air_3d_example.cpp

/*
 * Copyright (c) 2020, The Regents of the University of California (Regents).
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 * AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
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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 )
 */

///////////////////////////////////////////////////////////////////////////////
//
// Two player Air3D example from:
// https://www.cs.ubc.ca/~mitchell/Papers/publishedIEEEtac05.pdf.
//
///////////////////////////////////////////////////////////////////////////////

#include <ilqgames/constraint/single_dimension_constraint.h>
#include <ilqgames/cost/polyline2_signed_distance_cost.h>
#include <ilqgames/cost/quadratic_cost.h>
#include <ilqgames/dynamics/air_3d.h>
#include <ilqgames/examples/air_3d_example.h>
#include <ilqgames/geometry/draw_shapes.h>
#include <ilqgames/geometry/polyline2.h>
#include <ilqgames/solver/ilq_solver.h>
#include <ilqgames/solver/problem.h>
#include <ilqgames/solver/solver_params.h>
#include <ilqgames/utils/types.h>

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

// Initial state command-line flags.
DEFINE_double(rx0, 4.0, "Initial x-position (m).");
DEFINE_double(ry0, 3.0, "Initial y-position (m).");
DEFINE_double(rtheta0, M_PI / 4.0, "Initial heading (rad).");
DEFINE_double(ve, 1.0, "Evader speed (m/s).");
DEFINE_double(vp, 1.0, "Pursuer speed (m/s).");

namespace ilqgames {

namespace {

// Input cost and constraint.
static constexpr float kOmegaCostWeight = 0.1;
static constexpr float kOmegaMax = 1.0;  // rad/s

// State dimensions.
using Dyn = Air3D;

}  // anonymous namespace

void Air3DExample::ConstructDynamics() {
  dynamics_.reset(new Dyn(FLAGS_ve, FLAGS_vp));
}

void Air3DExample::ConstructInitialState() {
  x0_ = VectorXf::Zero(dynamics_->XDim());
  x0_(Dyn::kRxIdx) = FLAGS_rx0;
  x0_(Dyn::kRyIdx) = FLAGS_ry0;
  x0_(Dyn::kRThetaIdx) = FLAGS_rtheta0;
}

void Air3DExample::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];

  const auto control_cost =
      std::make_shared<QuadraticCost>(kOmegaCostWeight, -1, 0.0, "ControlCost");
  p1_cost.AddControlCost(0, control_cost);
  p2_cost.AddControlCost(1, control_cost);

  // Constrain control effort.
  const auto p1_omega_max_constraint =
      std::make_shared<SingleDimensionConstraint>(
          Dyn::kOmega1Idx, kOmegaMax, true, "Omega Constraint (Max)");
  const auto p1_omega_min_constraint =
      std::make_shared<SingleDimensionConstraint>(
          Dyn::kOmega1Idx, -kOmegaMax, false, "Omega Constraint (Min)");
  p1_cost.AddControlConstraint(0, p1_omega_max_constraint);
  p1_cost.AddControlConstraint(0, p1_omega_min_constraint);

  const auto p2_omega_max_constraint =
      std::make_shared<SingleDimensionConstraint>(
          Dyn::kOmega1Idx, kOmegaMax, true, "Omega Constraint (Max)");
  const auto p2_omega_min_constraint =
      std::make_shared<SingleDimensionConstraint>(
          Dyn::kOmega2Idx, -kOmegaMax, false, "Omega Constraint (Min)");
  p2_cost.AddControlConstraint(1, p2_omega_max_constraint);
  p2_cost.AddControlConstraint(1, p2_omega_min_constraint);

  // Target cost.
  const float kTargetRadius = 5.0;
  const Polyline2 circle = DrawCircle(Point2::Zero(), kTargetRadius, 10);

  constexpr bool kReach = true;
  const std::shared_ptr<Polyline2SignedDistanceCost> p1_target_cost(
      new Polyline2SignedDistanceCost(circle, {Dyn::kRxIdx, Dyn::kRyIdx},
                                      !kReach, "Target"));
  const std::shared_ptr<Polyline2SignedDistanceCost> p2_target_cost(
      new Polyline2SignedDistanceCost(circle, {Dyn::kRxIdx, Dyn::kRyIdx},
                                      kReach, "Target"));

  p1_cost.AddStateCost(p1_target_cost);
  p2_cost.AddStateCost(p2_target_cost);

  // Make sure evader's cost is a max-over-time and pursuer's is a
  // min-over-time.
  p1_cost.SetMaxOverTime();
  p2_cost.SetMinOverTime();
}

inline std::vector<float> Air3DExample::Xs(const VectorXf& x) const {
  return {0.0, x(Dyn::kRxIdx)};
}

inline std::vector<float> Air3DExample::Ys(const VectorXf& x) const {
  return {0.0, x(Dyn::kRyIdx)};
}

inline std::vector<float> Air3DExample::Thetas(const VectorXf& x) const {
  return {0.0, x(Dyn::kRThetaIdx)};
}

}  // namespace ilqgames