MPC.cpp

#include "MPC.h"
#include <cppad/cppad.hpp>
#include <cppad/ipopt/solve.hpp>
#include "Eigen-3.3/Eigen/Core"

using CppAD::AD;

size_t N = 10;
double dt = 0.1;

// Reference velocity below which if the vehicle goes it is penalized.
double ref_v = 100;

// The solver takes all the state variables and actuator
// variables in a singular vector. Thus, we should to establish
// when one variable starts and another ends to make our lifes easier.
size_t x_start = 0;
size_t y_start = x_start + N;
size_t psi_start = y_start + N;
size_t v_start = psi_start + N;
size_t cte_start = v_start + N;
size_t epsi_start = cte_start + N;
size_t delta_start = epsi_start + N;
size_t a_start = delta_start + N - 1;

class FG_eval {
 public:
  // Fitted polynomial coefficients
  Eigen::VectorXd coeffs;
  FG_eval(Eigen::VectorXd coeffs) { this->coeffs = coeffs; }

  typedef CPPAD_TESTVECTOR(AD<double>) ADvector;
  void operator()(ADvector& fg, const ADvector& vars) {
    // The cost is stored is the first element of `fg`.
    // Any additions to the cost should be added to `fg[0]`.
    fg[0] = 0;

    // Cost based on state.
    for (unsigned int i=0; i < N; ++i) {
      fg[0] += 1000 * CppAD::pow(vars[cte_start+i], 2);
      fg[0] += 1000 * CppAD::pow(vars[epsi_start+i], 2);
      fg[0] += CppAD::pow(vars[v_start+i] - ref_v, 2);
    }

    // Cost based on use of actuators.
    for (unsigned int i=0; i < N-1; ++i) {
      fg[0] += 50 * CppAD::pow(vars[delta_start+i], 2);
      fg[0] += 50 * CppAD::pow(vars[a_start+i], 2);
    }

    // Error between two consecutive actuations; affecting steering.
    for (unsigned int i=0; i < N-2; ++i) {
      fg[0] += 250000 * CppAD::pow(vars[delta_start+i+1] - vars[delta_start+i], 2);
      fg[0] += 5000 * CppAD::pow(vars[a_start+i+1] - vars[a_start+i], 2);  // reducing abrupt jumps in steering
    }

    //// Setup Constraints
    // Initial constraints.
    fg[1 + x_start] = vars[x_start];
    fg[1 + y_start] = vars[y_start];
    fg[1 + psi_start] = vars[psi_start];
    fg[1 + v_start] = vars[v_start];
    fg[1 + cte_start] = vars[cte_start];
    fg[1 + epsi_start] = vars[epsi_start];

    // The rest of the constraints
    for (unsigned int t = 1; t < N; ++t) {
      // State at time t+1 .
      AD<double> x1 = vars[x_start + t];
      AD<double> y1 = vars[y_start + t];
      AD<double> psi1 = vars[psi_start + t];
      AD<double> v1 = vars[v_start + t];
      AD<double> cte1 = vars[cte_start + t];
      AD<double> epsi1 = vars[epsi_start + t];

      // State at time t.
      AD<double> x0 = vars[x_start + t - 1];
      AD<double> y0 = vars[y_start + t - 1];
      AD<double> psi0 = vars[psi_start + t - 1];
      AD<double> v0 = vars[v_start + t - 1];
      AD<double> cte0 = vars[cte_start + t - 1];
      AD<double> epsi0 = vars[epsi_start + t - 1];

      // Actuation at time t.
      AD<double> delta0 = vars[delta_start + t - 1];
      AD<double> a0 = vars[a_start + t - 1];

      // f(x) polynomial of degree 3.
      AD<double> f0 = coeffs[0] + coeffs[1] * x0 + coeffs[2] * CppAD::pow(x0, 2) + coeffs[3] * CppAD::pow(x0, 3);
      AD<double> psides0 = CppAD::atan(coeffs[1] + 2 * coeffs[2] * x0 + 3 * coeffs[3] * CppAD::pow(x0, 2));

      // Constraints for the state at time t.
      fg[1 + x_start + t] = x1 - (x0 + v0 * CppAD::cos(psi0) * dt);
      fg[1 + y_start + t] = y1 - (y0 + v0 * CppAD::sin(psi0) * dt);
      fg[1 + psi_start + t] = psi1 - (psi0 - v0 / Lf * delta0 * dt);
      fg[1 + v_start + t] = v1 - (v0 + a0 * dt);
      fg[1 + cte_start + t] = cte1 - ((f0 - y0) + (v0 * CppAD::sin(epsi0) * dt));
      fg[1 + epsi_start + t] = epsi1 - ((psi0 - psides0) - v0 / Lf * delta0 * dt);
    }
  }
};

//
// MPC class definition implementation.
//
MPC::MPC() {}
MPC::~MPC() {}

vector<double> MPC::Solve(Eigen::VectorXd state, Eigen::VectorXd coeffs) {
  bool ok = true;
  size_t i;
  typedef CPPAD_TESTVECTOR(double) Dvector;

  // Set the number of model variables (includes both state and actuators).
  size_t n_vars = 6 * N + 2 * (N-1);
  // Set the number of constraints
  size_t n_constraints = 6 * N;

  // Extract state variables.
  const double x = state[0];
  const double y = state[1];
  const double psi = state[2];
  const double v = state[3];
  const double cte = state[4];
  const double epsi = state[5];

  // Initial value of the independent variables.
  // SHOULD BE 0 besides initial state.
  Dvector vars(n_vars);
  for (i = 0; i < n_vars; i++) {
    vars[i] = 0;
  }

  Dvector vars_lowerbound(n_vars);
  Dvector vars_upperbound(n_vars);

  // Set all state variables' lower and upper limits to the max negative and positive values.
  for (i = 0; i < delta_start; ++i) {
    vars_lowerbound[i] = -1.0e19;
    vars_upperbound[i] = 1.0e19;
  }

  // Set heading variable's lower and upper limits to 25 degrees.
  for (i = delta_start; i < a_start; ++i) {
    vars_lowerbound[i] = -0.436332 * Lf;
    vars_upperbound[i] = 0.436332 * Lf;
  }

  // Set throttle actuator's limits.
  for (i = a_start; i < n_vars; ++i) {
    vars_lowerbound[i] = -1.;
    vars_upperbound[i] = 1.;
  }

  // Lower and upper limits for the constraints
  // Should be 0 besides initial state.
  Dvector constraints_lowerbound(n_constraints);
  Dvector constraints_upperbound(n_constraints);
  for (i = 0; i < n_constraints; i++) {
    constraints_lowerbound[i] = 0;
    constraints_upperbound[i] = 0;
  }
  constraints_lowerbound[x_start] = x;
  constraints_lowerbound[y_start] = y;
  constraints_lowerbound[psi_start] = psi;
  constraints_lowerbound[v_start] = v;
  constraints_lowerbound[cte_start] = cte;
  constraints_lowerbound[epsi_start] = epsi;

  constraints_upperbound[x_start] = x;
  constraints_upperbound[y_start] = y;
  constraints_upperbound[psi_start] = psi;
  constraints_upperbound[v_start] = v;
  constraints_upperbound[cte_start] = cte;
  constraints_upperbound[epsi_start] = epsi;

  // object that computes objective and constraints
  FG_eval fg_eval(coeffs);

  // options for IPOPT solver
  std::string options;
  // Uncomment this if you'd like more print information
  options += "Integer print_level  0\n";
  // NOTE: Setting sparse to true allows the solver to take advantage
  // of sparse routines, this makes the computation MUCH FASTER. If you
  // can uncomment 1 of these and see if it makes a difference or not but
  // if you uncomment both the computation time should go up in orders of
  // magnitude.
  options += "Sparse  true        forward\n";
  options += "Sparse  true        reverse\n";
  // NOTE: Currently the solver has a maximum time limit of 0.5 seconds.
  // Change this as you see fit.
  options += "Numeric max_cpu_time          0.5\n";

  // place to return solution
  CppAD::ipopt::solve_result<Dvector> solution;

  // solve the problem
  CppAD::ipopt::solve<Dvector, FG_eval>(
      options, vars, vars_lowerbound, vars_upperbound, constraints_lowerbound,
      constraints_upperbound, fg_eval, solution);

  // Check some of the solution values
  ok &= solution.status == CppAD::ipopt::solve_result<Dvector>::success;

  //// DEBUG
  // Cost
  // auto cost = solution.obj_value;
  // std::cout << "Cost " << cost << std::endl;

  // Return actuator values for the next time-step.
  vector<double> result;
  result.push_back(solution.x[delta_start]);
  result.push_back(solution.x[a_start]);

  // Append the x, y coordinates of N-steps in the predicted curve.
  for (i = 0; i < N - 2; ++i) {
    result.push_back(solution.x[x_start + i + 1]);
    result.push_back(solution.x[y_start + i + 1]);
  }

  return result;
}