multiple_shooting.hpp

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#ifndef INCLUDE_METHOD_INTERFACES_MULTIPLE_SHOOTING_HPP_
#define INCLUDE_METHOD_INTERFACES_MULTIPLE_SHOOTING_HPP_

#define infy 1e20

#include <Eigen/Dense>
#include <boost/numeric/odeint.hpp>
#include <method_interfaces/multiple_shooting/shooting_constraint.hpp>
#include <method_interfaces/base_method_interface.hpp>

namespace DirectTrajectoryOptimization {

template <typename DIMENSIONS>
class DTOMultipleShooting;

template<typename DIMENSIONS>
class DTOMultipleShooting: public DTOMethodInterface<DIMENSIONS>, public std::enable_shared_from_this<DTOMultipleShooting<DIMENSIONS>>{

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;

    DTOMultipleShooting(
            std::vector<std::shared_ptr<DynamicsBase<DIMENSIONS> > > dynamics,
            std::vector<std::shared_ptr<DerivativesBaseDS<DIMENSIONS> > > derivatives,
            std::shared_ptr<BaseClass::CostFunctionBase<DIMENSIONS> > costFunction,
            std::vector<std::shared_ptr<BaseClass::ConstraintsBase<DIMENSIONS> > > constraints,
            Eigen::Vector2d duration, int number_of_nodes, bool methodVerbose) :
                DTOMethodInterface<DIMENSIONS>(dynamics, derivatives, costFunction,
                        constraints, duration, number_of_nodes, methodVerbose) { }

    virtual ~DTOMultipleShooting() {}

    virtual void Method_specific_initialization() override {
        _shootingconstraint_ = std::shared_ptr<ShootingConstraint<DIMENSIONS> >(new ShootingConstraint<DIMENSIONS>(this->num_defects,this->myNLP.num_vars,
                std::enable_shared_from_this<DTOMultipleShooting<DIMENSIONS>>::shared_from_this()));
        _shootingconstraint_->initialize();

    }

    // Sparsity structure is the same as the one in direct transcription
    virtual void evalSparseJacobianConstraint(double* val) override;
    virtual void evaluateDefects(Eigen::VectorXd & defect_vector) override;

    std::shared_ptr<ShootingConstraint<DIMENSIONS> > _shootingconstraint_; 
};

template<class DIMENSIONS>
void DTOMultipleShooting<DIMENSIONS>::evalSparseJacobianConstraint(double* val) {

  Eigen::Map<Eigen::VectorXd> val_vec(val,this->myNLP.lenG);
  val_vec.setZero();
  Eigen::MatrixXd Jacobian;

  Eigen::VectorXd x_local;
  this->SetDecisionVariablesFromStateControlIncrementsTrajectories(x_local,this->_y_trajectory,
                                                                   this->_u_trajectory,
                                                                   this->_h_trajectory);

  _shootingconstraint_->evalDefectGradient(x_local,Jacobian);


    int constraint_row = 0; // row of the constraint
    int G_index = 0;        // current index of the sparsity structure
    int nnz_per_row;

    /* defect constraints */

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

        int set_of_defects = k * this->_numStates;
        // for each defect
        for (int jj = 0; jj < this->_numStates; jj++) {
            int current_state = set_of_defects + jj;
            // w.r.t. h_k
            val_vec(G_index) = Jacobian(set_of_defects + jj , this->h_inds(k));//Jac_h(jj);
            G_index += 1;

            // w.r.t. y_k
            val_vec.segment(G_index, this->_numStates) = Jacobian.block(current_state , this->y_inds(0,k) , 1 , this->_numStates).transpose();//Jac_yk.row(jj);
            G_index += this->_numStates;

            // w.r.t. y_k+1
            val_vec.segment(G_index, this->_numStates) = Jacobian.block(current_state , this->y_inds(0,k+1) , 1 , this->_numStates).transpose();//Jac_ykp1.row(jj);
            G_index += this->_numStates;

            // w.r.t. u_k
            val_vec.segment(G_index, this->_numControls) = Jacobian.block(current_state , this->u_inds(0,k) , 1 , this->_numControls).transpose();//Jac_uk.row(jj);
            G_index += this->_numControls;

            // w.r.t. u_k+1
            val_vec.segment(G_index, this->_numControls) = Jacobian.block(current_state , this->u_inds(0,k+1) , 1 , this->_numControls).transpose();//row(jj);
            G_index += this->_numControls;

            constraint_row++;
            }
    }


    if (constraint_row != this->num_defects) {
        std::cout << "Error evaluating the Jacobian of constraints (DEFECTS)"
                << std::endl;
        exit(EXIT_FAILURE);
    }

    // ToDo: The following constraint jacobian is common to direct_transcription, but here is replicated.
    //       This should be centralized in base_method_interface

    /* parametric constraints */
        // Time constraint
        val_vec.segment(G_index, this->n_inc) = Eigen::VectorXd::Ones(this->n_inc);
        G_index += this->n_inc;
        constraint_row++;

        // increments constraint
        nnz_per_row = 2;
        if (this->_evenTimeIncr) {

            for (int k = 0 ; k < this->n_inc -1 ; k++) {
                //iGfun.segment(G_index,nnz_per_row) = Eigen::VectorXi::Constant(nnz_per_row,constraint_row);

                Eigen::VectorXd aux_value(nnz_per_row);
                aux_value << 1 , -1;
                val_vec.segment(G_index,nnz_per_row) = aux_value;

                G_index+=nnz_per_row;
                constraint_row++;
            }
        }

        if (constraint_row != this->num_parametric_constraints + this->num_defects) {
            std::cout << "Error evaluating the Jacobian of constraints (PARAMETRIC)" << std::endl;
            std::cout << "contratint_row : " << constraint_row << std::endl;
            std::cout << "num_parametric_constraints : " << this->num_parametric_constraints << std::endl;
            exit(EXIT_FAILURE);
        }

    /* User Constraints */

        for (int k=0; k< this->_numberOfNodes; k++) {

            //val_vec.segment(G_index,this->num_nonzero_jacobian_user_per_node)  = this->_constraints[this->node_to_phase_map[k]]->evalConstraintsFctDerivatives(y_trajectory[k], u_trajectory[k]);
            val_vec.segment(G_index,this->num_nonzero_jacobian_user_per_node_in_phase[this->node_to_phase_map[k]])  = this->_constraints[this->node_to_phase_map[k]]->evalConstraintsFctDerivatives(this->_y_trajectory[k],this->_u_trajectory[k]);
            G_index += this->num_nonzero_jacobian_user_per_node_in_phase[this->node_to_phase_map[k]];

            constraint_row += this->num_user_constraints_per_node_in_phase[this->node_to_phase_map[k]];
        }

    // ToDo Guard Constraints
        if (this->_usingGuardFunction) {
            //we have this number already!
            //ToDo: Move this!
            int num_nnz_jac_guards = this->num_guards * this->_numStates;
            Eigen::VectorXi guard_derivatives;
            guard_derivatives.resize(this->_numStates);
            val_vec.segment(G_index,num_nnz_jac_guards).setZero();
            G_index +=num_nnz_jac_guards;
            constraint_row += this->num_guards;
        }

    if (constraint_row!=this->myNLP.num_F) {
        std::cout << "Error evaluating the Jacobian of constraints (USER)" << std::endl;
        std::cout << "constraint_row : " << constraint_row << std::endl;
        std::cout << "num_F : " << this->myNLP.num_F << std::endl;
        std::cout << "lenG : " << this->myNLP.lenG << std::endl;
        exit(EXIT_FAILURE);
    }
}

template<class DIMENSIONS>
void DTOMultipleShooting<DIMENSIONS>::evaluateDefects(
        Eigen::VectorXd & defect_vector) {

    Eigen::VectorXd x_local;
    this->SetDecisionVariablesFromStateControlIncrementsTrajectories(x_local,this->_y_trajectory,this->_u_trajectory,this->_h_trajectory);

    defect_vector = _shootingconstraint_->Evalfx(x_local);
}

} // namespace DirectTrajectoryOptimization

#endif /* INCLUDE_METHOD_INTERFACES_MULTIPLE_SHOOTING_HPP_ */