WSDLSSolver.cpp

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/* SPDX-FileCopyrightText: 2009 Ruben Smits
 *
 * SPDX-License-Identifier: LGPL-2.1-or-later */
 
#include "WSDLSSolver.hpp"
#include "kdl/utilities/svd_eigen_HH.hpp"
#include <cstdio>
 
namespace iTaSC {
 
WSDLSSolver::WSDLSSolver() :
    m_ns(0), m_nc(0), m_nq(0)
 
{
    // default maximum speed: 50 rad/s
    m_qmax = 50.0;
}
 
WSDLSSolver::~WSDLSSolver() {
}
 
bool WSDLSSolver::init(unsigned int _nq, unsigned int _nc, const std::vector<bool>& gc)
{
    if (_nc == 0 || _nq == 0 || gc.size() != _nc)
        return false;
    m_nc = _nc;
    m_nq = _nq;
    m_ns = std::min(m_nc,m_nq);
    m_AWq = e_zero_matrix(m_nc,m_nq);
    m_WyAWq = e_zero_matrix(m_nc,m_nq);
    m_WyAWqt = e_zero_matrix(m_nq,m_nc);
    m_S = e_zero_vector(std::max(m_nc,m_nq));
    m_Wy_ydot = e_zero_vector(m_nc);
    m_ytask = gc;
    if (m_nq > m_nc) {
        m_transpose = true;
        m_temp = e_zero_vector(m_nc);
        m_U = e_zero_matrix(m_nc,m_nc);
        m_V = e_zero_matrix(m_nq,m_nc);
        m_WqV = e_zero_matrix(m_nq,m_nc);
    } else {
        m_transpose = false;
        m_temp = e_zero_vector(m_nq);
        m_U = e_zero_matrix(m_nc,m_nq);
        m_V = e_zero_matrix(m_nq,m_nq);
        m_WqV = e_zero_matrix(m_nq,m_nq);
    }
    return true;
}
 
bool WSDLSSolver::solve(const e_matrix& A, const e_vector& Wy, const e_vector& ydot, const e_matrix& Wq, e_vector& qdot, e_scalar& nlcoef)
{
    unsigned int i, j, l;
    e_scalar N, M;
 
    // Create the Weighted jacobian
    m_AWq.noalias() = A*Wq;
    for (i=0; i<m_nc; 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_Wy_ydot = Wy.array() * ydot.array();
    m_WqV.noalias() = Wq*m_V;
    qdot.setZero();
    e_scalar maxDeltaS = e_scalar(0.0);
    e_scalar prevS = e_scalar(0.0);
    e_scalar maxS = e_scalar(1.0);
    for(i=0;i<m_ns;++i) {
        e_scalar norm, mag, alpha, _qmax, Sinv, vmax, damp;
        e_scalar S = m_S(i);
        bool prev;
        if (S < KDL::epsilon)
            break;
        Sinv = e_scalar(1.)/S;
        if (i > 0) {
            if ((prevS-S) > maxDeltaS) {
                maxDeltaS = (prevS-S);
                maxS = prevS;
            }
        }
        N = M = e_scalar(0.);
        for (l=0, prev=m_ytask[0], norm=e_scalar(0.); l<m_nc; l++) {
            if (prev == m_ytask[l]) {
                norm += m_U(l,i)*m_U(l,i);
            } else {
                N += std::sqrt(norm);
                norm = m_U(l,i)*m_U(l,i);
            }
            prev = m_ytask[l];
        }
        N += std::sqrt(norm);
        for (j=0; j<m_nq; j++) {
            for (l=0, prev=m_ytask[0], norm=e_scalar(0.), mag=e_scalar(0.); l<m_nc; l++) {
                if (prev == m_ytask[l]) {
                    norm += m_WyAWq(l,j)*m_WyAWq(l,j);
                } else {
                    mag += std::sqrt(norm);
                    norm = m_WyAWq(l,j)*m_WyAWq(l,j);
                }
                prev = m_ytask[l];
            }
            mag += std::sqrt(norm);
            M += fabs(m_V(j,i))*mag;
        }
        M *= Sinv;
        alpha = m_U.col(i).dot(m_Wy_ydot);
        _qmax = (N < M) ? m_qmax*N/M : m_qmax;
        vmax = m_WqV.col(i).array().abs().maxCoeff();
        norm = fabs(Sinv*alpha*vmax);
        if (norm > _qmax) {
            damp = Sinv*alpha*_qmax/norm;
        } else {
            damp = Sinv*alpha;
        }
        qdot += m_WqV.col(i)*damp;
        prevS = S;
    }
    if (maxDeltaS == e_scalar(0.0))
        nlcoef = e_scalar(KDL::epsilon);
    else
        nlcoef = (maxS-maxDeltaS)/maxS;
    return true;
}
 
}