kinematics_metrics.cpp

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/* Author: Sachin Chitta */

#include <moveit/kinematics_metrics/kinematics_metrics.h>
#include <Eigen/Eigenvalues>
#include <boost/math/constants/constants.hpp>

namespace kinematics_metrics
{
double KinematicsMetrics::getJointLimitsPenalty(const robot_state::RobotState& state,
                                                const robot_model::JointModelGroup* joint_model_group) const
{
  if (fabs(penalty_multiplier_) <= boost::math::tools::epsilon<double>())
    return 1.0;
  double joint_limits_multiplier(1.0);
  const std::vector<const robot_model::JointModel*>& joint_model_vector = joint_model_group->getJointModels();
  for (std::size_t i = 0; i < joint_model_vector.size(); ++i)
  {
    if (joint_model_vector[i]->getType() == robot_model::JointModel::REVOLUTE)
    {
      const robot_model::RevoluteJointModel* revolute_model =
          static_cast<const robot_model::RevoluteJointModel*>(joint_model_vector[i]);
      if (revolute_model->isContinuous())
        continue;
    }
    if (joint_model_vector[i]->getType() == robot_model::JointModel::PLANAR)
    {
      const robot_model::JointModel::Bounds& bounds = joint_model_vector[i]->getVariableBounds();
      if (bounds[0].min_position_ == -std::numeric_limits<double>::max() ||
          bounds[0].max_position_ == std::numeric_limits<double>::max() ||
          bounds[1].min_position_ == -std::numeric_limits<double>::max() ||
          bounds[1].max_position_ == std::numeric_limits<double>::max() ||
          bounds[2].min_position_ == -boost::math::constants::pi<double>() ||
          bounds[2].max_position_ == boost::math::constants::pi<double>())
        continue;
    }
    if (joint_model_vector[i]->getType() == robot_model::JointModel::FLOATING)
    {
      // Joint limits are not well-defined for floating joints
      continue;
    }
    const double* joint_values = state.getJointPositions(joint_model_vector[i]);
    const robot_model::JointModel::Bounds& bounds = joint_model_vector[i]->getVariableBounds();
    std::vector<double> lower_bounds, upper_bounds;
    for (std::size_t j = 0; j < bounds.size(); ++j)
    {
      lower_bounds.push_back(bounds[j].min_position_);
      upper_bounds.push_back(bounds[j].max_position_);
    }
    double lower_bound_distance = joint_model_vector[i]->distance(joint_values, &lower_bounds[0]);
    double upper_bound_distance = joint_model_vector[i]->distance(joint_values, &upper_bounds[0]);
    double range = lower_bound_distance + upper_bound_distance;
    if (range <= boost::math::tools::epsilon<double>())
      continue;
    joint_limits_multiplier *= (lower_bound_distance * upper_bound_distance / (range * range));
  }
  return (1.0 - exp(-penalty_multiplier_ * joint_limits_multiplier));
}

bool KinematicsMetrics::getManipulabilityIndex(const robot_state::RobotState& state, const std::string& group_name,
                                               double& manipulability_index, bool translation) const
{
  const robot_model::JointModelGroup* joint_model_group = robot_model_->getJointModelGroup(group_name);
  if (joint_model_group)
    return getManipulabilityIndex(state, joint_model_group, manipulability_index, translation);
  else
    return false;
}

bool KinematicsMetrics::getManipulabilityIndex(const robot_state::RobotState& state,
                                               const robot_model::JointModelGroup* joint_model_group,
                                               double& manipulability_index, bool translation) const
{
  // state.getJacobian() only works for chain groups.
  if (!joint_model_group->isChain())
  {
    return false;
  }

  Eigen::MatrixXd jacobian = state.getJacobian(joint_model_group);
  // Get joint limits penalty
  double penalty = getJointLimitsPenalty(state, joint_model_group);
  if (translation)
  {
    if (jacobian.cols() < 6)
    {
      Eigen::JacobiSVD<Eigen::MatrixXd> svdsolver(jacobian.topLeftCorner(3, jacobian.cols()));
      Eigen::MatrixXd singular_values = svdsolver.singularValues();
      manipulability_index = 1.0;
      for (unsigned int i = 0; i < singular_values.rows(); ++i)
      {
        logDebug("moveit.kin_metrics: Singular value: %d %f", i, singular_values(i, 0));
        manipulability_index *= singular_values(i, 0);
      }
      // Get manipulability index
      manipulability_index = penalty * manipulability_index;
    }
    else
    {
      Eigen::MatrixXd jacobian_2 = jacobian.topLeftCorner(3, jacobian.cols());
      Eigen::MatrixXd matrix = jacobian_2 * jacobian_2.transpose();
      // Get manipulability index
      manipulability_index = penalty * sqrt(matrix.determinant());
    }
  }
  else
  {
    if (jacobian.cols() < 6)
    {
      Eigen::JacobiSVD<Eigen::MatrixXd> svdsolver(jacobian);
      Eigen::MatrixXd singular_values = svdsolver.singularValues();
      manipulability_index = 1.0;
      for (unsigned int i = 0; i < singular_values.rows(); ++i)
      {
        logDebug("moveit.kin_metrics: Singular value: %d %f", i, singular_values(i, 0));
        manipulability_index *= singular_values(i, 0);
      }
      // Get manipulability index
      manipulability_index = penalty * manipulability_index;
    }
    else
    {
      Eigen::MatrixXd matrix = jacobian * jacobian.transpose();
      // Get manipulability index
      manipulability_index = penalty * sqrt(matrix.determinant());
    }
  }
  return true;
}

bool KinematicsMetrics::getManipulabilityEllipsoid(const robot_state::RobotState& state, const std::string& group_name,
                                                   Eigen::MatrixXcd& eigen_values,
                                                   Eigen::MatrixXcd& eigen_vectors) const
{
  const robot_model::JointModelGroup* joint_model_group = robot_model_->getJointModelGroup(group_name);
  if (joint_model_group)
    return getManipulabilityEllipsoid(state, joint_model_group, eigen_values, eigen_vectors);
  else
    return false;
}

bool KinematicsMetrics::getManipulabilityEllipsoid(const robot_state::RobotState& state,
                                                   const robot_model::JointModelGroup* joint_model_group,
                                                   Eigen::MatrixXcd& eigen_values,
                                                   Eigen::MatrixXcd& eigen_vectors) const
{
  // state.getJacobian() only works for chain groups.
  if (!joint_model_group->isChain())
  {
    return false;
  }

  Eigen::MatrixXd jacobian = state.getJacobian(joint_model_group);
  Eigen::MatrixXd matrix = jacobian * jacobian.transpose();
  Eigen::EigenSolver<Eigen::MatrixXd> eigensolver(matrix.block(0, 0, 3, 3));
  eigen_values = eigensolver.eigenvalues();
  eigen_vectors = eigensolver.eigenvectors();
  return true;
}

bool KinematicsMetrics::getManipulability(const robot_state::RobotState& state, const std::string& group_name,
                                          double& manipulability, bool translation) const
{
  const robot_model::JointModelGroup* joint_model_group = robot_model_->getJointModelGroup(group_name);
  if (joint_model_group)
    return getManipulability(state, joint_model_group, manipulability, translation);
  else
    return false;
}

bool KinematicsMetrics::getManipulability(const robot_state::RobotState& state,
                                          const robot_model::JointModelGroup* joint_model_group, double& manipulability,
                                          bool translation) const
{
  // state.getJacobian() only works for chain groups.
  if (!joint_model_group->isChain())
  {
    return false;
  }
  // Get joint limits penalty
  double penalty = getJointLimitsPenalty(state, joint_model_group);
  if (translation)
  {
    Eigen::MatrixXd jacobian = state.getJacobian(joint_model_group);
    Eigen::JacobiSVD<Eigen::MatrixXd> svdsolver(jacobian.topLeftCorner(3, jacobian.cols()));
    Eigen::MatrixXd singular_values = svdsolver.singularValues();
    for (int i = 0; i < singular_values.rows(); ++i)
      logDebug("moveit.kin_metrics: Singular value: %d %f", i, singular_values(i, 0));
    manipulability = penalty * singular_values.minCoeff() / singular_values.maxCoeff();
  }
  else
  {
    Eigen::MatrixXd jacobian = state.getJacobian(joint_model_group);
    Eigen::JacobiSVD<Eigen::MatrixXd> svdsolver(jacobian);
    Eigen::MatrixXd singular_values = svdsolver.singularValues();
    for (int i = 0; i < singular_values.rows(); ++i)
      logDebug("moveit.kin_metrics: Singular value: %d %f", i, singular_values(i, 0));
    manipulability = penalty * singular_values.minCoeff() / singular_values.maxCoeff();
  }
  return true;
}

}  // namespace