import numpy as np import sympy as sp import os from laika.constants import EARTH_GM from .kalman_helpers import ObservationKind from .ekf_sym import gen_code from common.sympy_helpers import cross, euler_rotate, quat_rotate, quat_matrix_l, quat_matrix_r def gen_model(name, N, dim_main, dim_main_err, dim_augment, dim_augment_err, dim_state, dim_state_err, maha_test_kinds): # check if rebuild is needed try: dir_path = os.path.dirname(__file__) deps = [dir_path + '/' + 'ekf_c.c', dir_path + '/' + 'ekf_sym.py', dir_path + '/' + 'loc_model.py', dir_path + '/' + 'loc_kf.py'] outs = [dir_path + '/' + name + '.o', dir_path + '/' + name + '.so', dir_path + '/' + name + '.cpp'] out_times = list(map(os.path.getmtime, outs)) dep_times = list(map(os.path.getmtime, deps)) rebuild = os.getenv("REBUILD", False) if min(out_times) > max(dep_times) and not rebuild: return list(map(os.remove, outs)) except OSError as e: pass # make functions and jacobians with sympy # state variables state_sym = sp.MatrixSymbol('state', dim_state, 1) state = sp.Matrix(state_sym) x,y,z = state[0:3,:] q = state[3:7,:] v = state[7:10,:] vx, vy, vz = v omega = state[10:13,:] vroll, vpitch, vyaw = omega cb, cd = state[13:15,:] roll_bias, pitch_bias, yaw_bias = state[15:18,:] odo_scale = state[18,:] acceleration = state[19:22,:] focal_scale = state[22,:] imu_angles= state[23:26,:] glonass_bias, glonass_freq_slope = state[26:28,:] ca = state[28,0] dt = sp.Symbol('dt') # calibration and attitude rotation matrices quat_rot = quat_rotate(*q) # Got the quat predict equations from here # A New Quaternion-Based Kalman Filter for # Real-Time Attitude Estimation Using the Two-Step # Geometrically-Intuitive Correction Algorithm A = 0.5*sp.Matrix([[0, -vroll, -vpitch, -vyaw], [vroll, 0, vyaw, -vpitch], [vpitch, -vyaw, 0, vroll], [vyaw, vpitch, -vroll, 0]]) q_dot = A * q # Time derivative of the state as a function of state state_dot = sp.Matrix(np.zeros((dim_state, 1))) state_dot[:3,:] = v state_dot[3:7,:] = q_dot state_dot[7:10,0] = quat_rot * acceleration state_dot[13,0] = cd state_dot[14,0] = ca # Basic descretization, 1st order intergrator # Can be pretty bad if dt is big f_sym = state + dt*state_dot state_err_sym = sp.MatrixSymbol('state_err',dim_state_err,1) state_err = sp.Matrix(state_err_sym) quat_err = state_err[3:6,:] v_err = state_err[6:9,:] omega_err = state_err[9:12,:] cd_err = state_err[13,:] acceleration_err = state_err[18:21,:] ca_err = state_err[27,:] # Time derivative of the state error as a function of state error and state quat_err_matrix = euler_rotate(quat_err[0], quat_err[1], quat_err[2]) q_err_dot = quat_err_matrix * quat_rot * (omega + omega_err) state_err_dot = sp.Matrix(np.zeros((dim_state_err, 1))) state_err_dot[:3,:] = v_err state_err_dot[3:6,:] = q_err_dot state_err_dot[6:9,:] = quat_err_matrix * quat_rot * (acceleration + acceleration_err) state_err_dot[12,:] = cd_err state_err_dot[13,:] = ca_err f_err_sym = state_err + dt*state_err_dot # convenient indexing # q idxs are for quats and p idxs are for other q_idxs = [[3, dim_augment]] + [[dim_main + n*dim_augment + 3, dim_main + (n+1)*dim_augment] for n in range(N)] q_err_idxs = [[3, dim_augment_err]] + [[dim_main_err + n*dim_augment_err + 3, dim_main_err + (n+1)*dim_augment_err] for n in range(N)] p_idxs = [[0, 3]] + [[dim_augment, dim_main]] + [[dim_main + n*dim_augment , dim_main + n*dim_augment + 3] for n in range(N)] p_err_idxs = [[0, 3]] + [[dim_augment_err, dim_main_err]] + [[dim_main_err + n*dim_augment_err, dim_main_err + n*dim_augment_err + 3] for n in range(N)] # Observation matrix modifier H_mod_sym = sp.Matrix(np.zeros((dim_state, dim_state_err))) for p_idx, p_err_idx in zip(p_idxs, p_err_idxs): H_mod_sym[p_idx[0]:p_idx[1],p_err_idx[0]:p_err_idx[1]] = np.eye(p_idx[1]-p_idx[0]) for q_idx, q_err_idx in zip(q_idxs, q_err_idxs): H_mod_sym[q_idx[0]:q_idx[1],q_err_idx[0]:q_err_idx[1]] = 0.5*quat_matrix_r(state[q_idx[0]:q_idx[1]])[:,1:] # these error functions are defined so that say there # is a nominal x and true x: # true x = err_function(nominal x, delta x) # delta x = inv_err_function(nominal x, true x) nom_x = sp.MatrixSymbol('nom_x',dim_state,1) true_x = sp.MatrixSymbol('true_x',dim_state,1) delta_x = sp.MatrixSymbol('delta_x',dim_state_err,1) err_function_sym = sp.Matrix(np.zeros((dim_state,1))) for q_idx, q_err_idx in zip(q_idxs, q_err_idxs): delta_quat = sp.Matrix(np.ones((4))) delta_quat[1:,:] = sp.Matrix(0.5*delta_x[q_err_idx[0]: q_err_idx[1],:]) err_function_sym[q_idx[0]:q_idx[1],0] = quat_matrix_r(nom_x[q_idx[0]:q_idx[1],0])*delta_quat for p_idx, p_err_idx in zip(p_idxs, p_err_idxs): err_function_sym[p_idx[0]:p_idx[1],:] = sp.Matrix(nom_x[p_idx[0]:p_idx[1],:] + delta_x[p_err_idx[0]:p_err_idx[1],:]) inv_err_function_sym = sp.Matrix(np.zeros((dim_state_err,1))) for p_idx, p_err_idx in zip(p_idxs, p_err_idxs): inv_err_function_sym[p_err_idx[0]:p_err_idx[1],0] = sp.Matrix(-nom_x[p_idx[0]:p_idx[1],0] + true_x[p_idx[0]:p_idx[1],0]) for q_idx, q_err_idx in zip(q_idxs, q_err_idxs): delta_quat = quat_matrix_r(nom_x[q_idx[0]:q_idx[1],0]).T*true_x[q_idx[0]:q_idx[1],0] inv_err_function_sym[q_err_idx[0]:q_err_idx[1],0] = sp.Matrix(2*delta_quat[1:]) eskf_params = [[err_function_sym, nom_x, delta_x], [inv_err_function_sym, nom_x, true_x], H_mod_sym, f_err_sym, state_err_sym] # # Observation functions # # extra args sat_pos_freq_sym = sp.MatrixSymbol('sat_pos', 4, 1) sat_pos_vel_sym = sp.MatrixSymbol('sat_pos_vel', 6, 1) sat_los_sym = sp.MatrixSymbol('sat_los', 3, 1) orb_epos_sym = sp.MatrixSymbol('orb_epos_sym', 3, 1) # expand extra args sat_x, sat_y, sat_z, glonass_freq = sat_pos_freq_sym sat_vx, sat_vy, sat_vz = sat_pos_vel_sym[3:] los_x, los_y, los_z = sat_los_sym orb_x, orb_y, orb_z = orb_epos_sym h_pseudorange_sym = sp.Matrix([sp.sqrt( (x - sat_x)**2 + (y - sat_y)**2 + (z - sat_z)**2) + cb]) h_pseudorange_glonass_sym = sp.Matrix([sp.sqrt( (x - sat_x)**2 + (y - sat_y)**2 + (z - sat_z)**2) + cb + glonass_bias + glonass_freq_slope*glonass_freq]) los_vector = (sp.Matrix(sat_pos_vel_sym[0:3]) - sp.Matrix([x, y, z])) los_vector = los_vector / sp.sqrt(los_vector[0]**2 + los_vector[1]**2 + los_vector[2]**2) h_pseudorange_rate_sym = sp.Matrix([los_vector[0]*(sat_vx - vx) + los_vector[1]*(sat_vy - vy) + los_vector[2]*(sat_vz - vz) + cd]) imu_rot = euler_rotate(*imu_angles) h_gyro_sym = imu_rot*sp.Matrix([vroll + roll_bias, vpitch + pitch_bias, vyaw + yaw_bias]) pos = sp.Matrix([x, y, z]) gravity = quat_rot.T * ((EARTH_GM/((x**2 + y**2 + z**2)**(3.0/2.0)))*pos) h_acc_sym = imu_rot*(gravity + acceleration) h_phone_rot_sym = sp.Matrix([vroll, vpitch, vyaw]) speed = vx**2 + vy**2 + vz**2 h_speed_sym = sp.Matrix([sp.sqrt(speed)*odo_scale]) # orb stuff orb_pos_sym = sp.Matrix([orb_x - x, orb_y - y, orb_z - z]) orb_pos_rot_sym = quat_rot.T * orb_pos_sym s = orb_pos_rot_sym[0] h_orb_point_sym = sp.Matrix([(1/s)*(orb_pos_rot_sym[1]), (1/s)*(orb_pos_rot_sym[2])]) h_pos_sym = sp.Matrix([x, y, z]) h_imu_frame_sym = sp.Matrix(imu_angles) h_relative_motion = sp.Matrix(quat_rot.T * v) obs_eqs = [[h_speed_sym, ObservationKind.ODOMETRIC_SPEED, None], [h_gyro_sym, ObservationKind.PHONE_GYRO, None], [h_phone_rot_sym, ObservationKind.NO_ROT, None], [h_acc_sym, ObservationKind.PHONE_ACCEL, None], [h_pseudorange_sym, ObservationKind.PSEUDORANGE_GPS, sat_pos_freq_sym], [h_pseudorange_glonass_sym, ObservationKind.PSEUDORANGE_GLONASS, sat_pos_freq_sym], [h_pseudorange_rate_sym, ObservationKind.PSEUDORANGE_RATE_GPS, sat_pos_vel_sym], [h_pseudorange_rate_sym, ObservationKind.PSEUDORANGE_RATE_GLONASS, sat_pos_vel_sym], [h_pos_sym, ObservationKind.ECEF_POS, None], [h_relative_motion, ObservationKind.CAMERA_ODO_TRANSLATION, None], [h_phone_rot_sym, ObservationKind.CAMERA_ODO_ROTATION, None], [h_imu_frame_sym, ObservationKind.IMU_FRAME, None], [h_orb_point_sym, ObservationKind.ORB_POINT, orb_epos_sym]] # MSCKF configuration if N > 0: focal_scale =1 # Add observation functions for orb feature tracks track_epos_sym = sp.MatrixSymbol('track_epos_sym', 3, 1) track_x, track_y, track_z = track_epos_sym h_track_sym = sp.Matrix(np.zeros(((1 + N)*2, 1))) track_pos_sym = sp.Matrix([track_x - x, track_y - y, track_z - z]) track_pos_rot_sym = quat_rot.T * track_pos_sym h_track_sym[-2:,:] = sp.Matrix([focal_scale*(track_pos_rot_sym[1]/track_pos_rot_sym[0]), focal_scale*(track_pos_rot_sym[2]/track_pos_rot_sym[0])]) h_msckf_test_sym = sp.Matrix(np.zeros(((1 + N)*3, 1))) h_msckf_test_sym[-3:,:] = sp.Matrix([track_x - x,track_y - y , track_z - z]) for n in range(N): idx = dim_main + n*dim_augment err_idx = dim_main_err + n*dim_augment_err x, y, z = state[idx:idx+3] q = state[idx+3:idx+7] quat_rot = quat_rotate(*q) track_pos_sym = sp.Matrix([track_x - x, track_y - y, track_z - z]) track_pos_rot_sym = quat_rot.T * track_pos_sym h_track_sym[n*2:n*2+2,:] = sp.Matrix([focal_scale*(track_pos_rot_sym[1]/track_pos_rot_sym[0]), focal_scale*(track_pos_rot_sym[2]/track_pos_rot_sym[0])]) h_msckf_test_sym[n*3:n*3+3,:] = sp.Matrix([track_x - x, track_y - y, track_z - z]) obs_eqs.append([h_msckf_test_sym, ObservationKind.MSCKF_TEST, track_epos_sym]) obs_eqs.append([h_track_sym, ObservationKind.ORB_FEATURES, track_epos_sym]) obs_eqs.append([h_track_sym, ObservationKind.FEATURE_TRACK_TEST, track_epos_sym]) msckf_params = [dim_main, dim_augment, dim_main_err, dim_augment_err, N, [ObservationKind.MSCKF_TEST, ObservationKind.ORB_FEATURES]] else: msckf_params = None gen_code(name, f_sym, dt, state_sym, obs_eqs, dim_state, dim_state_err, eskf_params, msckf_params, maha_test_kinds)