Created
March 31, 2020 13:23
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## slam takes in 6 arguments and returns mu, | |
## mu is the entire path traversed by a robot (all x,y poses) *and* all landmarks locations | |
def slam(data, N, num_landmarks, world_size, motion_noise, measurement_noise): | |
## TODO: Use your initilization to create constraint matrices, omega and xi | |
omega, xi = initialize_constraints(N, num_landmarks, world_size) | |
## TODO: Iterate through each time step in the data | |
for time_step in range(len(data)): | |
## get all the motion and measurement data as you iterate through each time step | |
measurement = data[time_step][0] | |
motion = data[time_step][1] | |
dx = motion[0] # distance to be moved along x in this time_step | |
dy = motion[1] # distance to be moved along y in this time_step | |
#Consider the robot moves from (x0,y0) to (x1,y1) in this time_step | |
#even numbered columns of omega correspond to x values | |
x0 = (time_step * 2) #x0 = 0,2,4,... | |
x1 = x0 + 2 #x1 = 2,4,6,... | |
#odd numbered columns of omega correspond to y values | |
y0 = x0 + 1 #y0 = 1,3,5,... | |
y1 = y0 + 2 #y1 = 3,5,7,... | |
actual_m_noise = 1.0/measurement_noise | |
actual_n_noise = 1.0/motion_noise | |
## TODO: update the constraint matrix/vector(omega/xi) to account for all *measurements* | |
## this should be a series of additions that take into account the measurement noise | |
for landmark in measurement: | |
lM = landmark[0] # landmark id | |
dx_lM = landmark[1] # separation along x from current position | |
dy_lM = landmark[2] # separation along y from current position | |
L_x0 = (N*2) + (lM*2) # even-numbered columns have x values of landmarks | |
L_y0 = L_x0 + 1 # odd-numbered columns have y values of landmarks | |
# update omega values corresponding to measurement between x0 and Lx0 | |
omega[x0][x0] += actual_m_noise | |
omega[L_x0][L_x0] += actual_m_noise | |
omega[x0][L_x0] += -actual_m_noise | |
omega[L_x0][x0] += -actual_m_noise | |
# update omega values corresponding to measurement between y0 and Ly0 | |
omega[y0][y0] += actual_m_noise | |
omega[L_y0][L_y0] += actual_m_noise | |
omega[y0][L_y0] += -actual_m_noise | |
omega[L_y0][y0] += -actual_m_noise | |
# update xi values corresponding to measurement between x0 and Lx0 | |
xi[x0] -= dx_lM/measurement_noise | |
xi[L_x0] += dx_lM/measurement_noise | |
# update xi values corresponding to measurement between y0 and Ly0 | |
xi[y0] -= dy_lM/measurement_noise | |
xi[L_y0] += dy_lM/measurement_noise | |
## TODO: update the constraint matrix/vector(omega/xi) to account for all *motion* from from (x0,y0) to (x1,y1) and motion noise | |
omega[x0][x0] += actual_n_noise | |
omega[x1][x1] += actual_n_noise | |
omega[x0][x1] += -actual_n_noise | |
omega[x1][x0] += -actual_n_noise | |
omega[y0][y0] += actual_n_noise | |
omega[y1][y1] += actual_n_noise | |
omega[y0][y1] += -actual_n_noise | |
omega[y1][y0] += -actual_n_noise | |
xi[x0] -= dx/motion_noise | |
xi[y0] -= dy/motion_noise | |
xi[x1] += dx/motion_noise | |
xi[y1] += dy/motion_noise | |
## TODO: After iterating through all the data | |
## Compute the best estimate of poses and landmark positions | |
## using the formula, omega_inverse * Xi | |
inverse_of_omega = np.linalg.inv(np.matrix(omega)) | |
mu = inverse_of_omega * xi | |
return mu |
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