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CTRA_mm.py
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CTRA_mm.py
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import torch
import src.parameters as params
T = params.T_ctra
T_dec = T
#T_dec = T*params.ratio_ctra
q = params.q_ctra
sin = torch.sin
cos = torch.cos
# state = [x, y, phi, s, a, w]
sa = params.sa
sw = params.sw
#######################
### DATA GENERATION ###
#######################
def F_gen(state):
x = state[0] # pos x
y = state[1] # pos y
p = state[2] # phi
s = state[3] # speed
a = state[4] # longitudinal acceleration
w = state[5] # yaw rate
motion = torch.zeros_like(state)
motion[0] = (1/w)*(s+a*T)*sin(p+w*T) + (a/w**2)*cos(p+w*T) - (s/w)*sin(p) - (a/w**2)*cos(p)
motion[1] = (1/w)*(-s-a*T)*cos(p+w*T) + (a/w**2)*sin(p+w*T) + (s/w)*cos(p) - (a/w**2)*sin(p)
motion[2] = w*T
motion[3] = a*T
new_state = state + motion
return new_state.float()
def Q_gen(state):
Q_gen = torch.tensor([[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0], ]).float()
return Q_gen
def H_gen(state):
H_gen = torch.tensor([[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1]]).float()
return H_gen
def R_gen(state):
R_gen = torch.tensor([[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0],
[0, 0, 0, 0, 0, 0]]).float()
return R_gen
##############################
### FULL OBSERVATION MODEL ###
##############################
def F_FO(state):
x = state[0] # pos x
y = state[1] # pos y
p = state[2] # phi
s = state[3] # speed
a = state[4] # longitudinal acceleration
w = state[5] # yaw rate
motion = torch.zeros_like(state)
motion[0] = (1 / w) * (s + a * T_dec) * sin(p + w * T_dec) + (a / w ** 2) * cos(p + w * T_dec) - (s / w) * sin(p) - (
a / w ** 2) * cos(p)
motion[1] = (1 / w) * (-s - a * T_dec) * cos(p + w * T_dec) + (a / w ** 2) * sin(p + w * T_dec) + (s / w) * cos(p) - (
a / w ** 2) * sin(p)
motion[2] = w * T_dec
motion[3] = a * T_dec
new_state = state + motion
return new_state.float()
def Q_FO(state):
x = state[0] # pos x
y = state[1] # pos y
p = state[2] # phi
s = state[3] # speed
a = state[4] # longitudinal acceleration
w = state[5] # yaw rate
x1 = (T_dec**5/20)*(sw**2*s**2*(sin(p)**2) + sa**2*(cos(p))**2) # xx
x2 = (T_dec**5/20)*sin(p)*cos(p)*(sa**2 - sw**2*s**2) # xy
x3 = -(T_dec**4/8)*sw**2*s*sin(p) # xphi
x4 = (T_dec**4/8)*sa**2*cos(p) # xs
x5 = (T_dec**3/6)*sa**2*cos(p) # xa
x6 = -(T_dec**3/6)*sw**2*s*sin(p) # xw
y1 = (T_dec**5/20)*sin(p)*cos(p)*(sa**2 - sw**2*s**2)
y2 = (T_dec**5/20)*(sw**2*s**2*(cos(p)**2) + sa**2*(sin(p))**2)
y3 = (T_dec**4/8)*sw**2*s*cos(p)
y4 = (T_dec**4/8)*sa**2*sin(p)
y5 = (T_dec**3/6)*sa**2*sin(p)
y6 = (T_dec**3/6)*sw**2*s*cos(p)
p1 = -(T_dec**4/8)*sw**2*s*sin(p)
p2 = (T_dec**4/8)*sw**2*s*cos(p)
p3 = (T_dec**3/3)*sw**2
p4 = 0
p5 = 0
p6 = (T_dec**2/2)*sw**2
s1 = (T_dec**4/8)*sa**2*cos(p)
s2 = (T_dec**4/8)*sa**2*sin(p)
s3 = 0
s4 = (T_dec**3/3)*sa**2
s5 = (T_dec**2/2)*sa**2
s6 = 0
a1 = (T_dec**3/6)*sa**2*cos(p)
a2 = (T_dec**3/6)*sa**2*sin(p)
a3 = 0
a4 = (T_dec**2/2)*sa**2
a5 = T_dec**sa
a6 = 0
w1 = -(T_dec**3/6)*sw**2*s*sin(p)
w2 = (T_dec**3/6)*sw**2*s*cos(p)
w3 = (T_dec**2/2)*sw**2
w4 = 0
w5 = 0
w6 = T_dec*sw**2
Q_FO = torch.tensor([[x1, x2, x3, x4, x5, x6],
[y1, y2, y3, y4, y5, y6],
[p1, p2, p3, p4, p5, p6],
[s1, s2, s3, s4, s5, s6],
[a1, a2, a3, a4, a5, a6],
[w1, w2, w3, w4, w5, w6]]).float()
return Q_FO
def H_FO(state):
H_FO = torch.tensor([ [1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1]]).float()
return H_FO
def R_FO(state):
R_FO = torch.tensor([[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1]]).float()
return R_FO
############################
### POSITION OBSERVATION ###
############################
def F_PO(state):
x = state[0] # pos x
y = state[1] # pos y
p = state[2] # phi
s = state[3] # speed
a = state[4] # longitudinal acceleration
w = state[5] # yaw rate
motion = torch.zeros_like(state)
motion[0] = (1 / w) * (s + a * T_dec) * sin(p + w * T_dec) + (a / w ** 2) * cos(p + w * T_dec) - (s / w) * sin(p) - (
a / w ** 2) * cos(p)
motion[1] = (1 / w) * (-s - a * T_dec) * cos(p + w * T_dec) + (a / w ** 2) * sin(p + w * T_dec) + (s / w) * cos(p) - (
a / w ** 2) * sin(p)
motion[2] = w * T_dec
motion[3] = a * T_dec
new_state = state + motion
return new_state.float()
def Q_PO(state):
x = state[0] # pos x
y = state[1] # pos y
p = state[2] # phi
s = state[3] # speed
a = state[4] # longitudinal acceleration
w = state[5] # yaw rate
x1 = (T_dec**5/20)*(sw**2*s**2*(sin(p)**2) + sa**2*(cos(p))**2) # xx
x2 = (T_dec**5/20)*sin(p)*cos(p)*(sa**2 - sw**2*s**2) # xy
x3 = -(T_dec**4/8)*sw**2*s*sin(p) # xphi
x4 = (T_dec**4/8)*sa**2*cos(p) # xs
x5 = (T_dec**3/6)*sa**2*cos(p) # xa
x6 = -(T_dec**3/6)*sw**2*s*sin(p) # xw
y1 = (T_dec**5/20)*sin(p)*cos(p)*(sa**2 - sw**2*s**2)
y2 = (T_dec**5/20)*(sw**2*s**2*(cos(p)**2) + sa**2*(sin(p))**2)
y3 = (T_dec**4/8)*sw**2*s*cos(p)
y4 = (T_dec**4/8)*sa**2*sin(p)
y5 = (T_dec**3/6)*sa**2*sin(p)
y6 = (T_dec**3/6)*sw**2*s*cos(p)
p1 = -(T_dec**4/8)*sw**2*s*sin(p)
p2 = (T_dec**4/8)*sw**2*s*cos(p)
p3 = (T_dec**3/3)*sw**2
p4 = 0
p5 = 0
p6 = (T_dec**2/2)*sw**2
s1 = (T_dec**4/8)*sa**2*cos(p)
s2 = (T_dec**4/8)*sa**2*sin(p)
s3 = 0
s4 = (T_dec**3/3)*sa**2
s5 = (T_dec**2/2)*sa**2
s6 = 0
a1 = (T_dec**3/6)*sa**2*cos(p)
a2 = (T_dec**3/6)*sa**2*sin(p)
a3 = 0
a4 = (T_dec**2/2)*sa**2
a5 = T_dec**sa
a6 = 0
w1 = -(T_dec**3/6)*sw**2*s*sin(p)
w2 = (T_dec**3/6)*sw**2*s*cos(p)
w3 = (T_dec**2/2)*sw**2
w4 = 0
w5 = 0
w6 = T_dec*sw**2
Q_PO = torch.tensor([[x1, x2, x3, x4, x5, x6],
[y1, y2, y3, y4, y5, y6],
[p1, p2, p3, p4, p5, p6],
[s1, s2, s3, s4, s5, s6],
[a1, a2, a3, a4, a5, a6],
[w1, w2, w3, w4, w5, w6]]).float()
return Q_PO
def H_PO(state):
H_PO = torch.tensor([[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0]]).float()
return H_PO
def R_PO(state):
R_PO = torch.tensor([[1, 0],
[0, 1]]).float()
return R_PO
################################
### ACCELERATION OBSERVATION ###
################################
def F_AO(state):
x = state[0] # pos x
y = state[1] # pos y
p = state[2] # phi
s = state[3] # speed
a = state[4] # longitudinal acceleration
w = state[5] # yaw rate
motion = torch.zeros_like(state)
motion[0] = (1 / w) * (s + a * T_dec) * sin(p + w * T_dec) + (a / w ** 2) * cos(p + w * T_dec) - (s / w) * sin(p) - (
a / w ** 2) * cos(p)
motion[1] = (1 / w) * (-s - a * T_dec) * cos(p + w * T_dec) + (a / w ** 2) * sin(p + w * T_dec) + (s / w) * cos(p) - (
a / w ** 2) * sin(p)
motion[2] = w * T_dec
motion[3] = a * T_dec
new_state = state + motion
return new_state.float()
def Q_AO(state):
x = state[0] # pos x
y = state[1] # pos y
p = state[2] # phi
s = state[3] # speed
a = state[4] # longitudinal acceleration
w = state[5] # yaw rate
x1 = (T_dec**5/20)*(sw**2*s**2*(sin(p)**2) + sa**2*(cos(p))**2) # xx
x2 = (T_dec**5/20)*sin(p)*cos(p)*(sa**2 - sw**2*s**2) # xy
x3 = -(T_dec**4/8)*sw**2*s*sin(p) # xphi
x4 = (T_dec**4/8)*sa**2*cos(p) # xs
x5 = (T_dec**3/6)*sa**2*cos(p) # xa
x6 = -(T_dec**3/6)*sw**2*s*sin(p) # xw
y1 = (T_dec**5/20)*sin(p)*cos(p)*(sa**2 - sw**2*s**2)
y2 = (T_dec**5/20)*(sw**2*s**2*(cos(p)**2) + sa**2*(sin(p))**2)
y3 = (T_dec**4/8)*sw**2*s*cos(p)
y4 = (T_dec**4/8)*sa**2*sin(p)
y5 = (T_dec**3/6)*sa**2*sin(p)
y6 = (T_dec**3/6)*sw**2*s*cos(p)
p1 = -(T_dec**4/8)*sw**2*s*sin(p)
p2 = (T_dec**4/8)*sw**2*s*cos(p)
p3 = (T_dec**3/3)*sw**2
p4 = 0
p5 = 0
p6 = (T_dec**2/2)*sw**2
s1 = (T_dec**4/8)*sa**2*cos(p)
s2 = (T_dec**4/8)*sa**2*sin(p)
s3 = 0
s4 = (T_dec**3/3)*sa**2
s5 = (T_dec**2/2)*sa**2
s6 = 0
a1 = (T_dec**3/6)*sa**2*cos(p)
a2 = (T_dec**3/6)*sa**2*sin(p)
a3 = 0
a4 = (T_dec**2/2)*sa**2
a5 = T_dec**sa
a6 = 0
w1 = -(T_dec**3/6)*sw**2*s*sin(p)
w2 = (T_dec**3/6)*sw**2*s*cos(p)
w3 = (T_dec**2/2)*sw**2
w4 = 0
w5 = 0
w6 = T_dec*sw**2
Q_PO = torch.tensor([[x1, x2, x3, x4, x5, x6],
[y1, y2, y3, y4, y5, y6],
[p1, p2, p3, p4, p5, p6],
[s1, s2, s3, s4, s5, s6],
[a1, a2, a3, a4, a5, a6],
[w1, w2, w3, w4, w5, w6]]).float()
return Q_PO
def H_AO(state):
H_AO = torch.tensor([[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1]]).float()
return H_AO
def R_AO(state):
R_AO = torch.tensor([[1, 0],
[0, 1]]).float()
return R_AO
#############################################
### POSITION AND ACCELERATION OBSERVATION ###
#############################################
def F_PAO(state):
x = state[0] # pos x
y = state[1] # pos y
p = state[2] # phi
s = state[3] # speed
a = state[4] # longitudinal acceleration
w = state[5] # yaw rate
motion = torch.zeros_like(state)
motion[0] = (1 / w) * (s + a * T_dec) * sin(p + w * T_dec) + (a / w ** 2) * cos(p + w * T_dec) - (s / w) * sin(p) - (
a / w ** 2) * cos(p)
motion[1] = (1 / w) * (-s - a * T_dec) * cos(p + w * T_dec) + (a / w ** 2) * sin(p + w * T_dec) + (s / w) * cos(p) - (
a / w ** 2) * sin(p)
motion[2] = w * T_dec
motion[3] = a * T_dec
new_state = state + motion
return new_state.float()
def Q_PAO(state):
x = state[0] # pos x
y = state[1] # pos y
p = state[2] # phi
s = state[3] # speed
a = state[4] # longitudinal acceleration
w = state[5] # yaw rate
x1 = (T_dec**5/20)*(sw**2*s**2*(sin(p)**2) + sa**2*(cos(p))**2) # xx
x2 = (T_dec**5/20)*sin(p)*cos(p)*(sa**2 - sw**2*s**2) # xy
x3 = -(T_dec**4/8)*sw**2*s*sin(p) # xphi
x4 = (T_dec**4/8)*sa**2*cos(p) # xs
x5 = (T_dec**3/6)*sa**2*cos(p) # xa
x6 = -(T_dec**3/6)*sw**2*s*sin(p) # xw
y1 = (T_dec**5/20)*sin(p)*cos(p)*(sa**2 - sw**2*s**2)
y2 = (T_dec**5/20)*(sw**2*s**2*(cos(p)**2) + sa**2*(sin(p))**2)
y3 = (T_dec**4/8)*sw**2*s*cos(p)
y4 = (T_dec**4/8)*sa**2*sin(p)
y5 = (T_dec**3/6)*sa**2*sin(p)
y6 = (T_dec**3/6)*sw**2*s*cos(p)
p1 = -(T_dec**4/8)*sw**2*s*sin(p)
p2 = (T_dec**4/8)*sw**2*s*cos(p)
p3 = (T_dec**3/3)*sw**2
p4 = 0
p5 = 0
p6 = (T_dec**2/2)*sw**2
s1 = (T_dec**4/8)*sa**2*cos(p)
s2 = (T_dec**4/8)*sa**2*sin(p)
s3 = 0
s4 = (T_dec**3/3)*sa**2
s5 = (T_dec**2/2)*sa**2
s6 = 0
a1 = (T_dec**3/6)*sa**2*cos(p)
a2 = (T_dec**3/6)*sa**2*sin(p)
a3 = 0
a4 = (T_dec**2/2)*sa**2
a5 = T_dec**sa
a6 = 0
w1 = -(T_dec**3/6)*sw**2*s*sin(p)
w2 = (T_dec**3/6)*sw**2*s*cos(p)
w3 = (T_dec**2/2)*sw**2
w4 = 0
w5 = 0
w6 = T_dec*sw**2
Q_PO = torch.tensor([[x1, x2, x3, x4, x5, x6],
[y1, y2, y3, y4, y5, y6],
[p1, p2, p3, p4, p5, p6],
[s1, s2, s3, s4, s5, s6],
[a1, a2, a3, a4, a5, a6],
[w1, w2, w3, w4, w5, w6]]).float()
return Q_PO
def H_PAO(state):
H_PAO = torch.tensor([[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1]]).float()
return H_PAO
def R_PAO(state):
R_PAO = torch.tensor([[1, 0, 0, 0],
[0, 1, 0, 0],
[0, 0, 1, 0],
[0, 0, 0, 1]]).float()
return R_PAO
r_FO = torch.tensor([[1, 0, 0, 0, 0, 0],
[0, 1, 0, 0, 0, 0],
[0, 0, 1, 0, 0, 0],
[0, 0, 0, 1, 0, 0],
[0, 0, 0, 0, 1, 0],
[0, 0, 0, 0, 0, 1]]).float()
################
### JACOBIAN ###
################
def F_jacobian(state):
x = state[0] # pos x
y = state[1] # pos y
p = state[2] # phi
s = state[3] # speed
a = state[4] # longitudinal acceleration
w = state[5] # yaw rate
f1x = 1
f1y = 0
f1p = (1/w)*(a*T_dec+s)*cos(p+T_dec*w) + (1/w**2)*a*(sin(p)-sin(p+T_dec*w)) - (1/w)*cos(p)*s
f1s = (1/w) * (sin(p+T_dec*w) - sin(p))
f1a = (1/w) * (T_dec*sin(p+T_dec*w)) + (1/w**2)*(cos(p+T_dec*w)-cos(p))
f1w = (1/w)* (T_dec*(T_dec*a + s)*cos(p+T_dec*w)) + (1/w**2)*(s*sin(p) - a*T_dec*sin(p+T_dec*w) - (a*T_dec+a)*sin(p+T_dec*w))
f2x = 0
f2y = 1
f2p = (1/w)*((a*T_dec+s)*sin(p+T_dec*w) - sin(p)*s) + (1/w**2)*(a*(cos(p+T_dec*w)-cos(p)))
f2s = (1/w)*( -cos(p+T_dec*w) + cos(p))
f2a = (1/w)*(-T_dec*cos(p+T_dec*w)) + (1/w**2)*(sin(p+T_dec*w)-sin(p))
f2w = (1/w)*T_dec*sin(p+w*T_dec)*(s+a*T_dec) + (1/w**2)*cos(p+T_dec*w)*(2*a*T_dec+s) -(1/w**2)*(s*cos(p)) + (1/w**3)*2*a*(sin(p)-sin(p+T_dec*w))
f3x = 0
f3y = 0
f3p = 1
f3s = 0
f3a = 0
f3w = T_dec
f4x = 0
f4y = 0
f4p = 0
f4s = 1
f4a = T_dec
f4w = 0
f5x = 0
f5y = 0
f5p = 0
f5s = 0
f5a = 1
f5w = 0
f6x = 0
f6y = 0
f6p = 0
f6s = 0
f6a = 0
f6w = 1
F = torch.tensor([[f1x, f1y, f1p, f1s, f1a, f1w],
[f2x, f2y, f2p, f2s, f2a, f2w],
[f3x, f3y, f3p, f3s, f3a, f3w],
[f4x, f4y, f4p, f4s, f4a, f4w],
[f5x, f5y, f5p, f5s, f5a, f5w],
[f6x, f6y, f6p, f6s, f6a, f6w]]).float()
return F
def F_jacobian_smooth(state):
x = state[0] # pos x
y = state[1] # pos y
p = state[2] # phi
s = state[3] # speed
a = state[4] # longitudinal acceleration
w = state[5] # yaw rate
f1x = 1
f1y = 0
f1p = (1/w)*(a*T+s)*cos(p+T*w) + (1/w**2)*a*(sin(p)-sin(p+T*w)) - (1/w)*cos(p)*s
f1s = (1/w) * (sin(p+T*w) - sin(p))
f1a = (1/w) * (T*sin(p+T*w)) + (1/w**2)*(cos(p+T*w)-cos(p))
f1w = (1/w)* (T*(T*a + s)*cos(p+T*w)) + (1/w**2)*(s*sin(p) - a*T*sin(p+T*w) - (a*T+a)*sin(p+T*w))
f2x = 0
f2y = 1
f2p = (1/w)*((a*T+s)*sin(p+T*w) - sin(p)*s) + (1/w**2)*(a*(cos(p+T*w)-cos(p)))
f2s = (1/w)*( -cos(p+T*w) + cos(p))
f2a = (1/w)*(-T*cos(p+T*w)) + (1/w**2)*(sin(p+T*w)-sin(p))
f2w = (1/w)*T*sin(p+w*T)*(s+a*T) + (1/w**2)*cos(p+T*w)*(2*a*T+s) -(1/w**2)*(s*cos(p)) + (1/w**3)*2*a*(sin(p)-sin(p+T*w))
f3x = 0
f3y = 0
f3p = 1
f3s = 0
f3a = 0
f3w = T
f4x = 0
f4y = 0
f4p = 0
f4s = 1
f4a = T
f4w = 0
f5x = 0
f5y = 0
f5p = 0
f5s = 0
f5a = 1
f5w = 0
f6x = 0
f6y = 0
f6p = 0
f6s = 0
f6a = 0
f6w = 1
F = torch.tensor([[f1x, f1y, f1p, f1s, f1a, f1w],
[f2x, f2y, f2p, f2s, f2a, f2w],
[f3x, f3y, f3p, f3s, f3a, f3w],
[f4x, f4y, f4p, f4s, f4a, f4w],
[f5x, f5y, f5p, f5s, f5a, f5w],
[f6x, f6y, f6p, f6s, f6a, f6w]]).float()
return F
sGPS = 0.5*8.8*T**2 # assume 8.8m/s2 as maximum acceleration, forcing the vehicle
sCourse = 0.1*T # assume 0.1rad/s as maximum turn rate for the vehicle
sVelocity= 8.8*T # assume 8.8m/s2 as maximum acceleration, forcing the vehicle
sYaw = 1.0*T # assume 1.0rad/s2 as the maximum turn rate acceleration for the vehicle
sAccel = 0.5
q_gen = torch.diag(torch.tensor([sGPS**2, sGPS**2, sCourse**2, sVelocity**2, sAccel**2, sYaw**2 ]))
sGPS = 0.5*8.8*T_dec**2 # assume 8.8m/s2 as maximum acceleration, forcing the vehicle
sCourse = 0.1*T_dec # assume 0.1rad/s as maximum turn rate for the vehicle
sVelocity= 8.8*T_dec # assume 8.8m/s2 as maximum acceleration, forcing the vehicle
sYaw = 1.0*T_dec # assume 1.0rad/s2 as the maximum turn rate acceleration for the vehicle
sAccel = 0.5
q_simple = torch.diag(torch.tensor([sGPS**2, sGPS**2, sCourse**2, sVelocity**2, sAccel**2, sYaw**2]))