direct_transcription_implementation.hpp

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#include <Eigen/Dense>
#include <cstdlib>
#include <iostream>

#include "direct_transcription.hpp"

namespace DirectTrajectoryOptimization {

template <class DIMENSIONS>
void DTODirectTranscription<DIMENSIONS>::SetDircolMethod(const int & dcm) {

    dircol_method = dcm;
}

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

  defect_vector.setZero();

    // ToDo : Move this to the update variables method and validate with : dircol==1
    state_vector_t y_kmid;
    state_vector_t F_kmid, ymid_dot;
    control_vector_t u_kmid;

    int node = 0;
    int current_defect_index = 0;
    int phase_first_node = 0;
    int inc_index=0;

    for(int p = 0; p < this->num_phases ; p++ ){

        for(int n = 0 ; n < this->number_nodes_phase[p] - 1 ; n++) {

            node = phase_first_node + n;

            // Trapezodial
            if (dircol_method == 0) {

                defect_vector.segment(current_defect_index, this->_numStates) = -this->_y_trajectory[node+1] + this->_y_trajectory[node] +
                        this->_h_trajectory(inc_index)*0.5*( this->_ydot_trajectory[node] + this->_ydot_trajectory[node+1] );

            } else if(dircol_method == 1) {

                // Hermitian interpolation of state at intermediate points
                y_kmid = 0.5*(this->_y_trajectory[node] + this->_y_trajectory[node+1]) + this->_h_trajectory(inc_index)*0.125*(this->_ydot_trajectory[node] - this->_ydot_trajectory[node+1]);
                // Midpoint rule for control at intermediate points
                u_kmid = 0.5*(this->_u_trajectory[node] + this->_u_trajectory[node+1]);

                // approximated dynamics at intermediate point assuming
                ymid_dot = (1.5/this->_h_trajectory(inc_index))*(this->_y_trajectory[node+1] - this->_y_trajectory[node]) - 0.25*(this->_ydot_trajectory[node] + this->_ydot_trajectory[node+1]);

                // dynamics at the intermediate points
                F_kmid = this->_dynamics[this->node_to_phase_map[node]]->systemDynamics(y_kmid, u_kmid);

                //finally the defect constraints
                defect_vector.segment(current_defect_index, this->_numStates) = F_kmid - ymid_dot;
            }
            current_defect_index += this->_numStates;
            inc_index++;

        }
        phase_first_node += this->number_nodes_phase[p];


    }
}

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

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

    int constraint_row = 0; // row of the constraint
    int G_index = 0;        // current index of the sparsity structure
    int nnz_per_row;
    
    // defect constraints
        // Trapezodial
        if (dircol_method == 0) {
            //state_vector_t F_k, F_kp1;
            state_vector_t Jac_h;
            state_matrix_t Jac_yk, Jac_ykp1;
            control_gain_matrix_t Jac_uk, Jac_ukp1;

            double alpha = 0;
            int node = 0;
            int phase_first_node = 0;
            int inc_index = 0;

            for(int p = 0; p < this->num_phases ; p++ ){

                // initialize iteration variables
                this->_derivatives[this->node_to_phase_map[phase_first_node]]->setCurrentStateAndControl(this->_y_trajectory[phase_first_node],this->_u_trajectory[phase_first_node]);
                state_matrix_t aux_s_matrix = this->_derivatives[this->node_to_phase_map[phase_first_node]]->getDerivativeState();
                control_gain_matrix_t aux_c_matrix = this->_derivatives[this->node_to_phase_map[phase_first_node]]->getDerivativeControl();


                for(int n = 0 ; n < this->number_nodes_phase[p] - 1 ; n++) {

                    node = phase_first_node + n;

                    alpha = 0.5*this->_h_trajectory(inc_index);

                    //F_kp1 = this->_dynamics[this->node_to_phase_map[k+1]]->systemDynamics(y_trajectory[k+1], u_trajectory[k+1]);

                    //w.r.t h (room for efficiency)
                    Jac_h = 0.5*(this->_ydot_trajectory[node]+ this->_ydot_trajectory[node+1]);
                    //w.r.t y_k
                    Jac_yk = I_y + alpha * aux_s_matrix;
                    //w.r.t u_k
                    Jac_uk = alpha * aux_c_matrix;

                    //Very important : Do not move this above previous Jac's.
                    this->_derivatives[this->node_to_phase_map[node+1]]->setCurrentStateAndControl(this->_y_trajectory[node+1],this->_u_trajectory[node+1]);
                    aux_s_matrix = this->_derivatives[this->node_to_phase_map[node+1]]->getDerivativeState();
                    aux_c_matrix = this->_derivatives[this->node_to_phase_map[node+1]]->getDerivativeControl();

                    //w.r.t y_kp1
                    Jac_ykp1 = -I_y + alpha * aux_s_matrix;
                    //w.r.t u_kp1
                    Jac_ukp1 = alpha * aux_c_matrix;

                    for(int jj=0; jj<this->_numStates; jj++) {

                        val_vec(G_index) = Jac_h(jj);
                        G_index += 1;
                        val_vec.segment(G_index, this->_numStates) = Jac_yk.row(jj);
                        G_index += this->_numStates;
                        val_vec.segment(G_index, this->_numStates) = Jac_ykp1.row(jj);
                        G_index += this->_numStates;
                        val_vec.segment(G_index, this->_numControls) = Jac_uk.row(jj);
                        G_index += this->_numControls;
                        val_vec.segment(G_index, this->_numControls) = Jac_ukp1.row(jj);
                        G_index += this->_numControls;

                        constraint_row++;
                    }
                    inc_index++;
                }
                phase_first_node += this->number_nodes_phase[p];
            }

        } else if (dircol_method == 1) { // Simpson-Hermite

            state_vector_t y_kmid, F_kmid;
            control_vector_t u_kmid;

            state_vector_t Jac_h;
            state_matrix_t Jac_yk, Jac_ykmid, Jac_ykp1;
            state_matrix_t dFk_dyk, dFkmid_dykmid, dFkp1_dykp1;
            control_gain_matrix_t Jac_uk, Jac_ukmid, Jac_ukp1;
            control_gain_matrix_t dFk_duk, dFkmid_dukmid, dFkp1_dukp1;

            double fac = 0.0;

            int node = 0;
            int phase_first_node = 0;
            int inc_index = 0;

            for(int p = 0; p < this->num_phases ; p++ ){

                for(int n = 0 ; n < this->number_nodes_phase[p] - 1 ; n++) {

                    node = phase_first_node + n;

                    fac = 3/(2*this->_h_trajectory(inc_index));

                    //F_k = this->_dynamics[this->node_to_phase_map[k]]->systemDynamics(y_trajectory[k], u_trajectory[k]);
                    //F_kp1 = this->_dynamics[this->node_to_phase_map[node+1]]->systemDynamics(y_trajectory[node+1], u_trajectory[node+1]);

                    y_kmid = 0.5*(this->_y_trajectory[node] + this->_y_trajectory[node+1]) + this->_h_trajectory(inc_index)*0.125*(this->_ydot_trajectory[node] - this->_ydot_trajectory[node+1]);

                    u_kmid = 0.5*(this->_u_trajectory[node] + this->_u_trajectory[node+1]);

                    F_kmid = this->_dynamics[this->node_to_phase_map[node]]->systemDynamics(y_kmid, u_kmid);

                    // Dynamic derivatives
                    this->_derivatives[this->node_to_phase_map[node]]->setCurrentStateAndControl(this->_y_trajectory[node],this->_u_trajectory[node]);
                    dFk_dyk = this->_derivatives[this->node_to_phase_map[node]]->getDerivativeState();
                    dFk_duk = this->_derivatives[this->node_to_phase_map[node]]->getDerivativeControl();

                    this->_derivatives[this->node_to_phase_map[node]]->setCurrentStateAndControl(y_kmid,u_kmid);
                    dFkmid_dykmid = this->_derivatives[this->node_to_phase_map[node]]->getDerivativeState();
                    dFkmid_dukmid = this->_derivatives[this->node_to_phase_map[node]]->getDerivativeControl();

                    this->_derivatives[this->node_to_phase_map[node+1]]->setCurrentStateAndControl(this->_y_trajectory[node+1],this->_u_trajectory[node+1]);
                    dFkp1_dykp1 = this->_derivatives[this->node_to_phase_map[node+1]]->getDerivativeState();
                    dFkp1_dukp1 = this->_derivatives[this->node_to_phase_map[node+1]]->getDerivativeControl();

                    //Elements of Jacobian
                        //w.r.t h
                    Jac_h = 0.125 * dFkmid_dykmid * (this->_ydot_trajectory[node] - this->_ydot_trajectory[node+1])
                            - (fac/this->_h_trajectory(inc_index))*(this->_y_trajectory[node] - this->_y_trajectory[node+1]); //
                        //w.r.t y_k
                    Jac_yk = this->_h_trajectory(inc_index)*0.125*dFkmid_dykmid*dFk_dyk + 0.5*dFkmid_dykmid + I_y*fac + 0.25*dFk_dyk; //
                        //w.r.t u_k
                    Jac_uk = this->_h_trajectory(inc_index)*0.125*dFkmid_dykmid*dFk_duk + 0.5*dFkmid_dukmid + 0.25*dFk_duk; //
                        //w.r.t y_kp1
                    Jac_ykp1 = -this->_h_trajectory(inc_index)*0.125*dFkmid_dykmid*dFkp1_dykp1 + 0.5*dFkmid_dykmid - fac*I_y + 0.25*dFkp1_dykp1; //
                        //w.r.t u_kp1
                    Jac_ukp1 = -this->_h_trajectory(inc_index)*0.125*dFkmid_dykmid*dFkp1_dukp1 + 0.5*dFkmid_dukmid + 0.25*dFkp1_dukp1; //


                    for (int jj = 0 ; jj < this->_numStates; jj++) {
                        val_vec(G_index) = Jac_h(jj);
                        G_index += 1;
                        val_vec.segment(G_index, this->_numStates) = Jac_yk.row(jj);
                        G_index += this->_numStates;
                        val_vec.segment(G_index, this->_numStates) = Jac_ykp1.row(jj);
                        G_index += this->_numStates;
                        val_vec.segment(G_index, this->_numControls) = Jac_uk.row(jj);
                        G_index += this->_numControls;
                        val_vec.segment(G_index, this->_numControls) = Jac_ukp1.row(jj);
                        G_index += this->_numControls;

                        constraint_row++;
                    }
                    inc_index++;
                }
            phase_first_node += this->number_nodes_phase[p];
            }
        }

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

    // 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++) {

                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_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]];
        }

        if (this->_multiphaseproblem) {

            state_vector_t gJac;
            /* Guard Constraints */
            for(int i = 0; i < this->num_phases -1 ; i++) {

                // nnz per guard
                int nnz_per_guard = this->_numStates*this->size_guard[i];

                    // state at the left
                    state_vector_t   y_l = this->_y_trajectory[this->leftphase_nodes(i)];

                    // guard->evalJacobian should return a single-row Jacobian
                    val_vec.segment(G_index,nnz_per_guard) = this->_guards[i]->evalConstraintsFctDerivatives(y_l);
                    G_index += nnz_per_guard;
                    constraint_row += this->size_guard[i];

            }

            /* Interphase constraints */

            for(int i = 0 ; i < this->num_phases - 1 ; i++) {
                int nnz_interphase_constraint = 2 * (this->_numStates + this->_numControls) * this->size_interphase_constraint[i];

                //ToDo: Set this outside this method!
                state_vector_t   y_l = this->_y_trajectory[this->leftphase_nodes(i)];
                control_vector_t u_l = this->_u_trajectory[this->leftphase_nodes(i)];
                state_vector_t   y_r = this->_y_trajectory[this->rightphase_nodes(i)];
                control_vector_t u_r = this->_u_trajectory[this->rightphase_nodes(i)];

                // _interphase_constraint->getJacobian() should return Jacobian matrix row-wise
                val_vec.segment(G_index,nnz_interphase_constraint) = this->_interphase_constraint[i]->evalConstraintsFctDerivatives(y_l,y_r,u_l,u_r);
                G_index += nnz_interphase_constraint;
                constraint_row += this->size_interphase_constraint[i];
            }

        }

    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);
    }
}

} // namespace DirectTrajectoryOptimization