Add vehicle_model.py

opendbc/car/vehicle_model.py

@@ -0,0 +1,230 @@
+#!/usr/bin/env python3
+"""
+Dynamic bicycle model from "The Science of Vehicle Dynamics (2014), M. Guiggiani"
+
+The state is x = [v, r]^T
+with v lateral speed [m/s], and r rotational speed [rad/s]
+
+The input u is the steering angle [rad], and roll [rad]
+
+The system is defined by
+x_dot = A*x + B*u
+
+A depends on longitudinal speed, u [m/s], and vehicle parameters CP
+"""
+
+import numpy as np
+from numpy.linalg import solve
+
+from cereal import car
+
+ACCELERATION_DUE_TO_GRAVITY = 9.8
+
+
+class VehicleModel:
+  def __init__(self, CP: car.CarParams):
+    """
+    Args:
+      CP: Car Parameters
+    """
+    # for math readability, convert long names car params into short names
+    self.m: float = CP.mass
+    self.j: float = CP.rotationalInertia
+    self.l: float = CP.wheelbase
+    self.aF: float = CP.centerToFront
+    self.aR: float = CP.wheelbase - CP.centerToFront
+    self.chi: float = CP.steerRatioRear
+
+    self.cF_orig: float = CP.tireStiffnessFront
+    self.cR_orig: float = CP.tireStiffnessRear
+    self.update_params(1.0, CP.steerRatio)
+
+  def update_params(self, stiffness_factor: float, steer_ratio: float) -> None:
+    """Update the vehicle model with a new stiffness factor and steer ratio"""
+    self.cF: float = stiffness_factor * self.cF_orig
+    self.cR: float = stiffness_factor * self.cR_orig
+    self.sR: float = steer_ratio
+
+  def steady_state_sol(self, sa: float, u: float, roll: float) -> np.ndarray:
+    """Returns the steady state solution.
+
+    If the speed is too low we can't use the dynamic model (tire slip is undefined),
+    we then have to use the kinematic model
+
+    Args:
+      sa: Steering wheel angle [rad]
+      u: Speed [m/s]
+      roll: Road Roll [rad]
+
+    Returns:
+      2x1 matrix with steady state solution (lateral speed, rotational speed)
+    """
+    if u > 0.1:
+      return dyn_ss_sol(sa, u, roll, self)
+    else:
+      return kin_ss_sol(sa, u, self)
+
+  def calc_curvature(self, sa: float, u: float, roll: float) -> float:
+    """Returns the curvature. Multiplied by the speed this will give the yaw rate.
+
+    Args:
+      sa: Steering wheel angle [rad]
+      u: Speed [m/s]
+      roll: Road Roll [rad]
+
+    Returns:
+      Curvature factor [1/m]
+    """
+    return (self.curvature_factor(u) * sa / self.sR) + self.roll_compensation(roll, u)
+
+  def curvature_factor(self, u: float) -> float:
+    """Returns the curvature factor.
+    Multiplied by wheel angle (not steering wheel angle) this will give the curvature.
+
+    Args:
+      u: Speed [m/s]
+
+    Returns:
+      Curvature factor [1/m]
+    """
+    sf = calc_slip_factor(self)
+    return (1. - self.chi) / (1. - sf * u**2) / self.l
+
+  def get_steer_from_curvature(self, curv: float, u: float, roll: float) -> float:
+    """Calculates the required steering wheel angle for a given curvature
+
+    Args:
+      curv: Desired curvature [1/m]
+      u: Speed [m/s]
+      roll: Road Roll [rad]
+
+    Returns:
+      Steering wheel angle [rad]
+    """
+
+    return (curv - self.roll_compensation(roll, u)) * self.sR * 1.0 / self.curvature_factor(u)
+
+  def roll_compensation(self, roll: float, u: float) -> float:
+    """Calculates the roll-compensation to curvature
+
+    Args:
+      roll: Road Roll [rad]
+      u: Speed [m/s]
+
+    Returns:
+      Roll compensation curvature [rad]
+    """
+    sf = calc_slip_factor(self)
+
+    if abs(sf) < 1e-6:
+      return 0
+    else:
+      return (ACCELERATION_DUE_TO_GRAVITY * roll) / ((1 / sf) - u**2)
+
+  def get_steer_from_yaw_rate(self, yaw_rate: float, u: float, roll: float) -> float:
+    """Calculates the required steering wheel angle for a given yaw_rate
+
+    Args:
+      yaw_rate: Desired yaw rate [rad/s]
+      u: Speed [m/s]
+      roll: Road Roll [rad]
+
+    Returns:
+      Steering wheel angle [rad]
+    """
+    curv = yaw_rate / u
+    return self.get_steer_from_curvature(curv, u, roll)
+
+  def yaw_rate(self, sa: float, u: float, roll: float) -> float:
+    """Calculate yaw rate
+
+    Args:
+      sa: Steering wheel angle [rad]
+      u: Speed [m/s]
+      roll: Road Roll [rad]
+
+    Returns:
+      Yaw rate [rad/s]
+    """
+    return self.calc_curvature(sa, u, roll) * u
+
+
+def kin_ss_sol(sa: float, u: float, VM: VehicleModel) -> np.ndarray:
+  """Calculate the steady state solution at low speeds
+  At low speeds the tire slip is undefined, so a kinematic
+  model is used.
+
+  Args:
+    sa: Steering angle [rad]
+    u: Speed [m/s]
+    VM: Vehicle model
+
+  Returns:
+    2x1 matrix with steady state solution
+  """
+  K = np.zeros((2, 1))
+  K[0, 0] = VM.aR / VM.sR / VM.l * u
+  K[1, 0] = 1. / VM.sR / VM.l * u
+  return K * sa
+
+
+def create_dyn_state_matrices(u: float, VM: VehicleModel) -> tuple[np.ndarray, np.ndarray]:
+  """Returns the A and B matrix for the dynamics system
+
+  Args:
+    u: Vehicle speed [m/s]
+    VM: Vehicle model
+
+  Returns:
+    A tuple with the 2x2 A matrix, and 2x2 B matrix
+
+  Parameters in the vehicle model:
+    cF: Tire stiffness Front [N/rad]
+    cR: Tire stiffness Front [N/rad]
+    aF: Distance from CG to front wheels [m]
+    aR: Distance from CG to rear wheels [m]
+    m: Mass [kg]
+    j: Rotational inertia [kg m^2]
+    sR: Steering ratio [-]
+    chi: Steer ratio rear [-]
+  """
+  A = np.zeros((2, 2))
+  B = np.zeros((2, 2))
+  A[0, 0] = - (VM.cF + VM.cR) / (VM.m * u)
+  A[0, 1] = - (VM.cF * VM.aF - VM.cR * VM.aR) / (VM.m * u) - u
+  A[1, 0] = - (VM.cF * VM.aF - VM.cR * VM.aR) / (VM.j * u)
+  A[1, 1] = - (VM.cF * VM.aF**2 + VM.cR * VM.aR**2) / (VM.j * u)
+
+  # Steering input
+  B[0, 0] = (VM.cF + VM.chi * VM.cR) / VM.m / VM.sR
+  B[1, 0] = (VM.cF * VM.aF - VM.chi * VM.cR * VM.aR) / VM.j / VM.sR
+
+  # Roll input
+  B[0, 1] = -ACCELERATION_DUE_TO_GRAVITY
+
+  return A, B
+
+
+def dyn_ss_sol(sa: float, u: float, roll: float, VM: VehicleModel) -> np.ndarray:
+  """Calculate the steady state solution when x_dot = 0,
+  Ax + Bu = 0 => x = -A^{-1} B u
+
+  Args:
+    sa: Steering angle [rad]
+    u: Speed [m/s]
+    roll: Road Roll [rad]
+    VM: Vehicle model
+
+  Returns:
+    2x1 matrix with steady state solution
+  """
+  A, B = create_dyn_state_matrices(u, VM)
+  inp = np.array([[sa], [roll]])
+  return -solve(A, B) @ inp  # type: ignore
+
+
+def calc_slip_factor(VM: VehicleModel) -> float:
+  """The slip factor is a measure of how the curvature changes with speed
+  it's positive for Oversteering vehicle, negative (usual case) otherwise.
+  """
+  return VM.m * (VM.cF * VM.aF - VM.cR * VM.aR) / (VM.l**2 * VM.cF * VM.cR)