # [m/s]
yaw_rate = 0.1 # [rad/s]
u = np.array([[v, yaw_rate]]).T
return u
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/particle_filter/particle_filter.py#L38-L42
| 2 |
[
0,
1,
2,
3,
4
] | 100 |
[] | 0 | true | 88.888889 | 5 | 1 | 100 | 0 |
def calc_input():
v = 1.0 # [m/s]
yaw_rate = 0.1 # [rad/s]
u = np.array([[v, yaw_rate]]).T
return u
| 570 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/particle_filter/particle_filter.py
|
observation
|
(x_true, xd, u, rf_id)
|
return x_true, z, xd, ud
| 45 | 68 |
def observation(x_true, xd, u, rf_id):
x_true = motion_model(x_true, u)
# add noise to gps x-y
z = np.zeros((0, 3))
for i in range(len(rf_id[:, 0])):
dx = x_true[0, 0] - rf_id[i, 0]
dy = x_true[1, 0] - rf_id[i, 1]
d = math.hypot(dx, dy)
if d <= MAX_RANGE:
dn = d + np.random.randn() * Q_sim[0, 0] ** 0.5 # add noise
zi = np.array([[dn, rf_id[i, 0], rf_id[i, 1]]])
z = np.vstack((z, zi))
# add noise to input
ud1 = u[0, 0] + np.random.randn() * R_sim[0, 0] ** 0.5
ud2 = u[1, 0] + np.random.randn() * R_sim[1, 1] ** 0.5
ud = np.array([[ud1, ud2]]).T
xd = motion_model(xd, ud)
return x_true, z, xd, ud
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/particle_filter/particle_filter.py#L45-L68
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23
] | 100 |
[] | 0 | true | 88.888889 | 24 | 3 | 100 | 0 |
def observation(x_true, xd, u, rf_id):
x_true = motion_model(x_true, u)
# add noise to gps x-y
z = np.zeros((0, 3))
for i in range(len(rf_id[:, 0])):
dx = x_true[0, 0] - rf_id[i, 0]
dy = x_true[1, 0] - rf_id[i, 1]
d = math.hypot(dx, dy)
if d <= MAX_RANGE:
dn = d + np.random.randn() * Q_sim[0, 0] ** 0.5 # add noise
zi = np.array([[dn, rf_id[i, 0], rf_id[i, 1]]])
z = np.vstack((z, zi))
# add noise to input
ud1 = u[0, 0] + np.random.randn() * R_sim[0, 0] ** 0.5
ud2 = u[1, 0] + np.random.randn() * R_sim[1, 1] ** 0.5
ud = np.array([[ud1, ud2]]).T
xd = motion_model(xd, ud)
return x_true, z, xd, ud
| 571 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/particle_filter/particle_filter.py
|
motion_model
|
(x, u)
|
return x
| 71 | 84 |
def motion_model(x, u):
F = np.array([[1.0, 0, 0, 0],
[0, 1.0, 0, 0],
[0, 0, 1.0, 0],
[0, 0, 0, 0]])
B = np.array([[DT * math.cos(x[2, 0]), 0],
[DT * math.sin(x[2, 0]), 0],
[0.0, DT],
[1.0, 0.0]])
x = F.dot(x) + B.dot(u)
return x
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/particle_filter/particle_filter.py#L71-L84
| 2 |
[
0,
1,
5,
6,
10,
11,
12,
13
] | 57.142857 |
[] | 0 | false | 88.888889 | 14 | 1 | 100 | 0 |
def motion_model(x, u):
F = np.array([[1.0, 0, 0, 0],
[0, 1.0, 0, 0],
[0, 0, 1.0, 0],
[0, 0, 0, 0]])
B = np.array([[DT * math.cos(x[2, 0]), 0],
[DT * math.sin(x[2, 0]), 0],
[0.0, DT],
[1.0, 0.0]])
x = F.dot(x) + B.dot(u)
return x
| 572 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/particle_filter/particle_filter.py
|
gauss_likelihood
|
(x, sigma)
|
return p
| 87 | 91 |
def gauss_likelihood(x, sigma):
p = 1.0 / math.sqrt(2.0 * math.pi * sigma ** 2) * \
math.exp(-x ** 2 / (2 * sigma ** 2))
return p
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/particle_filter/particle_filter.py#L87-L91
| 2 |
[
0,
1,
3,
4
] | 80 |
[] | 0 | false | 88.888889 | 5 | 1 | 100 | 0 |
def gauss_likelihood(x, sigma):
p = 1.0 / math.sqrt(2.0 * math.pi * sigma ** 2) * \
math.exp(-x ** 2 / (2 * sigma ** 2))
return p
| 573 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/particle_filter/particle_filter.py
|
calc_covariance
|
(x_est, px, pw)
|
return cov
|
calculate covariance matrix
see ipynb doc
|
calculate covariance matrix
see ipynb doc
| 94 | 106 |
def calc_covariance(x_est, px, pw):
"""
calculate covariance matrix
see ipynb doc
"""
cov = np.zeros((3, 3))
n_particle = px.shape[1]
for i in range(n_particle):
dx = (px[:, i:i + 1] - x_est)[0:3]
cov += pw[0, i] * dx @ dx.T
cov *= 1.0 / (1.0 - pw @ pw.T)
return cov
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/particle_filter/particle_filter.py#L94-L106
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12
] | 100 |
[] | 0 | true | 88.888889 | 13 | 2 | 100 | 2 |
def calc_covariance(x_est, px, pw):
cov = np.zeros((3, 3))
n_particle = px.shape[1]
for i in range(n_particle):
dx = (px[:, i:i + 1] - x_est)[0:3]
cov += pw[0, i] * dx @ dx.T
cov *= 1.0 / (1.0 - pw @ pw.T)
return cov
| 574 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/particle_filter/particle_filter.py
|
pf_localization
|
(px, pw, z, u)
|
return x_est, p_est, px, pw
|
Localization with Particle filter
|
Localization with Particle filter
| 109 | 143 |
def pf_localization(px, pw, z, u):
"""
Localization with Particle filter
"""
for ip in range(NP):
x = np.array([px[:, ip]]).T
w = pw[0, ip]
# Predict with random input sampling
ud1 = u[0, 0] + np.random.randn() * R[0, 0] ** 0.5
ud2 = u[1, 0] + np.random.randn() * R[1, 1] ** 0.5
ud = np.array([[ud1, ud2]]).T
x = motion_model(x, ud)
# Calc Importance Weight
for i in range(len(z[:, 0])):
dx = x[0, 0] - z[i, 1]
dy = x[1, 0] - z[i, 2]
pre_z = math.hypot(dx, dy)
dz = pre_z - z[i, 0]
w = w * gauss_likelihood(dz, math.sqrt(Q[0, 0]))
px[:, ip] = x[:, 0]
pw[0, ip] = w
pw = pw / pw.sum() # normalize
x_est = px.dot(pw.T)
p_est = calc_covariance(x_est, px, pw)
N_eff = 1.0 / (pw.dot(pw.T))[0, 0] # Effective particle number
if N_eff < NTh:
px, pw = re_sampling(px, pw)
return x_est, p_est, px, pw
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/particle_filter/particle_filter.py#L109-L143
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34
] | 100 |
[] | 0 | true | 88.888889 | 35 | 4 | 100 | 1 |
def pf_localization(px, pw, z, u):
for ip in range(NP):
x = np.array([px[:, ip]]).T
w = pw[0, ip]
# Predict with random input sampling
ud1 = u[0, 0] + np.random.randn() * R[0, 0] ** 0.5
ud2 = u[1, 0] + np.random.randn() * R[1, 1] ** 0.5
ud = np.array([[ud1, ud2]]).T
x = motion_model(x, ud)
# Calc Importance Weight
for i in range(len(z[:, 0])):
dx = x[0, 0] - z[i, 1]
dy = x[1, 0] - z[i, 2]
pre_z = math.hypot(dx, dy)
dz = pre_z - z[i, 0]
w = w * gauss_likelihood(dz, math.sqrt(Q[0, 0]))
px[:, ip] = x[:, 0]
pw[0, ip] = w
pw = pw / pw.sum() # normalize
x_est = px.dot(pw.T)
p_est = calc_covariance(x_est, px, pw)
N_eff = 1.0 / (pw.dot(pw.T))[0, 0] # Effective particle number
if N_eff < NTh:
px, pw = re_sampling(px, pw)
return x_est, p_est, px, pw
| 575 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/particle_filter/particle_filter.py
|
re_sampling
|
(px, pw)
|
return px, pw
|
low variance re-sampling
|
low variance re-sampling
| 146 | 164 |
def re_sampling(px, pw):
"""
low variance re-sampling
"""
w_cum = np.cumsum(pw)
base = np.arange(0.0, 1.0, 1 / NP)
re_sample_id = base + np.random.uniform(0, 1 / NP)
indexes = []
ind = 0
for ip in range(NP):
while re_sample_id[ip] > w_cum[ind]:
ind += 1
indexes.append(ind)
px = px[:, indexes]
pw = np.zeros((1, NP)) + 1.0 / NP # init weight
return px, pw
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/particle_filter/particle_filter.py#L146-L164
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18
] | 100 |
[] | 0 | true | 88.888889 | 19 | 3 | 100 | 1 |
def re_sampling(px, pw):
w_cum = np.cumsum(pw)
base = np.arange(0.0, 1.0, 1 / NP)
re_sample_id = base + np.random.uniform(0, 1 / NP)
indexes = []
ind = 0
for ip in range(NP):
while re_sample_id[ip] > w_cum[ind]:
ind += 1
indexes.append(ind)
px = px[:, indexes]
pw = np.zeros((1, NP)) + 1.0 / NP # init weight
return px, pw
| 576 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/particle_filter/particle_filter.py
|
plot_covariance_ellipse
|
(x_est, p_est)
| 167 | 199 |
def plot_covariance_ellipse(x_est, p_est): # pragma: no cover
p_xy = p_est[0:2, 0:2]
eig_val, eig_vec = np.linalg.eig(p_xy)
if eig_val[0] >= eig_val[1]:
big_ind = 0
small_ind = 1
else:
big_ind = 1
small_ind = 0
t = np.arange(0, 2 * math.pi + 0.1, 0.1)
# eig_val[big_ind] or eiq_val[small_ind] were occasionally negative
# numbers extremely close to 0 (~10^-20), catch these cases and set the
# respective variable to 0
try:
a = math.sqrt(eig_val[big_ind])
except ValueError:
a = 0
try:
b = math.sqrt(eig_val[small_ind])
except ValueError:
b = 0
x = [a * math.cos(it) for it in t]
y = [b * math.sin(it) for it in t]
angle = math.atan2(eig_vec[1, big_ind], eig_vec[0, big_ind])
fx = rot_mat_2d(angle) @ np.array([[x, y]])
px = np.array(fx[:, 0] + x_est[0, 0]).flatten()
py = np.array(fx[:, 1] + x_est[1, 0]).flatten()
plt.plot(px, py, "--r")
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/particle_filter/particle_filter.py#L167-L199
| 2 |
[] | 0 |
[] | 0 | false | 88.888889 | 33 | 6 | 100 | 0 |
def plot_covariance_ellipse(x_est, p_est): # pragma: no cover
p_xy = p_est[0:2, 0:2]
eig_val, eig_vec = np.linalg.eig(p_xy)
if eig_val[0] >= eig_val[1]:
big_ind = 0
small_ind = 1
else:
big_ind = 1
small_ind = 0
t = np.arange(0, 2 * math.pi + 0.1, 0.1)
# eig_val[big_ind] or eiq_val[small_ind] were occasionally negative
# numbers extremely close to 0 (~10^-20), catch these cases and set the
# respective variable to 0
try:
a = math.sqrt(eig_val[big_ind])
except ValueError:
a = 0
try:
b = math.sqrt(eig_val[small_ind])
except ValueError:
b = 0
x = [a * math.cos(it) for it in t]
y = [b * math.sin(it) for it in t]
angle = math.atan2(eig_vec[1, big_ind], eig_vec[0, big_ind])
fx = rot_mat_2d(angle) @ np.array([[x, y]])
px = np.array(fx[:, 0] + x_est[0, 0]).flatten()
py = np.array(fx[:, 1] + x_est[1, 0]).flatten()
plt.plot(px, py, "--r")
| 577 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Localization/particle_filter/particle_filter.py
|
main
|
()
| 202 | 259 |
def main():
print(__file__ + " start!!")
time = 0.0
# RF_ID positions [x, y]
rf_id = np.array([[10.0, 0.0],
[10.0, 10.0],
[0.0, 15.0],
[-5.0, 20.0]])
# State Vector [x y yaw v]'
x_est = np.zeros((4, 1))
x_true = np.zeros((4, 1))
px = np.zeros((4, NP)) # Particle store
pw = np.zeros((1, NP)) + 1.0 / NP # Particle weight
x_dr = np.zeros((4, 1)) # Dead reckoning
# history
h_x_est = x_est
h_x_true = x_true
h_x_dr = x_true
while SIM_TIME >= time:
time += DT
u = calc_input()
x_true, z, x_dr, ud = observation(x_true, x_dr, u, rf_id)
x_est, PEst, px, pw = pf_localization(px, pw, z, ud)
# store data history
h_x_est = np.hstack((h_x_est, x_est))
h_x_dr = np.hstack((h_x_dr, x_dr))
h_x_true = np.hstack((h_x_true, x_true))
if show_animation:
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
for i in range(len(z[:, 0])):
plt.plot([x_true[0, 0], z[i, 1]], [x_true[1, 0], z[i, 2]], "-k")
plt.plot(rf_id[:, 0], rf_id[:, 1], "*k")
plt.plot(px[0, :], px[1, :], ".r")
plt.plot(np.array(h_x_true[0, :]).flatten(),
np.array(h_x_true[1, :]).flatten(), "-b")
plt.plot(np.array(h_x_dr[0, :]).flatten(),
np.array(h_x_dr[1, :]).flatten(), "-k")
plt.plot(np.array(h_x_est[0, :]).flatten(),
np.array(h_x_est[1, :]).flatten(), "-r")
plot_covariance_ellipse(x_est, PEst)
plt.axis("equal")
plt.grid(True)
plt.pause(0.001)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Localization/particle_filter/particle_filter.py#L202-L259
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37
] | 58.62069 |
[
38,
40,
44,
45,
46,
47,
48,
50,
52,
54,
55,
56,
57
] | 22.413793 | false | 88.888889 | 58 | 4 | 77.586207 | 0 |
def main():
print(__file__ + " start!!")
time = 0.0
# RF_ID positions [x, y]
rf_id = np.array([[10.0, 0.0],
[10.0, 10.0],
[0.0, 15.0],
[-5.0, 20.0]])
# State Vector [x y yaw v]'
x_est = np.zeros((4, 1))
x_true = np.zeros((4, 1))
px = np.zeros((4, NP)) # Particle store
pw = np.zeros((1, NP)) + 1.0 / NP # Particle weight
x_dr = np.zeros((4, 1)) # Dead reckoning
# history
h_x_est = x_est
h_x_true = x_true
h_x_dr = x_true
while SIM_TIME >= time:
time += DT
u = calc_input()
x_true, z, x_dr, ud = observation(x_true, x_dr, u, rf_id)
x_est, PEst, px, pw = pf_localization(px, pw, z, ud)
# store data history
h_x_est = np.hstack((h_x_est, x_est))
h_x_dr = np.hstack((h_x_dr, x_dr))
h_x_true = np.hstack((h_x_true, x_true))
if show_animation:
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
for i in range(len(z[:, 0])):
plt.plot([x_true[0, 0], z[i, 1]], [x_true[1, 0], z[i, 2]], "-k")
plt.plot(rf_id[:, 0], rf_id[:, 1], "*k")
plt.plot(px[0, :], px[1, :], ".r")
plt.plot(np.array(h_x_true[0, :]).flatten(),
np.array(h_x_true[1, :]).flatten(), "-b")
plt.plot(np.array(h_x_dr[0, :]).flatten(),
np.array(h_x_dr[1, :]).flatten(), "-k")
plt.plot(np.array(h_x_est[0, :]).flatten(),
np.array(h_x_est[1, :]).flatten(), "-r")
plot_covariance_ellipse(x_est, PEst)
plt.axis("equal")
plt.grid(True)
plt.pause(0.001)
| 578 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_mpc_control.py
|
main
|
()
| 32 | 67 |
def main():
x0 = np.array([
[0.0],
[0.0],
[0.3],
[0.0]
])
x = np.copy(x0)
time = 0.0
while sim_time > time:
time += delta_t
# calc control input
opt_x, opt_delta_x, opt_theta, opt_delta_theta, opt_input = \
mpc_control(x)
# get input
u = opt_input[0]
# simulate inverted pendulum cart
x = simulation(x, u)
if show_animation:
plt.clf()
px = float(x[0])
theta = float(x[2])
plot_cart(px, theta)
plt.xlim([-5.0, 2.0])
plt.pause(0.001)
print("Finish")
print(f"x={float(x[0]):.2f} [m] , theta={math.degrees(x[2]):.2f} [deg]")
if show_animation:
plt.show()
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_mpc_control.py#L32-L67
| 2 |
[
0,
1,
7,
8,
9,
10,
11,
12,
13,
14,
15,
18,
19,
20,
21,
22,
23,
24,
31,
32,
33,
34
] | 61.111111 |
[
25,
26,
27,
28,
29,
30,
35
] | 19.444444 | false | 64.150943 | 36 | 4 | 80.555556 | 0 |
def main():
x0 = np.array([
[0.0],
[0.0],
[0.3],
[0.0]
])
x = np.copy(x0)
time = 0.0
while sim_time > time:
time += delta_t
# calc control input
opt_x, opt_delta_x, opt_theta, opt_delta_theta, opt_input = \
mpc_control(x)
# get input
u = opt_input[0]
# simulate inverted pendulum cart
x = simulation(x, u)
if show_animation:
plt.clf()
px = float(x[0])
theta = float(x[2])
plot_cart(px, theta)
plt.xlim([-5.0, 2.0])
plt.pause(0.001)
print("Finish")
print(f"x={float(x[0]):.2f} [m] , theta={math.degrees(x[2]):.2f} [deg]")
if show_animation:
plt.show()
| 579 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_mpc_control.py
|
simulation
|
(x, u)
|
return x
| 70 | 74 |
def simulation(x, u):
A, B = get_model_matrix()
x = np.dot(A, x) + np.dot(B, u)
return x
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_mpc_control.py#L70-L74
| 2 |
[
0,
1,
2,
3,
4
] | 100 |
[] | 0 | true | 64.150943 | 5 | 1 | 100 | 0 |
def simulation(x, u):
A, B = get_model_matrix()
x = np.dot(A, x) + np.dot(B, u)
return x
| 580 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_mpc_control.py
|
mpc_control
|
(x0)
|
return ox, dx, theta, d_theta, ou
| 77 | 108 |
def mpc_control(x0):
x = cvxpy.Variable((nx, T + 1))
u = cvxpy.Variable((nu, T))
A, B = get_model_matrix()
cost = 0.0
constr = []
for t in range(T):
cost += cvxpy.quad_form(x[:, t + 1], Q)
cost += cvxpy.quad_form(u[:, t], R)
constr += [x[:, t + 1] == A @ x[:, t] + B @ u[:, t]]
constr += [x[:, 0] == x0[:, 0]]
prob = cvxpy.Problem(cvxpy.Minimize(cost), constr)
start = time.time()
prob.solve(verbose=False)
elapsed_time = time.time() - start
print(f"calc time:{elapsed_time:.6f} [sec]")
if prob.status == cvxpy.OPTIMAL:
ox = get_numpy_array_from_matrix(x.value[0, :])
dx = get_numpy_array_from_matrix(x.value[1, :])
theta = get_numpy_array_from_matrix(x.value[2, :])
d_theta = get_numpy_array_from_matrix(x.value[3, :])
ou = get_numpy_array_from_matrix(u.value[0, :])
else:
ox, dx, theta, d_theta, ou = None, None, None, None, None
return ox, dx, theta, d_theta, ou
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_mpc_control.py#L77-L108
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
30,
31
] | 93.75 |
[
29
] | 3.125 | false | 64.150943 | 32 | 3 | 96.875 | 0 |
def mpc_control(x0):
x = cvxpy.Variable((nx, T + 1))
u = cvxpy.Variable((nu, T))
A, B = get_model_matrix()
cost = 0.0
constr = []
for t in range(T):
cost += cvxpy.quad_form(x[:, t + 1], Q)
cost += cvxpy.quad_form(u[:, t], R)
constr += [x[:, t + 1] == A @ x[:, t] + B @ u[:, t]]
constr += [x[:, 0] == x0[:, 0]]
prob = cvxpy.Problem(cvxpy.Minimize(cost), constr)
start = time.time()
prob.solve(verbose=False)
elapsed_time = time.time() - start
print(f"calc time:{elapsed_time:.6f} [sec]")
if prob.status == cvxpy.OPTIMAL:
ox = get_numpy_array_from_matrix(x.value[0, :])
dx = get_numpy_array_from_matrix(x.value[1, :])
theta = get_numpy_array_from_matrix(x.value[2, :])
d_theta = get_numpy_array_from_matrix(x.value[3, :])
ou = get_numpy_array_from_matrix(u.value[0, :])
else:
ox, dx, theta, d_theta, ou = None, None, None, None, None
return ox, dx, theta, d_theta, ou
| 581 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_mpc_control.py
|
get_numpy_array_from_matrix
|
(x)
|
return np.array(x).flatten()
|
get build-in list from matrix
|
get build-in list from matrix
| 111 | 115 |
def get_numpy_array_from_matrix(x):
"""
get build-in list from matrix
"""
return np.array(x).flatten()
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_mpc_control.py#L111-L115
| 2 |
[
0,
1,
2,
3,
4
] | 100 |
[] | 0 | true | 64.150943 | 5 | 1 | 100 | 1 |
def get_numpy_array_from_matrix(x):
return np.array(x).flatten()
| 582 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_mpc_control.py
|
get_model_matrix
|
()
|
return A, B
| 118 | 135 |
def get_model_matrix():
A = np.array([
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, m * g / M, 0.0],
[0.0, 0.0, 0.0, 1.0],
[0.0, 0.0, g * (M + m) / (l_bar * M), 0.0]
])
A = np.eye(nx) + delta_t * A
B = np.array([
[0.0],
[1.0 / M],
[0.0],
[1.0 / (l_bar * M)]
])
B = delta_t * B
return A, B
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_mpc_control.py#L118-L135
| 2 |
[
0,
1,
7,
8,
9,
15,
16,
17
] | 44.444444 |
[] | 0 | false | 64.150943 | 18 | 1 | 100 | 0 |
def get_model_matrix():
A = np.array([
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, m * g / M, 0.0],
[0.0, 0.0, 0.0, 1.0],
[0.0, 0.0, g * (M + m) / (l_bar * M), 0.0]
])
A = np.eye(nx) + delta_t * A
B = np.array([
[0.0],
[1.0 / M],
[0.0],
[1.0 / (l_bar * M)]
])
B = delta_t * B
return A, B
| 583 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_mpc_control.py
|
flatten
|
(a)
|
return np.array(a).flatten()
| 138 | 139 |
def flatten(a):
return np.array(a).flatten()
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_mpc_control.py#L138-L139
| 2 |
[
0
] | 50 |
[
1
] | 50 | false | 64.150943 | 2 | 1 | 50 | 0 |
def flatten(a):
return np.array(a).flatten()
| 584 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_mpc_control.py
|
plot_cart
|
(xt, theta)
| 142 | 183 |
def plot_cart(xt, theta):
cart_w = 1.0
cart_h = 0.5
radius = 0.1
cx = np.array([-cart_w / 2.0, cart_w / 2.0, cart_w /
2.0, -cart_w / 2.0, -cart_w / 2.0])
cy = np.array([0.0, 0.0, cart_h, cart_h, 0.0])
cy += radius * 2.0
cx = cx + xt
bx = np.array([0.0, l_bar * math.sin(-theta)])
bx += xt
by = np.array([cart_h, l_bar * math.cos(-theta) + cart_h])
by += radius * 2.0
angles = np.arange(0.0, math.pi * 2.0, math.radians(3.0))
ox = np.array([radius * math.cos(a) for a in angles])
oy = np.array([radius * math.sin(a) for a in angles])
rwx = np.copy(ox) + cart_w / 4.0 + xt
rwy = np.copy(oy) + radius
lwx = np.copy(ox) - cart_w / 4.0 + xt
lwy = np.copy(oy) + radius
wx = np.copy(ox) + bx[-1]
wy = np.copy(oy) + by[-1]
plt.plot(flatten(cx), flatten(cy), "-b")
plt.plot(flatten(bx), flatten(by), "-k")
plt.plot(flatten(rwx), flatten(rwy), "-k")
plt.plot(flatten(lwx), flatten(lwy), "-k")
plt.plot(flatten(wx), flatten(wy), "-k")
plt.title(f"x: {xt:.2f} , theta: {math.degrees(theta):.2f}")
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.axis("equal")
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_mpc_control.py#L142-L183
| 2 |
[
0
] | 2.380952 |
[
1,
2,
3,
5,
7,
8,
10,
12,
13,
14,
15,
17,
18,
19,
21,
22,
23,
24,
26,
27,
29,
30,
31,
32,
33,
34,
37,
41
] | 66.666667 | false | 64.150943 | 42 | 3 | 33.333333 | 0 |
def plot_cart(xt, theta):
cart_w = 1.0
cart_h = 0.5
radius = 0.1
cx = np.array([-cart_w / 2.0, cart_w / 2.0, cart_w /
2.0, -cart_w / 2.0, -cart_w / 2.0])
cy = np.array([0.0, 0.0, cart_h, cart_h, 0.0])
cy += radius * 2.0
cx = cx + xt
bx = np.array([0.0, l_bar * math.sin(-theta)])
bx += xt
by = np.array([cart_h, l_bar * math.cos(-theta) + cart_h])
by += radius * 2.0
angles = np.arange(0.0, math.pi * 2.0, math.radians(3.0))
ox = np.array([radius * math.cos(a) for a in angles])
oy = np.array([radius * math.sin(a) for a in angles])
rwx = np.copy(ox) + cart_w / 4.0 + xt
rwy = np.copy(oy) + radius
lwx = np.copy(ox) - cart_w / 4.0 + xt
lwy = np.copy(oy) + radius
wx = np.copy(ox) + bx[-1]
wy = np.copy(oy) + by[-1]
plt.plot(flatten(cx), flatten(cy), "-b")
plt.plot(flatten(bx), flatten(by), "-k")
plt.plot(flatten(rwx), flatten(rwy), "-k")
plt.plot(flatten(lwx), flatten(lwy), "-k")
plt.plot(flatten(wx), flatten(wy), "-k")
plt.title(f"x: {xt:.2f} , theta: {math.degrees(theta):.2f}")
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.axis("equal")
| 585 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_lqr_control.py
|
main
|
()
| 31 | 62 |
def main():
x0 = np.array([
[0.0],
[0.0],
[0.3],
[0.0]
])
x = np.copy(x0)
time = 0.0
while sim_time > time:
time += delta_t
# calc control input
u = lqr_control(x)
# simulate inverted pendulum cart
x = simulation(x, u)
if show_animation:
plt.clf()
px = float(x[0])
theta = float(x[2])
plot_cart(px, theta)
plt.xlim([-5.0, 2.0])
plt.pause(0.001)
print("Finish")
print(f"x={float(x[0]):.2f} [m] , theta={math.degrees(x[2]):.2f} [deg]")
if show_animation:
plt.show()
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_lqr_control.py#L31-L62
| 2 |
[
0,
1,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
27,
28,
29,
30
] | 62.5 |
[
21,
22,
23,
24,
25,
26,
31
] | 21.875 | false | 62.376238 | 32 | 4 | 78.125 | 0 |
def main():
x0 = np.array([
[0.0],
[0.0],
[0.3],
[0.0]
])
x = np.copy(x0)
time = 0.0
while sim_time > time:
time += delta_t
# calc control input
u = lqr_control(x)
# simulate inverted pendulum cart
x = simulation(x, u)
if show_animation:
plt.clf()
px = float(x[0])
theta = float(x[2])
plot_cart(px, theta)
plt.xlim([-5.0, 2.0])
plt.pause(0.001)
print("Finish")
print(f"x={float(x[0]):.2f} [m] , theta={math.degrees(x[2]):.2f} [deg]")
if show_animation:
plt.show()
| 586 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_lqr_control.py
|
simulation
|
(x, u)
|
return x
| 65 | 69 |
def simulation(x, u):
A, B = get_model_matrix()
x = A @ x + B @ u
return x
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_lqr_control.py#L65-L69
| 2 |
[
0,
1,
2,
3,
4
] | 100 |
[] | 0 | true | 62.376238 | 5 | 1 | 100 | 0 |
def simulation(x, u):
A, B = get_model_matrix()
x = A @ x + B @ u
return x
| 587 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_lqr_control.py
|
solve_DARE
|
(A, B, Q, R, maxiter=150, eps=0.01)
|
return Pn
|
Solve a discrete time_Algebraic Riccati equation (DARE)
|
Solve a discrete time_Algebraic Riccati equation (DARE)
| 72 | 85 |
def solve_DARE(A, B, Q, R, maxiter=150, eps=0.01):
"""
Solve a discrete time_Algebraic Riccati equation (DARE)
"""
P = Q
for i in range(maxiter):
Pn = A.T @ P @ A - A.T @ P @ B @ \
inv(R + B.T @ P @ B) @ B.T @ P @ A + Q
if (abs(Pn - P)).max() < eps:
break
P = Pn
return Pn
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_lqr_control.py#L72-L85
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13
] | 100 |
[] | 0 | true | 62.376238 | 14 | 3 | 100 | 1 |
def solve_DARE(A, B, Q, R, maxiter=150, eps=0.01):
P = Q
for i in range(maxiter):
Pn = A.T @ P @ A - A.T @ P @ B @ \
inv(R + B.T @ P @ B) @ B.T @ P @ A + Q
if (abs(Pn - P)).max() < eps:
break
P = Pn
return Pn
| 588 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_lqr_control.py
|
dlqr
|
(A, B, Q, R)
|
return K, P, eigVals
|
Solve the discrete time lqr controller.
x[k+1] = A x[k] + B u[k]
cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
# ref Bertsekas, p.151
|
Solve the discrete time lqr controller.
x[k+1] = A x[k] + B u[k]
cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
# ref Bertsekas, p.151
| 88 | 103 |
def dlqr(A, B, Q, R):
"""
Solve the discrete time lqr controller.
x[k+1] = A x[k] + B u[k]
cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
# ref Bertsekas, p.151
"""
# first, try to solve the ricatti equation
P = solve_DARE(A, B, Q, R)
# compute the LQR gain
K = inv(B.T @ P @ B + R) @ (B.T @ P @ A)
eigVals, eigVecs = eig(A - B @ K)
return K, P, eigVals
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_lqr_control.py#L88-L103
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15
] | 100 |
[] | 0 | true | 62.376238 | 16 | 1 | 100 | 4 |
def dlqr(A, B, Q, R):
# first, try to solve the ricatti equation
P = solve_DARE(A, B, Q, R)
# compute the LQR gain
K = inv(B.T @ P @ B + R) @ (B.T @ P @ A)
eigVals, eigVecs = eig(A - B @ K)
return K, P, eigVals
| 589 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_lqr_control.py
|
lqr_control
|
(x)
|
return u
| 106 | 113 |
def lqr_control(x):
A, B = get_model_matrix()
start = time.time()
K, _, _ = dlqr(A, B, Q, R)
u = -K @ x
elapsed_time = time.time() - start
print(f"calc time:{elapsed_time:.6f} [sec]")
return u
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_lqr_control.py#L106-L113
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7
] | 100 |
[] | 0 | true | 62.376238 | 8 | 1 | 100 | 0 |
def lqr_control(x):
A, B = get_model_matrix()
start = time.time()
K, _, _ = dlqr(A, B, Q, R)
u = -K @ x
elapsed_time = time.time() - start
print(f"calc time:{elapsed_time:.6f} [sec]")
return u
| 590 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_lqr_control.py
|
get_numpy_array_from_matrix
|
(x)
|
return np.array(x).flatten()
|
get build-in list from matrix
|
get build-in list from matrix
| 116 | 120 |
def get_numpy_array_from_matrix(x):
"""
get build-in list from matrix
"""
return np.array(x).flatten()
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_lqr_control.py#L116-L120
| 2 |
[
0,
1,
2,
3
] | 80 |
[
4
] | 20 | false | 62.376238 | 5 | 1 | 80 | 1 |
def get_numpy_array_from_matrix(x):
return np.array(x).flatten()
| 591 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_lqr_control.py
|
get_model_matrix
|
()
|
return A, B
| 123 | 140 |
def get_model_matrix():
A = np.array([
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, m * g / M, 0.0],
[0.0, 0.0, 0.0, 1.0],
[0.0, 0.0, g * (M + m) / (l_bar * M), 0.0]
])
A = np.eye(nx) + delta_t * A
B = np.array([
[0.0],
[1.0 / M],
[0.0],
[1.0 / (l_bar * M)]
])
B = delta_t * B
return A, B
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_lqr_control.py#L123-L140
| 2 |
[
0,
1,
7,
8,
9,
15,
16,
17
] | 44.444444 |
[] | 0 | false | 62.376238 | 18 | 1 | 100 | 0 |
def get_model_matrix():
A = np.array([
[0.0, 1.0, 0.0, 0.0],
[0.0, 0.0, m * g / M, 0.0],
[0.0, 0.0, 0.0, 1.0],
[0.0, 0.0, g * (M + m) / (l_bar * M), 0.0]
])
A = np.eye(nx) + delta_t * A
B = np.array([
[0.0],
[1.0 / M],
[0.0],
[1.0 / (l_bar * M)]
])
B = delta_t * B
return A, B
| 592 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_lqr_control.py
|
flatten
|
(a)
|
return np.array(a).flatten()
| 143 | 144 |
def flatten(a):
return np.array(a).flatten()
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_lqr_control.py#L143-L144
| 2 |
[
0
] | 50 |
[
1
] | 50 | false | 62.376238 | 2 | 1 | 50 | 0 |
def flatten(a):
return np.array(a).flatten()
| 593 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/inverted_pendulum/inverted_pendulum_lqr_control.py
|
plot_cart
|
(xt, theta)
| 147 | 188 |
def plot_cart(xt, theta):
cart_w = 1.0
cart_h = 0.5
radius = 0.1
cx = np.array([-cart_w / 2.0, cart_w / 2.0, cart_w /
2.0, -cart_w / 2.0, -cart_w / 2.0])
cy = np.array([0.0, 0.0, cart_h, cart_h, 0.0])
cy += radius * 2.0
cx = cx + xt
bx = np.array([0.0, l_bar * math.sin(-theta)])
bx += xt
by = np.array([cart_h, l_bar * math.cos(-theta) + cart_h])
by += radius * 2.0
angles = np.arange(0.0, math.pi * 2.0, math.radians(3.0))
ox = np.array([radius * math.cos(a) for a in angles])
oy = np.array([radius * math.sin(a) for a in angles])
rwx = np.copy(ox) + cart_w / 4.0 + xt
rwy = np.copy(oy) + radius
lwx = np.copy(ox) - cart_w / 4.0 + xt
lwy = np.copy(oy) + radius
wx = np.copy(ox) + bx[-1]
wy = np.copy(oy) + by[-1]
plt.plot(flatten(cx), flatten(cy), "-b")
plt.plot(flatten(bx), flatten(by), "-k")
plt.plot(flatten(rwx), flatten(rwy), "-k")
plt.plot(flatten(lwx), flatten(lwy), "-k")
plt.plot(flatten(wx), flatten(wy), "-k")
plt.title(f"x: {xt:.2f} , theta: {math.degrees(theta):.2f}")
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.axis("equal")
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/inverted_pendulum/inverted_pendulum_lqr_control.py#L147-L188
| 2 |
[
0
] | 2.380952 |
[
1,
2,
3,
5,
7,
8,
10,
12,
13,
14,
15,
17,
18,
19,
21,
22,
23,
24,
26,
27,
29,
30,
31,
32,
33,
34,
37,
41
] | 66.666667 | false | 62.376238 | 42 | 3 | 33.333333 | 0 |
def plot_cart(xt, theta):
cart_w = 1.0
cart_h = 0.5
radius = 0.1
cx = np.array([-cart_w / 2.0, cart_w / 2.0, cart_w /
2.0, -cart_w / 2.0, -cart_w / 2.0])
cy = np.array([0.0, 0.0, cart_h, cart_h, 0.0])
cy += radius * 2.0
cx = cx + xt
bx = np.array([0.0, l_bar * math.sin(-theta)])
bx += xt
by = np.array([cart_h, l_bar * math.cos(-theta) + cart_h])
by += radius * 2.0
angles = np.arange(0.0, math.pi * 2.0, math.radians(3.0))
ox = np.array([radius * math.cos(a) for a in angles])
oy = np.array([radius * math.sin(a) for a in angles])
rwx = np.copy(ox) + cart_w / 4.0 + xt
rwy = np.copy(oy) + radius
lwx = np.copy(ox) - cart_w / 4.0 + xt
lwy = np.copy(oy) + radius
wx = np.copy(ox) + bx[-1]
wy = np.copy(oy) + by[-1]
plt.plot(flatten(cx), flatten(cy), "-b")
plt.plot(flatten(bx), flatten(by), "-k")
plt.plot(flatten(rwx), flatten(rwy), "-k")
plt.plot(flatten(lwx), flatten(lwy), "-k")
plt.plot(flatten(wx), flatten(wy), "-k")
plt.title(f"x: {xt:.2f} , theta: {math.degrees(theta):.2f}")
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.axis("equal")
| 594 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/move_to_pose/move_to_pose.py
|
move_to_pose
|
(x_start, y_start, theta_start, x_goal, y_goal, theta_goal)
| 97 | 134 |
def move_to_pose(x_start, y_start, theta_start, x_goal, y_goal, theta_goal):
x = x_start
y = y_start
theta = theta_start
x_diff = x_goal - x
y_diff = y_goal - y
x_traj, y_traj = [], []
rho = np.hypot(x_diff, y_diff)
while rho > 0.001:
x_traj.append(x)
y_traj.append(y)
x_diff = x_goal - x
y_diff = y_goal - y
rho, v, w = controller.calc_control_command(
x_diff, y_diff, theta, theta_goal)
if abs(v) > MAX_LINEAR_SPEED:
v = np.sign(v) * MAX_LINEAR_SPEED
if abs(w) > MAX_ANGULAR_SPEED:
w = np.sign(w) * MAX_ANGULAR_SPEED
theta = theta + w * dt
x = x + v * np.cos(theta) * dt
y = y + v * np.sin(theta) * dt
if show_animation: # pragma: no cover
plt.cla()
plt.arrow(x_start, y_start, np.cos(theta_start),
np.sin(theta_start), color='r', width=0.1)
plt.arrow(x_goal, y_goal, np.cos(theta_goal),
np.sin(theta_goal), color='g', width=0.1)
plot_vehicle(x, y, theta, x_traj, y_traj)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/move_to_pose/move_to_pose.py#L97-L134
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30
] | 90.909091 |
[] | 0 | false | 96.551724 | 38 | 5 | 100 | 0 |
def move_to_pose(x_start, y_start, theta_start, x_goal, y_goal, theta_goal):
x = x_start
y = y_start
theta = theta_start
x_diff = x_goal - x
y_diff = y_goal - y
x_traj, y_traj = [], []
rho = np.hypot(x_diff, y_diff)
while rho > 0.001:
x_traj.append(x)
y_traj.append(y)
x_diff = x_goal - x
y_diff = y_goal - y
rho, v, w = controller.calc_control_command(
x_diff, y_diff, theta, theta_goal)
if abs(v) > MAX_LINEAR_SPEED:
v = np.sign(v) * MAX_LINEAR_SPEED
if abs(w) > MAX_ANGULAR_SPEED:
w = np.sign(w) * MAX_ANGULAR_SPEED
theta = theta + w * dt
x = x + v * np.cos(theta) * dt
y = y + v * np.sin(theta) * dt
if show_animation: # pragma: no cover
plt.cla()
plt.arrow(x_start, y_start, np.cos(theta_start),
np.sin(theta_start), color='r', width=0.1)
plt.arrow(x_goal, y_goal, np.cos(theta_goal),
np.sin(theta_goal), color='g', width=0.1)
plot_vehicle(x, y, theta, x_traj, y_traj)
| 603 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/move_to_pose/move_to_pose.py
|
plot_vehicle
|
(x, y, theta, x_traj, y_traj)
| 137 | 162 |
def plot_vehicle(x, y, theta, x_traj, y_traj): # pragma: no cover
# Corners of triangular vehicle when pointing to the right (0 radians)
p1_i = np.array([0.5, 0, 1]).T
p2_i = np.array([-0.5, 0.25, 1]).T
p3_i = np.array([-0.5, -0.25, 1]).T
T = transformation_matrix(x, y, theta)
p1 = np.matmul(T, p1_i)
p2 = np.matmul(T, p2_i)
p3 = np.matmul(T, p3_i)
plt.plot([p1[0], p2[0]], [p1[1], p2[1]], 'k-')
plt.plot([p2[0], p3[0]], [p2[1], p3[1]], 'k-')
plt.plot([p3[0], p1[0]], [p3[1], p1[1]], 'k-')
plt.plot(x_traj, y_traj, 'b--')
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.xlim(0, 20)
plt.ylim(0, 20)
plt.pause(dt)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/move_to_pose/move_to_pose.py#L137-L162
| 2 |
[] | 0 |
[] | 0 | false | 96.551724 | 26 | 1 | 100 | 0 |
def plot_vehicle(x, y, theta, x_traj, y_traj): # pragma: no cover
# Corners of triangular vehicle when pointing to the right (0 radians)
p1_i = np.array([0.5, 0, 1]).T
p2_i = np.array([-0.5, 0.25, 1]).T
p3_i = np.array([-0.5, -0.25, 1]).T
T = transformation_matrix(x, y, theta)
p1 = np.matmul(T, p1_i)
p2 = np.matmul(T, p2_i)
p3 = np.matmul(T, p3_i)
plt.plot([p1[0], p2[0]], [p1[1], p2[1]], 'k-')
plt.plot([p2[0], p3[0]], [p2[1], p3[1]], 'k-')
plt.plot([p3[0], p1[0]], [p3[1], p1[1]], 'k-')
plt.plot(x_traj, y_traj, 'b--')
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.xlim(0, 20)
plt.ylim(0, 20)
plt.pause(dt)
| 604 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/move_to_pose/move_to_pose.py
|
transformation_matrix
|
(x, y, theta)
|
return np.array([
[np.cos(theta), -np.sin(theta), x],
[np.sin(theta), np.cos(theta), y],
[0, 0, 1]
])
| 165 | 170 |
def transformation_matrix(x, y, theta):
return np.array([
[np.cos(theta), -np.sin(theta), x],
[np.sin(theta), np.cos(theta), y],
[0, 0, 1]
])
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/move_to_pose/move_to_pose.py#L165-L170
| 2 |
[
0
] | 16.666667 |
[
1
] | 16.666667 | false | 96.551724 | 6 | 1 | 83.333333 | 0 |
def transformation_matrix(x, y, theta):
return np.array([
[np.cos(theta), -np.sin(theta), x],
[np.sin(theta), np.cos(theta), y],
[0, 0, 1]
])
| 605 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/move_to_pose/move_to_pose.py
|
main
|
()
| 173 | 186 |
def main():
for i in range(5):
x_start = 20 * random()
y_start = 20 * random()
theta_start = 2 * np.pi * random() - np.pi
x_goal = 20 * random()
y_goal = 20 * random()
theta_goal = 2 * np.pi * random() - np.pi
print("Initial x: %.2f m\nInitial y: %.2f m\nInitial theta: %.2f rad\n" %
(x_start, y_start, theta_start))
print("Goal x: %.2f m\nGoal y: %.2f m\nGoal theta: %.2f rad\n" %
(x_goal, y_goal, theta_goal))
move_to_pose(x_start, y_start, theta_start, x_goal, y_goal, theta_goal)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/move_to_pose/move_to_pose.py#L173-L186
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
11,
13
] | 85.714286 |
[] | 0 | false | 96.551724 | 14 | 2 | 100 | 0 |
def main():
for i in range(5):
x_start = 20 * random()
y_start = 20 * random()
theta_start = 2 * np.pi * random() - np.pi
x_goal = 20 * random()
y_goal = 20 * random()
theta_goal = 2 * np.pi * random() - np.pi
print("Initial x: %.2f m\nInitial y: %.2f m\nInitial theta: %.2f rad\n" %
(x_start, y_start, theta_start))
print("Goal x: %.2f m\nGoal y: %.2f m\nGoal theta: %.2f rad\n" %
(x_goal, y_goal, theta_goal))
move_to_pose(x_start, y_start, theta_start, x_goal, y_goal, theta_goal)
| 606 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/move_to_pose/move_to_pose.py
|
PathFinderController.__init__
|
(self, Kp_rho, Kp_alpha, Kp_beta)
| 33 | 36 |
def __init__(self, Kp_rho, Kp_alpha, Kp_beta):
self.Kp_rho = Kp_rho
self.Kp_alpha = Kp_alpha
self.Kp_beta = Kp_beta
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/move_to_pose/move_to_pose.py#L33-L36
| 2 |
[
0,
1,
2,
3
] | 100 |
[] | 0 | true | 96.551724 | 4 | 1 | 100 | 0 |
def __init__(self, Kp_rho, Kp_alpha, Kp_beta):
self.Kp_rho = Kp_rho
self.Kp_alpha = Kp_alpha
self.Kp_beta = Kp_beta
| 607 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
Control/move_to_pose/move_to_pose.py
|
PathFinderController.calc_control_command
|
(self, x_diff, y_diff, theta, theta_goal)
|
return rho, v, w
|
Returns the control command for the linear and angular velocities as
well as the distance to goal
Parameters
----------
x_diff : The position of target with respect to current robot position
in x direction
y_diff : The position of target with respect to current robot position
in y direction
theta : The current heading angle of robot with respect to x axis
theta_goal: The target angle of robot with respect to x axis
Returns
-------
rho : The distance between the robot and the goal position
v : Command linear velocity
w : Command angular velocity
|
Returns the control command for the linear and angular velocities as
well as the distance to goal
| 38 | 83 |
def calc_control_command(self, x_diff, y_diff, theta, theta_goal):
"""
Returns the control command for the linear and angular velocities as
well as the distance to goal
Parameters
----------
x_diff : The position of target with respect to current robot position
in x direction
y_diff : The position of target with respect to current robot position
in y direction
theta : The current heading angle of robot with respect to x axis
theta_goal: The target angle of robot with respect to x axis
Returns
-------
rho : The distance between the robot and the goal position
v : Command linear velocity
w : Command angular velocity
"""
# Description of local variables:
# - alpha is the angle to the goal relative to the heading of the robot
# - beta is the angle between the robot's position and the goal
# position plus the goal angle
# - Kp_rho*rho and Kp_alpha*alpha drive the robot along a line towards
# the goal
# - Kp_beta*beta rotates the line so that it is parallel to the goal
# angle
#
# Note:
# we restrict alpha and beta (angle differences) to the range
# [-pi, pi] to prevent unstable behavior e.g. difference going
# from 0 rad to 2*pi rad with slight turn
rho = np.hypot(x_diff, y_diff)
alpha = (np.arctan2(y_diff, x_diff)
- theta + np.pi) % (2 * np.pi) - np.pi
beta = (theta_goal - theta - alpha + np.pi) % (2 * np.pi) - np.pi
v = self.Kp_rho * rho
w = self.Kp_alpha * alpha - controller.Kp_beta * beta
if alpha > np.pi / 2 or alpha < -np.pi / 2:
v = -v
return rho, v, w
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/Control/move_to_pose/move_to_pose.py#L38-L83
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41,
42,
43,
44,
45
] | 100 |
[] | 0 | true | 96.551724 | 46 | 3 | 100 | 17 |
def calc_control_command(self, x_diff, y_diff, theta, theta_goal):
# Description of local variables:
# - alpha is the angle to the goal relative to the heading of the robot
# - beta is the angle between the robot's position and the goal
# position plus the goal angle
# - Kp_rho*rho and Kp_alpha*alpha drive the robot along a line towards
# the goal
# - Kp_beta*beta rotates the line so that it is parallel to the goal
# angle
#
# Note:
# we restrict alpha and beta (angle differences) to the range
# [-pi, pi] to prevent unstable behavior e.g. difference going
# from 0 rad to 2*pi rad with slight turn
rho = np.hypot(x_diff, y_diff)
alpha = (np.arctan2(y_diff, x_diff)
- theta + np.pi) % (2 * np.pi) - np.pi
beta = (theta_goal - theta - alpha + np.pi) % (2 * np.pi) - np.pi
v = self.Kp_rho * rho
w = self.Kp_alpha * alpha - controller.Kp_beta * beta
if alpha > np.pi / 2 or alpha < -np.pi / 2:
v = -v
return rho, v, w
| 608 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
utils/plot.py
|
plot_arrow
|
(x, y, yaw, arrow_length=1.0,
origin_point_plot_style="xr",
head_width=0.1, fc="r", ec="k", **kwargs)
|
Plot an arrow or arrows based on 2D state (x, y, yaw)
All optional settings of matplotlib.pyplot.arrow can be used.
- matplotlib.pyplot.arrow:
https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.arrow.html
Parameters
----------
x : a float or array_like
a value or a list of arrow origin x position.
y : a float or array_like
a value or a list of arrow origin y position.
yaw : a float or array_like
a value or a list of arrow yaw angle (orientation).
arrow_length : a float (optional)
arrow length. default is 1.0
origin_point_plot_style : str (optional)
origin point plot style. If None, not plotting.
head_width : a float (optional)
arrow head width. default is 0.1
fc : string (optional)
face color
ec : string (optional)
edge color
|
Plot an arrow or arrows based on 2D state (x, y, yaw)
| 9 | 50 |
def plot_arrow(x, y, yaw, arrow_length=1.0,
origin_point_plot_style="xr",
head_width=0.1, fc="r", ec="k", **kwargs):
"""
Plot an arrow or arrows based on 2D state (x, y, yaw)
All optional settings of matplotlib.pyplot.arrow can be used.
- matplotlib.pyplot.arrow:
https://matplotlib.org/stable/api/_as_gen/matplotlib.pyplot.arrow.html
Parameters
----------
x : a float or array_like
a value or a list of arrow origin x position.
y : a float or array_like
a value or a list of arrow origin y position.
yaw : a float or array_like
a value or a list of arrow yaw angle (orientation).
arrow_length : a float (optional)
arrow length. default is 1.0
origin_point_plot_style : str (optional)
origin point plot style. If None, not plotting.
head_width : a float (optional)
arrow head width. default is 0.1
fc : string (optional)
face color
ec : string (optional)
edge color
"""
if not isinstance(x, float):
for (i_x, i_y, i_yaw) in zip(x, y, yaw):
plot_arrow(i_x, i_y, i_yaw, head_width=head_width,
fc=fc, ec=ec, **kwargs)
else:
plt.arrow(x, y,
arrow_length * math.cos(yaw),
arrow_length * math.sin(yaw),
head_width=head_width,
fc=fc, ec=ec,
**kwargs)
if origin_point_plot_style is not None:
plt.plot(x, y, origin_point_plot_style)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/utils/plot.py#L9-L50
| 2 |
[
0
] | 2.380952 |
[
29,
30,
31,
34,
40,
41
] | 14.285714 | false | 31.25 | 42 | 4 | 85.714286 | 24 |
def plot_arrow(x, y, yaw, arrow_length=1.0,
origin_point_plot_style="xr",
head_width=0.1, fc="r", ec="k", **kwargs):
if not isinstance(x, float):
for (i_x, i_y, i_yaw) in zip(x, y, yaw):
plot_arrow(i_x, i_y, i_yaw, head_width=head_width,
fc=fc, ec=ec, **kwargs)
else:
plt.arrow(x, y,
arrow_length * math.cos(yaw),
arrow_length * math.sin(yaw),
head_width=head_width,
fc=fc, ec=ec,
**kwargs)
if origin_point_plot_style is not None:
plt.plot(x, y, origin_point_plot_style)
| 609 |
|
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
utils/plot.py
|
plot_curvature
|
(x_list, y_list, heading_list, curvature,
k=0.01, c="-c", label="Curvature")
|
Plot curvature on 2D path. This plot is a line from the original path,
the lateral distance from the original path shows curvature magnitude.
Left turning shows right side plot, right turning shows left side plot.
For straight path, the curvature plot will be on the path, because
curvature is 0 on the straight path.
Parameters
----------
x_list : array_like
x position list of the path
y_list : array_like
y position list of the path
heading_list : array_like
heading list of the path
curvature : array_like
curvature list of the path
k : float
curvature scale factor to calculate distance from the original path
c : string
color of the plot
label : string
label of the plot
|
Plot curvature on 2D path. This plot is a line from the original path,
the lateral distance from the original path shows curvature magnitude.
Left turning shows right side plot, right turning shows left side plot.
For straight path, the curvature plot will be on the path, because
curvature is 0 on the straight path.
| 53 | 86 |
def plot_curvature(x_list, y_list, heading_list, curvature,
k=0.01, c="-c", label="Curvature"):
"""
Plot curvature on 2D path. This plot is a line from the original path,
the lateral distance from the original path shows curvature magnitude.
Left turning shows right side plot, right turning shows left side plot.
For straight path, the curvature plot will be on the path, because
curvature is 0 on the straight path.
Parameters
----------
x_list : array_like
x position list of the path
y_list : array_like
y position list of the path
heading_list : array_like
heading list of the path
curvature : array_like
curvature list of the path
k : float
curvature scale factor to calculate distance from the original path
c : string
color of the plot
label : string
label of the plot
"""
cx = [x + d * k * np.cos(yaw - np.pi / 2.0) for x, y, yaw, d in
zip(x_list, y_list, heading_list, curvature)]
cy = [y + d * k * np.sin(yaw - np.pi / 2.0) for x, y, yaw, d in
zip(x_list, y_list, heading_list, curvature)]
plt.plot(cx, cy, c, label=label)
for ix, iy, icx, icy in zip(x_list, y_list, cx, cy):
plt.plot([ix, icx], [iy, icy], c)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/utils/plot.py#L53-L86
| 2 |
[
0
] | 2.941176 |
[
26,
28,
31,
32,
33
] | 14.705882 | false | 31.25 | 34 | 4 | 85.294118 | 22 |
def plot_curvature(x_list, y_list, heading_list, curvature,
k=0.01, c="-c", label="Curvature"):
cx = [x + d * k * np.cos(yaw - np.pi / 2.0) for x, y, yaw, d in
zip(x_list, y_list, heading_list, curvature)]
cy = [y + d * k * np.sin(yaw - np.pi / 2.0) for x, y, yaw, d in
zip(x_list, y_list, heading_list, curvature)]
plt.plot(cx, cy, c, label=label)
for ix, iy, icx, icy in zip(x_list, y_list, cx, cy):
plt.plot([ix, icx], [iy, icy], c)
| 610 |
|
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
utils/angle.py
|
rot_mat_2d
|
(angle)
|
return Rot.from_euler('z', angle).as_matrix()[0:2, 0:2]
|
Create 2D rotation matrix from an angle
Parameters
----------
angle :
Returns
-------
A 2D rotation matrix
Examples
--------
>>> angle_mod(-4.0)
|
Create 2D rotation matrix from an angle
| 5 | 23 |
def rot_mat_2d(angle):
"""
Create 2D rotation matrix from an angle
Parameters
----------
angle :
Returns
-------
A 2D rotation matrix
Examples
--------
>>> angle_mod(-4.0)
"""
return Rot.from_euler('z', angle).as_matrix()[0:2, 0:2]
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/utils/angle.py#L5-L23
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18
] | 100 |
[] | 0 | true | 100 | 19 | 1 | 100 | 13 |
def rot_mat_2d(angle):
return Rot.from_euler('z', angle).as_matrix()[0:2, 0:2]
| 611 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
utils/angle.py
|
angle_mod
|
(x, zero_2_2pi=False, degree=False)
|
Angle modulo operation
Default angle modulo range is [-pi, pi)
Parameters
----------
x : float or array_like
A angle or an array of angles. This array is flattened for
the calculation. When an angle is provided, a float angle is returned.
zero_2_2pi : bool, optional
Change angle modulo range to [0, 2pi)
Default is False.
degree : bool, optional
If True, then the given angles are assumed to be in degrees.
Default is False.
Returns
-------
ret : float or ndarray
an angle or an array of modulated angle.
Examples
--------
>>> angle_mod(-4.0)
2.28318531
>>> angle_mod([-4.0])
np.array(2.28318531)
>>> angle_mod([-150.0, 190.0, 350], degree=True)
array([-150., -170., -10.])
>>> angle_mod(-60.0, zero_2_2pi=True, degree=True)
array([300.])
|
Angle modulo operation
Default angle modulo range is [-pi, pi)
| 26 | 83 |
def angle_mod(x, zero_2_2pi=False, degree=False):
"""
Angle modulo operation
Default angle modulo range is [-pi, pi)
Parameters
----------
x : float or array_like
A angle or an array of angles. This array is flattened for
the calculation. When an angle is provided, a float angle is returned.
zero_2_2pi : bool, optional
Change angle modulo range to [0, 2pi)
Default is False.
degree : bool, optional
If True, then the given angles are assumed to be in degrees.
Default is False.
Returns
-------
ret : float or ndarray
an angle or an array of modulated angle.
Examples
--------
>>> angle_mod(-4.0)
2.28318531
>>> angle_mod([-4.0])
np.array(2.28318531)
>>> angle_mod([-150.0, 190.0, 350], degree=True)
array([-150., -170., -10.])
>>> angle_mod(-60.0, zero_2_2pi=True, degree=True)
array([300.])
"""
if isinstance(x, float):
is_float = True
else:
is_float = False
x = np.asarray(x).flatten()
if degree:
x = np.deg2rad(x)
if zero_2_2pi:
mod_angle = x % (2 * np.pi)
else:
mod_angle = (x + np.pi) % (2 * np.pi) - np.pi
if degree:
mod_angle = np.rad2deg(mod_angle)
if is_float:
return mod_angle.item()
else:
return mod_angle
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/utils/angle.py#L26-L83
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41,
42,
43,
44,
45,
46,
47,
48,
49,
50,
51,
52,
53,
54,
55,
56,
57
] | 100 |
[] | 0 | true | 100 | 58 | 6 | 100 | 33 |
def angle_mod(x, zero_2_2pi=False, degree=False):
if isinstance(x, float):
is_float = True
else:
is_float = False
x = np.asarray(x).flatten()
if degree:
x = np.deg2rad(x)
if zero_2_2pi:
mod_angle = x % (2 * np.pi)
else:
mod_angle = (x + np.pi) % (2 * np.pi) - np.pi
if degree:
mod_angle = np.rad2deg(mod_angle)
if is_float:
return mod_angle.item()
else:
return mod_angle
| 612 |
|
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_steer_control/lqr_steer_control.py
|
update
|
(state, a, delta)
|
return state
| 42 | 54 |
def update(state, a, delta):
if delta >= max_steer:
delta = max_steer
if delta <= - max_steer:
delta = - max_steer
state.x = state.x + state.v * math.cos(state.yaw) * dt
state.y = state.y + state.v * math.sin(state.yaw) * dt
state.yaw = state.yaw + state.v / L * math.tan(delta) * dt
state.v = state.v + a * dt
return state
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_steer_control/lqr_steer_control.py#L42-L54
| 2 |
[
0,
1,
2,
4,
6,
7,
8,
9,
10,
11,
12
] | 84.615385 |
[
3,
5
] | 15.384615 | false | 89.542484 | 13 | 3 | 84.615385 | 0 |
def update(state, a, delta):
if delta >= max_steer:
delta = max_steer
if delta <= - max_steer:
delta = - max_steer
state.x = state.x + state.v * math.cos(state.yaw) * dt
state.y = state.y + state.v * math.sin(state.yaw) * dt
state.yaw = state.yaw + state.v / L * math.tan(delta) * dt
state.v = state.v + a * dt
return state
| 613 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_steer_control/lqr_steer_control.py
|
PIDControl
|
(target, current)
|
return a
| 57 | 60 |
def PIDControl(target, current):
a = Kp * (target - current)
return a
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_steer_control/lqr_steer_control.py#L57-L60
| 2 |
[
0,
1,
2,
3
] | 100 |
[] | 0 | true | 89.542484 | 4 | 1 | 100 | 0 |
def PIDControl(target, current):
a = Kp * (target - current)
return a
| 614 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_steer_control/lqr_steer_control.py
|
pi_2_pi
|
(angle)
|
return (angle + math.pi) % (2 * math.pi) - math.pi
| 63 | 64 |
def pi_2_pi(angle):
return (angle + math.pi) % (2 * math.pi) - math.pi
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_steer_control/lqr_steer_control.py#L63-L64
| 2 |
[
0,
1
] | 100 |
[] | 0 | true | 89.542484 | 2 | 1 | 100 | 0 |
def pi_2_pi(angle):
return (angle + math.pi) % (2 * math.pi) - math.pi
| 615 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_steer_control/lqr_steer_control.py
|
solve_DARE
|
(A, B, Q, R)
|
return Xn
|
solve a discrete time_Algebraic Riccati equation (DARE)
|
solve a discrete time_Algebraic Riccati equation (DARE)
| 67 | 82 |
def solve_DARE(A, B, Q, R):
"""
solve a discrete time_Algebraic Riccati equation (DARE)
"""
X = Q
maxiter = 150
eps = 0.01
for i in range(maxiter):
Xn = A.T @ X @ A - A.T @ X @ B @ \
la.inv(R + B.T @ X @ B) @ B.T @ X @ A + Q
if (abs(Xn - X)).max() < eps:
break
X = Xn
return Xn
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_steer_control/lqr_steer_control.py#L67-L82
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15
] | 100 |
[] | 0 | true | 89.542484 | 16 | 3 | 100 | 1 |
def solve_DARE(A, B, Q, R):
X = Q
maxiter = 150
eps = 0.01
for i in range(maxiter):
Xn = A.T @ X @ A - A.T @ X @ B @ \
la.inv(R + B.T @ X @ B) @ B.T @ X @ A + Q
if (abs(Xn - X)).max() < eps:
break
X = Xn
return Xn
| 616 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_steer_control/lqr_steer_control.py
|
dlqr
|
(A, B, Q, R)
|
return K, X, eigVals
|
Solve the discrete time lqr controller.
x[k+1] = A x[k] + B u[k]
cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
# ref Bertsekas, p.151
|
Solve the discrete time lqr controller.
x[k+1] = A x[k] + B u[k]
cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
# ref Bertsekas, p.151
| 85 | 100 |
def dlqr(A, B, Q, R):
"""Solve the discrete time lqr controller.
x[k+1] = A x[k] + B u[k]
cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
# ref Bertsekas, p.151
"""
# first, try to solve the ricatti equation
X = solve_DARE(A, B, Q, R)
# compute the LQR gain
K = la.inv(B.T @ X @ B + R) @ (B.T @ X @ A)
eigVals, eigVecs = la.eig(A - B @ K)
return K, X, eigVals
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_steer_control/lqr_steer_control.py#L85-L100
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15
] | 100 |
[] | 0 | true | 89.542484 | 16 | 1 | 100 | 4 |
def dlqr(A, B, Q, R):
# first, try to solve the ricatti equation
X = solve_DARE(A, B, Q, R)
# compute the LQR gain
K = la.inv(B.T @ X @ B + R) @ (B.T @ X @ A)
eigVals, eigVecs = la.eig(A - B @ K)
return K, X, eigVals
| 617 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_steer_control/lqr_steer_control.py
|
lqr_steering_control
|
(state, cx, cy, cyaw, ck, pe, pth_e)
|
return delta, ind, e, th_e
| 103 | 135 |
def lqr_steering_control(state, cx, cy, cyaw, ck, pe, pth_e):
ind, e = calc_nearest_index(state, cx, cy, cyaw)
k = ck[ind]
v = state.v
th_e = pi_2_pi(state.yaw - cyaw[ind])
A = np.zeros((4, 4))
A[0, 0] = 1.0
A[0, 1] = dt
A[1, 2] = v
A[2, 2] = 1.0
A[2, 3] = dt
# print(A)
B = np.zeros((4, 1))
B[3, 0] = v / L
K, _, _ = dlqr(A, B, Q, R)
x = np.zeros((4, 1))
x[0, 0] = e
x[1, 0] = (e - pe) / dt
x[2, 0] = th_e
x[3, 0] = (th_e - pth_e) / dt
ff = math.atan2(L * k, 1)
fb = pi_2_pi((-K @ x)[0, 0])
delta = ff + fb
return delta, ind, e, th_e
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_steer_control/lqr_steer_control.py#L103-L135
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32
] | 100 |
[] | 0 | true | 89.542484 | 33 | 1 | 100 | 0 |
def lqr_steering_control(state, cx, cy, cyaw, ck, pe, pth_e):
ind, e = calc_nearest_index(state, cx, cy, cyaw)
k = ck[ind]
v = state.v
th_e = pi_2_pi(state.yaw - cyaw[ind])
A = np.zeros((4, 4))
A[0, 0] = 1.0
A[0, 1] = dt
A[1, 2] = v
A[2, 2] = 1.0
A[2, 3] = dt
# print(A)
B = np.zeros((4, 1))
B[3, 0] = v / L
K, _, _ = dlqr(A, B, Q, R)
x = np.zeros((4, 1))
x[0, 0] = e
x[1, 0] = (e - pe) / dt
x[2, 0] = th_e
x[3, 0] = (th_e - pth_e) / dt
ff = math.atan2(L * k, 1)
fb = pi_2_pi((-K @ x)[0, 0])
delta = ff + fb
return delta, ind, e, th_e
| 618 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_steer_control/lqr_steer_control.py
|
calc_nearest_index
|
(state, cx, cy, cyaw)
|
return ind, mind
| 138 | 157 |
def calc_nearest_index(state, cx, cy, cyaw):
dx = [state.x - icx for icx in cx]
dy = [state.y - icy for icy in cy]
d = [idx ** 2 + idy ** 2 for (idx, idy) in zip(dx, dy)]
mind = min(d)
ind = d.index(mind)
mind = math.sqrt(mind)
dxl = cx[ind] - state.x
dyl = cy[ind] - state.y
angle = pi_2_pi(cyaw[ind] - math.atan2(dyl, dxl))
if angle < 0:
mind *= -1
return ind, mind
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_steer_control/lqr_steer_control.py#L138-L157
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19
] | 100 |
[] | 0 | true | 89.542484 | 20 | 5 | 100 | 0 |
def calc_nearest_index(state, cx, cy, cyaw):
dx = [state.x - icx for icx in cx]
dy = [state.y - icy for icy in cy]
d = [idx ** 2 + idy ** 2 for (idx, idy) in zip(dx, dy)]
mind = min(d)
ind = d.index(mind)
mind = math.sqrt(mind)
dxl = cx[ind] - state.x
dyl = cy[ind] - state.y
angle = pi_2_pi(cyaw[ind] - math.atan2(dyl, dxl))
if angle < 0:
mind *= -1
return ind, mind
| 619 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_steer_control/lqr_steer_control.py
|
closed_loop_prediction
|
(cx, cy, cyaw, ck, speed_profile, goal)
|
return t, x, y, yaw, v
| 160 | 215 |
def closed_loop_prediction(cx, cy, cyaw, ck, speed_profile, goal):
T = 500.0 # max simulation time
goal_dis = 0.3
stop_speed = 0.05
state = State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
time = 0.0
x = [state.x]
y = [state.y]
yaw = [state.yaw]
v = [state.v]
t = [0.0]
e, e_th = 0.0, 0.0
while T >= time:
dl, target_ind, e, e_th = lqr_steering_control(
state, cx, cy, cyaw, ck, e, e_th)
ai = PIDControl(speed_profile[target_ind], state.v)
state = update(state, ai, dl)
if abs(state.v) <= stop_speed:
target_ind += 1
time = time + dt
# check goal
dx = state.x - goal[0]
dy = state.y - goal[1]
if math.hypot(dx, dy) <= goal_dis:
print("Goal")
break
x.append(state.x)
y.append(state.y)
yaw.append(state.yaw)
v.append(state.v)
t.append(time)
if target_ind % 1 == 0 and show_animation:
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect('key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.plot(cx, cy, "-r", label="course")
plt.plot(x, y, "ob", label="trajectory")
plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
plt.axis("equal")
plt.grid(True)
plt.title("speed[km/h]:" + str(round(state.v * 3.6, 2))
+ ",target index:" + str(target_ind))
plt.pause(0.0001)
return t, x, y, yaw, v
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_steer_control/lqr_steer_control.py#L160-L215
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
19,
20,
21,
22,
23,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41,
54,
55
] | 75 |
[
24,
42,
44,
46,
47,
48,
49,
50,
51,
53
] | 17.857143 | false | 89.542484 | 56 | 6 | 82.142857 | 0 |
def closed_loop_prediction(cx, cy, cyaw, ck, speed_profile, goal):
T = 500.0 # max simulation time
goal_dis = 0.3
stop_speed = 0.05
state = State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
time = 0.0
x = [state.x]
y = [state.y]
yaw = [state.yaw]
v = [state.v]
t = [0.0]
e, e_th = 0.0, 0.0
while T >= time:
dl, target_ind, e, e_th = lqr_steering_control(
state, cx, cy, cyaw, ck, e, e_th)
ai = PIDControl(speed_profile[target_ind], state.v)
state = update(state, ai, dl)
if abs(state.v) <= stop_speed:
target_ind += 1
time = time + dt
# check goal
dx = state.x - goal[0]
dy = state.y - goal[1]
if math.hypot(dx, dy) <= goal_dis:
print("Goal")
break
x.append(state.x)
y.append(state.y)
yaw.append(state.yaw)
v.append(state.v)
t.append(time)
if target_ind % 1 == 0 and show_animation:
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect('key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.plot(cx, cy, "-r", label="course")
plt.plot(x, y, "ob", label="trajectory")
plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
plt.axis("equal")
plt.grid(True)
plt.title("speed[km/h]:" + str(round(state.v * 3.6, 2))
+ ",target index:" + str(target_ind))
plt.pause(0.0001)
return t, x, y, yaw, v
| 620 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_steer_control/lqr_steer_control.py
|
calc_speed_profile
|
(cx, cy, cyaw, target_speed)
|
return speed_profile
| 218 | 241 |
def calc_speed_profile(cx, cy, cyaw, target_speed):
speed_profile = [target_speed] * len(cx)
direction = 1.0
# Set stop point
for i in range(len(cx) - 1):
dyaw = abs(cyaw[i + 1] - cyaw[i])
switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
if switch:
direction *= -1
if direction != 1.0:
speed_profile[i] = - target_speed
else:
speed_profile[i] = target_speed
if switch:
speed_profile[i] = 0.0
speed_profile[-1] = 0.0
return speed_profile
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_steer_control/lqr_steer_control.py#L218-L241
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
12,
13,
16,
17,
18,
20,
21,
22,
23
] | 83.333333 |
[
11,
14,
19
] | 12.5 | false | 89.542484 | 24 | 5 | 87.5 | 0 |
def calc_speed_profile(cx, cy, cyaw, target_speed):
speed_profile = [target_speed] * len(cx)
direction = 1.0
# Set stop point
for i in range(len(cx) - 1):
dyaw = abs(cyaw[i + 1] - cyaw[i])
switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
if switch:
direction *= -1
if direction != 1.0:
speed_profile[i] = - target_speed
else:
speed_profile[i] = target_speed
if switch:
speed_profile[i] = 0.0
speed_profile[-1] = 0.0
return speed_profile
| 621 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_steer_control/lqr_steer_control.py
|
main
|
()
| 244 | 284 |
def main():
print("LQR steering control tracking start!!")
ax = [0.0, 6.0, 12.5, 10.0, 7.5, 3.0, -1.0]
ay = [0.0, -3.0, -5.0, 6.5, 3.0, 5.0, -2.0]
goal = [ax[-1], ay[-1]]
cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
ax, ay, ds=0.1)
target_speed = 10.0 / 3.6 # simulation parameter km/h -> m/s
sp = calc_speed_profile(cx, cy, cyaw, target_speed)
t, x, y, yaw, v = closed_loop_prediction(cx, cy, cyaw, ck, sp, goal)
if show_animation: # pragma: no cover
plt.close()
plt.subplots(1)
plt.plot(ax, ay, "xb", label="input")
plt.plot(cx, cy, "-r", label="spline")
plt.plot(x, y, "-g", label="tracking")
plt.grid(True)
plt.axis("equal")
plt.xlabel("x[m]")
plt.ylabel("y[m]")
plt.legend()
plt.subplots(1)
plt.plot(s, [np.rad2deg(iyaw) for iyaw in cyaw], "-r", label="yaw")
plt.grid(True)
plt.legend()
plt.xlabel("line length[m]")
plt.ylabel("yaw angle[deg]")
plt.subplots(1)
plt.plot(s, ck, "-r", label="curvature")
plt.grid(True)
plt.legend()
plt.xlabel("line length[m]")
plt.ylabel("curvature [1/m]")
plt.show()
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_steer_control/lqr_steer_control.py#L244-L284
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
8,
9,
10,
11,
12,
13
] | 76.470588 |
[] | 0 | false | 89.542484 | 41 | 3 | 100 | 0 |
def main():
print("LQR steering control tracking start!!")
ax = [0.0, 6.0, 12.5, 10.0, 7.5, 3.0, -1.0]
ay = [0.0, -3.0, -5.0, 6.5, 3.0, 5.0, -2.0]
goal = [ax[-1], ay[-1]]
cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
ax, ay, ds=0.1)
target_speed = 10.0 / 3.6 # simulation parameter km/h -> m/s
sp = calc_speed_profile(cx, cy, cyaw, target_speed)
t, x, y, yaw, v = closed_loop_prediction(cx, cy, cyaw, ck, sp, goal)
if show_animation: # pragma: no cover
plt.close()
plt.subplots(1)
plt.plot(ax, ay, "xb", label="input")
plt.plot(cx, cy, "-r", label="spline")
plt.plot(x, y, "-g", label="tracking")
plt.grid(True)
plt.axis("equal")
plt.xlabel("x[m]")
plt.ylabel("y[m]")
plt.legend()
plt.subplots(1)
plt.plot(s, [np.rad2deg(iyaw) for iyaw in cyaw], "-r", label="yaw")
plt.grid(True)
plt.legend()
plt.xlabel("line length[m]")
plt.ylabel("yaw angle[deg]")
plt.subplots(1)
plt.plot(s, ck, "-r", label="curvature")
plt.grid(True)
plt.legend()
plt.xlabel("line length[m]")
plt.ylabel("curvature [1/m]")
plt.show()
| 622 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_steer_control/lqr_steer_control.py
|
State.__init__
|
(self, x=0.0, y=0.0, yaw=0.0, v=0.0)
| 35 | 39 |
def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
self.x = x
self.y = y
self.yaw = yaw
self.v = v
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_steer_control/lqr_steer_control.py#L35-L39
| 2 |
[
0,
1,
2,
3,
4
] | 100 |
[] | 0 | true | 89.542484 | 5 | 1 | 100 | 0 |
def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
self.x = x
self.y = y
self.yaw = yaw
self.v = v
| 623 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
differential_model
|
(v, yaw, u_1, u_2)
|
return dx, dy, d_yaw, dv
| 27 | 34 |
def differential_model(v, yaw, u_1, u_2):
dx = cos(yaw) * v
dy = sin(yaw) * v
dv = u_1
# tangent is not good for nonlinear optimization
d_yaw = v / WB * sin(u_2)
return dx, dy, d_yaw, dv
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L27-L34
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7
] | 100 |
[] | 0 | true | 90.987124 | 8 | 1 | 100 | 0 |
def differential_model(v, yaw, u_1, u_2):
dx = cos(yaw) * v
dy = sin(yaw) * v
dv = u_1
# tangent is not good for nonlinear optimization
d_yaw = v / WB * sin(u_2)
return dx, dy, d_yaw, dv
| 624 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
plot_figures
|
(plant_system, controller, iteration_num,
dt)
| 390 | 479 |
def plot_figures(plant_system, controller, iteration_num,
dt): # pragma: no cover
# figure
# time history
fig_p = plt.figure()
fig_u = plt.figure()
fig_f = plt.figure()
# trajectory
fig_t = plt.figure()
fig_trajectory = fig_t.add_subplot(111)
fig_trajectory.set_aspect('equal')
x_1_fig = fig_p.add_subplot(411)
x_2_fig = fig_p.add_subplot(412)
x_3_fig = fig_p.add_subplot(413)
x_4_fig = fig_p.add_subplot(414)
u_1_fig = fig_u.add_subplot(411)
u_2_fig = fig_u.add_subplot(412)
dummy_1_fig = fig_u.add_subplot(413)
dummy_2_fig = fig_u.add_subplot(414)
raw_1_fig = fig_f.add_subplot(311)
raw_2_fig = fig_f.add_subplot(312)
f_fig = fig_f.add_subplot(313)
x_1_fig.plot(np.arange(iteration_num) * dt, plant_system.history_x)
x_1_fig.set_xlabel("time [s]")
x_1_fig.set_ylabel("x")
x_2_fig.plot(np.arange(iteration_num) * dt, plant_system.history_y)
x_2_fig.set_xlabel("time [s]")
x_2_fig.set_ylabel("y")
x_3_fig.plot(np.arange(iteration_num) * dt, plant_system.history_yaw)
x_3_fig.set_xlabel("time [s]")
x_3_fig.set_ylabel("yaw")
x_4_fig.plot(np.arange(iteration_num) * dt, plant_system.history_v)
x_4_fig.set_xlabel("time [s]")
x_4_fig.set_ylabel("v")
u_1_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_u_1)
u_1_fig.set_xlabel("time [s]")
u_1_fig.set_ylabel("u_a")
u_2_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_u_2)
u_2_fig.set_xlabel("time [s]")
u_2_fig.set_ylabel("u_omega")
dummy_1_fig.plot(np.arange(iteration_num - 1) *
dt, controller.history_dummy_u_1)
dummy_1_fig.set_xlabel("time [s]")
dummy_1_fig.set_ylabel("dummy u_1")
dummy_2_fig.plot(np.arange(iteration_num - 1) *
dt, controller.history_dummy_u_2)
dummy_2_fig.set_xlabel("time [s]")
dummy_2_fig.set_ylabel("dummy u_2")
raw_1_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_raw_1)
raw_1_fig.set_xlabel("time [s]")
raw_1_fig.set_ylabel("raw_1")
raw_2_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_raw_2)
raw_2_fig.set_xlabel("time [s]")
raw_2_fig.set_ylabel("raw_2")
f_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_f)
f_fig.set_xlabel("time [s]")
f_fig.set_ylabel("optimal error")
fig_trajectory.plot(plant_system.history_x,
plant_system.history_y, "-r")
fig_trajectory.set_xlabel("x [m]")
fig_trajectory.set_ylabel("y [m]")
fig_trajectory.axis("equal")
# start state
plot_car(plant_system.history_x[0],
plant_system.history_y[0],
plant_system.history_yaw[0],
controller.history_u_2[0],
)
# goal state
plot_car(0.0, 0.0, 0.0, 0.0)
plt.show()
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L390-L479
| 2 |
[] | 0 |
[] | 0 | false | 90.987124 | 90 | 1 | 100 | 0 |
def plot_figures(plant_system, controller, iteration_num,
dt): # pragma: no cover
# figure
# time history
fig_p = plt.figure()
fig_u = plt.figure()
fig_f = plt.figure()
# trajectory
fig_t = plt.figure()
fig_trajectory = fig_t.add_subplot(111)
fig_trajectory.set_aspect('equal')
x_1_fig = fig_p.add_subplot(411)
x_2_fig = fig_p.add_subplot(412)
x_3_fig = fig_p.add_subplot(413)
x_4_fig = fig_p.add_subplot(414)
u_1_fig = fig_u.add_subplot(411)
u_2_fig = fig_u.add_subplot(412)
dummy_1_fig = fig_u.add_subplot(413)
dummy_2_fig = fig_u.add_subplot(414)
raw_1_fig = fig_f.add_subplot(311)
raw_2_fig = fig_f.add_subplot(312)
f_fig = fig_f.add_subplot(313)
x_1_fig.plot(np.arange(iteration_num) * dt, plant_system.history_x)
x_1_fig.set_xlabel("time [s]")
x_1_fig.set_ylabel("x")
x_2_fig.plot(np.arange(iteration_num) * dt, plant_system.history_y)
x_2_fig.set_xlabel("time [s]")
x_2_fig.set_ylabel("y")
x_3_fig.plot(np.arange(iteration_num) * dt, plant_system.history_yaw)
x_3_fig.set_xlabel("time [s]")
x_3_fig.set_ylabel("yaw")
x_4_fig.plot(np.arange(iteration_num) * dt, plant_system.history_v)
x_4_fig.set_xlabel("time [s]")
x_4_fig.set_ylabel("v")
u_1_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_u_1)
u_1_fig.set_xlabel("time [s]")
u_1_fig.set_ylabel("u_a")
u_2_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_u_2)
u_2_fig.set_xlabel("time [s]")
u_2_fig.set_ylabel("u_omega")
dummy_1_fig.plot(np.arange(iteration_num - 1) *
dt, controller.history_dummy_u_1)
dummy_1_fig.set_xlabel("time [s]")
dummy_1_fig.set_ylabel("dummy u_1")
dummy_2_fig.plot(np.arange(iteration_num - 1) *
dt, controller.history_dummy_u_2)
dummy_2_fig.set_xlabel("time [s]")
dummy_2_fig.set_ylabel("dummy u_2")
raw_1_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_raw_1)
raw_1_fig.set_xlabel("time [s]")
raw_1_fig.set_ylabel("raw_1")
raw_2_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_raw_2)
raw_2_fig.set_xlabel("time [s]")
raw_2_fig.set_ylabel("raw_2")
f_fig.plot(np.arange(iteration_num - 1) * dt, controller.history_f)
f_fig.set_xlabel("time [s]")
f_fig.set_ylabel("optimal error")
fig_trajectory.plot(plant_system.history_x,
plant_system.history_y, "-r")
fig_trajectory.set_xlabel("x [m]")
fig_trajectory.set_ylabel("y [m]")
fig_trajectory.axis("equal")
# start state
plot_car(plant_system.history_x[0],
plant_system.history_y[0],
plant_system.history_yaw[0],
controller.history_u_2[0],
)
# goal state
plot_car(0.0, 0.0, 0.0, 0.0)
plt.show()
| 625 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
plot_car
|
(x, y, yaw, steer=0.0, truck_color="-k")
| 482 | 547 |
def plot_car(x, y, yaw, steer=0.0, truck_color="-k"): # pragma: no cover
# Vehicle parameters
LENGTH = 0.4 # [m]
WIDTH = 0.2 # [m]
BACK_TO_WHEEL = 0.1 # [m]
WHEEL_LEN = 0.03 # [m]
WHEEL_WIDTH = 0.02 # [m]
TREAD = 0.07 # [m]
outline = np.array(
[[-BACK_TO_WHEEL, (LENGTH - BACK_TO_WHEEL), (LENGTH - BACK_TO_WHEEL),
-BACK_TO_WHEEL, -BACK_TO_WHEEL],
[WIDTH / 2, WIDTH / 2, - WIDTH / 2, -WIDTH / 2, WIDTH / 2]])
fr_wheel = np.array(
[[WHEEL_LEN, -WHEEL_LEN, -WHEEL_LEN, WHEEL_LEN, WHEEL_LEN],
[-WHEEL_WIDTH - TREAD, -WHEEL_WIDTH - TREAD, WHEEL_WIDTH -
TREAD, WHEEL_WIDTH - TREAD, -WHEEL_WIDTH - TREAD]])
rr_wheel = np.copy(fr_wheel)
fl_wheel = np.copy(fr_wheel)
fl_wheel[1, :] *= -1
rl_wheel = np.copy(rr_wheel)
rl_wheel[1, :] *= -1
Rot1 = np.array([[cos(yaw), sin(yaw)],
[-sin(yaw), cos(yaw)]])
Rot2 = np.array([[cos(steer), sin(steer)],
[-sin(steer), cos(steer)]])
fr_wheel = (fr_wheel.T.dot(Rot2)).T
fl_wheel = (fl_wheel.T.dot(Rot2)).T
fr_wheel[0, :] += WB
fl_wheel[0, :] += WB
fr_wheel = (fr_wheel.T.dot(Rot1)).T
fl_wheel = (fl_wheel.T.dot(Rot1)).T
outline = (outline.T.dot(Rot1)).T
rr_wheel = (rr_wheel.T.dot(Rot1)).T
rl_wheel = (rl_wheel.T.dot(Rot1)).T
outline[0, :] += x
outline[1, :] += y
fr_wheel[0, :] += x
fr_wheel[1, :] += y
rr_wheel[0, :] += x
rr_wheel[1, :] += y
fl_wheel[0, :] += x
fl_wheel[1, :] += y
rl_wheel[0, :] += x
rl_wheel[1, :] += y
plt.plot(np.array(outline[0, :]).flatten(),
np.array(outline[1, :]).flatten(), truck_color)
plt.plot(np.array(fr_wheel[0, :]).flatten(),
np.array(fr_wheel[1, :]).flatten(), truck_color)
plt.plot(np.array(rr_wheel[0, :]).flatten(),
np.array(rr_wheel[1, :]).flatten(), truck_color)
plt.plot(np.array(fl_wheel[0, :]).flatten(),
np.array(fl_wheel[1, :]).flatten(), truck_color)
plt.plot(np.array(rl_wheel[0, :]).flatten(),
np.array(rl_wheel[1, :]).flatten(), truck_color)
plt.plot(x, y, "*")
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L482-L547
| 2 |
[] | 0 |
[] | 0 | false | 90.987124 | 66 | 1 | 100 | 0 |
def plot_car(x, y, yaw, steer=0.0, truck_color="-k"): # pragma: no cover
# Vehicle parameters
LENGTH = 0.4 # [m]
WIDTH = 0.2 # [m]
BACK_TO_WHEEL = 0.1 # [m]
WHEEL_LEN = 0.03 # [m]
WHEEL_WIDTH = 0.02 # [m]
TREAD = 0.07 # [m]
outline = np.array(
[[-BACK_TO_WHEEL, (LENGTH - BACK_TO_WHEEL), (LENGTH - BACK_TO_WHEEL),
-BACK_TO_WHEEL, -BACK_TO_WHEEL],
[WIDTH / 2, WIDTH / 2, - WIDTH / 2, -WIDTH / 2, WIDTH / 2]])
fr_wheel = np.array(
[[WHEEL_LEN, -WHEEL_LEN, -WHEEL_LEN, WHEEL_LEN, WHEEL_LEN],
[-WHEEL_WIDTH - TREAD, -WHEEL_WIDTH - TREAD, WHEEL_WIDTH -
TREAD, WHEEL_WIDTH - TREAD, -WHEEL_WIDTH - TREAD]])
rr_wheel = np.copy(fr_wheel)
fl_wheel = np.copy(fr_wheel)
fl_wheel[1, :] *= -1
rl_wheel = np.copy(rr_wheel)
rl_wheel[1, :] *= -1
Rot1 = np.array([[cos(yaw), sin(yaw)],
[-sin(yaw), cos(yaw)]])
Rot2 = np.array([[cos(steer), sin(steer)],
[-sin(steer), cos(steer)]])
fr_wheel = (fr_wheel.T.dot(Rot2)).T
fl_wheel = (fl_wheel.T.dot(Rot2)).T
fr_wheel[0, :] += WB
fl_wheel[0, :] += WB
fr_wheel = (fr_wheel.T.dot(Rot1)).T
fl_wheel = (fl_wheel.T.dot(Rot1)).T
outline = (outline.T.dot(Rot1)).T
rr_wheel = (rr_wheel.T.dot(Rot1)).T
rl_wheel = (rl_wheel.T.dot(Rot1)).T
outline[0, :] += x
outline[1, :] += y
fr_wheel[0, :] += x
fr_wheel[1, :] += y
rr_wheel[0, :] += x
rr_wheel[1, :] += y
fl_wheel[0, :] += x
fl_wheel[1, :] += y
rl_wheel[0, :] += x
rl_wheel[1, :] += y
plt.plot(np.array(outline[0, :]).flatten(),
np.array(outline[1, :]).flatten(), truck_color)
plt.plot(np.array(fr_wheel[0, :]).flatten(),
np.array(fr_wheel[1, :]).flatten(), truck_color)
plt.plot(np.array(rr_wheel[0, :]).flatten(),
np.array(rr_wheel[1, :]).flatten(), truck_color)
plt.plot(np.array(fl_wheel[0, :]).flatten(),
np.array(fl_wheel[1, :]).flatten(), truck_color)
plt.plot(np.array(rl_wheel[0, :]).flatten(),
np.array(rl_wheel[1, :]).flatten(), truck_color)
plt.plot(x, y, "*")
| 626 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
animation
|
(plant, controller, dt)
| 550 | 580 |
def animation(plant, controller, dt):
skip = 2 # skip index for animation
for t in range(1, len(controller.history_u_1), skip):
x = plant.history_x[t]
y = plant.history_y[t]
yaw = plant.history_yaw[t]
v = plant.history_v[t]
accel = controller.history_u_1[t]
time = t * dt
if abs(v) <= 0.01:
steer = 0.0
else:
steer = atan2(controller.history_u_2[t] * WB / v, 1.0)
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.plot(plant.history_x, plant.history_y, "-r", label="trajectory")
plot_car(x, y, yaw, steer=steer)
plt.axis("equal")
plt.grid(True)
plt.title("Time[s]:" + str(round(time, 2)) +
", accel[m/s]:" + str(round(accel, 2)) +
", speed[km/h]:" + str(round(v * 3.6, 2)))
plt.pause(0.0001)
plt.close("all")
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L550-L580
| 2 |
[
0
] | 3.225806 |
[
1,
3,
4,
5,
6,
7,
8,
9,
11,
12,
14,
16,
18,
21,
22,
23,
24,
25,
28,
30
] | 64.516129 | false | 90.987124 | 31 | 3 | 35.483871 | 0 |
def animation(plant, controller, dt):
skip = 2 # skip index for animation
for t in range(1, len(controller.history_u_1), skip):
x = plant.history_x[t]
y = plant.history_y[t]
yaw = plant.history_yaw[t]
v = plant.history_v[t]
accel = controller.history_u_1[t]
time = t * dt
if abs(v) <= 0.01:
steer = 0.0
else:
steer = atan2(controller.history_u_2[t] * WB / v, 1.0)
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.plot(plant.history_x, plant.history_y, "-r", label="trajectory")
plot_car(x, y, yaw, steer=steer)
plt.axis("equal")
plt.grid(True)
plt.title("Time[s]:" + str(round(time, 2)) +
", accel[m/s]:" + str(round(accel, 2)) +
", speed[km/h]:" + str(round(v * 3.6, 2)))
plt.pause(0.0001)
plt.close("all")
| 627 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
main
|
()
| 583 | 612 |
def main():
# simulation time
dt = 0.1
iteration_time = 150.0 # [s]
init_x = -4.5
init_y = -2.5
init_yaw = radians(45.0)
init_v = -1.0
# plant
plant_system = TwoWheeledSystem(
init_x, init_y, init_yaw, init_v)
# controller
controller = NMPCControllerCGMRES()
iteration_num = int(iteration_time / dt)
for i in range(1, iteration_num):
time = float(i) * dt
# make input
u_1s, u_2s = controller.calc_input(
plant_system.x, plant_system.y, plant_system.yaw, plant_system.v,
time)
# update state
plant_system.update_state(u_1s[0], u_2s[0])
if show_animation: # pragma: no cover
animation(plant_system, controller, dt)
plot_figures(plant_system, controller, iteration_num, dt)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L583-L612
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
14,
15,
16,
17,
18,
19,
20,
21,
24,
25,
26
] | 85.185185 |
[] | 0 | false | 90.987124 | 30 | 3 | 100 | 0 |
def main():
# simulation time
dt = 0.1
iteration_time = 150.0 # [s]
init_x = -4.5
init_y = -2.5
init_yaw = radians(45.0)
init_v = -1.0
# plant
plant_system = TwoWheeledSystem(
init_x, init_y, init_yaw, init_v)
# controller
controller = NMPCControllerCGMRES()
iteration_num = int(iteration_time / dt)
for i in range(1, iteration_num):
time = float(i) * dt
# make input
u_1s, u_2s = controller.calc_input(
plant_system.x, plant_system.y, plant_system.yaw, plant_system.v,
time)
# update state
plant_system.update_state(u_1s[0], u_2s[0])
if show_animation: # pragma: no cover
animation(plant_system, controller, dt)
plot_figures(plant_system, controller, iteration_num, dt)
| 628 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
TwoWheeledSystem.__init__
|
(self, init_x, init_y, init_yaw, init_v)
| 39 | 47 |
def __init__(self, init_x, init_y, init_yaw, init_v):
self.x = init_x
self.y = init_y
self.yaw = init_yaw
self.v = init_v
self.history_x = [init_x]
self.history_y = [init_y]
self.history_yaw = [init_yaw]
self.history_v = [init_v]
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L39-L47
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8
] | 100 |
[] | 0 | true | 90.987124 | 9 | 1 | 100 | 0 |
def __init__(self, init_x, init_y, init_yaw, init_v):
self.x = init_x
self.y = init_y
self.yaw = init_yaw
self.v = init_v
self.history_x = [init_x]
self.history_y = [init_y]
self.history_yaw = [init_yaw]
self.history_v = [init_v]
| 629 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
TwoWheeledSystem.update_state
|
(self, u_1, u_2, dt=0.01)
| 49 | 61 |
def update_state(self, u_1, u_2, dt=0.01):
dx, dy, d_yaw, dv = differential_model(self.v, self.yaw, u_1, u_2)
self.x += dt * dx
self.y += dt * dy
self.yaw += dt * d_yaw
self.v += dt * dv
# save
self.history_x.append(self.x)
self.history_y.append(self.y)
self.history_yaw.append(self.yaw)
self.history_v.append(self.v)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L49-L61
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12
] | 100 |
[] | 0 | true | 90.987124 | 13 | 1 | 100 | 0 |
def update_state(self, u_1, u_2, dt=0.01):
dx, dy, d_yaw, dv = differential_model(self.v, self.yaw, u_1, u_2)
self.x += dt * dx
self.y += dt * dy
self.yaw += dt * d_yaw
self.v += dt * dv
# save
self.history_x.append(self.x)
self.history_y.append(self.y)
self.history_yaw.append(self.yaw)
self.history_v.append(self.v)
| 630 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
NMPCSimulatorSystem.calc_predict_and_adjoint_state
|
(self, x, y, yaw, v, u_1s, u_2s, N, dt)
|
return x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s
| 66 | 74 |
def calc_predict_and_adjoint_state(self, x, y, yaw, v, u_1s, u_2s, N, dt):
# by using state equation
x_s, y_s, yaw_s, v_s = self._calc_predict_states(
x, y, yaw, v, u_1s, u_2s, N, dt)
# by using adjoint equation
lam_1s, lam_2s, lam_3s, lam_4s = self._calc_adjoint_states(
x_s, y_s, yaw_s, v_s, u_2s, N, dt)
return x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L66-L74
| 2 |
[
0,
1,
2,
4,
5,
7,
8
] | 77.777778 |
[] | 0 | false | 90.987124 | 9 | 1 | 100 | 0 |
def calc_predict_and_adjoint_state(self, x, y, yaw, v, u_1s, u_2s, N, dt):
# by using state equation
x_s, y_s, yaw_s, v_s = self._calc_predict_states(
x, y, yaw, v, u_1s, u_2s, N, dt)
# by using adjoint equation
lam_1s, lam_2s, lam_3s, lam_4s = self._calc_adjoint_states(
x_s, y_s, yaw_s, v_s, u_2s, N, dt)
return x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s
| 631 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
NMPCSimulatorSystem._calc_predict_states
|
(self, x, y, yaw, v, u_1s, u_2s, N, dt)
|
return x_s, y_s, yaw_s, v_s
| 76 | 90 |
def _calc_predict_states(self, x, y, yaw, v, u_1s, u_2s, N, dt):
x_s = [x]
y_s = [y]
yaw_s = [yaw]
v_s = [v]
for i in range(N):
temp_x_1, temp_x_2, temp_x_3, temp_x_4 = self._predict_state_with_oylar(
x_s[i], y_s[i], yaw_s[i], v_s[i], u_1s[i], u_2s[i], dt)
x_s.append(temp_x_1)
y_s.append(temp_x_2)
yaw_s.append(temp_x_3)
v_s.append(temp_x_4)
return x_s, y_s, yaw_s, v_s
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L76-L90
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
9,
10,
11,
12,
13,
14
] | 93.333333 |
[] | 0 | false | 90.987124 | 15 | 2 | 100 | 0 |
def _calc_predict_states(self, x, y, yaw, v, u_1s, u_2s, N, dt):
x_s = [x]
y_s = [y]
yaw_s = [yaw]
v_s = [v]
for i in range(N):
temp_x_1, temp_x_2, temp_x_3, temp_x_4 = self._predict_state_with_oylar(
x_s[i], y_s[i], yaw_s[i], v_s[i], u_1s[i], u_2s[i], dt)
x_s.append(temp_x_1)
y_s.append(temp_x_2)
yaw_s.append(temp_x_3)
v_s.append(temp_x_4)
return x_s, y_s, yaw_s, v_s
| 632 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
NMPCSimulatorSystem._calc_adjoint_states
|
(self, x_s, y_s, yaw_s, v_s, u_2s, N, dt)
|
return lam_1s, lam_2s, lam_3s, lam_4s
| 92 | 108 |
def _calc_adjoint_states(self, x_s, y_s, yaw_s, v_s, u_2s, N, dt):
lam_1s = [x_s[-1]]
lam_2s = [y_s[-1]]
lam_3s = [yaw_s[-1]]
lam_4s = [v_s[-1]]
# backward adjoint state calc
for i in range(N - 1, 0, -1):
temp_lam_1, temp_lam_2, temp_lam_3, temp_lam_4 = self._adjoint_state_with_oylar(
yaw_s[i], v_s[i], lam_1s[0], lam_2s[0], lam_3s[0], lam_4s[0],
u_2s[i], dt)
lam_1s.insert(0, temp_lam_1)
lam_2s.insert(0, temp_lam_2)
lam_3s.insert(0, temp_lam_3)
lam_4s.insert(0, temp_lam_4)
return lam_1s, lam_2s, lam_3s, lam_4s
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L92-L108
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
11,
12,
13,
14,
15,
16
] | 88.235294 |
[] | 0 | false | 90.987124 | 17 | 2 | 100 | 0 |
def _calc_adjoint_states(self, x_s, y_s, yaw_s, v_s, u_2s, N, dt):
lam_1s = [x_s[-1]]
lam_2s = [y_s[-1]]
lam_3s = [yaw_s[-1]]
lam_4s = [v_s[-1]]
# backward adjoint state calc
for i in range(N - 1, 0, -1):
temp_lam_1, temp_lam_2, temp_lam_3, temp_lam_4 = self._adjoint_state_with_oylar(
yaw_s[i], v_s[i], lam_1s[0], lam_2s[0], lam_3s[0], lam_4s[0],
u_2s[i], dt)
lam_1s.insert(0, temp_lam_1)
lam_2s.insert(0, temp_lam_2)
lam_3s.insert(0, temp_lam_3)
lam_4s.insert(0, temp_lam_4)
return lam_1s, lam_2s, lam_3s, lam_4s
| 633 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
NMPCSimulatorSystem._predict_state_with_oylar
|
(x, y, yaw, v, u_1, u_2, dt)
|
return next_x_1, next_x_2, next_x_3, next_x_4
| 111 | 121 |
def _predict_state_with_oylar(x, y, yaw, v, u_1, u_2, dt):
dx, dy, dyaw, dv = differential_model(
v, yaw, u_1, u_2)
next_x_1 = x + dt * dx
next_x_2 = y + dt * dy
next_x_3 = yaw + dt * dyaw
next_x_4 = v + dt * dv
return next_x_1, next_x_2, next_x_3, next_x_4
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L111-L121
| 2 |
[
0,
1,
2,
4,
5,
6,
7,
8,
9,
10
] | 90.909091 |
[] | 0 | false | 90.987124 | 11 | 1 | 100 | 0 |
def _predict_state_with_oylar(x, y, yaw, v, u_1, u_2, dt):
dx, dy, dyaw, dv = differential_model(
v, yaw, u_1, u_2)
next_x_1 = x + dt * dx
next_x_2 = y + dt * dy
next_x_3 = yaw + dt * dyaw
next_x_4 = v + dt * dv
return next_x_1, next_x_2, next_x_3, next_x_4
| 634 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
NMPCSimulatorSystem._adjoint_state_with_oylar
|
(yaw, v, lam_1, lam_2, lam_3, lam_4, u_2, dt)
|
return pre_lam_1, pre_lam_2, pre_lam_3, pre_lam_4
| 124 | 134 |
def _adjoint_state_with_oylar(yaw, v, lam_1, lam_2, lam_3, lam_4, u_2, dt):
# ∂H/∂x
pre_lam_1 = lam_1 + dt * 0.0
pre_lam_2 = lam_2 + dt * 0.0
tmp1 = - lam_1 * sin(yaw) * v + lam_2 * cos(yaw) * v
pre_lam_3 = lam_3 + dt * tmp1
tmp2 = lam_1 * cos(yaw) + lam_2 * sin(yaw) + lam_3 * sin(u_2) / WB
pre_lam_4 = lam_4 + dt * tmp2
return pre_lam_1, pre_lam_2, pre_lam_3, pre_lam_4
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L124-L134
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10
] | 100 |
[] | 0 | true | 90.987124 | 11 | 1 | 100 | 0 |
def _adjoint_state_with_oylar(yaw, v, lam_1, lam_2, lam_3, lam_4, u_2, dt):
# ∂H/∂x
pre_lam_1 = lam_1 + dt * 0.0
pre_lam_2 = lam_2 + dt * 0.0
tmp1 = - lam_1 * sin(yaw) * v + lam_2 * cos(yaw) * v
pre_lam_3 = lam_3 + dt * tmp1
tmp2 = lam_1 * cos(yaw) + lam_2 * sin(yaw) + lam_3 * sin(u_2) / WB
pre_lam_4 = lam_4 + dt * tmp2
return pre_lam_1, pre_lam_2, pre_lam_3, pre_lam_4
| 635 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
NMPCControllerCGMRES.__init__
|
(self)
| 186 | 214 |
def __init__(self):
# parameters
self.zeta = 100. # stability gain
self.ht = 0.01 # difference approximation tick
self.tf = 3.0 # final time
self.alpha = 0.5 # time gain
self.N = 10 # division number
self.threshold = 0.001
self.input_num = 6 # input number of dummy, constraints
self.max_iteration = self.input_num * self.N
# simulator
self.simulator = NMPCSimulatorSystem()
# initial input, initialize as 1.0
self.u_1s = np.ones(self.N)
self.u_2s = np.ones(self.N)
self.dummy_u_1s = np.ones(self.N)
self.dummy_u_2s = np.ones(self.N)
self.raw_1s = np.zeros(self.N)
self.raw_2s = np.zeros(self.N)
self.history_u_1 = []
self.history_u_2 = []
self.history_dummy_u_1 = []
self.history_dummy_u_2 = []
self.history_raw_1 = []
self.history_raw_2 = []
self.history_f = []
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L186-L214
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28
] | 100 |
[] | 0 | true | 90.987124 | 29 | 1 | 100 | 0 |
def __init__(self):
# parameters
self.zeta = 100. # stability gain
self.ht = 0.01 # difference approximation tick
self.tf = 3.0 # final time
self.alpha = 0.5 # time gain
self.N = 10 # division number
self.threshold = 0.001
self.input_num = 6 # input number of dummy, constraints
self.max_iteration = self.input_num * self.N
# simulator
self.simulator = NMPCSimulatorSystem()
# initial input, initialize as 1.0
self.u_1s = np.ones(self.N)
self.u_2s = np.ones(self.N)
self.dummy_u_1s = np.ones(self.N)
self.dummy_u_2s = np.ones(self.N)
self.raw_1s = np.zeros(self.N)
self.raw_2s = np.zeros(self.N)
self.history_u_1 = []
self.history_u_2 = []
self.history_dummy_u_1 = []
self.history_dummy_u_2 = []
self.history_raw_1 = []
self.history_raw_2 = []
self.history_f = []
| 636 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
NMPCControllerCGMRES.calc_input
|
(self, x, y, yaw, v, time)
|
return self.u_1s, self.u_2s
| 216 | 368 |
def calc_input(self, x, y, yaw, v, time):
# calculating sampling time
dt = self.tf * (1. - np.exp(-self.alpha * time)) / float(self.N)
# x_dot
x_1_dot, x_2_dot, x_3_dot, x_4_dot = differential_model(
v, yaw, self.u_1s[0], self.u_2s[0])
dx_1 = x_1_dot * self.ht
dx_2 = x_2_dot * self.ht
dx_3 = x_3_dot * self.ht
dx_4 = x_4_dot * self.ht
x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
x + dx_1, y + dx_2, yaw + dx_3, v + dx_4, self.u_1s, self.u_2s,
self.N, dt)
# Fxt:F(U,x+hx˙,t+h)
Fxt = self._calc_f(v_s, lam_3s, lam_4s,
self.u_1s, self.u_2s, self.dummy_u_1s,
self.dummy_u_2s,
self.raw_1s, self.raw_2s, self.N)
# F:F(U,x,t)
x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
x, y, yaw, v, self.u_1s, self.u_2s, self.N, dt)
F = self._calc_f(v_s, lam_3s, lam_4s,
self.u_1s, self.u_2s, self.dummy_u_1s, self.dummy_u_2s,
self.raw_1s, self.raw_2s, self.N)
right = -self.zeta * F - ((Fxt - F) / self.ht)
du_1 = self.u_1s * self.ht
du_2 = self.u_2s * self.ht
ddummy_u_1 = self.dummy_u_1s * self.ht
ddummy_u_2 = self.dummy_u_2s * self.ht
draw_1 = self.raw_1s * self.ht
draw_2 = self.raw_2s * self.ht
x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
x + dx_1, y + dx_2, yaw + dx_3, v + dx_4, self.u_1s + du_1,
self.u_2s + du_2, self.N, dt)
# Fuxt:F(U+hdU(0),x+hx˙,t+h)
Fuxt = self._calc_f(v_s, lam_3s, lam_4s,
self.u_1s + du_1, self.u_2s + du_2,
self.dummy_u_1s + ddummy_u_1,
self.dummy_u_2s + ddummy_u_2,
self.raw_1s + draw_1, self.raw_2s + draw_2, self.N)
left = ((Fuxt - Fxt) / self.ht)
# calculating cgmres
r0 = right - left
r0_norm = np.linalg.norm(r0)
vs = np.zeros((self.max_iteration, self.max_iteration + 1))
vs[:, 0] = r0 / r0_norm
hs = np.zeros((self.max_iteration + 1, self.max_iteration + 1))
# in this case the state is 3(u and dummy_u)
e = np.zeros((self.max_iteration + 1, 1))
e[0] = 1.0
ys_pre = None
du_1_new, du_2_new, draw_1_new, draw_2_new = None, None, None, None
ddummy_u_1_new, ddummy_u_2_new = None, None
for i in range(self.max_iteration):
du_1 = vs[::self.input_num, i] * self.ht
du_2 = vs[1::self.input_num, i] * self.ht
ddummy_u_1 = vs[2::self.input_num, i] * self.ht
ddummy_u_2 = vs[3::self.input_num, i] * self.ht
draw_1 = vs[4::self.input_num, i] * self.ht
draw_2 = vs[5::self.input_num, i] * self.ht
x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
x + dx_1, y + dx_2, yaw + dx_3, v + dx_4, self.u_1s + du_1,
self.u_2s + du_2, self.N, dt)
Fuxt = self._calc_f(v_s, lam_3s, lam_4s,
self.u_1s + du_1, self.u_2s + du_2,
self.dummy_u_1s + ddummy_u_1,
self.dummy_u_2s + ddummy_u_2,
self.raw_1s + draw_1, self.raw_2s + draw_2,
self.N)
Av = ((Fuxt - Fxt) / self.ht)
sum_Av = np.zeros(self.max_iteration)
# Gram–Schmidt orthonormalization
for j in range(i + 1):
hs[j, i] = np.dot(Av, vs[:, j])
sum_Av = sum_Av + hs[j, i] * vs[:, j]
v_est = Av - sum_Av
hs[i + 1, i] = np.linalg.norm(v_est)
vs[:, i + 1] = v_est / hs[i + 1, i]
inv_hs = np.linalg.pinv(hs[:i + 1, :i])
ys = np.dot(inv_hs, r0_norm * e[:i + 1])
judge_value = r0_norm * e[:i + 1] - np.dot(hs[:i + 1, :i], ys[:i])
flag1 = np.linalg.norm(judge_value) < self.threshold
flag2 = i == self.max_iteration - 1
if flag1 or flag2:
update_val = np.dot(vs[:, :i - 1], ys_pre[:i - 1]).flatten()
du_1_new = du_1 + update_val[::self.input_num]
du_2_new = du_2 + update_val[1::self.input_num]
ddummy_u_1_new = ddummy_u_1 + update_val[2::self.input_num]
ddummy_u_2_new = ddummy_u_2 + update_val[3::self.input_num]
draw_1_new = draw_1 + update_val[4::self.input_num]
draw_2_new = draw_2 + update_val[5::self.input_num]
break
ys_pre = ys
# update input
self.u_1s += du_1_new * self.ht
self.u_2s += du_2_new * self.ht
self.dummy_u_1s += ddummy_u_1_new * self.ht
self.dummy_u_2s += ddummy_u_2_new * self.ht
self.raw_1s += draw_1_new * self.ht
self.raw_2s += draw_2_new * self.ht
x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
x, y, yaw, v, self.u_1s, self.u_2s, self.N, dt)
F = self._calc_f(v_s, lam_3s, lam_4s,
self.u_1s, self.u_2s, self.dummy_u_1s, self.dummy_u_2s,
self.raw_1s, self.raw_2s, self.N)
print("norm(F) = {0}".format(np.linalg.norm(F)))
# for save
self.history_f.append(np.linalg.norm(F))
self.history_u_1.append(self.u_1s[0])
self.history_u_2.append(self.u_2s[0])
self.history_dummy_u_1.append(self.dummy_u_1s[0])
self.history_dummy_u_2.append(self.dummy_u_2s[0])
self.history_raw_1.append(self.raw_1s[0])
self.history_raw_2.append(self.raw_2s[0])
return self.u_1s, self.u_2s
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L216-L368
| 2 |
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] | 81.699346 |
[] | 0 | false | 90.987124 | 153 | 5 | 100 | 0 |
def calc_input(self, x, y, yaw, v, time):
# calculating sampling time
dt = self.tf * (1. - np.exp(-self.alpha * time)) / float(self.N)
# x_dot
x_1_dot, x_2_dot, x_3_dot, x_4_dot = differential_model(
v, yaw, self.u_1s[0], self.u_2s[0])
dx_1 = x_1_dot * self.ht
dx_2 = x_2_dot * self.ht
dx_3 = x_3_dot * self.ht
dx_4 = x_4_dot * self.ht
x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
x + dx_1, y + dx_2, yaw + dx_3, v + dx_4, self.u_1s, self.u_2s,
self.N, dt)
# Fxt:F(U,x+hx˙,t+h)
Fxt = self._calc_f(v_s, lam_3s, lam_4s,
self.u_1s, self.u_2s, self.dummy_u_1s,
self.dummy_u_2s,
self.raw_1s, self.raw_2s, self.N)
# F:F(U,x,t)
x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
x, y, yaw, v, self.u_1s, self.u_2s, self.N, dt)
F = self._calc_f(v_s, lam_3s, lam_4s,
self.u_1s, self.u_2s, self.dummy_u_1s, self.dummy_u_2s,
self.raw_1s, self.raw_2s, self.N)
right = -self.zeta * F - ((Fxt - F) / self.ht)
du_1 = self.u_1s * self.ht
du_2 = self.u_2s * self.ht
ddummy_u_1 = self.dummy_u_1s * self.ht
ddummy_u_2 = self.dummy_u_2s * self.ht
draw_1 = self.raw_1s * self.ht
draw_2 = self.raw_2s * self.ht
x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
x + dx_1, y + dx_2, yaw + dx_3, v + dx_4, self.u_1s + du_1,
self.u_2s + du_2, self.N, dt)
# Fuxt:F(U+hdU(0),x+hx˙,t+h)
Fuxt = self._calc_f(v_s, lam_3s, lam_4s,
self.u_1s + du_1, self.u_2s + du_2,
self.dummy_u_1s + ddummy_u_1,
self.dummy_u_2s + ddummy_u_2,
self.raw_1s + draw_1, self.raw_2s + draw_2, self.N)
left = ((Fuxt - Fxt) / self.ht)
# calculating cgmres
r0 = right - left
r0_norm = np.linalg.norm(r0)
vs = np.zeros((self.max_iteration, self.max_iteration + 1))
vs[:, 0] = r0 / r0_norm
hs = np.zeros((self.max_iteration + 1, self.max_iteration + 1))
# in this case the state is 3(u and dummy_u)
e = np.zeros((self.max_iteration + 1, 1))
e[0] = 1.0
ys_pre = None
du_1_new, du_2_new, draw_1_new, draw_2_new = None, None, None, None
ddummy_u_1_new, ddummy_u_2_new = None, None
for i in range(self.max_iteration):
du_1 = vs[::self.input_num, i] * self.ht
du_2 = vs[1::self.input_num, i] * self.ht
ddummy_u_1 = vs[2::self.input_num, i] * self.ht
ddummy_u_2 = vs[3::self.input_num, i] * self.ht
draw_1 = vs[4::self.input_num, i] * self.ht
draw_2 = vs[5::self.input_num, i] * self.ht
x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
x + dx_1, y + dx_2, yaw + dx_3, v + dx_4, self.u_1s + du_1,
self.u_2s + du_2, self.N, dt)
Fuxt = self._calc_f(v_s, lam_3s, lam_4s,
self.u_1s + du_1, self.u_2s + du_2,
self.dummy_u_1s + ddummy_u_1,
self.dummy_u_2s + ddummy_u_2,
self.raw_1s + draw_1, self.raw_2s + draw_2,
self.N)
Av = ((Fuxt - Fxt) / self.ht)
sum_Av = np.zeros(self.max_iteration)
# Gram–Schmidt orthonormalization
for j in range(i + 1):
hs[j, i] = np.dot(Av, vs[:, j])
sum_Av = sum_Av + hs[j, i] * vs[:, j]
v_est = Av - sum_Av
hs[i + 1, i] = np.linalg.norm(v_est)
vs[:, i + 1] = v_est / hs[i + 1, i]
inv_hs = np.linalg.pinv(hs[:i + 1, :i])
ys = np.dot(inv_hs, r0_norm * e[:i + 1])
judge_value = r0_norm * e[:i + 1] - np.dot(hs[:i + 1, :i], ys[:i])
flag1 = np.linalg.norm(judge_value) < self.threshold
flag2 = i == self.max_iteration - 1
if flag1 or flag2:
update_val = np.dot(vs[:, :i - 1], ys_pre[:i - 1]).flatten()
du_1_new = du_1 + update_val[::self.input_num]
du_2_new = du_2 + update_val[1::self.input_num]
ddummy_u_1_new = ddummy_u_1 + update_val[2::self.input_num]
ddummy_u_2_new = ddummy_u_2 + update_val[3::self.input_num]
draw_1_new = draw_1 + update_val[4::self.input_num]
draw_2_new = draw_2 + update_val[5::self.input_num]
break
ys_pre = ys
# update input
self.u_1s += du_1_new * self.ht
self.u_2s += du_2_new * self.ht
self.dummy_u_1s += ddummy_u_1_new * self.ht
self.dummy_u_2s += ddummy_u_2_new * self.ht
self.raw_1s += draw_1_new * self.ht
self.raw_2s += draw_2_new * self.ht
x_s, y_s, yaw_s, v_s, lam_1s, lam_2s, lam_3s, lam_4s = self.simulator.calc_predict_and_adjoint_state(
x, y, yaw, v, self.u_1s, self.u_2s, self.N, dt)
F = self._calc_f(v_s, lam_3s, lam_4s,
self.u_1s, self.u_2s, self.dummy_u_1s, self.dummy_u_2s,
self.raw_1s, self.raw_2s, self.N)
print("norm(F) = {0}".format(np.linalg.norm(F)))
# for save
self.history_f.append(np.linalg.norm(F))
self.history_u_1.append(self.u_1s[0])
self.history_u_2.append(self.u_2s[0])
self.history_dummy_u_1.append(self.dummy_u_1s[0])
self.history_dummy_u_2.append(self.dummy_u_2s[0])
self.history_raw_1.append(self.raw_1s[0])
self.history_raw_2.append(self.raw_2s[0])
return self.u_1s, self.u_2s
| 637 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/cgmres_nmpc/cgmres_nmpc.py
|
NMPCControllerCGMRES._calc_f
|
(v_s, lam_3s, lam_4s, u_1s, u_2s, dummy_u_1s, dummy_u_2s,
raw_1s, raw_2s, N)
|
return np.array(F)
| 371 | 387 |
def _calc_f(v_s, lam_3s, lam_4s, u_1s, u_2s, dummy_u_1s, dummy_u_2s,
raw_1s, raw_2s, N):
F = []
for i in range(N):
# ∂H/∂u(xi, ui, λi)
F.append(u_1s[i] + lam_4s[i] + 2.0 * raw_1s[i] * u_1s[i])
F.append(u_2s[i] + lam_3s[i] * v_s[i] /
WB * cos(u_2s[i]) ** 2 + 2.0 * raw_2s[i] * u_2s[i])
F.append(-PHI_V + 2.0 * raw_1s[i] * dummy_u_1s[i])
F.append(-PHI_OMEGA + 2.0 * raw_2s[i] * dummy_u_2s[i])
# C(xi, ui, λi)
F.append(u_1s[i] ** 2 + dummy_u_1s[i] ** 2 - U_A_MAX ** 2)
F.append(u_2s[i] ** 2 + dummy_u_2s[i] ** 2 - U_OMEGA_MAX ** 2)
return np.array(F)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/cgmres_nmpc/cgmres_nmpc.py#L371-L387
| 2 |
[
0,
2,
3,
4,
5,
6,
7,
9,
10,
11,
12,
13,
14,
15,
16
] | 88.235294 |
[] | 0 | false | 90.987124 | 17 | 2 | 100 | 0 |
def _calc_f(v_s, lam_3s, lam_4s, u_1s, u_2s, dummy_u_1s, dummy_u_2s,
raw_1s, raw_2s, N):
F = []
for i in range(N):
# ∂H/∂u(xi, ui, λi)
F.append(u_1s[i] + lam_4s[i] + 2.0 * raw_1s[i] * u_1s[i])
F.append(u_2s[i] + lam_3s[i] * v_s[i] /
WB * cos(u_2s[i]) ** 2 + 2.0 * raw_2s[i] * u_2s[i])
F.append(-PHI_V + 2.0 * raw_1s[i] * dummy_u_1s[i])
F.append(-PHI_OMEGA + 2.0 * raw_2s[i] * dummy_u_2s[i])
# C(xi, ui, λi)
F.append(u_1s[i] ** 2 + dummy_u_1s[i] ** 2 - U_A_MAX ** 2)
F.append(u_2s[i] ** 2 + dummy_u_2s[i] ** 2 - U_OMEGA_MAX ** 2)
return np.array(F)
| 638 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
|
update
|
(state, a, delta)
|
return state
| 39 | 51 |
def update(state, a, delta):
if delta >= max_steer:
delta = max_steer
if delta <= - max_steer:
delta = - max_steer
state.x = state.x + state.v * math.cos(state.yaw) * dt
state.y = state.y + state.v * math.sin(state.yaw) * dt
state.yaw = state.yaw + state.v / L * math.tan(delta) * dt
state.v = state.v + a * dt
return state
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py#L39-L51
| 2 |
[
0,
1,
2,
4,
6,
7,
8,
9,
10,
11,
12
] | 84.615385 |
[
3,
5
] | 15.384615 | false | 90.506329 | 13 | 3 | 84.615385 | 0 |
def update(state, a, delta):
if delta >= max_steer:
delta = max_steer
if delta <= - max_steer:
delta = - max_steer
state.x = state.x + state.v * math.cos(state.yaw) * dt
state.y = state.y + state.v * math.sin(state.yaw) * dt
state.yaw = state.yaw + state.v / L * math.tan(delta) * dt
state.v = state.v + a * dt
return state
| 639 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
|
pi_2_pi
|
(angle)
|
return (angle + math.pi) % (2 * math.pi) - math.pi
| 54 | 55 |
def pi_2_pi(angle):
return (angle + math.pi) % (2 * math.pi) - math.pi
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py#L54-L55
| 2 |
[
0,
1
] | 100 |
[] | 0 | true | 90.506329 | 2 | 1 | 100 | 0 |
def pi_2_pi(angle):
return (angle + math.pi) % (2 * math.pi) - math.pi
| 640 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
|
solve_dare
|
(A, B, Q, R)
|
return x_next
|
solve a discrete time_Algebraic Riccati equation (DARE)
|
solve a discrete time_Algebraic Riccati equation (DARE)
| 58 | 74 |
def solve_dare(A, B, Q, R):
"""
solve a discrete time_Algebraic Riccati equation (DARE)
"""
x = Q
x_next = Q
max_iter = 150
eps = 0.01
for i in range(max_iter):
x_next = A.T @ x @ A - A.T @ x @ B @ \
la.inv(R + B.T @ x @ B) @ B.T @ x @ A + Q
if (abs(x_next - x)).max() < eps:
break
x = x_next
return x_next
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py#L58-L74
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16
] | 100 |
[] | 0 | true | 90.506329 | 17 | 3 | 100 | 1 |
def solve_dare(A, B, Q, R):
x = Q
x_next = Q
max_iter = 150
eps = 0.01
for i in range(max_iter):
x_next = A.T @ x @ A - A.T @ x @ B @ \
la.inv(R + B.T @ x @ B) @ B.T @ x @ A + Q
if (abs(x_next - x)).max() < eps:
break
x = x_next
return x_next
| 641 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
|
dlqr
|
(A, B, Q, R)
|
return K, X, eig_result[0]
|
Solve the discrete time lqr controller.
x[k+1] = A x[k] + B u[k]
cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
# ref Bertsekas, p.151
|
Solve the discrete time lqr controller.
x[k+1] = A x[k] + B u[k]
cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
# ref Bertsekas, p.151
| 77 | 92 |
def dlqr(A, B, Q, R):
"""Solve the discrete time lqr controller.
x[k+1] = A x[k] + B u[k]
cost = sum x[k].T*Q*x[k] + u[k].T*R*u[k]
# ref Bertsekas, p.151
"""
# first, try to solve the ricatti equation
X = solve_dare(A, B, Q, R)
# compute the LQR gain
K = la.inv(B.T @ X @ B + R) @ (B.T @ X @ A)
eig_result = la.eig(A - B @ K)
return K, X, eig_result[0]
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py#L77-L92
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15
] | 100 |
[] | 0 | true | 90.506329 | 16 | 1 | 100 | 4 |
def dlqr(A, B, Q, R):
# first, try to solve the ricatti equation
X = solve_dare(A, B, Q, R)
# compute the LQR gain
K = la.inv(B.T @ X @ B + R) @ (B.T @ X @ A)
eig_result = la.eig(A - B @ K)
return K, X, eig_result[0]
| 642 |
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
|
lqr_speed_steering_control
|
(state, cx, cy, cyaw, ck, pe, pth_e, sp, Q, R)
|
return delta, ind, e, th_e, accel
| 95 | 156 |
def lqr_speed_steering_control(state, cx, cy, cyaw, ck, pe, pth_e, sp, Q, R):
ind, e = calc_nearest_index(state, cx, cy, cyaw)
tv = sp[ind]
k = ck[ind]
v = state.v
th_e = pi_2_pi(state.yaw - cyaw[ind])
# A = [1.0, dt, 0.0, 0.0, 0.0
# 0.0, 0.0, v, 0.0, 0.0]
# 0.0, 0.0, 1.0, dt, 0.0]
# 0.0, 0.0, 0.0, 0.0, 0.0]
# 0.0, 0.0, 0.0, 0.0, 1.0]
A = np.zeros((5, 5))
A[0, 0] = 1.0
A[0, 1] = dt
A[1, 2] = v
A[2, 2] = 1.0
A[2, 3] = dt
A[4, 4] = 1.0
# B = [0.0, 0.0
# 0.0, 0.0
# 0.0, 0.0
# v/L, 0.0
# 0.0, dt]
B = np.zeros((5, 2))
B[3, 0] = v / L
B[4, 1] = dt
K, _, _ = dlqr(A, B, Q, R)
# state vector
# x = [e, dot_e, th_e, dot_th_e, delta_v]
# e: lateral distance to the path
# dot_e: derivative of e
# th_e: angle difference to the path
# dot_th_e: derivative of th_e
# delta_v: difference between current speed and target speed
x = np.zeros((5, 1))
x[0, 0] = e
x[1, 0] = (e - pe) / dt
x[2, 0] = th_e
x[3, 0] = (th_e - pth_e) / dt
x[4, 0] = v - tv
# input vector
# u = [delta, accel]
# delta: steering angle
# accel: acceleration
ustar = -K @ x
# calc steering input
ff = math.atan2(L * k, 1) # feedforward steering angle
fb = pi_2_pi(ustar[0, 0]) # feedback steering angle
delta = ff + fb
# calc accel input
accel = ustar[1, 0]
return delta, ind, e, th_e, accel
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py#L95-L156
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
41,
42,
43,
44,
45,
46,
47,
48,
49,
50,
51,
52,
53,
54,
55,
56,
57,
58,
59,
60,
61
] | 100 |
[] | 0 | true | 90.506329 | 62 | 1 | 100 | 0 |
def lqr_speed_steering_control(state, cx, cy, cyaw, ck, pe, pth_e, sp, Q, R):
ind, e = calc_nearest_index(state, cx, cy, cyaw)
tv = sp[ind]
k = ck[ind]
v = state.v
th_e = pi_2_pi(state.yaw - cyaw[ind])
# A = [1.0, dt, 0.0, 0.0, 0.0
# 0.0, 0.0, v, 0.0, 0.0]
# 0.0, 0.0, 1.0, dt, 0.0]
# 0.0, 0.0, 0.0, 0.0, 0.0]
# 0.0, 0.0, 0.0, 0.0, 1.0]
A = np.zeros((5, 5))
A[0, 0] = 1.0
A[0, 1] = dt
A[1, 2] = v
A[2, 2] = 1.0
A[2, 3] = dt
A[4, 4] = 1.0
# B = [0.0, 0.0
# 0.0, 0.0
# 0.0, 0.0
# v/L, 0.0
# 0.0, dt]
B = np.zeros((5, 2))
B[3, 0] = v / L
B[4, 1] = dt
K, _, _ = dlqr(A, B, Q, R)
# state vector
# x = [e, dot_e, th_e, dot_th_e, delta_v]
# e: lateral distance to the path
# dot_e: derivative of e
# th_e: angle difference to the path
# dot_th_e: derivative of th_e
# delta_v: difference between current speed and target speed
x = np.zeros((5, 1))
x[0, 0] = e
x[1, 0] = (e - pe) / dt
x[2, 0] = th_e
x[3, 0] = (th_e - pth_e) / dt
x[4, 0] = v - tv
# input vector
# u = [delta, accel]
# delta: steering angle
# accel: acceleration
ustar = -K @ x
# calc steering input
ff = math.atan2(L * k, 1) # feedforward steering angle
fb = pi_2_pi(ustar[0, 0]) # feedback steering angle
delta = ff + fb
# calc accel input
accel = ustar[1, 0]
return delta, ind, e, th_e, accel
| 643 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
|
calc_nearest_index
|
(state, cx, cy, cyaw)
|
return ind, mind
| 159 | 178 |
def calc_nearest_index(state, cx, cy, cyaw):
dx = [state.x - icx for icx in cx]
dy = [state.y - icy for icy in cy]
d = [idx ** 2 + idy ** 2 for (idx, idy) in zip(dx, dy)]
mind = min(d)
ind = d.index(mind)
mind = math.sqrt(mind)
dxl = cx[ind] - state.x
dyl = cy[ind] - state.y
angle = pi_2_pi(cyaw[ind] - math.atan2(dyl, dxl))
if angle < 0:
mind *= -1
return ind, mind
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py#L159-L178
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19
] | 100 |
[] | 0 | true | 90.506329 | 20 | 5 | 100 | 0 |
def calc_nearest_index(state, cx, cy, cyaw):
dx = [state.x - icx for icx in cx]
dy = [state.y - icy for icy in cy]
d = [idx ** 2 + idy ** 2 for (idx, idy) in zip(dx, dy)]
mind = min(d)
ind = d.index(mind)
mind = math.sqrt(mind)
dxl = cx[ind] - state.x
dyl = cy[ind] - state.y
angle = pi_2_pi(cyaw[ind] - math.atan2(dyl, dxl))
if angle < 0:
mind *= -1
return ind, mind
| 644 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
|
do_simulation
|
(cx, cy, cyaw, ck, speed_profile, goal)
|
return t, x, y, yaw, v
| 181 | 235 |
def do_simulation(cx, cy, cyaw, ck, speed_profile, goal):
T = 500.0 # max simulation time
goal_dis = 0.3
stop_speed = 0.05
state = State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
time = 0.0
x = [state.x]
y = [state.y]
yaw = [state.yaw]
v = [state.v]
t = [0.0]
e, e_th = 0.0, 0.0
while T >= time:
dl, target_ind, e, e_th, ai = lqr_speed_steering_control(
state, cx, cy, cyaw, ck, e, e_th, speed_profile, lqr_Q, lqr_R)
state = update(state, ai, dl)
if abs(state.v) <= stop_speed:
target_ind += 1
time = time + dt
# check goal
dx = state.x - goal[0]
dy = state.y - goal[1]
if math.hypot(dx, dy) <= goal_dis:
print("Goal")
break
x.append(state.x)
y.append(state.y)
yaw.append(state.yaw)
v.append(state.v)
t.append(time)
if target_ind % 1 == 0 and show_animation:
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect('key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.plot(cx, cy, "-r", label="course")
plt.plot(x, y, "ob", label="trajectory")
plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
plt.axis("equal")
plt.grid(True)
plt.title("speed[km/h]:" + str(round(state.v * 3.6, 2))
+ ",target index:" + str(target_ind))
plt.pause(0.0001)
return t, x, y, yaw, v
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py#L181-L235
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
19,
20,
21,
22,
23,
24,
25,
26,
27,
28,
29,
30,
31,
32,
33,
34,
35,
36,
37,
38,
39,
40,
53,
54
] | 76.363636 |
[
41,
43,
45,
46,
47,
48,
49,
50,
52
] | 16.363636 | false | 90.506329 | 55 | 6 | 83.636364 | 0 |
def do_simulation(cx, cy, cyaw, ck, speed_profile, goal):
T = 500.0 # max simulation time
goal_dis = 0.3
stop_speed = 0.05
state = State(x=-0.0, y=-0.0, yaw=0.0, v=0.0)
time = 0.0
x = [state.x]
y = [state.y]
yaw = [state.yaw]
v = [state.v]
t = [0.0]
e, e_th = 0.0, 0.0
while T >= time:
dl, target_ind, e, e_th, ai = lqr_speed_steering_control(
state, cx, cy, cyaw, ck, e, e_th, speed_profile, lqr_Q, lqr_R)
state = update(state, ai, dl)
if abs(state.v) <= stop_speed:
target_ind += 1
time = time + dt
# check goal
dx = state.x - goal[0]
dy = state.y - goal[1]
if math.hypot(dx, dy) <= goal_dis:
print("Goal")
break
x.append(state.x)
y.append(state.y)
yaw.append(state.yaw)
v.append(state.v)
t.append(time)
if target_ind % 1 == 0 and show_animation:
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect('key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plt.plot(cx, cy, "-r", label="course")
plt.plot(x, y, "ob", label="trajectory")
plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
plt.axis("equal")
plt.grid(True)
plt.title("speed[km/h]:" + str(round(state.v * 3.6, 2))
+ ",target index:" + str(target_ind))
plt.pause(0.0001)
return t, x, y, yaw, v
| 645 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
|
calc_speed_profile
|
(cyaw, target_speed)
|
return speed_profile
| 238 | 265 |
def calc_speed_profile(cyaw, target_speed):
speed_profile = [target_speed] * len(cyaw)
direction = 1.0
# Set stop point
for i in range(len(cyaw) - 1):
dyaw = abs(cyaw[i + 1] - cyaw[i])
switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
if switch:
direction *= -1
if direction != 1.0:
speed_profile[i] = - target_speed
else:
speed_profile[i] = target_speed
if switch:
speed_profile[i] = 0.0
# speed down
for i in range(40):
speed_profile[-i] = target_speed / (50 - i)
if speed_profile[-i] <= 1.0 / 3.6:
speed_profile[-i] = 1.0 / 3.6
return speed_profile
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py#L238-L265
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
12,
13,
16,
17,
18,
21,
22,
23,
24,
25,
26,
27
] | 82.142857 |
[
11,
14,
19
] | 10.714286 | false | 90.506329 | 28 | 7 | 89.285714 | 0 |
def calc_speed_profile(cyaw, target_speed):
speed_profile = [target_speed] * len(cyaw)
direction = 1.0
# Set stop point
for i in range(len(cyaw) - 1):
dyaw = abs(cyaw[i + 1] - cyaw[i])
switch = math.pi / 4.0 <= dyaw < math.pi / 2.0
if switch:
direction *= -1
if direction != 1.0:
speed_profile[i] = - target_speed
else:
speed_profile[i] = target_speed
if switch:
speed_profile[i] = 0.0
# speed down
for i in range(40):
speed_profile[-i] = target_speed / (50 - i)
if speed_profile[-i] <= 1.0 / 3.6:
speed_profile[-i] = 1.0 / 3.6
return speed_profile
| 646 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
|
main
|
()
| 268 | 308 |
def main():
print("LQR steering control tracking start!!")
ax = [0.0, 6.0, 12.5, 10.0, 17.5, 20.0, 25.0]
ay = [0.0, -3.0, -5.0, 6.5, 3.0, 0.0, 0.0]
goal = [ax[-1], ay[-1]]
cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
ax, ay, ds=0.1)
target_speed = 10.0 / 3.6 # simulation parameter km/h -> m/s
sp = calc_speed_profile(cyaw, target_speed)
t, x, y, yaw, v = do_simulation(cx, cy, cyaw, ck, sp, goal)
if show_animation: # pragma: no cover
plt.close()
plt.subplots(1)
plt.plot(ax, ay, "xb", label="waypoints")
plt.plot(cx, cy, "-r", label="target course")
plt.plot(x, y, "-g", label="tracking")
plt.grid(True)
plt.axis("equal")
plt.xlabel("x[m]")
plt.ylabel("y[m]")
plt.legend()
plt.subplots(1)
plt.plot(s, [np.rad2deg(iyaw) for iyaw in cyaw], "-r", label="yaw")
plt.grid(True)
plt.legend()
plt.xlabel("line length[m]")
plt.ylabel("yaw angle[deg]")
plt.subplots(1)
plt.plot(s, ck, "-r", label="curvature")
plt.grid(True)
plt.legend()
plt.xlabel("line length[m]")
plt.ylabel("curvature [1/m]")
plt.show()
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py#L268-L308
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
8,
9,
10,
11,
12,
13
] | 76.470588 |
[] | 0 | false | 90.506329 | 41 | 3 | 100 | 0 |
def main():
print("LQR steering control tracking start!!")
ax = [0.0, 6.0, 12.5, 10.0, 17.5, 20.0, 25.0]
ay = [0.0, -3.0, -5.0, 6.5, 3.0, 0.0, 0.0]
goal = [ax[-1], ay[-1]]
cx, cy, cyaw, ck, s = cubic_spline_planner.calc_spline_course(
ax, ay, ds=0.1)
target_speed = 10.0 / 3.6 # simulation parameter km/h -> m/s
sp = calc_speed_profile(cyaw, target_speed)
t, x, y, yaw, v = do_simulation(cx, cy, cyaw, ck, sp, goal)
if show_animation: # pragma: no cover
plt.close()
plt.subplots(1)
plt.plot(ax, ay, "xb", label="waypoints")
plt.plot(cx, cy, "-r", label="target course")
plt.plot(x, y, "-g", label="tracking")
plt.grid(True)
plt.axis("equal")
plt.xlabel("x[m]")
plt.ylabel("y[m]")
plt.legend()
plt.subplots(1)
plt.plot(s, [np.rad2deg(iyaw) for iyaw in cyaw], "-r", label="yaw")
plt.grid(True)
plt.legend()
plt.xlabel("line length[m]")
plt.ylabel("yaw angle[deg]")
plt.subplots(1)
plt.plot(s, ck, "-r", label="curvature")
plt.grid(True)
plt.legend()
plt.xlabel("line length[m]")
plt.ylabel("curvature [1/m]")
plt.show()
| 647 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py
|
State.__init__
|
(self, x=0.0, y=0.0, yaw=0.0, v=0.0)
| 32 | 36 |
def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
self.x = x
self.y = y
self.yaw = yaw
self.v = v
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/lqr_speed_steer_control/lqr_speed_steer_control.py#L32-L36
| 2 |
[
0,
1,
2,
3,
4
] | 100 |
[] | 0 | true | 90.506329 | 5 | 1 | 100 | 0 |
def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
self.x = x
self.y = y
self.yaw = yaw
self.v = v
| 648 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/pure_pursuit/pure_pursuit.py
|
proportional_control
|
(target, current)
|
return a
| 64 | 67 |
def proportional_control(target, current):
a = Kp * (target - current)
return a
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/pure_pursuit/pure_pursuit.py#L64-L67
| 2 |
[
0,
1,
2,
3
] | 100 |
[] | 0 | true | 90.178571 | 4 | 1 | 100 | 0 |
def proportional_control(target, current):
a = Kp * (target - current)
return a
| 649 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/pure_pursuit/pure_pursuit.py
|
pure_pursuit_steer_control
|
(state, trajectory, pind)
|
return delta, ind
| 111 | 129 |
def pure_pursuit_steer_control(state, trajectory, pind):
ind, Lf = trajectory.search_target_index(state)
if pind >= ind:
ind = pind
if ind < len(trajectory.cx):
tx = trajectory.cx[ind]
ty = trajectory.cy[ind]
else: # toward goal
tx = trajectory.cx[-1]
ty = trajectory.cy[-1]
ind = len(trajectory.cx) - 1
alpha = math.atan2(ty - state.rear_y, tx - state.rear_x) - state.yaw
delta = math.atan2(2.0 * WB * math.sin(alpha) / Lf, 1.0)
return delta, ind
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/pure_pursuit/pure_pursuit.py#L111-L129
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
13,
14,
15,
16,
17,
18
] | 78.947368 |
[
10,
11,
12
] | 15.789474 | false | 90.178571 | 19 | 3 | 84.210526 | 0 |
def pure_pursuit_steer_control(state, trajectory, pind):
ind, Lf = trajectory.search_target_index(state)
if pind >= ind:
ind = pind
if ind < len(trajectory.cx):
tx = trajectory.cx[ind]
ty = trajectory.cy[ind]
else: # toward goal
tx = trajectory.cx[-1]
ty = trajectory.cy[-1]
ind = len(trajectory.cx) - 1
alpha = math.atan2(ty - state.rear_y, tx - state.rear_x) - state.yaw
delta = math.atan2(2.0 * WB * math.sin(alpha) / Lf, 1.0)
return delta, ind
| 650 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/pure_pursuit/pure_pursuit.py
|
plot_arrow
|
(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k")
|
Plot arrow
|
Plot arrow
| 132 | 143 |
def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"):
"""
Plot arrow
"""
if not isinstance(x, float):
for ix, iy, iyaw in zip(x, y, yaw):
plot_arrow(ix, iy, iyaw)
else:
plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),
fc=fc, ec=ec, head_width=width, head_length=width)
plt.plot(x, y)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/pure_pursuit/pure_pursuit.py#L132-L143
| 2 |
[
0,
1,
2,
3,
4
] | 41.666667 |
[
5,
6,
7,
9,
11
] | 41.666667 | false | 90.178571 | 12 | 3 | 58.333333 | 1 |
def plot_arrow(x, y, yaw, length=1.0, width=0.5, fc="r", ec="k"):
if not isinstance(x, float):
for ix, iy, iyaw in zip(x, y, yaw):
plot_arrow(ix, iy, iyaw)
else:
plt.arrow(x, y, length * math.cos(yaw), length * math.sin(yaw),
fc=fc, ec=ec, head_width=width, head_length=width)
plt.plot(x, y)
| 651 |
|
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/pure_pursuit/pure_pursuit.py
|
main
|
()
| 146 | 210 |
def main():
# target course
cx = np.arange(0, 50, 0.5)
cy = [math.sin(ix / 5.0) * ix / 2.0 for ix in cx]
target_speed = 10.0 / 3.6 # [m/s]
T = 100.0 # max simulation time
# initial state
state = State(x=-0.0, y=-3.0, yaw=0.0, v=0.0)
lastIndex = len(cx) - 1
time = 0.0
states = States()
states.append(time, state)
target_course = TargetCourse(cx, cy)
target_ind, _ = target_course.search_target_index(state)
while T >= time and lastIndex > target_ind:
# Calc control input
ai = proportional_control(target_speed, state.v)
di, target_ind = pure_pursuit_steer_control(
state, target_course, target_ind)
state.update(ai, di) # Control vehicle
time += dt
states.append(time, state)
if show_animation: # pragma: no cover
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plot_arrow(state.x, state.y, state.yaw)
plt.plot(cx, cy, "-r", label="course")
plt.plot(states.x, states.y, "-b", label="trajectory")
plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
plt.axis("equal")
plt.grid(True)
plt.title("Speed[km/h]:" + str(state.v * 3.6)[:4])
plt.pause(0.001)
# Test
assert lastIndex >= target_ind, "Cannot goal"
if show_animation: # pragma: no cover
plt.cla()
plt.plot(cx, cy, ".r", label="course")
plt.plot(states.x, states.y, "-b", label="trajectory")
plt.legend()
plt.xlabel("x[m]")
plt.ylabel("y[m]")
plt.axis("equal")
plt.grid(True)
plt.subplots(1)
plt.plot(states.t, [iv * 3.6 for iv in states.v], "-r")
plt.xlabel("Time[s]")
plt.ylabel("Speed[km/h]")
plt.grid(True)
plt.show()
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/pure_pursuit/pure_pursuit.py#L146-L210
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
10,
11,
12,
13,
14,
15,
16,
17,
18,
19,
20,
21,
22,
23,
25,
26,
27,
28,
29,
30,
46,
47,
48
] | 84.615385 |
[] | 0 | false | 90.178571 | 65 | 8 | 100 | 0 |
def main():
# target course
cx = np.arange(0, 50, 0.5)
cy = [math.sin(ix / 5.0) * ix / 2.0 for ix in cx]
target_speed = 10.0 / 3.6 # [m/s]
T = 100.0 # max simulation time
# initial state
state = State(x=-0.0, y=-3.0, yaw=0.0, v=0.0)
lastIndex = len(cx) - 1
time = 0.0
states = States()
states.append(time, state)
target_course = TargetCourse(cx, cy)
target_ind, _ = target_course.search_target_index(state)
while T >= time and lastIndex > target_ind:
# Calc control input
ai = proportional_control(target_speed, state.v)
di, target_ind = pure_pursuit_steer_control(
state, target_course, target_ind)
state.update(ai, di) # Control vehicle
time += dt
states.append(time, state)
if show_animation: # pragma: no cover
plt.cla()
# for stopping simulation with the esc key.
plt.gcf().canvas.mpl_connect(
'key_release_event',
lambda event: [exit(0) if event.key == 'escape' else None])
plot_arrow(state.x, state.y, state.yaw)
plt.plot(cx, cy, "-r", label="course")
plt.plot(states.x, states.y, "-b", label="trajectory")
plt.plot(cx[target_ind], cy[target_ind], "xg", label="target")
plt.axis("equal")
plt.grid(True)
plt.title("Speed[km/h]:" + str(state.v * 3.6)[:4])
plt.pause(0.001)
# Test
assert lastIndex >= target_ind, "Cannot goal"
if show_animation: # pragma: no cover
plt.cla()
plt.plot(cx, cy, ".r", label="course")
plt.plot(states.x, states.y, "-b", label="trajectory")
plt.legend()
plt.xlabel("x[m]")
plt.ylabel("y[m]")
plt.axis("equal")
plt.grid(True)
plt.subplots(1)
plt.plot(states.t, [iv * 3.6 for iv in states.v], "-r")
plt.xlabel("Time[s]")
plt.ylabel("Speed[km/h]")
plt.grid(True)
plt.show()
| 652 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/pure_pursuit/pure_pursuit.py
|
State.__init__
|
(self, x=0.0, y=0.0, yaw=0.0, v=0.0)
| 25 | 31 |
def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
self.x = x
self.y = y
self.yaw = yaw
self.v = v
self.rear_x = self.x - ((WB / 2) * math.cos(self.yaw))
self.rear_y = self.y - ((WB / 2) * math.sin(self.yaw))
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/pure_pursuit/pure_pursuit.py#L25-L31
| 2 |
[
0,
1,
2,
3,
4,
5,
6
] | 100 |
[] | 0 | true | 90.178571 | 7 | 1 | 100 | 0 |
def __init__(self, x=0.0, y=0.0, yaw=0.0, v=0.0):
self.x = x
self.y = y
self.yaw = yaw
self.v = v
self.rear_x = self.x - ((WB / 2) * math.cos(self.yaw))
self.rear_y = self.y - ((WB / 2) * math.sin(self.yaw))
| 653 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/pure_pursuit/pure_pursuit.py
|
State.update
|
(self, a, delta)
| 33 | 39 |
def update(self, a, delta):
self.x += self.v * math.cos(self.yaw) * dt
self.y += self.v * math.sin(self.yaw) * dt
self.yaw += self.v / WB * math.tan(delta) * dt
self.v += a * dt
self.rear_x = self.x - ((WB / 2) * math.cos(self.yaw))
self.rear_y = self.y - ((WB / 2) * math.sin(self.yaw))
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/pure_pursuit/pure_pursuit.py#L33-L39
| 2 |
[
0,
1,
2,
3,
4,
5,
6
] | 100 |
[] | 0 | true | 90.178571 | 7 | 1 | 100 | 0 |
def update(self, a, delta):
self.x += self.v * math.cos(self.yaw) * dt
self.y += self.v * math.sin(self.yaw) * dt
self.yaw += self.v / WB * math.tan(delta) * dt
self.v += a * dt
self.rear_x = self.x - ((WB / 2) * math.cos(self.yaw))
self.rear_y = self.y - ((WB / 2) * math.sin(self.yaw))
| 654 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/pure_pursuit/pure_pursuit.py
|
State.calc_distance
|
(self, point_x, point_y)
|
return math.hypot(dx, dy)
| 41 | 44 |
def calc_distance(self, point_x, point_y):
dx = self.rear_x - point_x
dy = self.rear_y - point_y
return math.hypot(dx, dy)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/pure_pursuit/pure_pursuit.py#L41-L44
| 2 |
[
0,
1,
2,
3
] | 100 |
[] | 0 | true | 90.178571 | 4 | 1 | 100 | 0 |
def calc_distance(self, point_x, point_y):
dx = self.rear_x - point_x
dy = self.rear_y - point_y
return math.hypot(dx, dy)
| 655 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/pure_pursuit/pure_pursuit.py
|
States.__init__
|
(self)
| 49 | 54 |
def __init__(self):
self.x = []
self.y = []
self.yaw = []
self.v = []
self.t = []
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/pure_pursuit/pure_pursuit.py#L49-L54
| 2 |
[
0,
1,
2,
3,
4,
5
] | 100 |
[] | 0 | true | 90.178571 | 6 | 1 | 100 | 0 |
def __init__(self):
self.x = []
self.y = []
self.yaw = []
self.v = []
self.t = []
| 656 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/pure_pursuit/pure_pursuit.py
|
States.append
|
(self, t, state)
| 56 | 61 |
def append(self, t, state):
self.x.append(state.x)
self.y.append(state.y)
self.yaw.append(state.yaw)
self.v.append(state.v)
self.t.append(t)
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/pure_pursuit/pure_pursuit.py#L56-L61
| 2 |
[
0,
1,
2,
3,
4,
5
] | 100 |
[] | 0 | true | 90.178571 | 6 | 1 | 100 | 0 |
def append(self, t, state):
self.x.append(state.x)
self.y.append(state.y)
self.yaw.append(state.yaw)
self.v.append(state.v)
self.t.append(t)
| 657 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/pure_pursuit/pure_pursuit.py
|
TargetCourse.__init__
|
(self, cx, cy)
| 72 | 75 |
def __init__(self, cx, cy):
self.cx = cx
self.cy = cy
self.old_nearest_point_index = None
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/pure_pursuit/pure_pursuit.py#L72-L75
| 2 |
[
0,
1,
2,
3
] | 100 |
[] | 0 | true | 90.178571 | 4 | 1 | 100 | 0 |
def __init__(self, cx, cy):
self.cx = cx
self.cy = cy
self.old_nearest_point_index = None
| 658 |
|||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/pure_pursuit/pure_pursuit.py
|
TargetCourse.search_target_index
|
(self, state)
|
return ind, Lf
| 77 | 108 |
def search_target_index(self, state):
# To speed up nearest point search, doing it at only first time.
if self.old_nearest_point_index is None:
# search nearest point index
dx = [state.rear_x - icx for icx in self.cx]
dy = [state.rear_y - icy for icy in self.cy]
d = np.hypot(dx, dy)
ind = np.argmin(d)
self.old_nearest_point_index = ind
else:
ind = self.old_nearest_point_index
distance_this_index = state.calc_distance(self.cx[ind],
self.cy[ind])
while True:
distance_next_index = state.calc_distance(self.cx[ind + 1],
self.cy[ind + 1])
if distance_this_index < distance_next_index:
break
ind = ind + 1 if (ind + 1) < len(self.cx) else ind
distance_this_index = distance_next_index
self.old_nearest_point_index = ind
Lf = k * state.v + Lfc # update look ahead distance
# search look ahead target point index
while Lf > state.calc_distance(self.cx[ind], self.cy[ind]):
if (ind + 1) >= len(self.cx):
break # not exceed goal
ind += 1
return ind, Lf
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/pure_pursuit/pure_pursuit.py#L77-L108
| 2 |
[
0,
1,
2,
3,
4,
5,
6,
7,
8,
9,
11,
12,
14,
15,
17,
18,
19,
20,
21,
22,
23,
24,
25,
26,
27,
29,
30,
31
] | 87.5 |
[
28
] | 3.125 | false | 90.178571 | 32 | 8 | 96.875 | 0 |
def search_target_index(self, state):
# To speed up nearest point search, doing it at only first time.
if self.old_nearest_point_index is None:
# search nearest point index
dx = [state.rear_x - icx for icx in self.cx]
dy = [state.rear_y - icy for icy in self.cy]
d = np.hypot(dx, dy)
ind = np.argmin(d)
self.old_nearest_point_index = ind
else:
ind = self.old_nearest_point_index
distance_this_index = state.calc_distance(self.cx[ind],
self.cy[ind])
while True:
distance_next_index = state.calc_distance(self.cx[ind + 1],
self.cy[ind + 1])
if distance_this_index < distance_next_index:
break
ind = ind + 1 if (ind + 1) < len(self.cx) else ind
distance_this_index = distance_next_index
self.old_nearest_point_index = ind
Lf = k * state.v + Lfc # update look ahead distance
# search look ahead target point index
while Lf > state.calc_distance(self.cx[ind], self.cy[ind]):
if (ind + 1) >= len(self.cx):
break # not exceed goal
ind += 1
return ind, Lf
| 659 |
||
AtsushiSakai/PythonRobotics
|
15ab19688b2f6c03ee91a853f1f8cc9def84d162
|
PathTracking/rear_wheel_feedback/rear_wheel_feedback.py
|
pid_control
|
(target, current)
|
return a
| 94 | 96 |
def pid_control(target, current):
a = Kp * (target - current)
return a
|
https://github.com/AtsushiSakai/PythonRobotics/blob/15ab19688b2f6c03ee91a853f1f8cc9def84d162/project2/PathTracking/rear_wheel_feedback/rear_wheel_feedback.py#L94-L96
| 2 |
[
0,
1,
2
] | 100 |
[] | 0 | true | 92.307692 | 3 | 1 | 100 | 0 |
def pid_control(target, current):
a = Kp * (target - current)
return a
| 660 |
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