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								import math
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								from cereal import log
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								from common.numpy_fast import interp
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								from selfdrive.controls.lib.latcontrol import LatControl, MIN_STEER_SPEED
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								from selfdrive.controls.lib.pid import PIDController
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								from selfdrive.controls.lib.drive_helpers import apply_deadzone
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								from selfdrive.controls.lib.vehicle_model import ACCELERATION_DUE_TO_GRAVITY
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								# At higher speeds (25+mph) we can assume:
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								# Lateral acceleration achieved by a specific car correlates to
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								# torque applied to the steering rack. It does not correlate to
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								# wheel slip, or to speed.
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								# This controller applies torque to achieve desired lateral
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								# accelerations. To compensate for the low speed effects we
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								# use a LOW_SPEED_FACTOR in the error. Additionally, there is
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								# friction in the steering wheel that needs to be overcome to
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								# move it at all, this is compensated for too.
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								FRICTION_THRESHOLD = 0.2
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								class LatControlTorque(LatControl):
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								  def __init__(self, CP, CI):
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								    super().__init__(CP, CI)
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								    self.pid = PIDController(CP.lateralTuning.torque.kp, CP.lateralTuning.torque.ki,
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								                             k_f=CP.lateralTuning.torque.kf, pos_limit=self.steer_max, neg_limit=-self.steer_max)
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								    self.get_steer_feedforward = CI.get_steer_feedforward_function()
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								    self.use_steering_angle = CP.lateralTuning.torque.useSteeringAngle
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								    self.friction = CP.lateralTuning.torque.friction
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								    self.kf = CP.lateralTuning.torque.kf
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								    self.steering_angle_deadzone_deg = CP.lateralTuning.torque.steeringAngleDeadzoneDeg
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								  def update(self, active, CS, VM, params, last_actuators, desired_curvature, desired_curvature_rate, llk):
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								    pid_log = log.ControlsState.LateralTorqueState.new_message()
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								    if CS.vEgo < MIN_STEER_SPEED or not active:
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								      output_torque = 0.0
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								      pid_log.active = False
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								    else:
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								      if self.use_steering_angle:
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								        actual_curvature = -VM.calc_curvature(math.radians(CS.steeringAngleDeg - params.angleOffsetDeg), CS.vEgo, params.roll)
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								        curvature_deadzone = abs(VM.calc_curvature(math.radians(self.steering_angle_deadzone_deg), CS.vEgo, 0.0))
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								      else:
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								        actual_curvature_vm = -VM.calc_curvature(math.radians(CS.steeringAngleDeg - params.angleOffsetDeg), CS.vEgo, params.roll)
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								        actual_curvature_llk = llk.angularVelocityCalibrated.value[2] / CS.vEgo
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								        actual_curvature = interp(CS.vEgo, [2.0, 5.0], [actual_curvature_vm, actual_curvature_llk])
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								        curvature_deadzone = 0.0
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								      desired_lateral_accel = desired_curvature * CS.vEgo ** 2
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								      # desired rate is the desired rate of change in the setpoint, not the absolute desired curvature
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								      #desired_lateral_jerk = desired_curvature_rate * CS.vEgo ** 2
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								      actual_lateral_accel = actual_curvature * CS.vEgo ** 2
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								      lateral_accel_deadzone = curvature_deadzone * CS.vEgo ** 2
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								      low_speed_factor = interp(CS.vEgo, [0, 10, 20], [500, 500, 200])
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								      setpoint = desired_lateral_accel + low_speed_factor * desired_curvature
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								      measurement = actual_lateral_accel + low_speed_factor * actual_curvature
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								      error = setpoint - measurement
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								      pid_log.error = error
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								      ff = desired_lateral_accel - params.roll * ACCELERATION_DUE_TO_GRAVITY
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								      # convert friction into lateral accel units for feedforward
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								      friction_compensation = interp(apply_deadzone(error, lateral_accel_deadzone), [-FRICTION_THRESHOLD, FRICTION_THRESHOLD], [-self.friction, self.friction])
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								      ff += friction_compensation / self.kf
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								      freeze_integrator = CS.steeringRateLimited or CS.steeringPressed or CS.vEgo < 5
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								      output_torque = self.pid.update(error,
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								                                      feedforward=ff,
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								                                      speed=CS.vEgo,
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								                                      freeze_integrator=freeze_integrator)
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								      pid_log.active = True
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								      pid_log.p = self.pid.p
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								      pid_log.i = self.pid.i
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								      pid_log.d = self.pid.d
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								      pid_log.f = self.pid.f
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								      pid_log.output = -output_torque
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								      pid_log.saturated = self._check_saturation(self.steer_max - abs(output_torque) < 1e-3, CS)
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								      pid_log.actualLateralAccel = actual_lateral_accel
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								      pid_log.desiredLateralAccel = desired_lateral_accel
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								    # TODO left is positive in this convention
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								    return -output_torque, 0.0, pid_log
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