shooting_constraint.hpp

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#ifndef SHOOTINGCONSTRAINT_HPP_
#define SHOOTINGCONSTRAINT_HPP_

#include <Eigen/Dense>
#include <method_interfaces/multiple_shooting/multiple_shooting.hpp>
#include <optimization/constraints/GenericConstraintsBase.hpp>
#include <boost/numeric/odeint.hpp>
#include <dynamical_systems/tools/eigenIntegration.h>

namespace DirectTrajectoryOptimization {
template <typename DIMENSIONS>
class DTOMultipleShooting;

template<class DIMENSIONS>
class ShootingConstraint : public BaseClass::GenericConstraintsBase {

public:

    EIGEN_MAKE_ALIGNED_OPERATOR_NEW

    typedef typename DIMENSIONS::state_vector_t state_vector_t;
    typedef typename DIMENSIONS::control_vector_t control_vector_t;
    typedef typename DIMENSIONS::state_vector_array_t state_vector_array_t;
    typedef typename DIMENSIONS::control_vector_array_t control_vector_array_t;

    ShootingConstraint(const int & n_func, const int & n_vars, std::shared_ptr<DTOMultipleShooting<DIMENSIONS>>  my_owner):
        _dms_(my_owner),GenericConstraintsBase(n_func, n_vars)  { }

    virtual Eigen::VectorXd Evalfx(const Eigen::VectorXd & in_vect) override;

    void forwardIntegrateForTimeRange(const state_vector_t & curr_state, const control_vector_t & curr_control,
            const control_vector_t & next_control, const double & total_t, state_vector_t & integrated_state);

    void evalDefectGradient(const Eigen::VectorXd & inputspace, Eigen::MatrixXd &jacobianMatrix);

    Eigen::VectorXd evalDefectVector(const state_vector_array_t & y_trajectory,
            const control_vector_array_t & u_trajectory, const Eigen::VectorXd & h_trajectory);

    ~ShootingConstraint() {}

    void initialize() {
        this->initialize_num_diff();
        _ms_defect_vector.resize(_dms_->num_defects);
    }

    double ms_dt_ = 0.001;  
    Eigen::VectorXd _ms_defect_vector;

    std::shared_ptr<DTOMultipleShooting<DIMENSIONS> > _dms_;
    std::shared_ptr<DynamicsBase<DIMENSIONS> > _local_dynamics_;

    //ToDo : Try with different steppers!
    boost::numeric::odeint::runge_kutta4<state_vector_t, double,
                state_vector_t, double,
                boost::numeric::odeint::vector_space_algebra> ms_stepper_;
};

template<class DIMENSIONS>
typename Eigen::VectorXd ShootingConstraint<DIMENSIONS>::Evalfx(const Eigen::VectorXd & in_vector) {

    state_vector_array_t y_trajectory;
    control_vector_array_t u_trajectory;
    Eigen::VectorXd  h_trajectory;

    _dms_->getStateControlIncrementsTrajectoriesFromDecisionVariables(in_vector,y_trajectory,u_trajectory,h_trajectory);

    Eigen::VectorXd defect = evalDefectVector(y_trajectory,u_trajectory,h_trajectory);

    return(defect);
}

template<class DIMENSIONS>
Eigen::VectorXd ShootingConstraint<DIMENSIONS>::evalDefectVector(const state_vector_array_t & y_trajectory,
        const control_vector_array_t & u_trajectory , const Eigen::VectorXd & h_trajectory) {

    state_vector_t integrated_state;
    _ms_defect_vector.setZero();

    int current_defect_index = 0;

    for (int k = 0; k < _dms_->n_inc ;  k++) {

        _local_dynamics_ = _dms_->_dynamics[_dms_->node_to_phase_map[k]];

        forwardIntegrateForTimeRange(y_trajectory[k], u_trajectory[k],
                u_trajectory[k+1], h_trajectory[k],integrated_state);

        state_vector_t defect = (y_trajectory[k+1] - integrated_state);

        _ms_defect_vector.segment<DIMENSIONS::kTotalStates>(current_defect_index) = defect;

        current_defect_index +=  DIMENSIONS::kTotalStates;
    }

    return(_ms_defect_vector);
}

template<class DIMENSIONS>
void ShootingConstraint<DIMENSIONS>::evalDefectGradient(const Eigen::VectorXd& input, Eigen::MatrixXd &defect_jacobian) {
    // User can still override the function EVALFXJACOBIAN in this class and write an analytical version

    defect_jacobian = this->EvalFxJacobian(input);
}

template<class DIMENSIONS>
void ShootingConstraint<DIMENSIONS>::forwardIntegrateForTimeRange(
        const state_vector_t & curr_state, const control_vector_t & curr_control,
        const control_vector_t & next_control, const double & total_t, state_vector_t & integrated_state) {

    // generate stepper and lambda for forward integration
    integrated_state = curr_state;

    auto f = [=](const state_vector_t &x, state_vector_t &dxdt, const double t) {

        double t_percentage = t/total_t;
        control_vector_t control =
                next_control * t_percentage +
                curr_control * (1-t_percentage);

        dxdt = _local_dynamics_->systemDynamics(x, control);
    };

    // run the integration
    boost::numeric::odeint::integrate_const(ms_stepper_, f, integrated_state,
            0.0,total_t,ms_dt_);
}

} // namespace DirectTrajectoryOptimization
#endif /* SHOOTINGCONSTRAINT_HPP_ */