single_player_delayed_dubins_car.h

/*
 * Copyright (c) 2020, The Regents of the University of California (Regents).
 * All rights reserved.
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 *       notice, this list of conditions and the following disclaimer.
 *
 *    2. Redistributions in binary form must reproduce the above
 *       copyright notice, this list of conditions and the following
 *       disclaimer in the documentation and/or other materials provided
 *       with the distribution.
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 *    3. Neither the name of the copyright holder nor the names of its
 *       contributors may be used to endorse or promote products derived
 *       from this software without specific prior written permission.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS AS IS
 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE
 * LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
 * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
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 * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
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 *
 * Please contact the author(s) of this library if you have any questions.
 * Authors: David Fridovich-Keil   ( dfk@eecs.berkeley.edu )
 */

///////////////////////////////////////////////////////////////////////////////
//
// Single player dynamics modeling a Dubins car with input delay. 4 states and 1
// control input. State is [x, y, theta, omega], control is [alpha], and
// dynamics are:
//                     \dot px    = v cos theta
//                     \dot py    = v sin theta
//                     \dot theta = omega
//                     \dot omega = alpha
//
///////////////////////////////////////////////////////////////////////////////

#ifndef ILQGAMES_DYNAMICS_SINGLE_PLAYER_DELAYED_DUBINS_CAR_H
#define ILQGAMES_DYNAMICS_SINGLE_PLAYER_DELAYED_DUBINS_CAR_H

#include <ilqgames/dynamics/single_player_dynamical_system.h>
#include <ilqgames/utils/types.h>

#include <glog/logging.h>

namespace ilqgames {

class SinglePlayerDelayedDubinsCar : public SinglePlayerDynamicalSystem {
 public:
  ~SinglePlayerDelayedDubinsCar() {}
  SinglePlayerDelayedDubinsCar(float v)
      : SinglePlayerDynamicalSystem(kNumXDims, kNumUDims), v_(v) {
    CHECK_GT(v_, 0.0);
  }

  // Compute time derivative of state.
  VectorXf Evaluate(Time t, const VectorXf& x, const VectorXf& u) const;

  // Compute a discrete-time Jacobian linearization.
  void Linearize(Time t, const VectorXf& x, const VectorXf& u,
                 Eigen::Ref<MatrixXf> A, Eigen::Ref<MatrixXf> B) const;

  // Position dimensions.
  std::vector<Dimension> PositionDimensions() const { return {kPxIdx, kPyIdx}; }

  // Constexprs for state indices.
  static const Dimension kNumXDims;
  static const Dimension kPxIdx;
  static const Dimension kPyIdx;
  static const Dimension kThetaIdx;
  static const Dimension kOmegaIdx;

  // Constexprs for control indices.
  static const Dimension kNumUDims;
  static const Dimension kAlphaIdx;

 private:
  // Constant speed of the car.
  const float v_;
};  //\class SinglePlayerDelayedDubinsCar

// ----------------------------- IMPLEMENTATION ----------------------------- //

inline VectorXf SinglePlayerDelayedDubinsCar::Evaluate(
    Time t, const VectorXf& x, const VectorXf& u) const {
  VectorXf xdot(xdim_);
  xdot(kPxIdx) = v_ * std::cos(x(kThetaIdx));
  xdot(kPyIdx) = v_ * std::sin(x(kThetaIdx));
  xdot(kThetaIdx) = x(kOmegaIdx);
  xdot(kOmegaIdx) = u(kAlphaIdx);

  return xdot;
}

inline void SinglePlayerDelayedDubinsCar::Linearize(
    Time t, const VectorXf& x, const VectorXf& u, Eigen::Ref<MatrixXf> A,
    Eigen::Ref<MatrixXf> B) const {
  const float ctheta = std::cos(x(kThetaIdx)) * time::kTimeStep;
  const float stheta = std::sin(x(kThetaIdx)) * time::kTimeStep;

  A(kPxIdx, kThetaIdx) += -v_ * stheta;
  A(kPyIdx, kThetaIdx) += v_ * ctheta;
  A(kThetaIdx, kOmegaIdx) += time::kTimeStep;

  B(kOmegaIdx, kAlphaIdx) = time::kTimeStep;
}

}  // namespace ilqgames

#endif