chainiksolverpos_lma.cpp

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/**************************************************************************
    begin                : May 2012
    copyright            : (C) 2012 Erwin Aertbelien
    email                : firstname.lastname@mech.kuleuven.ac.be

 History (only major changes)( AUTHOR-Description ) :

 ***************************************************************************
 *   This library is free software; you can redistribute it and/or         *
 *   modify it under the terms of the GNU Lesser General Public            *
 *   License as published by the Free Software Foundation; either          *
 *   version 2.1 of the License, or (at your option) any later version.    *
 *                                                                         *
 *   This library is distributed in the hope that it will be useful,       *
 *   but WITHOUT ANY WARRANTY; without even the implied warranty of        *
 *   MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU     *
 *   Lesser General Public License for more details.                       *
 *                                                                         *
 *   You should have received a copy of the GNU Lesser General Public      *
 *   License along with this library; if not, write to the Free Software   *
 *   Foundation, Inc., 59 Temple Place,                                    *
 *   Suite 330, Boston, MA  02111-1307  USA                                *
 *                                                                         *
 ***************************************************************************/

#include "chainiksolverpos_lma.hpp"
#include <iostream>

namespace KDL {




template <typename Derived>
inline void Twist_to_Eigen(const KDL::Twist& t,Eigen::MatrixBase<Derived>& e) {
        e(0)=t.vel.data[0];
        e(1)=t.vel.data[1];
        e(2)=t.vel.data[2];
        e(3)=t.rot.data[0];
        e(4)=t.rot.data[1];
        e(5)=t.rot.data[2];
}


ChainIkSolverPos_LMA::ChainIkSolverPos_LMA(
                const KDL::Chain& _chain,
                const Eigen::Matrix<double,6,1>& _L,
                double _eps,
                int _maxiter,
                double _eps_joints
) :
        lastNrOfIter(0),
        lastSV(_chain.getNrOfJoints()),
        jac(6, _chain.getNrOfJoints()),
        grad(_chain.getNrOfJoints()),
        display_information(false),
        maxiter(_maxiter),
        eps(_eps),
        eps_joints(_eps_joints),
        L(_L.cast<ScalarType>()),
        chain(_chain),
        T_base_jointroot(_chain.getNrOfJoints()),
        T_base_jointtip(_chain.getNrOfJoints()),
        q(_chain.getNrOfJoints()),
        A(_chain.getNrOfJoints(), _chain.getNrOfJoints()),
        tmp(_chain.getNrOfJoints()),
        ldlt(_chain.getNrOfJoints()),
        svd(6, _chain.getNrOfJoints(),Eigen::ComputeThinU | Eigen::ComputeThinV),
        diffq(_chain.getNrOfJoints()),
        q_new(_chain.getNrOfJoints()),
        original_Aii(_chain.getNrOfJoints())
{}

ChainIkSolverPos_LMA::ChainIkSolverPos_LMA(
                const KDL::Chain& _chain,
                double _eps,
                int _maxiter,
                double _eps_joints
) :
        lastNrOfIter(0),
        lastSV(_chain.getNrOfJoints()>6?6:_chain.getNrOfJoints()),
        jac(6, _chain.getNrOfJoints()),
        grad(_chain.getNrOfJoints()),
        display_information(false),
        maxiter(_maxiter),
        eps(_eps),
        eps_joints(_eps_joints),
        chain(_chain),
        T_base_jointroot(_chain.getNrOfJoints()),
        T_base_jointtip(_chain.getNrOfJoints()),
        q(_chain.getNrOfJoints()),
        A(_chain.getNrOfJoints(), _chain.getNrOfJoints()),
        ldlt(_chain.getNrOfJoints()),
        svd(6, _chain.getNrOfJoints(),Eigen::ComputeThinU | Eigen::ComputeThinV),
        diffq(_chain.getNrOfJoints()),
        q_new(_chain.getNrOfJoints()),
        original_Aii(_chain.getNrOfJoints())
{
        L(0)=1;
        L(1)=1;
        L(2)=1;
        L(3)=0.01;
        L(4)=0.01;
        L(5)=0.01;
}

ChainIkSolverPos_LMA::~ChainIkSolverPos_LMA() {}

void ChainIkSolverPos_LMA::compute_fwdpos(const VectorXq& q) {
        using namespace KDL;
        unsigned int jointndx=0;
        T_base_head = Frame::Identity(); // frame w.r.t. base of head
        for (unsigned int i=0;i<chain.getNrOfSegments();i++) {
                const Segment& segment = chain.getSegment(i);
                if (segment.getJoint().getType()!=Joint::None) {
                        T_base_jointroot[jointndx] = T_base_head;
                        T_base_head = T_base_head * segment.pose(q(jointndx));
                        T_base_jointtip[jointndx] = T_base_head;
                        jointndx++;
                } else {
                        T_base_head = T_base_head * segment.pose(0.0);
                }
        }
}

void ChainIkSolverPos_LMA::compute_jacobian(const VectorXq& q) {
        using namespace KDL;
        unsigned int jointndx=0;
        for (unsigned int i=0;i<chain.getNrOfSegments();i++) {
                const Segment& segment = chain.getSegment(i);
                if (segment.getJoint().getType()!=Joint::None) {
                        // compute twist of the end effector motion caused by joint [jointndx]; expressed in base frame, with vel. ref. point equal to the end effector
                        KDL::Twist t = ( T_base_jointroot[jointndx].M * segment.twist(q(jointndx),1.0) ).RefPoint( T_base_head.p - T_base_jointtip[jointndx].p);
                        jac(0,jointndx)=t[0];
                        jac(1,jointndx)=t[1];
                        jac(2,jointndx)=t[2];
                        jac(3,jointndx)=t[3];
                        jac(4,jointndx)=t[4];
                        jac(5,jointndx)=t[5];
                        jointndx++;
                }
        }
}

void ChainIkSolverPos_LMA::display_jac(const KDL::JntArray& jval) {
        VectorXq q;
        q = jval.data.cast<ScalarType>();
        compute_fwdpos(q);
        compute_jacobian(q);
        svd.compute(jac);
        std::cout << "Singular values : " << svd.singularValues().transpose()<<"\n";
}


int ChainIkSolverPos_LMA::CartToJnt(const KDL::JntArray& q_init, const KDL::Frame& T_base_goal, KDL::JntArray& q_out) {
        using namespace KDL;
        double v      = 2;
        double tau    = 10;
        double rho;
        double lambda;
        Twist t;
        double delta_pos_norm;
        Eigen::Matrix<ScalarType,6,1> delta_pos;
        Eigen::Matrix<ScalarType,6,1> delta_pos_new;


        q=q_init.data.cast<ScalarType>();
        compute_fwdpos(q);
        Twist_to_Eigen( diff( T_base_head, T_base_goal), delta_pos );
        delta_pos=L.asDiagonal()*delta_pos;
        delta_pos_norm = delta_pos.norm();
        if (delta_pos_norm<eps) {
                lastNrOfIter    =0 ;
                Twist_to_Eigen( diff( T_base_head, T_base_goal), delta_pos );
                lastDifference  = delta_pos.norm();
                lastTransDiff   = delta_pos.topRows(3).norm();
                lastRotDiff     = delta_pos.bottomRows(3).norm();
                svd.compute(jac);
                original_Aii    = svd.singularValues();
                lastSV          = svd.singularValues();
                q_out.data      = q.cast<double>();
                return 0;
        }
        compute_jacobian(q);
        jac = L.asDiagonal()*jac;

        lambda = tau;
        double dnorm = 1;
        for (unsigned int i=0;i<maxiter;++i) {

                svd.compute(jac);
                original_Aii = svd.singularValues();
                for (unsigned int j=0;j<original_Aii.rows();++j) {
                        original_Aii(j) = original_Aii(j)/( original_Aii(j)*original_Aii(j)+lambda);

                }
                tmp = svd.matrixU().transpose()*delta_pos;
                tmp = original_Aii.cwiseProduct(tmp);
                diffq = svd.matrixV()*tmp;
                grad = jac.transpose()*delta_pos;
                if (display_information) {
                        std::cout << "------- iteration " << i << " ----------------\n"
                                          << "  q              = " << q.transpose() << "\n"
                                          << "  weighted jac   = \n" << jac << "\n"
                                          << "  lambda         = " << lambda << "\n"
                                          << "  eigenvalues    = " << svd.singularValues().transpose() << "\n"
                                          << "  difference     = "   << delta_pos.transpose() << "\n"
                                          << "  difference norm= "   << delta_pos_norm << "\n"
                                          << "  proj. on grad. = "   << grad << "\n";
                        std::cout << std::endl;
                }
                dnorm = diffq.lpNorm<Eigen::Infinity>();
                if (dnorm < eps_joints) {
                                lastDifference = delta_pos_norm;
                                lastNrOfIter   = i;
                                lastSV         = svd.singularValues();
                                q_out.data     = q.cast<double>();
                                compute_fwdpos(q);
                                Twist_to_Eigen( diff( T_base_head, T_base_goal), delta_pos );
                                lastTransDiff  = delta_pos.topRows(3).norm();
                                lastRotDiff    = delta_pos.bottomRows(3).norm();
                                return -2;
                }


                if (grad.transpose()*grad < eps_joints*eps_joints ) {
                        compute_fwdpos(q);
                        Twist_to_Eigen( diff( T_base_head, T_base_goal), delta_pos );
                        lastDifference = delta_pos_norm;
                        lastTransDiff = delta_pos.topRows(3).norm();
                        lastRotDiff   = delta_pos.bottomRows(3).norm();
                        lastSV        = svd.singularValues();
                        lastNrOfIter  = i;
                        q_out.data    = q.cast<double>();
                        return -1;
                }

                q_new = q+diffq;
                compute_fwdpos(q_new);
                Twist_to_Eigen( diff( T_base_head, T_base_goal), delta_pos_new );
                delta_pos_new             = L.asDiagonal()*delta_pos_new;
                double delta_pos_new_norm = delta_pos_new.norm();
                rho                       = delta_pos_norm*delta_pos_norm - delta_pos_new_norm*delta_pos_new_norm;
                rho                      /= diffq.transpose()*(lambda*diffq + grad);
                if (rho > 0) {
                        q               = q_new;
                        delta_pos       = delta_pos_new;
                        delta_pos_norm  = delta_pos_new_norm;
                        if (delta_pos_norm<eps) {
                                Twist_to_Eigen( diff( T_base_head, T_base_goal), delta_pos );
                                lastDifference = delta_pos_norm;
                                lastTransDiff  = delta_pos.topRows(3).norm();
                                lastRotDiff    = delta_pos.bottomRows(3).norm();
                                lastSV         = svd.singularValues();
                                lastNrOfIter   = i;
                                q_out.data     = q.cast<double>();
                                return 0;
                        }
                        compute_jacobian(q_new);
                        jac = L.asDiagonal()*jac;
                        double tmp=2*rho-1;
                        lambda = lambda*max(1/3.0, 1-tmp*tmp*tmp);
                        v = 2;
                } else {
                        lambda = lambda*v;
                        v      = 2*v;
                }
        }
        lastDifference = delta_pos_norm;
        lastTransDiff  = delta_pos.topRows(3).norm();
        lastRotDiff    = delta_pos.bottomRows(3).norm();
        lastSV         = svd.singularValues();
        lastNrOfIter   = maxiter;
        q_out.data     = q.cast<double>();
        return -3;

}



};//namespace KDL