#!/usr/bin/env python3
import math
import sys
from typing import Any
import numpy as np
from openpilot.selfdrive.controls.lib.vehicle_model import ACCELERATION_DUE_TO_GRAVITY
from openpilot.selfdrive.locationd.models.constants import ObservationKind
from openpilot.common.swaglog import cloudlog
from rednose.helpers.kalmanfilter import KalmanFilter
if __name__ == '__main__': # Generating sympy
import sympy as sp
from rednose.helpers.ekf_sym import gen_code
else:
from rednose.helpers.ekf_sym_pyx import EKF_sym_pyx
i = 0
def _slice(n):
global i
s = slice(i, i + n)
i += n
return s
[docs]
class States():
# Vehicle model params
STIFFNESS = _slice(1) # [-]
STEER_RATIO = _slice(1) # [-]
ANGLE_OFFSET = _slice(1) # [rad]
ANGLE_OFFSET_FAST = _slice(1) # [rad]
VELOCITY = _slice(2) # (x, y) [m/s]
YAW_RATE = _slice(1) # [rad/s]
STEER_ANGLE = _slice(1) # [rad]
ROAD_ROLL = _slice(1) # [rad]
[docs]
class CarKalman(KalmanFilter):
name = 'car'
initial_x = np.array([
1.0,
15.0,
0.0,
0.0,
10.0, 0.0,
0.0,
0.0,
0.0
])
# process noise
Q = np.diag([
(.05 / 100)**2,
.01**2,
math.radians(0.02)**2,
math.radians(0.25)**2,
.1**2, .01**2,
math.radians(0.1)**2,
math.radians(0.1)**2,
math.radians(1)**2,
])
P_initial = Q.copy()
obs_noise: dict[int, Any] = {
ObservationKind.STEER_ANGLE: np.atleast_2d(math.radians(0.05)**2),
ObservationKind.ANGLE_OFFSET_FAST: np.atleast_2d(math.radians(10.0)**2),
ObservationKind.ROAD_ROLL: np.atleast_2d(math.radians(1.0)**2),
ObservationKind.STEER_RATIO: np.atleast_2d(5.0**2),
ObservationKind.STIFFNESS: np.atleast_2d(0.5**2),
ObservationKind.ROAD_FRAME_X_SPEED: np.atleast_2d(0.1**2),
}
global_vars = [
'mass',
'rotational_inertia',
'center_to_front',
'center_to_rear',
'stiffness_front',
'stiffness_rear',
]
[docs]
@staticmethod
def generate_code(generated_dir):
dim_state = CarKalman.initial_x.shape[0]
name = CarKalman.name
# vehicle models comes from The Science of Vehicle Dynamics: Handling, Braking, and Ride of Road and Race Cars
# Model used is in 6.15 with formula from 6.198
# globals
global_vars = [sp.Symbol(name) for name in CarKalman.global_vars]
m, j, aF, aR, cF_orig, cR_orig = global_vars
# make functions and jacobians with sympy
# state variables
state_sym = sp.MatrixSymbol('state', dim_state, 1)
state = sp.Matrix(state_sym)
# Vehicle model constants
sf = state[States.STIFFNESS, :][0, 0]
cF, cR = sf * cF_orig, sf * cR_orig
angle_offset = state[States.ANGLE_OFFSET, :][0, 0]
angle_offset_fast = state[States.ANGLE_OFFSET_FAST, :][0, 0]
theta = state[States.ROAD_ROLL, :][0, 0]
sa = state[States.STEER_ANGLE, :][0, 0]
sR = state[States.STEER_RATIO, :][0, 0]
u, v = state[States.VELOCITY, :]
r = state[States.YAW_RATE, :][0, 0]
A = sp.Matrix(np.zeros((2, 2)))
A[0, 0] = -(cF + cR) / (m * u)
A[0, 1] = -(cF * aF - cR * aR) / (m * u) - u
A[1, 0] = -(cF * aF - cR * aR) / (j * u)
A[1, 1] = -(cF * aF**2 + cR * aR**2) / (j * u)
B = sp.Matrix(np.zeros((2, 1)))
B[0, 0] = cF / m / sR
B[1, 0] = (cF * aF) / j / sR
C = sp.Matrix(np.zeros((2, 1)))
C[0, 0] = ACCELERATION_DUE_TO_GRAVITY
C[1, 0] = 0
x = sp.Matrix([v, r]) # lateral velocity, yaw rate
x_dot = A * x + B * (sa - angle_offset - angle_offset_fast) - C * theta
dt = sp.Symbol('dt')
state_dot = sp.Matrix(np.zeros((dim_state, 1)))
state_dot[States.VELOCITY.start + 1, 0] = x_dot[0]
state_dot[States.YAW_RATE.start, 0] = x_dot[1]
# Basic descretization, 1st order integrator
# Can be pretty bad if dt is big
f_sym = state + dt * state_dot
#
# Observation functions
#
obs_eqs = [
[sp.Matrix([r]), ObservationKind.ROAD_FRAME_YAW_RATE, None],
[sp.Matrix([u, v]), ObservationKind.ROAD_FRAME_XY_SPEED, None],
[sp.Matrix([u]), ObservationKind.ROAD_FRAME_X_SPEED, None],
[sp.Matrix([sa]), ObservationKind.STEER_ANGLE, None],
[sp.Matrix([angle_offset_fast]), ObservationKind.ANGLE_OFFSET_FAST, None],
[sp.Matrix([sR]), ObservationKind.STEER_RATIO, None],
[sp.Matrix([sf]), ObservationKind.STIFFNESS, None],
[sp.Matrix([theta]), ObservationKind.ROAD_ROLL, None],
]
gen_code(generated_dir, name, f_sym, dt, state_sym, obs_eqs, dim_state, dim_state, global_vars=global_vars)
def __init__(self, generated_dir, steer_ratio=15, stiffness_factor=1, angle_offset=0, P_initial=None):
dim_state = self.initial_x.shape[0]
dim_state_err = self.P_initial.shape[0]
x_init = self.initial_x
x_init[States.STEER_RATIO] = steer_ratio
x_init[States.STIFFNESS] = stiffness_factor
x_init[States.ANGLE_OFFSET] = angle_offset
if P_initial is not None:
self.P_initial = P_initial
# init filter
self.filter = EKF_sym_pyx(generated_dir, self.name, self.Q, self.initial_x, self.P_initial,
dim_state, dim_state_err, global_vars=self.global_vars, logger=cloudlog)
if __name__ == "__main__":
generated_dir = sys.argv[2]
CarKalman.generate_code(generated_dir)