vpViper.cpp

/****************************************************************************
 *
 * $Id: vpViper.cpp 3834 2012-07-03 10:36:30Z fspindle $
 *
 * This file is part of the ViSP software.
 * Copyright (C) 2005 - 2012 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
 * ("GPL") version 2 as published by the Free Software Foundation.
 * 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 http://www.irisa.fr/lagadic/visp/visp.html for more information.
 * 
 * This software was developed at:
 * INRIA Rennes - Bretagne Atlantique
 * Campus Universitaire de Beaulieu
 * 35042 Rennes Cedex
 * France
 * http://www.irisa.fr/lagadic
 *
 * 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:
 * Interface for a  generic ADEPT Viper (either 650 or 850) robot.
 *
 * Authors:
 * Fabien Spindler
 *
 *****************************************************************************/

#include <visp/vpDebug.h>
#include <visp/vpVelocityTwistMatrix.h>
#include <visp/vpRobotException.h>
#include <visp/vpCameraParameters.h>
#include <visp/vpRxyzVector.h>
#include <visp/vpTranslationVector.h>
#include <visp/vpRotationMatrix.h>
#include <visp/vpViper.h>
#include <cmath>    // std::fabs
#include <limits>   // numeric_limits

const unsigned int vpViper::njoint = 6;

vpViper::vpViper()
{
  // Default values are initialized

  // Denavit Hartenberg parameters
  a1 = 0.075;
  a2 = 0.365;
  a3 = 0.090;
  d1 = 0.335;
  d4 = 0.405;
  d6 = 0.080;
  c56 = -341.33 / 9102.22;

  // Software joint limits in radians
  joint_min.resize(njoint);
  joint_min[0] = vpMath::rad(-170);
  joint_min[1] = vpMath::rad(-190);
  joint_min[2] = vpMath::rad(-29);
  joint_min[3] = vpMath::rad(-190);
  joint_min[4] = vpMath::rad(-120);
  joint_min[5] = vpMath::rad(-360);
  joint_max.resize(njoint);
  joint_max[0] = vpMath::rad(170);
  joint_max[1] = vpMath::rad(45);
  joint_max[2] = vpMath::rad(256);
  joint_max[3] = vpMath::rad(190);
  joint_max[4] = vpMath::rad(120);
  joint_max[5] = vpMath::rad(360);

  // End effector to camera transformation
  eMc.setIdentity(); 
}




vpHomogeneousMatrix
vpViper::getForwardKinematics(const vpColVector & q)
{
  vpHomogeneousMatrix fMc;
  fMc = get_fMc(q);

  return fMc;
}

bool 
vpViper::convertJointPositionInLimits(unsigned int joint, const double &q, double &q_mod)
{
  double eps = 0.01;
  if (q >= joint_min[joint]-eps && q <= joint_max[joint]+eps ) {
    q_mod = q;
    return true;
  }

  q_mod = q + 2*M_PI;
  if (q_mod >= joint_min[joint]-eps && q_mod <= joint_max[joint]+eps ) {
    return true;
  } 

  q_mod = q - 2*M_PI;
  if (q_mod >= joint_min[joint]-eps && q_mod <= joint_max[joint]+eps ) {
    return true;
  } 

  return false;
}

unsigned int
vpViper::getInverseKinematicsWrist(const vpHomogeneousMatrix & fMw, vpColVector & q)
{
  vpColVector q_sol[8];

  for (unsigned int i=0; i<8; i++)
    q_sol[i].resize(6);

  double c1[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
  double s1[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
  double c3[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
  double s3[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
  double c23[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
  double s23[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
  double c4[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
  double s4[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
  double c5[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
  double s5[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
  double c6[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};
  double s6[8]={0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0};

  bool ok[8];

  if (q.getRows() != njoint)
    q.resize(6);

  for (unsigned int i=0; i< 8; i++)
    ok[i] = true;

  double px = fMw[0][3]; // a*c1
  double py = fMw[1][3]; // a*s1
  double pz = fMw[2][3];

  // Compute q1
  double a_2 = px*px+py*py; 
  //if (a_2 == 0) {// singularity
  if (std::fabs(a_2) <= std::numeric_limits<double>::epsilon()) {// singularity
    c1[0] = cos(q[0]);
    s1[0] = sin(q[0]);
    c1[4] = cos(q[0]+M_PI);
    s1[4] = sin(q[0]+M_PI);
  }
  else {
    double a = sqrt(a_2);
    c1[0] = px/a;
    s1[0] = py/a;
    c1[4] = -px/a;
    s1[4] = -py/a;
  }

  double q1_mod;
  for(unsigned int i=0;i<8;i+=4) {
    q_sol[i][0] = atan2(s1[i],c1[i]);
    if (convertJointPositionInLimits(0, q_sol[i][0], q1_mod) == true) {
      q_sol[i][0] = q1_mod;
      for(unsigned int j=1;j<4;j++) {
    c1[i+j] = c1[i];
    s1[i+j] = s1[i];
    q_sol[i+j][0] = q_sol[i][0];
      }
    }
    else {
      for(unsigned int j=1;j<4;j++) 
    ok[i+j] = false;
    }
  }

//   std::cout << "ok apres q1: ";
//   for (unsigned int i=0; i< 8; i++)
//     std::cout << ok[i] << " ";
//   std::cout << std::endl;

  // Compute q3
  double K, q3_mod;
  for(unsigned int i=0; i<8; i+=4) {
    if(ok[i] == true) {
      K = (px*px+py*py+pz*pz+a1*a1-a2*a2-a3*a3+d1*d1-d4*d4
       - 2*(a1*c1[i]*px + a1*s1[i]*py + d1*pz)) / (2*a2);
      q_sol[i][2]   = atan2(a3, d4) + atan2(K, sqrt(d4*d4+a3*a3-K*K));
      q_sol[i+2][2] = atan2(a3, d4) + atan2(K, -sqrt(d4*d4+a3*a3-K*K));

      for (unsigned int j=0; j<4; j+=2) {
    if (convertJointPositionInLimits(2, q_sol[i+j][2], q3_mod) == true) {
      for(unsigned int k=0; k<2; k++) {
        q_sol[i+j+k][2] = q3_mod;
        c3[i+j+k] = cos(q3_mod);
        s3[i+j+k] = sin(q3_mod);
      }
    }
    else {
      for(unsigned int k=0; k<2; k++) 
        ok[i+j+k] = false;
    }
      }
    }
  }
//   std::cout << "ok apres q3: ";
//   for (unsigned int i=0; i< 8; i++)
//     std::cout << ok[i] << " ";
//   std::cout << std::endl;

  // Compute q2
  double q23[8], q2_mod;
  for (unsigned int i=0; i<8; i+=2) {
    if (ok[i] == true) {
      // Compute q23 = q2+q3
      c23[i] = (-(a3-a2*c3[i])*(c1[i]*px+s1[i]*py-a1)-(d1-pz)*(d4+a2*s3[i]))
    / ( (c1[i]*px+s1[i]*py-a1)*(c1[i]*px+s1[i]*py-a1) +(d1-pz)*(d1-pz) );
      s23[i] = ((d4+a2*s3[i])*(c1[i]*px+s1[i]*py-a1)-(d1-pz)*(a3-a2*c3[i]))
    / ( (c1[i]*px+s1[i]*py-a1)*(c1[i]*px+s1[i]*py-a1) +(d1-pz)*(d1-pz) );
      q23[i] = atan2(s23[i],c23[i]);
      //std::cout << i << " c23 = " << c23[i] << " s23 = " << s23[i] << std::endl;
      // q2 = q23 - q3
      q_sol[i][1] = q23[i] - q_sol[i][2];

      if (convertJointPositionInLimits(1, q_sol[i][1], q2_mod) == true) {
    for(unsigned int j=0; j<2; j++) {
      q_sol[i+j][1] = q2_mod;
      c23[i+j] = c23[i];
      s23[i+j] = s23[i];
    }
      }
      else {
    for(unsigned int j=0; j<2; j++)
      ok[i+j] = false;
      }
    }
  }
//   std::cout << "ok apres q2: ";
//   for (unsigned int i=0; i< 8; i++)
//     std::cout << ok[i] << " ";
//   std::cout << std::endl;

  // Compute q4 as long as s5 != 0
  double r13 = fMw[0][2];
  double r23 = fMw[1][2];
  double r33 = fMw[2][2];
  double s4s5, c4s5, q4_mod, q5_mod;
  for (unsigned int i=0; i<8; i+=2) { 
    if (ok[i] == true) {
      s4s5 = -s1[i]*r13+c1[i]*r23;
      c4s5 =  c1[i]*c23[i]*r13+s1[i]*c23[i]*r23-s23[i]*r33;
      if (fabs(s4s5) < vpMath::rad(0.5) && fabs(c4s5) < vpMath::rad(0.5)) {
    // s5 = 0
    c5[i] = c1[i]*s23[i]*r13+s1[i]*s23[i]*r23+c23[i]*r33;
    //std::cout << "Singularity: s5 near 0: ";
    if (c5[i] > 0.)
      q_sol[i][4] = 0.0;
    else 
      q_sol[i][4] = M_PI;
    
    if (convertJointPositionInLimits(4, q_sol[i][4], q5_mod) == true) {
      for(unsigned int j=0; j<2; j++) {
        q_sol[i+j][3] = q[3]; // keep current q4
        q_sol[i+j][4] = q5_mod;
        c4[i] = cos(q_sol[i+j][3]);
        s4[i] = sin(q_sol[i+j][3]);
      }
    }
    else {
      for(unsigned int j=0; j<2; j++)
        ok[i+j] = false;
    }
      }
      else {
    // s5 != 0
    //if (c4s5 == 0) {
    if (std::fabs(c4s5) <= std::numeric_limits<double>::epsilon()) {
      // c4 = 0
      //  vpTRACE("c4 = 0");
      // q_sol[i][3] = q[3]; // keep current position
      q_sol[i][3] = atan2(s4s5, c4s5);
    }
    else {
      q_sol[i][3] = atan2(s4s5, c4s5);
    }
    if (convertJointPositionInLimits(3, q_sol[i][3], q4_mod) == true) {
      q_sol[i][3] = q4_mod;
      c4[i] = cos(q4_mod);
      s4[i] = sin(q4_mod);
    }
    else {
      ok[i] = false;
    }
    if (q_sol[i][3] > 0.) 
      q_sol[i+1][3] = q_sol[i][3] + M_PI;
    else
      q_sol[i+1][3] = q_sol[i][3] - M_PI;
    if (convertJointPositionInLimits(3, q_sol[i+1][3], q4_mod) == true) {
      q_sol[i+1][3] = q4_mod;
      c4[i+1] = cos(q4_mod);
      s4[i+1] = sin(q4_mod);
    }
    else {
      ok[i+1] = false;
    }
    
    // Compute q5
    for (unsigned int j=0; j<2; j++) { 
      if (ok[i+j] == true) {
        c5[i+j] = c1[i+j]*s23[i+j]*r13+s1[i+j]*s23[i+j]*r23+c23[i+j]*r33;
        s5[i+j] = (c1[i+j]*c23[i+j]*c4[i+j]-s1[i+j]*s4[i+j])*r13
          +(s1[i+j]*c23[i+j]*c4[i+j]+c1[i+j]*s4[i+j])*r23-s23[i+j]*c4[i+j]*r33;
        
        q_sol[i+j][4] = atan2(s5[i+j], c5[i+j]);
        if (convertJointPositionInLimits(4, q_sol[i+j][4], q5_mod) == true) {
          q_sol[i+j][4] = q5_mod;
        }
        else {
          
          ok[i+j] = false;
        }
      }
    }
      }
    }
  }

  // Compute q6
  // 4 solutions for q6 and 4 more solutions by flipping the wrist (see below)
  double r12 = fMw[0][1];
  double r22 = fMw[1][1];
  double r32 = fMw[2][1];
  double q6_mod;
  for (unsigned int i=0; i<8; i++) { 
    c6[i] = -(c1[i]*c23[i]*s4[i]+s1[i]*c4[i])*r12 
      +(c1[i]*c4[i]-s1[i]*c23[i]*s4[i])*r22+s23[i]*s4[i]*r32;
    s6[i] = -(c1[i]*c23[i]*c4[i]*c5[i]-c1[i]*s23[i]*s5[i]
          -s1[i]*s4[i]*c5[i])*r12
      -(s1[i]*c23[i]*c4[i]*c5[i]-s1[i]*s23[i]*s5[i]+c1[i]*s4[i]*c5[i])*r22
      +(c23[i]*s5[i]+s23[i]*c4[i]*c5[i])*r32;
 
    q_sol[i][5] = atan2(s6[i], c6[i]);
    if (convertJointPositionInLimits(5, q_sol[i][5], q6_mod) == true) {
      q_sol[i][5] = q6_mod;
    }
    else {
      ok[i] = false;
    }
  }

  // Select the best config in terms of distance from the current position
  unsigned int nbsol = 0;
  unsigned int sol = 0;
  vpColVector dist(8);
  for (unsigned int i=0; i<8; i++) {
    if (ok[i] == true) {
      nbsol ++;
      sol = i;
      //      dist[i] = vpColVector::distance(q, q_sol[i]);
      vpColVector weight(6);
      weight = 1;
      weight[0] = 8; 
      weight[1] = weight[2] = 4; 
      dist[i] = 0;
      for (unsigned int j=0; j< 6; j++) {
    double rought_dist = q[j]- q_sol[i][j];
    double modulo_dist = rought_dist; 
    if (rought_dist > 0) {
      if (fabs(rought_dist - 2*M_PI) < fabs(rought_dist))
        modulo_dist = rought_dist - 2*M_PI;
    }
    else {
      if (fabs(rought_dist + 2*M_PI) < fabs(rought_dist))
        modulo_dist = rought_dist + 2*M_PI;
    }
    //std::cout << "dist " << i << ": " << rought_dist << " modulo: " << modulo_dist << std::endl;
    dist[i] += weight[j]*vpMath::sqr(modulo_dist);
      }
    }
    //  std::cout << "sol " << i << " [" << ok[i] << "] dist: " << dist[i] << " q: " << q_sol[i].t() << std::endl;
  }
  //std::cout << "dist: " << dist.t() << std::endl;
  if (nbsol) {
    for (unsigned int i=0; i<8; i++) {
      if (ok[i] == true) 
    if (dist[i] < dist[sol]) sol = i;
    }
    // Update the inverse kinematics solution
    q = q_sol[sol];

//     std::cout << "Nearest solution (" << sol << ") with distance (" 
//        << dist[sol] << "): " << q_sol[sol].t() << std::endl;
  }
  return nbsol;

}

unsigned int
vpViper::getInverseKinematics(const vpHomogeneousMatrix & fMc, vpColVector & q)
{
  vpHomogeneousMatrix fMw;
  vpHomogeneousMatrix wMe;
  vpHomogeneousMatrix eMc;
  this->get_wMe(wMe);
  this->get_eMc(eMc);
  fMw = fMc * eMc.inverse() * wMe.inverse();
  
  return (getInverseKinematicsWrist(fMw,q));
}

vpHomogeneousMatrix
vpViper::get_fMc (const vpColVector & q)
{
  vpHomogeneousMatrix fMc;
  get_fMc(q, fMc);

  return fMc;
}

void
vpViper::get_fMc(const vpColVector & q, vpHomogeneousMatrix & fMc)
{

  // Compute the direct geometric model: fMe = transformation between
  // fix and end effector frame.
  vpHomogeneousMatrix fMe;

  get_fMe(q, fMe);

  fMc = fMe * this->eMc;

  return;
}

void
vpViper::get_fMe(const vpColVector & q, vpHomogeneousMatrix & fMe)
{
  double q1 = q[0];
  double q2 = q[1];
  double q3 = q[2];
  double q4 = q[3];
  double q5 = q[4];
  double q6 = q[5];
  //  We turn off the coupling since the measured positions are joint position
  //  taking into account the coupling factor. The coupling factor is relevant
  //  if positions are motor position.
  // double q6 = q[5] + c56 * q[4];

//   std::cout << "q6 motor: " << q[5] << " rad " 
//      << vpMath::deg(q[5]) << " deg" << std::endl;
//   std::cout << "q6 joint: " << q6 << " rad " 
//      << vpMath::deg(q6) << " deg" << std::endl;

  double c1 = cos(q1);
  double s1 = sin(q1);
  double c2 = cos(q2);
  double s2 = sin(q2);
  //double c3 = cos(q3);
  //double s3 = sin(q3);
  double c4 = cos(q4);
  double s4 = sin(q4);
  double c5 = cos(q5);
  double s5 = sin(q5);
  double c6 = cos(q6);
  double s6 = sin(q6);
  double c23 = cos(q2+q3);
  double s23 = sin(q2+q3);

  fMe[0][0] = c1*(c23*(c4*c5*c6-s4*s6)-s23*s5*c6)-s1*(s4*c5*c6+c4*s6);
  fMe[1][0] = -s1*(c23*(-c4*c5*c6+s4*s6)+s23*s5*c6)+c1*(s4*c5*c6+c4*s6);
  fMe[2][0] = s23*(s4*s6-c4*c5*c6)-c23*s5*c6;

  fMe[0][1] = -c1*(c23*(c4*c5*s6+s4*c6)-s23*s5*s6)+s1*(s4*c5*s6-c4*c6);
  fMe[1][1] = -s1*(c23*(c4*c5*s6+s4*c6)-s23*s5*s6)-c1*(s4*c5*s6-c4*c6);
  fMe[2][1] = s23*(c4*c5*s6+s4*c6)+c23*s5*s6;

  fMe[0][2] = c1*(c23*c4*s5+s23*c5)-s1*s4*s5;
  fMe[1][2] = s1*(c23*c4*s5+s23*c5)+c1*s4*s5;
  fMe[2][2] = -s23*c4*s5+c23*c5;

  fMe[0][3] = c1*(c23*(c4*s5*d6-a3)+s23*(c5*d6+d4)+a1+a2*c2)-s1*s4*s5*d6;
  fMe[1][3] = s1*(c23*(c4*s5*d6-a3)+s23*(c5*d6+d4)+a1+a2*c2)+c1*s4*s5*d6;
  fMe[2][3] = s23*(a3-c4*s5*d6)+c23*(c5*d6+d4)-a2*s2+d1;

  // std::cout << "Effector position fMe: " << std::endl << fMe;

  return;
}
void
vpViper::get_fMw(const vpColVector & q, vpHomogeneousMatrix & fMw)
{
  double q1 = q[0];
  double q2 = q[1];
  double q3 = q[2];
  double q4 = q[3];
  double q5 = q[4];
  double q6 = q[5];
  //  We turn off the coupling since the measured positions are joint position
  //  taking into account the coupling factor. The coupling factor is relevant
  //  if positions are motor position.
  // double q6 = q[5] + c56 * q[4];

//   std::cout << "q6 motor: " << q[5] << " rad " 
//      << vpMath::deg(q[5]) << " deg" << std::endl;
//   std::cout << "q6 joint: " << q6 << " rad " 
//      << vpMath::deg(q6) << " deg" << std::endl;

  double c1 = cos(q1);
  double s1 = sin(q1);
  double c2 = cos(q2);
  double s2 = sin(q2);
  //  double c3 = cos(q3);
  //double s3 = sin(q3);
  double c4 = cos(q4);
  double s4 = sin(q4);
  double c5 = cos(q5);
  double s5 = sin(q5);
  double c6 = cos(q6);
  double s6 = sin(q6);
  double c23 = cos(q2+q3);
  double s23 = sin(q2+q3);


  fMw[0][0] = c1*(c23*(c4*c5*c6-s4*s6)-s23*s5*c6)-s1*(s4*c5*c6+c4*s6);
  fMw[1][0] = -s1*(c23*(-c4*c5*c6+s4*s6)+s23*s5*c6)+c1*(s4*c5*c6+c4*s6);
  fMw[2][0] = s23*(s4*s6-c4*c5*c6)-c23*s5*c6;

  fMw[0][1] = -c1*(c23*(c4*c5*s6+s4*c6)-s23*s5*s6)+s1*(s4*c5*s6-c4*c6);
  fMw[1][1] = -s1*(c23*(c4*c5*s6+s4*c6)-s23*s5*s6)-c1*(s4*c5*s6-c4*c6);
  fMw[2][1] = s23*(c4*c5*s6+s4*c6)+c23*s5*s6;

  fMw[0][2] = c1*(c23*c4*s5+s23*c5)-s1*s4*s5;
  fMw[1][2] = s1*(c23*c4*s5+s23*c5)+c1*s4*s5;
  fMw[2][2] = -s23*c4*s5+c23*c5;

  fMw[0][3] = c1*(-c23*a3+s23*d4+a1+a2*c2);
  fMw[1][3] = s1*(-c23*a3+s23*d4+a1+a2*c2);
  fMw[2][3] = s23*a3+c23*d4-a2*s2+d1;

  //std::cout << "Wrist position fMw: " << std::endl << fMw;

  return;
}

void
vpViper::get_wMe(vpHomogeneousMatrix & wMe)
{
  // Set the rotation as identity
  wMe.setIdentity();

  // Set the translation
  wMe[2][3] = d6;
}

void
vpViper::get_eMc(vpHomogeneousMatrix &eMc)
{
  eMc = this->eMc;
}

void
vpViper::get_cMe(vpHomogeneousMatrix &cMe)
{
  cMe = this->eMc.inverse();
}

void
vpViper::get_cVe(vpVelocityTwistMatrix &cVe)
{
  vpHomogeneousMatrix cMe ;
  get_cMe(cMe) ;

  cVe.buildFrom(cMe) ;

  return;
}

void
vpViper::get_eJe(const vpColVector &q, vpMatrix &eJe)
{
  vpMatrix V(6,6);
  V = 0;
  // Compute the first and last block of V
  vpHomogeneousMatrix fMw;
  get_fMw(q, fMw);
  vpRotationMatrix fRw;
  fMw.extract(fRw);
  vpRotationMatrix wRf;
  wRf = fRw.inverse();
  for (unsigned int i=0; i<3; i++ ) {
    for (unsigned int j=0; j<3; j++ ) {
      V[i][j] = V[i+3][j+3] = wRf[i][j];
    }
  }
  // Compute the second block of V
  vpHomogeneousMatrix wMe;
  get_wMe(wMe);
  vpHomogeneousMatrix eMw;
  eMw = wMe.inverse();
  vpTranslationVector etw;
  eMw.extract(etw);
  vpMatrix block2 = etw.skew()*wRf;
  for (unsigned int i=0; i<3; i++ ) {
    for (unsigned int j=0; j<3; j++ ) {
      V[i][j+3] = block2[i][j];
    }
  }
  // Compute eJe
  vpMatrix fJw;
  get_fJw(q, fJw);  
  eJe = V * fJw;

  return;
}


void
vpViper::get_fJw(const vpColVector &q, vpMatrix &fJw)
{
  double q1 = q[0];
  double q2 = q[1];
  double q3 = q[2];
  double q4 = q[3];
  double q5 = q[4];

  double c1 = cos(q1);
  double s1 = sin(q1);
  double c2 = cos(q2);
  double s2 = sin(q2);
  double c3 = cos(q3);
  double s3 = sin(q3);
  double c4 = cos(q4);
  double s4 = sin(q4);
  double c5 = cos(q5);
  double s5 = sin(q5);
  double c23 = cos(q2+q3);
  double s23 = sin(q2+q3);

  vpColVector J1(6);
  vpColVector J2(6);
  vpColVector J3(6);
  vpColVector J4(6);
  vpColVector J5(6);
  vpColVector J6(6);

  // Jacobian when d6 is set to zero
  J1[0] = -s1*(-c23*a3+s23*d4+a1+a2*c2);
  J1[1] =  c1*(-c23*a3+s23*d4+a1+a2*c2);
  J1[2] = 0;
  J1[3] = 0;
  J1[4] = 0;
  J1[5] = 1;

  J2[0] = c1*(s23*a3+c23*d4-a2*s2);
  J2[1] = s1*(s23*a3+c23*d4-a2*s2);
  J2[2] = c23*a3-s23*d4-a2*c2;
  J2[3] = -s1;
  J2[4] = c1;
  J2[5] = 0;

  J3[0] = c1*(a3*(s2*c3+c2*s3)+(-s2*s3+c2*c3)*d4);
  J3[1] = s1*(a3*(s2*c3+c2*s3)+(-s2*s3+c2*c3)*d4);
  J3[2] = -a3*(s2*s3-c2*c3)-d4*(s2*c3+c2*s3);
  J3[3] = -s1;
  J3[4] = c1;
  J3[5] = 0;

  J4[0] = 0;
  J4[1] = 0;
  J4[2] = 0;
  J4[3] = c1*s23;
  J4[4] = s1*s23;
  J4[5] = c23;

  J5[0] = 0;
  J5[1] = 0;
  J5[2] = 0;
  J5[3] = -c23*c1*s4-s1*c4;
  J5[4] = c1*c4-c23*s1*s4;
  J5[5] = s23*s4;

  J6[0] = 0;
  J6[1] = 0;
  J6[2] = 0;
  J6[3] = (c1*c23*c4-s1*s4)*s5+c1*s23*c5;
  J6[4] = (s1*c23*c4+c1*s4)*s5+s1*s23*c5;
  J6[5] = -s23*c4*s5+c23*c5;

  fJw.resize(6,6) ;
  for (unsigned int i=0;i<6;i++) {
    fJw[i][0] = J1[i];
    fJw[i][1] = J2[i];
    fJw[i][2] = J3[i];
    fJw[i][3] = J4[i];
    fJw[i][4] = J5[i];
    fJw[i][5] = J6[i];
  }
  return;
}
void
vpViper::get_fJe(const vpColVector &q, vpMatrix &fJe)
{
  vpMatrix V(6,6);
  V = 0;
  // Set the first and last block to identity
  for (unsigned int i=0; i<6; i++ )
    V[i][i] = 1;
  
  // Compute the second block of V
  vpHomogeneousMatrix fMw;
  get_fMw(q, fMw);
  vpRotationMatrix fRw;
  fMw.extract(fRw);
  vpHomogeneousMatrix wMe;
  get_wMe(wMe);
  vpHomogeneousMatrix eMw;
  eMw = wMe.inverse();
  vpTranslationVector etw;
  eMw.extract(etw);
  vpMatrix block2 = (fRw*etw).skew();
  // Set the second block
  for (unsigned int i=0; i<3; i++ )
    for (unsigned int j=0; j<3; j++ )
      V[i][j+3] = block2[i][j];

  // Compute fJe
  vpMatrix fJw;
  get_fJw(q, fJw);  
  fJe = V * fJw;

  return;
}


vpColVector
vpViper::getJointMin()
{
  return joint_min;
}

vpColVector
vpViper::getJointMax()
{
  return joint_max;
}

double
vpViper::getCoupl56()
{
  return c56;
}



std::ostream & operator << (std::ostream & os, const vpViper & viper)
{
  vpRotationMatrix eRc;
  viper.eMc.extract(eRc);
  vpRxyzVector rxyz(eRc);

  // Convert joint limits in degrees
  vpColVector jmax = viper.joint_max;
  vpColVector jmin = viper.joint_min;
  jmax.rad2deg();
  jmin.rad2deg();

  os
    << "Joint Max (deg):" << std::endl
    << "\t" << jmax.t() << std::endl

    << "Joint Min (deg): " << std::endl
    << "\t" << jmin.t() << std::endl

    << "Coupling 5-6:" << std::endl
    << "\t" << viper.c56 << std::endl

    << "eMc: "<< std::endl
    << "\tTranslation (m): "
    << viper.eMc[0][3] << " "
    << viper.eMc[1][3] << " "
    << viper.eMc[2][3]
    << "\t" << std::endl
    << "\tRotation Rxyz (rad) : "
    << rxyz[0] << " "
    << rxyz[1] << " "
    << rxyz[2]
    << "\t" << std::endl
    << "\tRotation Rxyz (deg) : "
    << vpMath::deg(rxyz[0])  << " "
    << vpMath::deg(rxyz[1])  << " "
    << vpMath::deg(rxyz[2])
    << "\t" << std::endl;

  return os;
}
/*
 * Local variables:
 * c-basic-offset: 2
 * End:
 */