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
) :
    chain(_chain),
    nj(chain.getNrOfJoints()),
    ns(chain.getNrOfSegments()),
    lastNrOfIter(0),
    lastDifference(0),
    lastTransDiff(0),
    lastRotDiff(0),
    lastSV(nj),
    jac(6, nj),
    grad(nj),
    display_information(false),
    maxiter(_maxiter),
    eps(_eps),
    eps_joints(_eps_joints),
    L(_L.cast<ScalarType>()),
    T_base_jointroot(nj),
    T_base_jointtip(nj),
    q(nj),
    A(nj, nj),
    tmp(nj),
    ldlt(nj),
    svd(6, nj,Eigen::ComputeThinU | Eigen::ComputeThinV),
    diffq(nj),
    q_new(nj),
    original_Aii(nj)
{}

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

void ChainIkSolverPos_LMA::updateInternalDataStructures() {
    nj = chain.getNrOfJoints();
    ns = chain.getNrOfSegments();
    lastSV.conservativeResize(nj>6?6:nj);
    jac.conservativeResize(Eigen::NoChange, nj);
    grad.conservativeResize(nj);
    T_base_jointroot.resize(nj);
    T_base_jointtip.resize(nj);
    q.conservativeResize(nj);
    A.conservativeResize(nj, nj);
    ldlt = Eigen::LDLT<MatrixXq>(nj);
    svd = Eigen::JacobiSVD<MatrixXq>(6, nj,Eigen::ComputeThinU | Eigen::ComputeThinV);
    diffq.conservativeResize(nj);
    q_new.conservativeResize(nj);
    original_Aii.conservativeResize(nj);
}

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::Fixed) {
            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::Fixed) {
            // 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) {
  if (nj != chain.getNrOfJoints())
    return (error = E_NOT_UP_TO_DATE);

  if (nj != q_init.rows() || nj != q_out.rows())
    return (error = E_SIZE_MISMATCH);

    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 (error = E_NOERROR);
    }
    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 (error = E_INCREMENT_JOINTS_TOO_SMALL);
        }


        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 (error = E_GRADIENT_JOINTS_TOO_SMALL);
        }

        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 (error = E_NOERROR);
            }
            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 (error = E_MAX_ITERATIONS_EXCEEDED);

}

const char* ChainIkSolverPos_LMA::strError(const int error) const
    {
        if (E_GRADIENT_JOINTS_TOO_SMALL == error) return "The gradient of E towards the joints is to small";
        else if (E_INCREMENT_JOINTS_TOO_SMALL == error) return "The joint position increments are to small";
        else return SolverI::strError(error);
    }

}//namespace KDL