nlopt_ik.cpp

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#include <trac_ik/nlopt_ik.hpp>
#include <ros/ros.h>
#include <limits>
#include <boost/date_time.hpp>
#include <trac_ik/dual_quaternion.h>
#include <cmath>



namespace NLOPT_IK
{

dual_quaternion targetDQ;

double minfunc(const std::vector<double>& x, std::vector<double>& grad, void* data)
{
  // Auxilory function to minimize (Sum of Squared joint angle error
  // from the requested configuration).  Because we wanted a Class
  // without static members, but NLOpt library does not support
  // passing methods of Classes, we use these auxilary functions.

  NLOPT_IK *c = (NLOPT_IK *) data;

  return c->minJoints(x, grad);
}

double minfuncDQ(const std::vector<double>& x, std::vector<double>& grad, void* data)
{
  // Auxilory function to minimize (Sum of Squared joint angle error
  // from the requested configuration).  Because we wanted a Class
  // without static members, but NLOpt library does not support
  // passing methods of Classes, we use these auxilary functions.
  NLOPT_IK *c = (NLOPT_IK *) data;

  std::vector<double> vals(x);

  double jump = boost::math::tools::epsilon<float>();
  double result[1];
  c->cartDQError(vals, result);

  if (!grad.empty())
  {
    double v1[1];
    for (uint i = 0; i < x.size(); i++)
    {
      double original = vals[i];

      vals[i] = original + jump;
      c->cartDQError(vals, v1);

      vals[i] = original;
      grad[i] = (v1[0] - result[0]) / (2 * jump);
    }
  }

  return result[0];
}


double minfuncSumSquared(const std::vector<double>& x, std::vector<double>& grad, void* data)
{
  // Auxilory function to minimize (Sum of Squared joint angle error
  // from the requested configuration).  Because we wanted a Class
  // without static members, but NLOpt library does not support
  // passing methods of Classes, we use these auxilary functions.

  NLOPT_IK *c = (NLOPT_IK *) data;

  std::vector<double> vals(x);

  double jump = boost::math::tools::epsilon<float>();
  double result[1];
  c->cartSumSquaredError(vals, result);

  if (!grad.empty())
  {
    double v1[1];
    for (uint i = 0; i < x.size(); i++)
    {
      double original = vals[i];

      vals[i] = original + jump;
      c->cartSumSquaredError(vals, v1);

      vals[i] = original;
      grad[i] = (v1[0] - result[0]) / (2.0 * jump);
    }
  }

  return result[0];
}


double minfuncL2(const std::vector<double>& x, std::vector<double>& grad, void* data)
{
  // Auxilory function to minimize (Sum of Squared joint angle error
  // from the requested configuration).  Because we wanted a Class
  // without static members, but NLOpt library does not support
  // passing methods of Classes, we use these auxilary functions.

  NLOPT_IK *c = (NLOPT_IK *) data;

  std::vector<double> vals(x);

  double jump = boost::math::tools::epsilon<float>();
  double result[1];
  c->cartL2NormError(vals, result);

  if (!grad.empty())
  {
    double v1[1];
    for (uint i = 0; i < x.size(); i++)
    {
      double original = vals[i];

      vals[i] = original + jump;
      c->cartL2NormError(vals, v1);

      vals[i] = original;
      grad[i] = (v1[0] - result[0]) / (2.0 * jump);
    }
  }

  return result[0];
}



void constrainfuncm(uint m, double* result, uint n, const double* x, double* grad, void* data)
{
  //Equality constraint auxilary function for Euclidean distance .
  //This also uses a small walk to approximate the gradient of the
  //constraint function at the current joint angles.

  NLOPT_IK *c = (NLOPT_IK *) data;

  std::vector<double> vals(n);

  for (uint i = 0; i < n; i++)
  {
    vals[i] = x[i];
  }

  double jump = boost::math::tools::epsilon<float>();

  c->cartSumSquaredError(vals, result);

  if (grad != NULL)
  {
    std::vector<double> v1(m);
    for (uint i = 0; i < n; i++)
    {
      double o = vals[i];
      vals[i] = o + jump;
      c->cartSumSquaredError(vals, v1.data());
      vals[i] = o;
      for (uint j = 0; j < m; j++)
      {
        grad[j * n + i] = (v1[j] - result[j]) / (2 * jump);
      }
    }
  }
}


NLOPT_IK::NLOPT_IK(const KDL::Chain& _chain, const KDL::JntArray& _q_min, const KDL::JntArray& _q_max, double _maxtime, double _eps, OptType _type):
  chain(_chain), fksolver(_chain), maxtime(_maxtime), eps(std::abs(_eps)), TYPE(_type)
{
  assert(chain.getNrOfJoints() == _q_min.data.size());
  assert(chain.getNrOfJoints() == _q_max.data.size());

  //Constructor for an IK Class.  Takes in a Chain to operate on,
  //the min and max joint limits, an (optional) maximum number of
  //iterations, and an (optional) desired error.
  reset();

  if (chain.getNrOfJoints() < 2)
  {
    ROS_WARN_THROTTLE(1.0, "NLOpt_IK can only be run for chains of length 2 or more");
    return;
  }
  opt = nlopt::opt(nlopt::LD_SLSQP, _chain.getNrOfJoints());

  for (uint i = 0; i < chain.getNrOfJoints(); i++)
  {
    lb.push_back(_q_min(i));
    ub.push_back(_q_max(i));
  }

  for (uint i = 0; i < chain.segments.size(); i++)
  {
    std::string type = chain.segments[i].getJoint().getTypeName();
    if (type.find("Rot") != std::string::npos)
    {
      if (_q_max(types.size()) >= std::numeric_limits<float>::max() &&
          _q_min(types.size()) <= std::numeric_limits<float>::lowest())
        types.push_back(KDL::BasicJointType::Continuous);
      else
        types.push_back(KDL::BasicJointType::RotJoint);
    }
    else if (type.find("Trans") != std::string::npos)
      types.push_back(KDL::BasicJointType::TransJoint);
  }

  assert(types.size() == lb.size());

  std::vector<double> tolerance(1, boost::math::tools::epsilon<float>());
  opt.set_xtol_abs(tolerance[0]);


  switch (TYPE)
  {
  case Joint:
    opt.set_min_objective(minfunc, this);
    opt.add_equality_mconstraint(constrainfuncm, this, tolerance);
    break;
  case DualQuat:
    opt.set_min_objective(minfuncDQ, this);
    break;
  case SumSq:
    opt.set_min_objective(minfuncSumSquared, this);
    break;
  case L2:
    opt.set_min_objective(minfuncL2, this);
    break;
  }
}


double NLOPT_IK::minJoints(const std::vector<double>& x, std::vector<double>& grad)
{
  // Actual function to compute the error between the current joint
  // configuration and the desired.  The SSE is easy to provide a
  // closed form gradient for.

  bool gradient = !grad.empty();

  double err = 0;
  for (uint i = 0; i < x.size(); i++)
  {
    err += pow(x[i] - des[i], 2);
    if (gradient)
      grad[i] = 2.0 * (x[i] - des[i]);
  }

  return err;

}


void NLOPT_IK::cartSumSquaredError(const std::vector<double>& x, double error[])
{
  // Actual function to compute Euclidean distance error.  This uses
  // the KDL Forward Kinematics solver to compute the Cartesian pose
  // of the current joint configuration and compares that to the
  // desired Cartesian pose for the IK solve.

  if (aborted || progress != -3)
  {
    opt.force_stop();
    return;
  }


  KDL::JntArray q(x.size());

  for (uint i = 0; i < x.size(); i++)
    q(i) = x[i];

  int rc = fksolver.JntToCart(q, currentPose);

  if (rc < 0)
    ROS_FATAL_STREAM("KDL FKSolver is failing: " << q.data);

  if (std::isnan(currentPose.p.x()))
  {
    ROS_ERROR("NaNs from NLOpt!!");
    error[0] = std::numeric_limits<float>::max();
    progress = -1;
    return;
  }

  KDL::Twist delta_twist = KDL::diffRelative(targetPose, currentPose);

  for (int i = 0; i < 6; i++)
  {
    if (std::abs(delta_twist[i]) <= std::abs(bounds[i]))
      delta_twist[i] = 0.0;
  }

  error[0] = KDL::dot(delta_twist.vel, delta_twist.vel) + KDL::dot(delta_twist.rot, delta_twist.rot);

  if (KDL::Equal(delta_twist, KDL::Twist::Zero(), eps))
  {
    progress = 1;
    best_x = x;
    return;
  }
}



void NLOPT_IK::cartL2NormError(const std::vector<double>& x, double error[])
{
  // Actual function to compute Euclidean distance error.  This uses
  // the KDL Forward Kinematics solver to compute the Cartesian pose
  // of the current joint configuration and compares that to the
  // desired Cartesian pose for the IK solve.

  if (aborted || progress != -3)
  {
    opt.force_stop();
    return;
  }

  KDL::JntArray q(x.size());

  for (uint i = 0; i < x.size(); i++)
    q(i) = x[i];

  int rc = fksolver.JntToCart(q, currentPose);

  if (rc < 0)
    ROS_FATAL_STREAM("KDL FKSolver is failing: " << q.data);


  if (std::isnan(currentPose.p.x()))
  {
    ROS_ERROR("NaNs from NLOpt!!");
    error[0] = std::numeric_limits<float>::max();
    progress = -1;
    return;
  }

  KDL::Twist delta_twist = KDL::diffRelative(targetPose, currentPose);

  for (int i = 0; i < 6; i++)
  {
    if (std::abs(delta_twist[i]) <= std::abs(bounds[i]))
      delta_twist[i] = 0.0;
  }

  error[0] = std::sqrt(KDL::dot(delta_twist.vel, delta_twist.vel) + KDL::dot(delta_twist.rot, delta_twist.rot));

  if (KDL::Equal(delta_twist, KDL::Twist::Zero(), eps))
  {
    progress = 1;
    best_x = x;
    return;
  }
}




void NLOPT_IK::cartDQError(const std::vector<double>& x, double error[])
{
  // Actual function to compute Euclidean distance error.  This uses
  // the KDL Forward Kinematics solver to compute the Cartesian pose
  // of the current joint configuration and compares that to the
  // desired Cartesian pose for the IK solve.

  if (aborted || progress != -3)
  {
    opt.force_stop();
    return;
  }

  KDL::JntArray q(x.size());

  for (uint i = 0; i < x.size(); i++)
    q(i) = x[i];

  int rc = fksolver.JntToCart(q, currentPose);

  if (rc < 0)
    ROS_FATAL_STREAM("KDL FKSolver is failing: " << q.data);


  if (std::isnan(currentPose.p.x()))
  {
    ROS_ERROR("NaNs from NLOpt!!");
    error[0] = std::numeric_limits<float>::max();
    progress = -1;
    return;
  }

  KDL::Twist delta_twist = KDL::diffRelative(targetPose, currentPose);

  for (int i = 0; i < 6; i++)
  {
    if (std::abs(delta_twist[i]) <= std::abs(bounds[i]))
      delta_twist[i] = 0.0;
  }

  math3d::matrix3x3<double> currentRotationMatrix(currentPose.M.data);
  math3d::quaternion<double> currentQuaternion = math3d::rot_matrix_to_quaternion<double>(currentRotationMatrix);
  math3d::point3d currentTranslation(currentPose.p.data);
  dual_quaternion currentDQ = dual_quaternion::rigid_transformation(currentQuaternion, currentTranslation);

  dual_quaternion errorDQ = (currentDQ * !targetDQ).normalize();
  errorDQ.log();
  error[0] = 4.0f * dot(errorDQ, errorDQ);


  if (KDL::Equal(delta_twist, KDL::Twist::Zero(), eps))
  {
    progress = 1;
    best_x = x;
    return;
  }
}


int NLOPT_IK::CartToJnt(const KDL::JntArray &q_init, const KDL::Frame &p_in, KDL::JntArray &q_out, const KDL::Twist _bounds, const KDL::JntArray& q_desired)
{
  // User command to start an IK solve.  Takes in a seed
  // configuration, a Cartesian pose, and (optional) a desired
  // configuration.  If the desired is not provided, the seed is
  // used.  Outputs the joint configuration found that solves the
  // IK.

  // Returns -3 if a configuration could not be found within the eps
  // set up in the constructor.

  boost::posix_time::ptime start_time = boost::posix_time::microsec_clock::local_time();
  boost::posix_time::time_duration diff;

  bounds = _bounds;
  q_out = q_init;

  if (chain.getNrOfJoints() < 2)
  {
    ROS_ERROR_THROTTLE(1.0, "NLOpt_IK can only be run for chains of length 2 or more");
    return -3;
  }

  if (q_init.data.size() != types.size())
  {
    ROS_ERROR_THROTTLE(1.0, "IK seeded with wrong number of joints.  Expected %d but got %d", (int)types.size(), (int)q_init.data.size());
    return -3;
  }

  opt.set_maxtime(maxtime);


  double minf; /* the minimum objective value, upon return */

  targetPose = p_in;

  if (TYPE == 1)   // DQ
  {
    math3d::matrix3x3<double> targetRotationMatrix(targetPose.M.data);
    math3d::quaternion<double> targetQuaternion = math3d::rot_matrix_to_quaternion<double>(targetRotationMatrix);
    math3d::point3d targetTranslation(targetPose.p.data);
    targetDQ = dual_quaternion::rigid_transformation(targetQuaternion, targetTranslation);
  }
  // else if (TYPE == 1)
  // {
  //   z_target = targetPose*z_up;
  //   x_target = targetPose*x_out;
  //   y_target = targetPose*y_out;
  // }


  //    fksolver.JntToCart(q_init,currentPose);

  std::vector<double> x(chain.getNrOfJoints());

  for (uint i = 0; i < x.size(); i++)
  {
    x[i] = q_init(i);

    if (types[i] == KDL::BasicJointType::Continuous)
      continue;

    if (types[i] == KDL::BasicJointType::TransJoint)
    {
      x[i] = std::min(x[i], ub[i]);
      x[i] = std::max(x[i], lb[i]);
    }
    else
    {

      // Below is to handle bad seeds outside of limits

      if (x[i] > ub[i])
      {
        //Find actual angle offset
        double diffangle = fmod(x[i] - ub[i], 2 * M_PI);
        // Add that to upper bound and go back a full rotation
        x[i] = ub[i] + diffangle - 2 * M_PI;
      }

      if (x[i] < lb[i])
      {
        //Find actual angle offset
        double diffangle = fmod(lb[i] - x[i], 2 * M_PI);
        // Subtract that from lower bound and go forward a full rotation
        x[i] = lb[i] - diffangle + 2 * M_PI;
      }

      if (x[i] > ub[i])
        x[i] = (ub[i] + lb[i]) / 2.0;
    }
  }

  best_x = x;
  progress = -3;

  std::vector<double> artificial_lower_limits(lb.size());

  for (uint i = 0; i < lb.size(); i++)
    if (types[i] == KDL::BasicJointType::Continuous)
      artificial_lower_limits[i] = best_x[i] - 2 * M_PI;
    else if (types[i] == KDL::BasicJointType::TransJoint)
      artificial_lower_limits[i] = lb[i];
    else
      artificial_lower_limits[i] = std::max(lb[i], best_x[i] - 2 * M_PI);

  opt.set_lower_bounds(artificial_lower_limits);

  std::vector<double> artificial_upper_limits(lb.size());

  for (uint i = 0; i < ub.size(); i++)
    if (types[i] == KDL::BasicJointType::Continuous)
      artificial_upper_limits[i] = best_x[i] + 2 * M_PI;
    else if (types[i] == KDL::BasicJointType::TransJoint)
      artificial_upper_limits[i] = ub[i];
    else
      artificial_upper_limits[i] = std::min(ub[i], best_x[i] + 2 * M_PI);

  opt.set_upper_bounds(artificial_upper_limits);

  if (q_desired.data.size() == 0)
  {
    des = x;
  }
  else
  {
    des.resize(x.size());
    for (uint i = 0; i < des.size(); i++)
      des[i] = q_desired(i);
  }

  try
  {
    opt.optimize(x, minf);
  }
  catch (...)
  {
  }

  if (progress == -1) // Got NaNs
    progress = -3;


  if (!aborted && progress < 0)
  {

    double time_left;
    diff = boost::posix_time::microsec_clock::local_time() - start_time;
    time_left = maxtime - diff.total_nanoseconds() / 1000000000.0;

    while (time_left > 0 && !aborted && progress < 0)
    {

      for (uint i = 0; i < x.size(); i++)
        x[i] = fRand(artificial_lower_limits[i], artificial_upper_limits[i]);

      opt.set_maxtime(time_left);

      try
      {
        opt.optimize(x, minf);
      }
      catch (...) {}

      if (progress == -1) // Got NaNs
        progress = -3;

      diff = boost::posix_time::microsec_clock::local_time() - start_time;
      time_left = maxtime - diff.total_nanoseconds() / 1000000000.0;
    }
  }


  for (uint i = 0; i < x.size(); i++)
  {
    q_out(i) = best_x[i];
  }

  return progress;

}


}