# Setup for EKF
mus = np.mat(np.zeros((num_states, T)))
mus[:, 0] = np.mat(x0).T
Sigmas = np.zeros((Q.shape[0], Q.shape[1], T))
Sigmas[:, :, 0] = np.mat(np.diag([0.001] * num_states)) #arg
# Generate trajectory and obtain observations along trajectory
X_bar = np.mat(np.zeros((car.NX, T))) #arg
X_bar[:, 0] = np.mat(x0).T
U_bar = np.ones((car.NU, T - 1)) * 1.7 #arg
for t in xrange(1, T):
U_bar[1, t - 1] = 0
for t in xrange(1, T):
X_bar[:,t] = np.mat(car.dynamics(X_bar[:,t-1], U_bar[:, t-1])) +\
np.mat(dynamics_noise[:,t-1]).T
z = car.observe(s, x=X_bar[:, t]) + np.mat(measurement_noise[:, t - 1]).T
mus[:,
t], Sigmas[:, :,
t] = ekf_update(car.dynamics, lambda x: car.observe(s, x=x),
Q, R, mus[:, t - 1], Sigmas[:, :, t - 1],
U_bar[:, t - 1], z)
# Plot nominal trajectory with covariance ellipses
ax = plt.gca()
plt.title('Nominal')
s.draw(ax=ax)
#print Sigmas
car.draw_trajectory(mat2tuple(X_bar.T), mus=mus, Sigmas=Sigmas[0:2, 0:2, :])
car = SimpleCar(x0)
s.add_robot(car)
T = 30
X_bar = np.mat(np.zeros((car.NX, T)))
U_bar = np.mat(np.zeros((car.NU, T - 1)))
#U_bar = np.mat(np.random.random_sample((car.NU, T-1)))/5
for t in xrange(1, T):
U_bar[0, t - 1] = 0.3
U_bar[1, t - 1] = 0.1
if t > T / 2:
U_bar[0, t - 1] = 0
U_bar[1, t - 1] = -U_bar[1, t - 1]
X_bar[:, t] = car.dynamics(X_bar[:, t - 1], U_bar[:, t - 1])
# Plot nominal trajectory
ax = plt.subplot(221)
plt.title('Nominal')
s.draw(ax=ax)
car.draw_trajectory(mat2tuple(X_bar.T))
'''
X = np.mat(np.zeros((car.NX, T)))
As, Bs, Cs = car.linearize_dynamics_trajectory(X_bar, U_bar)
for t in xrange(T-1):
X[:,t+1] = As[:,:,t]*(X[:,t]-X_bar[:,t]) + Bs[:,:,t]*(U_bar[:,t]-U_bar[:,t]) +\
Cs[:,t]
s.draw()
car.draw_trajectory(mat2tuple(X.T))
# Generate nominal belief trajectory
'''
X_bar = np.mat(np.zeros((car.NX, T))) #arg
X_bar[:,0] = np.mat(x0).T
U_bar = np.load('data/nominal_trajectory.npy')
#U_bar = np.random.random((car.NU, T-1))
#for t in xrange(1,T):
#U_bar[1,t-1] = (U_bar[1,t-1] - 0.5)
#np.save('data/nominal_trajectory', U_bar)
'''
X_bar = np.mat(d['dat_states'])
U_bar = np.mat(d['dat_ctrls'])
for t in xrange(1,T):
X_bar[:,t] = np.mat(car.dynamics(X_bar[:,t-1], U_bar[:, t-1])) +\
np.mat(dynamics_noise[:,t-1]).T
mus[:,t], Sigmas[:,:,t] = ekf_update(car.dynamics,
lambda x: car.observe(s, x=x),
Q, R, mus[:,t-1], Sigmas[:,:,t-1],
U_bar[:,t-1], None) #NOTE No obs
# Plot nominal trajectory with covariance ellipses
ax = plt.gca()
s.draw(ax=ax)
#print Sigmas
#car.draw_trajectory(mat2tuple(X_bar.T), mus=X_bar, Sigmas=Sigmas[0:2,0:2,:])
Bel_bar = np.mat(np.zeros((car.NB, T)))
for t in xrange(T):
car = SimpleCar(x0)
s.add_robot(car)
T = 30
X_bar = np.mat(np.zeros((car.NX, T)))
U_bar = np.mat(np.zeros((car.NU, T-1)))
#U_bar = np.mat(np.random.random_sample((car.NU, T-1)))/5
for t in xrange(1,T):
U_bar[0,t-1] = 0.3
U_bar[1,t-1] = 0.1
if t > T / 2:
U_bar[0,t-1] = 0
U_bar[1,t-1] = -U_bar[1,t-1]
X_bar[:,t] = car.dynamics(X_bar[:,t-1], U_bar[:, t-1])
# Plot nominal trajectory
ax = plt.subplot(221)
plt.title('Nominal')
s.draw(ax=ax)
car.draw_trajectory(mat2tuple(X_bar.T))
'''
X = np.mat(np.zeros((car.NX, T)))
As, Bs, Cs = car.linearize_dynamics_trajectory(X_bar, U_bar)
for t in xrange(T-1):
X[:,t+1] = As[:,:,t]*(X[:,t]-X_bar[:,t]) + Bs[:,:,t]*(U_bar[:,t]-U_bar[:,t]) +\
Cs[:,t]
s.draw()
