dubins_origin_example.cpp

/*
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 * Authors: David Fridovich-Keil   ( dfk@eecs.berkeley.edu )
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///////////////////////////////////////////////////////////////////////////////
//
// Two Dubins cars. One tries to follow other one, which is trying to get to the
// origin. Both also have penalties on control input, and we are interested in
// the difference between open-loop and feedback Nash strategies for this
// situation. Example conceived by Forrest Laine ( forrest.laine@berkeley.edu ).
//
///////////////////////////////////////////////////////////////////////////////

#include <ilqgames/cost/quadratic_cost.h>
#include <ilqgames/cost/quadratic_difference_cost.h>
#include <ilqgames/dynamics/concatenated_dynamical_system.h>
#include <ilqgames/dynamics/single_player_dubins_car.h>
#include <ilqgames/examples/dubins_origin_example.h>
#include <ilqgames/solver/ilq_solver.h>
#include <ilqgames/solver/problem.h>
#include <ilqgames/solver/solver_params.h>
#include <ilqgames/utils/types.h>

#include <math.h>
#include <memory>
#include <vector>

namespace ilqgames {

namespace {

// Cost weights.
static constexpr float kOmegaCostWeight = 100.0;
static constexpr float kAttractionCostWeight = 10.0;
static constexpr float kGoalCostWeight = 10.0;

// Initial state.
static constexpr float kP1InitialX = 0.0;                // m
static constexpr float kP1InitialY = -10.0;              // m
static constexpr float kP1InitialHeading = M_PI - 0.01;  // rad

static constexpr float kP2InitialX = 0.0;               // m
static constexpr float kP2InitialY = 10.0;              // m
static constexpr float kP2InitialHeading = 1.5 * M_PI;  // rad

static constexpr float kSpeed = 1.0;  // m/s

// Goal position.
static constexpr float kP2GoalX = 0.0;
static constexpr float kP2GoalY = 0.0;

// State dimensions.
using P1 = SinglePlayerDubinsCar;
using P2 = SinglePlayerDubinsCar;

static const Dimension kP1XIdx = P1::kPxIdx;
static const Dimension kP1YIdx = P1::kPyIdx;
static const Dimension kP1HeadingIdx = P1::kThetaIdx;

static const Dimension kP2XIdx = P1::kNumXDims + P2::kPxIdx;
static const Dimension kP2YIdx = P1::kNumXDims + P2::kPyIdx;
static const Dimension kP2HeadingIdx = P1::kNumXDims + P2::kThetaIdx;

// Control dimensions.
static const Dimension kP1OmegaIdx = 0;
static const Dimension kP2OmegaIdx = 0;
}  // anonymous namespace

void DubinsOriginExample::ConstructDynamics() {
  dynamics_.reset(new ConcatenatedDynamicalSystem(
      {std::make_shared<P1>(kSpeed), std::make_shared<P2>(kSpeed)}));
}

void DubinsOriginExample::ConstructInitialState() {
  // Set up initial state.
  x0_ = VectorXf::Zero(dynamics_->XDim());
  x0_(kP1XIdx) = kP1InitialX;
  x0_(kP1YIdx) = kP1InitialY;
  x0_(kP1HeadingIdx) = kP1InitialHeading;
  x0_(kP2XIdx) = kP2InitialX;
  x0_(kP2YIdx) = kP2InitialY;
  x0_(kP2HeadingIdx) = kP2InitialHeading;
}

void DubinsOriginExample::ConstructPlayerCosts() {
  // Set up costs for all players.
  player_costs_.emplace_back("P1");
  player_costs_.emplace_back("P2");
  auto& p1_cost = player_costs_[0];
  auto& p2_cost = player_costs_[1];

  // Attract P2 to P1.
  const std::shared_ptr<QuadraticDifferenceCost> p2_attraction_cost =
      std::shared_ptr<QuadraticDifferenceCost>(
          new QuadraticDifferenceCost(kAttractionCostWeight, {kP1XIdx, kP1YIdx},
                                      {kP2XIdx, kP2YIdx}, "AttractionCost"));
  p2_cost.AddStateCost(p2_attraction_cost);

  // Penalize control effort.
  const auto p1_omega_cost = std::make_shared<QuadraticCost>(
      kOmegaCostWeight, kP1OmegaIdx, 0.0, "Steering");
  p1_cost.AddControlCost(0, p1_omega_cost);

  const auto p2_omega_cost = std::make_shared<QuadraticCost>(
      kOmegaCostWeight, kP2OmegaIdx, 0.0, "Steering");
  p2_cost.AddControlCost(1, p2_omega_cost);

  // Goal cost.
  const auto p1_goalx_cost = std::make_shared<QuadraticCost>(
      kGoalCostWeight, kP2XIdx, kP2GoalX, "GoalX");
  const auto p1_goaly_cost = std::make_shared<QuadraticCost>(
      kGoalCostWeight, kP2YIdx, kP2GoalY, "GoalY");
  p1_cost.AddStateCost(p1_goalx_cost);
  p1_cost.AddStateCost(p1_goaly_cost);
}

inline std::vector<float> DubinsOriginExample::Xs(const VectorXf& x) const {
  return {x(kP1XIdx), x(kP2XIdx)};
}

inline std::vector<float> DubinsOriginExample::Ys(const VectorXf& x) const {
  return {x(kP1YIdx), x(kP2YIdx)};
}

inline std::vector<float> DubinsOriginExample::Thetas(const VectorXf& x) const {
  return {x(kP1HeadingIdx), x(kP2HeadingIdx)};
}

}  // namespace ilqgames