WDLSSolver.cpp

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/*
 * WDLSSolver.hpp.cpp
 *
 *  Created on: Jan 8, 2009
 *      Author: rubensmits
 */

#include "WDLSSolver.hpp"
#include "kdl/utilities/svd_eigen_HH.hpp"

namespace iTaSC {

WDLSSolver::WDLSSolver() : m_lambda(0.5), m_epsilon(0.1) 
{
    // maximum joint velocity
    m_qmax = 50.0;
}

WDLSSolver::~WDLSSolver() {
}

bool WDLSSolver::init(unsigned int nq, unsigned int nc, const std::vector<bool>& gc)
{
    m_ns = std::min(nc,nq);
    m_AWq = e_zero_matrix(nc,nq);
    m_WyAWq = e_zero_matrix(nc,nq);
    m_WyAWqt = e_zero_matrix(nq,nc);
    m_S = e_zero_vector(std::max(nc,nq));
    m_Wy_ydot = e_zero_vector(nc);
    if (nq > nc) {
        m_transpose = true;
        m_temp = e_zero_vector(nc);
        m_U = e_zero_matrix(nc,nc);
        m_V = e_zero_matrix(nq,nc);
        m_WqV = e_zero_matrix(nq,nc);
    } else {
        m_transpose = false;
        m_temp = e_zero_vector(nq);
        m_U = e_zero_matrix(nc,nq);
        m_V = e_zero_matrix(nq,nq);
        m_WqV = e_zero_matrix(nq,nq);
    }
    return true;
}

bool WDLSSolver::solve(const e_matrix& A, const e_vector& Wy, const e_vector& ydot, const e_matrix& Wq, e_vector& qdot, e_scalar& nlcoef)
{
    double alpha, vmax, norm;
    // Create the Weighted jacobian
    m_AWq = A*Wq;
    for (int i=0; i<Wy.size(); i++)
        m_WyAWq.row(i) = Wy(i)*m_AWq.row(i);

    // Compute the SVD of the weighted jacobian
    int ret;
    if (m_transpose) {
        m_WyAWqt = m_WyAWq.transpose();
        ret = KDL::svd_eigen_HH(m_WyAWqt,m_V,m_S,m_U,m_temp);
    } else {
        ret = KDL::svd_eigen_HH(m_WyAWq,m_U,m_S,m_V,m_temp);
    }
    if(ret<0)
        return false;

    m_WqV.noalias() = Wq*m_V;

    //Wy*ydot
    m_Wy_ydot = Wy.array() * ydot.array();
    //S^-1*U'*Wy*ydot
    e_scalar maxDeltaS = e_scalar(0.0);
    e_scalar prevS = e_scalar(0.0);
    e_scalar maxS = e_scalar(1.0);
    e_scalar S, lambda;
    qdot.setZero();
    for(int i=0;i<m_ns;++i) {
        S = m_S(i);
        if (S <= KDL::epsilon)
            break;
        if (i > 0 && (prevS-S) > maxDeltaS) {
            maxDeltaS = (prevS-S);
            maxS = prevS;
        }
        lambda = (S < m_epsilon) ? (e_scalar(1.0)-KDL::sqr(S/m_epsilon))*m_lambda*m_lambda : e_scalar(0.0);
        alpha = m_U.col(i).dot(m_Wy_ydot)*S/(S*S+lambda);
        vmax = m_WqV.col(i).array().abs().maxCoeff();
        norm = fabs(alpha*vmax);
        if (norm > m_qmax) {
            qdot += m_WqV.col(i)*(alpha*m_qmax/norm);
        } else {
            qdot += m_WqV.col(i)*alpha;
        }
        prevS = S;
    }
    if (maxDeltaS == e_scalar(0.0))
        nlcoef = e_scalar(KDL::epsilon);
    else
        nlcoef = (maxS-maxDeltaS)/maxS;
    return true;
}

}