openpilot is an open source driver assistance system. openpilot performs the functions of Automated Lane Centering and Adaptive Cruise Control for over 200 supported car makes and models.
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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)