vpExponentialMap.cpp

/*
 * ViSP, open source Visual Servoing Platform software.
 * Copyright (C) 2005 - 2024 by Inria. All rights reserved.
 *
 * This software is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 * See the file LICENSE.txt at the root directory of this source
 * distribution for additional information about the GNU GPL.
 *
 * For using ViSP with software that can not be combined with the GNU
 * GPL, please contact Inria about acquiring a ViSP Professional
 * Edition License.
 *
 * See https://visp.inria.fr for more information.
 *
 * This software was developed at:
 * Inria Rennes - Bretagne Atlantique
 * Campus Universitaire de Beaulieu
 * 35042 Rennes Cedex
 * France
 *
 * If you have questions regarding the use of this file, please contact
 * Inria at visp@inria.fr
 *
 * This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
 * WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
 *
 * Description:
 * Exponential map.
 */
 
#include <visp3/core/vpExponentialMap.h>
 
BEGIN_VISP_NAMESPACE
vpHomogeneousMatrix vpExponentialMap::direct(const vpColVector &v) { return vpExponentialMap::direct(v, 1.0); }
 
vpHomogeneousMatrix vpExponentialMap::direct(const vpColVector &v, const double &delta_t)
{
  const unsigned int v_size = 6;
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
  const unsigned int index_3 = 3;
  const unsigned int index_4 = 4;
  const unsigned int index_5 = 5;
 
  if (v.size() != v_size) {
    throw(vpException(vpException::dimensionError,
                      "Cannot compute direct exponential map from a %d-dim velocity vector. Should be 6-dim.",
                      v.size()));
  }
  double theta, si, co, sinc, mcosc, msinc;
  vpThetaUVector u;
  vpRotationMatrix rd;
  vpTranslationVector dt;
 
  vpColVector v_dt = v * delta_t;
 
  u[index_0] = v_dt[index_3];
  u[index_1] = v_dt[index_4];
  u[index_2] = v_dt[index_5];
  rd.build(u);
 
  theta = sqrt((u[index_0] * u[index_0]) + (u[index_1] * u[index_1]) + (u[index_2] * u[index_2]));
  si = sin(theta);
  co = cos(theta);
  sinc = vpMath::sinc(si, theta);
  mcosc = vpMath::mcosc(co, theta);
  msinc = vpMath::msinc(si, theta);
 
  dt[index_0] = ((v_dt[index_0] * (sinc + (u[index_0] * u[index_0] * msinc))) +
          (v_dt[index_1] * ((u[index_0] * u[index_1] * msinc) - (u[index_2] * mcosc)))) +
    (v_dt[index_2] * ((u[index_0] * u[index_2] * msinc) + (u[index_1] * mcosc)));
 
  dt[index_1] = ((v_dt[index_0] * ((u[index_0] * u[index_1] * msinc) + (u[index_2] * mcosc))) +
          (v_dt[index_1] * (sinc + (u[index_1] * u[index_1] * msinc)))) +
    (v_dt[index_2] * ((u[index_1] * u[index_2] * msinc) - (u[index_0] * mcosc)));
 
  dt[index_2] = ((v_dt[index_0] * ((u[index_0] * u[index_2] * msinc) - (u[index_1] * mcosc))) +
          (v_dt[index_1] * ((u[index_1] * u[index_2] * msinc) + (u[index_0] * mcosc)))) +
    (v_dt[index_2] * (sinc + (u[index_2] * u[index_2] * msinc)));
 
  vpHomogeneousMatrix Delta;
  Delta.insert(rd);
  Delta.insert(dt);
 
  return Delta;
}
 
vpColVector vpExponentialMap::inverse(const vpHomogeneousMatrix &M) { return vpExponentialMap::inverse(M, 1.0); }
 
vpColVector vpExponentialMap::inverse(const vpHomogeneousMatrix &M, const double &delta_t)
{
  vpColVector v(6);
  unsigned int i;
  double theta, si, co, sinc, mcosc, msinc, det;
  vpThetaUVector u;
  vpRotationMatrix Rd, a;
  vpTranslationVector dt;
  const unsigned int index_0 = 0;
  const unsigned int index_1 = 1;
  const unsigned int index_2 = 2;
  const unsigned int index_3 = 3;
 
  M.extract(Rd);
  u.build(Rd);
  for (i = 0; i < 3; ++i) {
    v[3 + i] = u[i];
  }
 
  theta = sqrt((u[index_0] * u[index_0]) + (u[index_1] * u[index_1]) + (u[index_2] * u[index_2]));
  si = sin(theta);
  co = cos(theta);
  sinc = vpMath::sinc(si, theta);
  mcosc = vpMath::mcosc(co, theta);
  msinc = vpMath::msinc(si, theta);
 
  // a below is not a pure rotation matrix, even if not so far from
  // the Rodrigues formula : sinc I + (1-sinc)/t^2 VV^T + (1-cos)/t^2 [V]_X
  // with V = t.U
 
  a[index_0][index_0] = sinc + (u[index_0] * u[index_0] * msinc);
  a[index_0][index_1] = (u[index_0] * u[index_1] * msinc) - (u[index_2] * mcosc);
  a[index_0][index_2] = (u[index_0] * u[index_2] * msinc) + (u[index_1] * mcosc);
 
  a[index_1][index_0] = (u[index_0] * u[index_1] * msinc) + (u[index_2] * mcosc);
  a[index_1][index_1] = sinc + (u[index_1] * u[index_1] * msinc);
  a[index_1][index_2] = (u[index_1] * u[index_2] * msinc) - (u[index_0] * mcosc);
 
  a[index_2][index_0] = (u[index_0] * u[index_2] * msinc) - (u[index_1] * mcosc);
  a[index_2][index_1] = (u[index_1] * u[index_2] * msinc) + (u[index_0] * mcosc);
  a[index_2][index_2] = sinc + (u[index_2] * u[index_2] * msinc);
 
  det = (((((a[index_0][index_0] * a[index_1][index_1] * a[index_2][index_2]) + (a[index_1][index_0] * a[index_2][index_1] * a[index_0][index_2])) + (a[index_0][index_1] * a[index_1][index_2] * a[index_2][index_0])) -
          (a[index_2][index_0] * a[index_1][index_1] * a[index_0][index_2])) - (a[index_1][index_0] * a[index_0][index_1] * a[index_2][index_2])) - (a[index_0][index_0] * a[index_2][index_1] * a[index_1][index_2]);
 
  if (fabs(det) > 1.e-5) {
    v[index_0] = ((((((M[index_0][index_3] * a[index_1][index_1] * a[index_2][index_2]) + (M[index_1][index_3] * a[index_2][index_1] * a[index_0][index_2])) + (M[index_2][index_3] * a[index_0][index_1] * a[index_1][index_2])) -
                    (M[index_2][index_3] * a[index_1][index_1] * a[index_0][index_2])) - (M[index_1][index_3] * a[index_0][index_1] * a[index_2][index_2])) - (M[index_0][index_3] * a[index_2][index_1] * a[index_1][index_2])) /
      det;
    v[index_1] = ((((((a[index_0][index_0] * M[index_1][index_3] * a[index_2][index_2]) + (a[index_1][index_0] * M[index_2][index_3] * a[index_0][index_2])) + (M[index_0][index_3] * a[index_1][index_2] * a[index_2][index_0])) -
                    (a[index_2][index_0] * M[index_1][index_3] * a[index_0][index_2])) - (a[index_1][index_0] * M[index_0][index_3] * a[index_2][index_2])) - (a[index_0][index_0] * M[index_2][index_3] * a[index_1][index_2])) /
      det;
    v[index_2] = ((((((a[index_0][index_0] * a[index_1][index_1] * M[index_2][index_3]) + (a[index_1][index_0] * a[index_2][index_1] * M[index_0][index_3])) + (a[index_0][index_1] * M[index_1][index_3] * a[index_2][index_0])) -
                    (a[index_2][index_0] * a[index_1][index_1] * M[index_0][index_3])) - (a[index_1][index_0] * a[index_0][index_1] * M[index_2][index_3])) - (a[index_0][index_0] * a[index_2][index_1] * M[index_1][index_3])) /
      det;
  }
  else {
    v[index_0] = M[index_0][index_3];
    v[index_1] = M[index_1][index_3];
    v[index_2] = M[index_2][index_3];
  }
 
  // Apply the sampling time to the computed velocity
  v /= delta_t;
 
  return v;
}
END_VISP_NAMESPACE