chomp_optimizer.cpp

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#include <chomp_motion_planner/chomp_optimizer.h>
#include <ros/ros.h>
#include <visualization_msgs/MarkerArray.h>
#include <chomp_motion_planner/chomp_utils.h>
#include <planning_models/robot_model.h>
#include <eigen3/Eigen/LU>
#include <eigen3/Eigen/Core>

namespace chomp
{
double getRandomDouble()
{
  return ((double)random() / (double)RAND_MAX);
}

ChompOptimizer::ChompOptimizer(ChompTrajectory *trajectory,
                               const planning_scene::PlanningSceneConstPtr& planning_scene,
                               const std::string& planning_group,
                               const ChompParameters *parameters,
                               const planning_models::RobotState& start_state) :
  full_trajectory_(trajectory),
  kmodel_(planning_scene->getRobotModel()),
  planning_group_(planning_group),
  parameters_(parameters),
  group_trajectory_(*full_trajectory_,
                    planning_group_,
                    DIFF_RULE_LENGTH),
  planning_scene_(planning_scene),
  state_(start_state),
  start_state_(start_state),
  initialized_(false)
{
  hy_world_ = dynamic_cast<const collision_detection::CollisionWorldHybrid*>(planning_scene->getCollisionWorld().get());
  if(!hy_world_) {
    ROS_WARN_STREAM("Could not initialize hybrid collision world from planning scene");
    return;
  }

  hy_robot_ = dynamic_cast<const collision_detection::CollisionRobotHybrid*>(planning_scene->getCollisionRobot().get());
  if(!hy_robot_) {
    ROS_WARN_STREAM("Could not initialize hybrid collision robot from planning scene");
    return;
  }
  initialize();
}

void ChompOptimizer::initialize()
{
  // init some variables:
  num_vars_free_ = group_trajectory_.getNumFreePoints();
  num_vars_all_ = group_trajectory_.getNumPoints();
  num_joints_ = group_trajectory_.getNumJoints();

  free_vars_start_ = group_trajectory_.getStartIndex();
  free_vars_end_ = group_trajectory_.getEndIndex();

  collision_detection::CollisionRequest req;
  collision_detection::CollisionResult res;
  req.group_name = planning_group_;
  ros::WallTime wt = ros::WallTime::now();
  hy_world_->getCollisionGradients(req,
                                   res,
                                   *hy_robot_->getCollisionRobotDistanceField().get(),
                                   state_,
                                   &planning_scene_->getAllowedCollisionMatrix(),
                                   gsr_);
  ROS_INFO_STREAM("First coll check took " << (ros::WallTime::now()-wt));
  num_collision_points_ = 0;
  for(size_t i = 0; i < gsr_->gradients_.size(); i++)
  {
    num_collision_points_ += gsr_->gradients_[i].gradients.size();
  }

  // set up the joint costs:
  joint_costs_.reserve(num_joints_);

  double max_cost_scale = 0.0;

  joint_model_group_ = planning_scene_->getRobotModel()->getJointModelGroup(planning_group_);

  const std::vector<const planning_models::RobotModel::JointModel*> joint_models = joint_model_group_->getJointModels();
  for(size_t i = 0; i < joint_models.size(); i++)
  {
    const planning_models::RobotModel::JointModel* model = joint_models[i];
    double joint_cost = 1.0;
    std::string joint_name = model->getName();
    //nh.param("joint_costs/" + joint_name, joint_cost, 1.0);
    std::vector<double> derivative_costs(3);
    derivative_costs[0] = joint_cost * parameters_->getSmoothnessCostVelocity();
    derivative_costs[1] = joint_cost * parameters_->getSmoothnessCostAcceleration();
    derivative_costs[2] = joint_cost * parameters_->getSmoothnessCostJerk();
    joint_costs_.push_back(ChompCost(group_trajectory_, i, derivative_costs, parameters_->getRidgeFactor()));
    double cost_scale = joint_costs_[i].getMaxQuadCostInvValue();
    if(max_cost_scale < cost_scale)
      max_cost_scale = cost_scale;
  }

  // scale the smoothness costs
  for(int i = 0; i < num_joints_; i++)
  {
    joint_costs_[i].scale(max_cost_scale);
  }

  // allocate memory for matrices:
  smoothness_increments_ = Eigen::MatrixXd::Zero(num_vars_free_, num_joints_);
  collision_increments_ = Eigen::MatrixXd::Zero(num_vars_free_, num_joints_);
  final_increments_ = Eigen::MatrixXd::Zero(num_vars_free_, num_joints_);
  smoothness_derivative_ = Eigen::VectorXd::Zero(num_vars_all_);
  jacobian_ = Eigen::MatrixXd::Zero(3, num_joints_);
  jacobian_pseudo_inverse_ = Eigen::MatrixXd::Zero(num_joints_, 3);
  jacobian_jacobian_tranpose_ = Eigen::MatrixXd::Zero(3, 3);
  random_state_ = Eigen::VectorXd::Zero(num_joints_);
  joint_state_velocities_ = Eigen::VectorXd::Zero(num_joints_);

  group_trajectory_backup_ = group_trajectory_.getTrajectory();
  best_group_trajectory_ = group_trajectory_.getTrajectory();

  collision_point_joint_names_.resize(num_vars_all_, std::vector<std::string>(num_collision_points_));
  collision_point_pos_eigen_.resize(num_vars_all_, std::vector<Eigen::Vector3d>(num_collision_points_));
  collision_point_vel_eigen_.resize(num_vars_all_, std::vector<Eigen::Vector3d>(num_collision_points_));
  collision_point_acc_eigen_.resize(num_vars_all_, std::vector<Eigen::Vector3d>(num_collision_points_));
  joint_axes_.resize(num_vars_all_, std::vector<Eigen::Vector3d>(num_joints_));
  joint_positions_.resize(num_vars_all_, std::vector<Eigen::Vector3d>(num_joints_));

  collision_point_potential_.resize(num_vars_all_, std::vector<double>(num_collision_points_));
  collision_point_vel_mag_.resize(num_vars_all_, std::vector<double>(num_collision_points_));
  collision_point_potential_gradient_.resize(num_vars_all_, std::vector<Eigen::Vector3d>(num_collision_points_));

  collision_free_iteration_ = 0;
  is_collision_free_ = false;
  state_is_in_collision_.resize(num_vars_all_);
  point_is_in_collision_.resize(num_vars_all_, std::vector<int>(num_collision_points_));

  last_improvement_iteration_ = -1;

  // HMC initialization:
  momentum_ = Eigen::MatrixXd::Zero(num_vars_free_, num_joints_);
  random_momentum_ = Eigen::MatrixXd::Zero(num_vars_free_, num_joints_);
  random_joint_momentum_ = Eigen::VectorXd::Zero(num_vars_free_);
  multivariate_gaussian_.clear();
  stochasticity_factor_ = 1.0;
  for(int i = 0; i < num_joints_; i++)
  {
    multivariate_gaussian_.push_back(
                                     MultivariateGaussian(Eigen::VectorXd::Zero(num_vars_free_),
                                                          joint_costs_[i].getQuadraticCostInverse()));
  }

  std::map<std::string, std::string> fixed_link_resolution_map;
  for(int i = 0; i < num_joints_; i++)
  {
    joint_names_.push_back(joint_model_group_->getJointModels()[i]->getName());
    //ROS_INFO("Got joint %s", joint_names_[i].c_str());
    registerParents(joint_model_group_->getJointModels()[i]);
    fixed_link_resolution_map[joint_names_[i]] = joint_names_[i];
  }

  for(size_t i = 0; i < joint_model_group_->getFixedJointModels().size(); i ++)
  {
    const planning_models::RobotModel::JointModel* model = joint_model_group_->getFixedJointModels()[i];
    fixed_link_resolution_map[model->getName()] = model->getParentLinkModel()->getParentJointModel()->getName();
  }

  //TODO - is this just the joint_roots_?
  for(size_t i = 0; i < joint_model_group_->getUpdatedLinkModels().size(); i ++)
  {
    if(fixed_link_resolution_map.find(joint_model_group_->getUpdatedLinkModels()[i]->getParentJointModel()->getName()) == fixed_link_resolution_map.end())
    {
      const planning_models::RobotModel::JointModel* parent_model = NULL;
      bool found_root = false;

      while(!found_root)
      {
        if(parent_model == NULL)
        {
          parent_model = joint_model_group_->getUpdatedLinkModels()[i]->getParentJointModel();
        }
        else
        {
          parent_model = parent_model->getParentLinkModel()->getParentJointModel();
          for(size_t j = 0; j < joint_names_.size(); j++)
          {
            if(parent_model->getName() == joint_names_[j])
            {
              found_root = true;
            }
          }
        }
      }
      fixed_link_resolution_map[joint_model_group_->getUpdatedLinkModels()[i]->getParentJointModel()->getName()] = parent_model->getName();
    }
  }

  // for(map<string, map<string, bool> >::iterator it = joint_parent_map_.begin(); it != joint_parent_map_.end(); it++)
  // {
  //   stringstream ss;
  //   ss << it->first << " Parents : {";

  //   for(map<string, bool>::iterator it2 = it->second.begin(); it2 != it->second.end(); it2++)
  //   {
  //     ss << it2->first << ",";
  //   }
  //   ss << "}";
  //   ROS_INFO("%s",ss.str().c_str());
  // }

  int start = free_vars_start_;
  int end = free_vars_end_;
  for(int i = start; i <= end; ++i)
  {
    size_t j = 0;
    for(size_t g = 0; g < gsr_->gradients_.size(); g++)
    {
      collision_detection::GradientInfo& info = gsr_->gradients_[g];

      for(size_t k = 0; k < info.sphere_locations.size(); k++)
      {
        if(fixed_link_resolution_map.find(info.joint_name) != fixed_link_resolution_map.end())
        {
          collision_point_joint_names_[i][j] = fixed_link_resolution_map[info.joint_name];
        }
        else
        {
          ROS_ERROR("Couldn't find joint %s!", info.joint_name.c_str());
        }
        j++;
      }
    }
  }
  initialized_ = true;
}

ChompOptimizer::~ChompOptimizer()
{
  destroy();
}

void ChompOptimizer::registerParents(const planning_models::RobotModel::JointModel* model)
{
  const planning_models::RobotModel::JointModel* parent_model = NULL;
  bool found_root = false;

  if(model == kmodel_->getRoot()) return;

  while(!found_root)
  {
    if(parent_model == NULL)
    {
      if(model->getParentLinkModel() == NULL) {
        ROS_ERROR_STREAM("Model " << model->getName() << " not root but has NULL link model parent");
        return;
      } else if(model->getParentLinkModel()->getParentJointModel() == NULL) {
        ROS_ERROR_STREAM("Model " << model->getName() << " not root but has NULL joint model parent");
        return;
      }
      parent_model = model->getParentLinkModel()->getParentJointModel();
    } else
    {
      if(parent_model == kmodel_->getRoot())
      {
        found_root = true;
      } else {
        parent_model = parent_model->getParentLinkModel()->getParentJointModel();
      }
    }
    joint_parent_map_[model->getName()][parent_model->getName()] = true;
  }
}

void ChompOptimizer::optimize()
{
  ros::WallTime start_time = ros::WallTime::now();
  double averageCostVelocity = 0.0;
  int currentCostIter = 0;
  int costWindow = 10;
  std::vector<double>costs(costWindow, 0.0);
  double minimaThreshold = 0.05;
  bool should_break_out = false;

  // if(parameters_->getAnimatePath())
  // {
  //   animatePath();
  // }

  // iterate
  for(iteration_ = 0; iteration_ < parameters_->getMaxIterations(); iteration_++)
  {
    ros::WallTime for_time = ros::WallTime::now();
    performForwardKinematics();
    //ROS_INFO_STREAM("Forward kinematics took " << (ros::WallTime::now()-for_time));
    double cCost = getCollisionCost();
    double sCost = getSmoothnessCost();
    double cost = cCost + sCost;

    //ROS_INFO_STREAM("Collision cost " << cCost << " smoothness cost " << sCost);

    // if(parameters_->getAddRandomness() && currentCostIter != -1)
    // {
    //   costs[currentCostIter] = cCost;
    //   currentCostIter++;

    //   if(currentCostIter >= costWindow)
    //   {
    //     for(int i = 1; i < costWindow; i++)
    //     {
    //       averageCostVelocity += (costs.at(i) - costs.at(i - 1));
    //     }

    //     averageCostVelocity /= (double)(costWindow);
    //     currentCostIter = -1;
    //   }
    // }
    if(iteration_ == 0)
    {
      best_group_trajectory_ = group_trajectory_.getTrajectory();
      best_group_trajectory_cost_ = cost;
    }
    else
    {
      if(cost < best_group_trajectory_cost_)
      {
        best_group_trajectory_ = group_trajectory_.getTrajectory();
        best_group_trajectory_cost_ = cost;
        last_improvement_iteration_ = iteration_;
      }
    }
    calculateSmoothnessIncrements();
    ros::WallTime coll_time = ros::WallTime::now();
    calculateCollisionIncrements();
    ROS_DEBUG_STREAM("Collision increments took " << (ros::WallTime::now()-coll_time));
    calculateTotalIncrements();

    // if(!parameters_->getUseHamiltonianMonteCarlo())
    // {
    //   // non-stochastic version:
    addIncrementsToTrajectory();
    // }
    // else
    // {
    //   // hamiltonian monte carlo updates:
    //   getRandomMomentum();
    //   updateMomentum();
    //   updatePositionFromMomentum();
    //   stochasticity_factor_ *= parameters_->getHmcAnnealingFactor();
    // }
    handleJointLimits();
    updateFullTrajectory();

    if(iteration_ % 10 == 0)
    {
      if(isCurrentTrajectoryMeshToMeshCollisionFree()) {
        num_collision_free_iterations_ = 0;
        ROS_INFO("Chomp Got mesh to mesh safety at iter %d. Breaking out early.", iteration_);
        is_collision_free_ = true;
        iteration_++;
        should_break_out = true;
      }
      // } else if(safety == CollisionProximitySpace::InCollisionSafe) {

      // ROS_DEBUG("Trajectory cost: %f (s=%f, c=%f)", getTrajectoryCost(), getSmoothnessCost(), getCollisionCost());
      // CollisionProximitySpace::TrajectorySafety safety = checkCurrentIterValidity();
      // if(safety == CollisionProximitySpace::MeshToMeshSafe)
      // {
      //   num_collision_free_iterations_ = 0;
      //   ROS_INFO("Chomp Got mesh to mesh safety at iter %d. Breaking out early.", iteration_);
      //   is_collision_free_ = true;
      //   iteration_++;
      //   should_break_out = true;
      // } else if(safety == CollisionProximitySpace::InCollisionSafe) {
      //   num_collision_free_iterations_ = parameters_->getMaxIterationsAfterCollisionFree();
      //   ROS_INFO("Chomp Got in collision safety at iter %d. Breaking out soon.", iteration_);
      //   is_collision_free_ = true;
      //   iteration_++;
      //   should_break_out = true;
      // }
      // else
      // {
      //   is_collision_free_ = false;
      // }
    }

    if(!parameters_->getFilterMode())
    {
      if(cCost < parameters_->getCollisionThreshold())
      {
        num_collision_free_iterations_ = parameters_->getMaxIterationsAfterCollisionFree();
        is_collision_free_ = true;
        iteration_++;
        should_break_out = true;
      } else {
        //ROS_INFO_STREAM("cCost " << cCost << " over threshold " << parameters_->getCollisionThreshold());
      }
    }

    if((ros::WallTime::now() - start_time).toSec() > parameters_->getPlanningTimeLimit() && !parameters_->getAnimatePath() && !parameters_->getAnimateEndeffector())
    {
      ROS_WARN("Breaking out early due to time limit constraints.");
      break;
    }

    // if(fabs(averageCostVelocity) < minimaThreshold && currentCostIter == -1 && !is_collision_free_ && parameters_->getAddRandomness())
    // {
    //   ROS_INFO("Detected local minima. Attempting to break out!");
    //   int iter = 0;
    //   bool success = false;
    //   while(iter < 20 && !success)
    //   {
    //     performForwardKinematics();
    //     double original_cost = getTrajectoryCost();
    //     group_trajectory_backup_ = group_trajectory_.getTrajectory();
    //     perturbTrajectory();
    //     handleJointLimits();
    //     updateFullTrajectory();
    //     performForwardKinematics();
    //     double new_cost = getTrajectoryCost();
    //     iter ++;
    //     if(new_cost < original_cost)
    //     {
    //       ROS_INFO("Got out of minimum in %d iters!", iter);
    //       averageCostVelocity = 0.0;
    //       currentCostIter = 0;
    //       success = true;
    //     }
    //     else
    //     {
    //       group_trajectory_.getTrajectory() = group_trajectory_backup_;
    //       updateFullTrajectory();
    //       currentCostIter = 0;
    //       averageCostVelocity = 0.0;
    //       success = false;
    //     }

    //   }

    //   if(!success)
    //   {
    //     ROS_INFO("Failed to exit minimum!");
    //   }
    //}
    else if(currentCostIter == -1)
    {
      currentCostIter = 0;
      averageCostVelocity = 0.0;
    }

    // if(parameters_->getAnimateEndeffector())
    // {
    //   animateEndeffector();
    // }

    // if(parameters_->getAnimatePath() && iteration_ % 25 == 0)
    // {
    //   animatePath();
    // }

    if(should_break_out)
    {
      collision_free_iteration_++;
      if(num_collision_free_iterations_ == 0) {
        break;
      } else if(collision_free_iteration_ > num_collision_free_iterations_)
      {
        // CollisionProximitySpace::TrajectorySafety safety = checkCurrentIterValidity();
        // if(safety != CollisionProximitySpace::MeshToMeshSafe &&
        //    safety != CollisionProximitySpace::InCollisionSafe) {
        //   ROS_WARN_STREAM("Apparently regressed");
        // }
        break;
      }
    }
  }

  if(is_collision_free_)
  {
    ROS_INFO("Chomp path is collision free");
  }
  else
  {
    ROS_ERROR("Chomp path is not collision free!");
  }

  // if(parameters_->getAnimatePath())
  // {
  //   animatePath();
  // }

  group_trajectory_.getTrajectory() = best_group_trajectory_;
  updateFullTrajectory();

  // if(parameters_->getAnimatePath())
  //   animatePath();

  ROS_INFO("Terminated after %d iterations, using path from iteration %d", iteration_, last_improvement_iteration_);
  ROS_INFO("Optimization core finished in %f sec", (ros::WallTime::now() - start_time).toSec() );
  ROS_INFO_STREAM("Time per iteration " << (ros::WallTime::now() - start_time).toSec()/(iteration_*1.0));
}

bool ChompOptimizer::isCurrentTrajectoryMeshToMeshCollisionFree() const
{
  moveit_msgs::RobotTrajectory traj;
  traj.joint_trajectory.joint_names = joint_names_;
  for(int i = 0; i < group_trajectory_.getNumPoints(); i++) {
    trajectory_msgs::JointTrajectoryPoint point;
    for(int j = 0; j < group_trajectory_.getNumJoints(); j++) {
      point.positions.push_back(best_group_trajectory_(i,j));
    }
    traj.joint_trajectory.points.push_back(point);
  }
  return planning_scene_->isPathValid(start_state_,
                                      traj);
}

// CollisionProximitySpace::TrajectorySafety ChompOptimizer::checkCurrentIterValidity()
// {
//   JointTrajectory jointTrajectory;
//   jointTrajectory.joint_names = joint_names_;
//   jointTrajectory.header.frame_id = collision_space_->getCollisionModelsInterface()->getRobotFrameId();
//   jointTrajectory.header.stamp = ros::Time::now();
//   Constraints goalConstraints;
//   Constraints pathConstraints;
//   ArmNavigationErrorCodes errorCode;
//   vector<ArmNavigationErrorCodes> trajectoryErrorCodes;
//   for(int i = 0; i < group_trajectory_.getNumPoints(); i++)
//   {
//     JointTrajectoryPoint point;
//     for(int j = 0; j < group_trajectory_.getNumJoints(); j++)
//     {
//       point.positions.push_back(best_group_trajectory_(i, j));
//     }
//     jointTrajectory.points.push_back(point);
//   }

//   return collision_space_->isTrajectorySafe(jointTrajectory, goalConstraints, pathConstraints, planning_group_);
//   /*
//     bool valid = collision_space_->getCollisionModelsInterface()->isJointTrajectoryValid(*state_,
//     jointTrajectory,
//     goalConstraints,
//     pathConstraints, errorCode,
//     trajectoryErrorCodes, false);
//   */

// }

void ChompOptimizer::calculateSmoothnessIncrements()
{
  for(int i = 0; i < num_joints_; i++)
  {
    joint_costs_[i].getDerivative(group_trajectory_.getJointTrajectory(i), smoothness_derivative_);
    smoothness_increments_.col(i)
      = -smoothness_derivative_.segment(group_trajectory_.getStartIndex(), num_vars_free_);
  }
}

void ChompOptimizer::calculateCollisionIncrements()
{
  double potential;
  double vel_mag_sq;
  double vel_mag;
  Eigen::Vector3d potential_gradient;
  Eigen::Vector3d normalized_velocity;
  Eigen::Matrix3d orthogonal_projector;
  Eigen::Vector3d curvature_vector;
  Eigen::Vector3d cartesian_gradient;


  collision_increments_.setZero(num_vars_free_, num_joints_);

  int startPoint = 0;
  int endPoint = free_vars_end_;

  // In stochastic descent, simply use a random point in the trajectory, rather than all the trajectory points.
  // This is faster and guaranteed to converge, but it may take more iterations in the worst case.
  if(parameters_->getUseStochasticDescent())
  {
    startPoint =  (int)(((double)random() / (double)RAND_MAX)*(free_vars_end_ - free_vars_start_) + free_vars_start_);
    if(startPoint < free_vars_start_) startPoint = free_vars_start_;
    if(startPoint > free_vars_end_) startPoint = free_vars_end_;
    endPoint = startPoint;
  }
  else
  {
    startPoint = free_vars_start_;
  }

  for(int i = startPoint; i <= endPoint; i++)
  {
    for(int j = 0; j < num_collision_points_; j++)
    {
      potential = collision_point_potential_[i][j];

      if(potential < 0.0001)
        continue;

      potential_gradient = -collision_point_potential_gradient_[i][j];

      vel_mag = collision_point_vel_mag_[i][j];
      vel_mag_sq = vel_mag * vel_mag;

      // all math from the CHOMP paper:

      normalized_velocity = collision_point_vel_eigen_[i][j] / vel_mag;
      orthogonal_projector = Eigen::Matrix3d::Identity() - (normalized_velocity * normalized_velocity.transpose());
      curvature_vector = (orthogonal_projector * collision_point_acc_eigen_[i][j]) / vel_mag_sq;
      cartesian_gradient = vel_mag * (orthogonal_projector * potential_gradient - potential * curvature_vector);

      // pass it through the jacobian transpose to get the increments
      getJacobian(i, collision_point_pos_eigen_[i][j], collision_point_joint_names_[i][j] ,jacobian_);

      if(parameters_->getUsePseudoInverse())
      {
        calculatePseudoInverse();
        collision_increments_.row(i - free_vars_start_).transpose() -= jacobian_pseudo_inverse_ * cartesian_gradient;
      }
      else
      {
        collision_increments_.row(i - free_vars_start_).transpose() -= jacobian_.transpose() * cartesian_gradient;
      }

      /*
        if(point_is_in_collision_[i][j])
        {
        break;
        }
      */
    }
  }
  //cout << collision_increments_ << endl;
}

void ChompOptimizer::calculatePseudoInverse()
{
  jacobian_jacobian_tranpose_ = jacobian_ * jacobian_.transpose() + Eigen::MatrixXd::Identity(3, 3)
    * parameters_->getPseudoInverseRidgeFactor();
  jacobian_pseudo_inverse_ = jacobian_.transpose() * jacobian_jacobian_tranpose_.inverse();
}

void ChompOptimizer::calculateTotalIncrements()
{
  for(int i = 0; i < num_joints_; i++)
  {
    final_increments_.col(i) = parameters_->getLearningRate() * (joint_costs_[i].getQuadraticCostInverse()
                                                                 * (parameters_->getSmoothnessCostWeight() * smoothness_increments_.col(i)
                                                                    + parameters_->getObstacleCostWeight() * collision_increments_.col(i)));
  }

}

void ChompOptimizer::addIncrementsToTrajectory()
{
  const std::vector<const planning_models::RobotModel::JointModel*>& joint_models = joint_model_group_->getJointModels();
  for(size_t i = 0; i < joint_models.size(); i++)
  {
    double scale = 1.0;
    double max = final_increments_.col(i).maxCoeff();
    double min = final_increments_.col(i).minCoeff();
    double max_scale =  parameters_->getJointUpdateLimit() / fabs(max);
    double min_scale = parameters_->getJointUpdateLimit() / fabs(min);
    if(max_scale < scale)
      scale = max_scale;
    if(min_scale < scale)
      scale = min_scale;
    group_trajectory_.getFreeTrajectoryBlock().col(i) += scale * final_increments_.col(i);
  }
  //ROS_DEBUG("Scale: %f",scale);
  //group_trajectory_.getFreeTrajectoryBlock() += scale * final_increments_;
}

void ChompOptimizer::updateFullTrajectory()
{
  full_trajectory_->updateFromGroupTrajectory(group_trajectory_);
}

void ChompOptimizer::debugCost()
{
  double cost = 0.0;
  for(int i = 0; i < num_joints_; i++)
    cost += joint_costs_[i].getCost(group_trajectory_.getJointTrajectory(i));
  std::cout << "Cost = " << cost << std::endl;
}

double ChompOptimizer::getTrajectoryCost()
{
  return getSmoothnessCost() + getCollisionCost();
}

double ChompOptimizer::getSmoothnessCost()
{
  double smoothness_cost = 0.0;
  // joint costs:
  for(int i = 0; i < num_joints_; i++)
    smoothness_cost += joint_costs_[i].getCost(group_trajectory_.getJointTrajectory(i));

  return parameters_->getSmoothnessCostWeight() * smoothness_cost;
}

double ChompOptimizer::getCollisionCost()
{
  double collision_cost = 0.0;

  double worst_collision_cost = 0.0;
  worst_collision_cost_state_ = -1;

  // collision costs:
  for(int i = free_vars_start_; i <= free_vars_end_; i++)
  {
    double state_collision_cost = 0.0;
    for(int j = 0; j < num_collision_points_; j++)
    {
      state_collision_cost += collision_point_potential_[i][j] * collision_point_vel_mag_[i][j];
    }
    collision_cost += state_collision_cost;
    if(state_collision_cost > worst_collision_cost)
    {
      worst_collision_cost = state_collision_cost;
      worst_collision_cost_state_ = i;
    }
  }

  return parameters_->getObstacleCostWeight() * collision_cost;
}

void ChompOptimizer::computeJointProperties(int trajectory_point)
{
  //tf::Transform inverseWorldTransform = collision_space_->getInverseWorldTransform(*state_);
  for(int j = 0; j < num_joints_; j++)
  {
    const planning_models::RobotState *::JointState* joint_state = state_.getJointState(joint_names_[j]);
    const planning_models::RobotModel::JointModel* joint_model = joint_state->getJointModel();
    const planning_models::RobotModel::RevoluteJointModel* revolute_joint
      = dynamic_cast<const planning_models::RobotModel::RevoluteJointModel*>(joint_model);
    const planning_models::RobotModel::PrismaticJointModel* prismatic_joint
      = dynamic_cast<const planning_models::RobotModel::PrismaticJointModel*>(joint_model);

    std::string parent_link_name = joint_model->getParentLinkModel()->getName();
    std::string child_link_name = joint_model->getChildLinkModel()->getName();
    Eigen::Affine3d joint_transform =
      state_.getLinkState(parent_link_name)->getGlobalLinkTransform()
      * (kmodel_->getLinkModel(child_link_name)->getJointOriginTransform()
         * (state_.getJointState(joint_model->getName())->getVariableTransform()));


    //joint_transform = inverseWorldTransform * jointTransform;
    Eigen::Vector3d axis;

    if(revolute_joint != NULL)
    {
      axis = revolute_joint->getAxis();
    }
    else if(prismatic_joint != NULL)
    {
      axis = prismatic_joint->getAxis();
    } else {
      axis = Eigen::Vector3d::Identity();
    }

    axis = joint_transform * axis;

    joint_axes_[trajectory_point][j] = axis;
    joint_positions_[trajectory_point][j] = joint_transform.translation();
  }
}

template<typename Derived>
void ChompOptimizer::getJacobian(int trajectory_point,
                                 Eigen::Vector3d& collision_point_pos,
                                 std::string& joint_name,
                                 Eigen::MatrixBase<Derived>& jacobian) const
{
  for(int j = 0; j < num_joints_; j++)
  {
    if(isParent(joint_name, joint_names_[j]))
    {
      Eigen::Vector3d column = joint_axes_[trajectory_point][j].cross(Eigen::Vector3d(collision_point_pos(0),
                                                                                      collision_point_pos(1),
                                                                                      collision_point_pos(2))
                                                                      - joint_positions_[trajectory_point][j]);

      jacobian.col(j)[0] = column.x();
      jacobian.col(j)[1] = column.y();
      jacobian.col(j)[2] = column.z();
    }
    else
    {
      jacobian.col(j)[0] = 0.0;
      jacobian.col(j)[1] = 0.0;
      jacobian.col(j)[2] = 0.0;
    }
  }
}

void ChompOptimizer::handleJointLimits()
{
  const std::vector<const planning_models::RobotModel::JointModel*> joint_models = joint_model_group_->getJointModels();
  for(size_t joint_i = 0; joint_i < joint_models.size(); joint_i++) {
    const planning_models::RobotModel::JointModel* joint_model = joint_models[joint_i];
    const planning_models::RobotModel::RevoluteJointModel* revolute_joint
      = dynamic_cast<const planning_models::RobotModel::RevoluteJointModel*>(joint_model);

    if(revolute_joint->isContinuous())
    {
      continue;
    }

    const planning_models::RobotModel::JointModel::Bounds& bounds = joint_model->getVariableBounds();

    double joint_max = -DBL_MAX;
    double joint_min = DBL_MAX;

    for(planning_models::RobotModel::JointModel::Bounds::const_iterator it = bounds.begin(); it != bounds.end(); it ++)
    {
      if((*it).first < joint_min)
      {
        joint_min = (*it).first;
      }

      if((*it).second > joint_max)
      {
        joint_max = (*it).second;
      }
    }


    int count = 0;

    bool violation = false;
    do
    {
      double max_abs_violation = 1e-6;
      double max_violation = 0.0;
      int max_violation_index = 0;
      violation = false;
      for(int i = free_vars_start_; i <= free_vars_end_; i++)
      {
        double amount = 0.0;
        double absolute_amount = 0.0;
        if(group_trajectory_(i, joint_i) > joint_max)
        {
          amount = joint_max - group_trajectory_(i, joint_i);
          absolute_amount = fabs(amount);
        }
        else if(group_trajectory_(i, joint_i) < joint_min)
        {
          amount = joint_min - group_trajectory_(i, joint_i);
          absolute_amount = fabs(amount);
        }
        if(absolute_amount > max_abs_violation)
        {
          max_abs_violation = absolute_amount;
          max_violation = amount;
          max_violation_index = i;
          violation = true;
        }
      }

      if(violation)
      {
        int free_var_index = max_violation_index - free_vars_start_;
        double multiplier = max_violation / joint_costs_[joint_i].getQuadraticCostInverse()(free_var_index,
                                                                                            free_var_index);
        group_trajectory_.getFreeJointTrajectoryBlock(joint_i) += multiplier
          * joint_costs_[joint_i].getQuadraticCostInverse().col(free_var_index);
      }
      if(++count > 10)
        break;
    }
    while(violation);
  }
}

void ChompOptimizer::performForwardKinematics()
{
  double inv_time = 1.0 / group_trajectory_.getDiscretization();
  double inv_time_sq = inv_time * inv_time;

  // calculate the forward kinematics for the fixed states only in the first iteration:
  int start = free_vars_start_;
  int end = free_vars_end_;
  if(iteration_ == 0)
  {
    start = 0;
    end = num_vars_all_ - 1;
  }

  is_collision_free_ = true;

  ros::WallDuration total_dur(0.0);

  // for each point in the trajectory
  for(int i = start; i <= end; ++i)
  {
    // Set Robot state from trajectory point...
    collision_detection::CollisionRequest req;
    collision_detection::CollisionResult res;
    req.group_name = planning_group_;
    setRobotStateFromPoint(group_trajectory_, i);
    ros::WallTime grad = ros::WallTime::now();

    hy_world_->getCollisionGradients(req,
                                     res,
                                     *hy_robot_->getCollisionRobotDistanceField().get(),
                                     state_,
                                     NULL,
                                     gsr_);
    total_dur += (ros::WallTime::now()-grad);
    computeJointProperties(i);
    state_is_in_collision_[i] = false;

    //Keep vars in scope
    {
      size_t j = 0;
      for(size_t g = 0; g < gsr_->gradients_.size(); g++)
      {
        collision_detection::GradientInfo& info = gsr_->gradients_[g];

        for(size_t k = 0; k < info.sphere_locations.size(); k++)
        {
          collision_point_pos_eigen_[i][j][0] = info.sphere_locations[k].x();
          collision_point_pos_eigen_[i][j][1] = info.sphere_locations[k].y();
          collision_point_pos_eigen_[i][j][2] = info.sphere_locations[k].z();

          collision_point_potential_[i][j] = getPotential(info.distances[k], info.sphere_radii[k], parameters_->getMinClearence());
          collision_point_potential_gradient_[i][j][0] = info.gradients[k].x();
          collision_point_potential_gradient_[i][j][1] = info.gradients[k].y();
          collision_point_potential_gradient_[i][j][2] = info.gradients[k].z();

          point_is_in_collision_[i][j] = (info.distances[k] - info.sphere_radii[k] < info.sphere_radii[k]);

          if(point_is_in_collision_[i][j])
          {
            state_is_in_collision_[i] = true;
            // if(is_collision_free_ == true) {
            //   ROS_INFO_STREAM("We know it's not collision free " << g);
            //   ROS_INFO_STREAM("Sphere location " << info.sphere_locations[k].x() << " " << info.sphere_locations[k].y() << " " << info.sphere_locations[k].z());
            //   ROS_INFO_STREAM("Gradient " << info.gradients[k].x() << " " << info.gradients[k].y() << " " << info.gradients[k].z() << " distance " << info.distances[k] << " radii " << info.sphere_radii[k]);
            //   ROS_INFO_STREAM("Radius " << info.sphere_radii[k] << " potential " << collision_point_potential_[i][j]);
            // }
            is_collision_free_ = false;
          }
          j++;
        }
      }
    }
  }

  //ROS_INFO_STREAM("Total dur " << total_dur << " total checks " << end-start+1);

  // now, get the vel and acc for each collision point (using finite differencing)
  for(int i = free_vars_start_; i <= free_vars_end_; i++)
  {
    for(int j = 0; j < num_collision_points_; j++)
    {
      collision_point_vel_eigen_[i][j] = Eigen::Vector3d(0,0,0);
      collision_point_acc_eigen_[i][j] = Eigen::Vector3d(0,0,0);
      for(int k = -DIFF_RULE_LENGTH / 2; k <= DIFF_RULE_LENGTH / 2; k++)
      {
        collision_point_vel_eigen_[i][j] += (inv_time * DIFF_RULES[0][k + DIFF_RULE_LENGTH / 2]) * collision_point_pos_eigen_[i
                                                                                                                              + k][j];
        collision_point_acc_eigen_[i][j] += (inv_time_sq * DIFF_RULES[1][k + DIFF_RULE_LENGTH / 2]) * collision_point_pos_eigen_[i
                                                                                                                                 + k][j];
      }

      // get the norm of the velocity:
      collision_point_vel_mag_[i][j] = collision_point_vel_eigen_[i][j].norm();
    }
  }
}

void ChompOptimizer::setRobotStateFromPoint(ChompTrajectory& group_trajectory, int i)
{
  const Eigen::MatrixXd::RowXpr& point = group_trajectory.getTrajectoryPoint(i);

  std::vector<double> joint_states;
  for(int j = 0; j < group_trajectory.getNumJoints(); j ++)
  {
    joint_states.push_back(point(0,j));
  }

  //ros::WallTime timer = ros::WallTime::now();
  planning_models::RobotState *::JointStateGroup* group = state_.getJointStateGroup(planning_group_);
  group->setStateValues(joint_states);
  //timer = ros::WallTime::now();
}

void ChompOptimizer::perturbTrajectory()
{
  //int mid_point = (free_vars_start_ + free_vars_end_) / 2;
  if(worst_collision_cost_state_ < 0)
    return;
  int mid_point = worst_collision_cost_state_;
  planning_models::RobotState *random_state(state_);
  random_state.getJointStateGroup(planning_group_)->setToRandomValues();
  std::vector<double> vals;
  random_state.getJointStateGroup(planning_group_)->getGroupStateValues(vals);
  double* ptr = &vals[0];
  Eigen::Map<Eigen::VectorXd> random_matrix(ptr, vals.size());
  //Eigen::VectorXd random_matrix = vals;

  // convert the state into an increment
  random_matrix -= group_trajectory_.getTrajectoryPoint(mid_point).transpose();

  // project the increment orthogonal to joint velocities
  group_trajectory_.getJointVelocities(mid_point, joint_state_velocities_);
  joint_state_velocities_.normalize();
  random_matrix = (Eigen::MatrixXd::Identity(num_joints_, num_joints_) - joint_state_velocities_
                   * joint_state_velocities_.transpose()) * random_matrix;

  int mp_free_vars_index = mid_point - free_vars_start_;
  for(int i = 0; i < num_joints_; i++)
  {
    group_trajectory_.getFreeJointTrajectoryBlock(i)
      += joint_costs_[i].getQuadraticCostInverse().col(mp_free_vars_index) * random_state_(i);
  }
}

// void ChompOptimizer::getRandomState(const RobotState currentState, const string& groupName, Eigen::VectorXd& state_vec)
// {
//   const vector<RobotState *::JointState*>& jointStates =
//     currentState->getJointStateGroup(groupName)->getJointStateVector();
//   for(size_t i = 0; i < jointStates.size(); i++)
//   {

//     bool continuous = false;

//     RobotState *::JointState* jointState = jointStates[i];
//     const RobotModel::RevoluteJointModel* revolute_joint
//       = dynamic_cast<const RobotModel::RevoluteJointModel*>(jointState->getJointModel());
//     if(revolute_joint && revolute_joint->continuous_) {
//       continuous = true;
//     }

//     map<string, pair<double, double> > bounds = jointState->getJointModel()->getAllVariableBounds();
//     int j = 0;
//     for(map<string, pair<double, double> >::iterator it = bounds.begin(); it != bounds.end(); it++)
//     {
//       double randVal = jointState->getJointStateValues()[j] + (getRandomDouble()
//                                                                * (parameters_->getRandomJumpAmount()) - getRandomDouble() * (parameters_->getRandomJumpAmount()));

//       if(!continuous)
//       {
//         if(randVal > it->second.second)
//         {
//           randVal = it->second.second;
//         }
//         else if(randVal < it->second.first)
//         {
//           randVal = it->second.first;
//         }
//       }

//       ROS_DEBUG_STREAM("Joint " << it->first << " old value " << jointState->getJointStateValues()[j] << " new value " << randVal);
//       state_vec(i) = randVal;

//       j++;
//     }
//   }
// }

void ChompOptimizer::getRandomMomentum()
{
  if(is_collision_free_)
    random_momentum_.setZero(num_vars_free_, num_joints_);
  else
    for(int i = 0; i < num_joints_; ++i)
    {
      multivariate_gaussian_[i].sample(random_joint_momentum_);
      random_momentum_.col(i) = stochasticity_factor_ * random_joint_momentum_;
    }
}

void ChompOptimizer::updateMomentum()
{
  //double alpha = 1.0 - parameters_->getHmcStochasticity();
  double eps = parameters_->getHmcDiscretization();
  if(iteration_ > 0)
    momentum_ = (momentum_ + eps * final_increments_);
  else
    momentum_ = random_momentum_;
  //momentum_ = alpha * (momentum_ + eps*final_increments_) + sqrt(1.0-alpha*alpha)*random_momentum_;
}

void ChompOptimizer::updatePositionFromMomentum()
{
  double eps = parameters_->getHmcDiscretization();
  group_trajectory_.getFreeTrajectoryBlock() += eps * momentum_;
}

// void ChompOptimizer::animatePath()
// {
//   for(int i = free_vars_start_; i <= free_vars_end_; i++)
//   {
//     visualizeState(i);
//     //ros::WallDuration(group_trajectory_.getDiscretization()).sleep();
//     ros::WallDuration(.05).sleep();
//   }
// }

// void ChompOptimizer::animateEndeffector()
// {
//   visualization_msgs::Marker msg;
//   msg.points.resize(num_vars_free_);
//   // int joint_index = planning_group_->chomp_joints_[num_joints_-1].kdl_joint_index_;
//   int sn = (int)(num_collision_points_ - 1);
//   for(int i = 0; i < num_vars_free_; ++i)
//   {
//     int j = i + free_vars_start_;
//     msg.points[i].x = collision_point_pos_eigen_[j][sn][0];
//     msg.points[i].y = collision_point_pos_eigen_[j][sn][1];
//     msg.points[i].z = collision_point_pos_eigen_[j][sn][2];
//   }
//   msg.header.frame_id = collision_space_->getCollisionModelsInterface()->getRobotFrameId();
//   msg.header.stamp = ros::Time();
//   msg.ns = "chomp_endeffector";
//   msg.id = 0;
//   msg.type = visualization_msgs::Marker::SPHERE_LIST;
//   msg.action = visualization_msgs::Marker::ADD;
//   double scale = 0.05;
//   msg.scale.x = scale;
//   msg.scale.y = scale;
//   msg.scale.z = scale;
//   msg.color.a = 0.6;
//   msg.color.r = 0.5;
//   msg.color.g = 1.0;
//   msg.color.b = 0.3;
//   vis_marker_pub_.publish(msg);
//   ros::WallDuration(0.1).sleep();

// }

// void ChompOptimizer::visualizeState(int index)
// {

//   visualization_msgs::MarkerArray msg;
//   msg.markers.resize(num_collision_points_ + num_joints_);
//   int num_arrows = 0;
//   double potential_threshold = 1e-10;
//   for(int i = 0; i < num_collision_points_; i++)
//   {
//     msg.markers[i].header.frame_id = collision_space_->getCollisionModelsInterface()->getRobotFrameId();
//     msg.markers[i].header.stamp = ros::Time();
//     msg.markers[i].ns = "chomp_collisions";
//     msg.markers[i].id = i;
//     msg.markers[i].type = visualization_msgs::Marker::SPHERE;
//     msg.markers[i].action = visualization_msgs::Marker::ADD;
//     msg.markers[i].pose.position.x = collision_point_pos_eigen_[index][i][0];
//     msg.markers[i].pose.position.y = collision_point_pos_eigen_[index][i][1];
//     msg.markers[i].pose.position.z = collision_point_pos_eigen_[index][i][2];
//     msg.markers[i].pose.orientation.x = 0.0;
//     msg.markers[i].pose.orientation.y = 0.0;
//     msg.markers[i].pose.orientation.z = 0.0;
//     msg.markers[i].pose.orientation.w = 1.0;
//     double scale = 0.1;
//     msg.markers[i].scale.x = scale;
//     msg.markers[i].scale.y = scale;
//     msg.markers[i].scale.z = scale;
//     msg.markers[i].color.a = 0.6;
//     msg.markers[i].color.r = 0.5;
//     msg.markers[i].color.g = 1.0;
//     msg.markers[i].color.b = 0.3;
//     if(collision_point_potential_[index][i] > potential_threshold)
//       num_arrows++;
//   }

//   vis_marker_array_pub_.publish(msg);

//   // publish arrows for distance field:
//   msg.markers.resize(0);
//   msg.markers.resize(num_collision_points_);
//   for(int i = 0; i < num_collision_points_; i++)
//   {
//     msg.markers[i].header.frame_id = collision_space_->getCollisionModelsInterface()->getRobotFrameId();
//     msg.markers[i].header.stamp = ros::Time();
//     msg.markers[i].ns = "chomp_arrows";
//     msg.markers[i].id = i;
//     msg.markers[i].type = visualization_msgs::Marker::ARROW;
//     msg.markers[i].action = visualization_msgs::Marker::ADD;
//     msg.markers[i].points.resize(2);
//     msg.markers[i].points[0].x = collision_point_pos_eigen_[index][i](0);
//     msg.markers[i].points[0].y = collision_point_pos_eigen_[index][i](1);
//     msg.markers[i].points[0].z = collision_point_pos_eigen_[index][i](2);
//     msg.markers[i].points[1] = msg.markers[i].points[0];
//     double scale = 0.25f;
//     if(collision_point_potential_[index][i] <= potential_threshold)
//       scale = 0.0;
//     msg.markers[i].points[1].x += scale * collision_point_potential_gradient_[index][i](0);
//     msg.markers[i].points[1].y += scale * collision_point_potential_gradient_[index][i](1);
//     msg.markers[i].points[1].z += scale * collision_point_potential_gradient_[index][i](2);
//     msg.markers[i].scale.x = 0.01;
//     msg.markers[i].scale.y = 0.03;
//     msg.markers[i].color.a = 0.5;
//     msg.markers[i].color.r = 0.5;
//     msg.markers[i].color.g = 0.5;
//     msg.markers[i].color.b = 1.0;
//   }
//   vis_marker_array_pub_.publish(msg);

// }

} // namespace chomp