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dwa_planner.cpp

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* Author: Eitan Marder-Eppstein
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#include <dwa_local_planner/dwa_planner.h>
#include <angles/angles.h>

namespace dwa_local_planner {
  void DWAPlanner::reconfigureCB(DWAPlannerConfig &config, uint32_t level)
  {
    if(setup_ && config.restore_defaults) {
      config = default_config_;
      config.restore_defaults = false;
    }

    if(!setup_) {
      default_config_ = config;
      setup_ = true;
    }
    boost::mutex::scoped_lock l(configuration_mutex_);
 
    max_vel_x_ = config.max_vel_x;
    min_vel_x_ = config.min_vel_x;
 
    max_vel_y_ = config.max_vel_y;
    min_vel_y_ = config.min_vel_y;
 
    min_vel_trans_ = config.min_trans_vel;
    max_vel_trans_ = config.max_trans_vel;
 
    max_vel_th_ = config.max_rot_vel;
    min_vel_th_ = -1.0 * max_vel_th_;
 
    min_rot_vel_ = config.min_rot_vel;
 
    sim_time_ = config.sim_time;
    sim_granularity_ = config.sim_granularity;
    pdist_scale_ = config.path_distance_bias;
    gdist_scale_ = config.goal_distance_bias;
    occdist_scale_ = config.occdist_scale;
 
    stop_time_buffer_ = config.stop_time_buffer;
    oscillation_reset_dist_ = config.oscillation_reset_dist;
    forward_point_distance_ = config.forward_point_distance;
 
    scaling_speed_ = config.scaling_speed;
    max_scaling_factor_ = config.max_scaling_factor;
 
    int vx_samp, vy_samp, vth_samp;
    vx_samp = config.vx_samples;
    vy_samp = config.vy_samples;
    vth_samp = config.vth_samples;
 
    if(vx_samp <= 0){
      ROS_WARN("You've specified that you don't want any samples in the x dimension. We'll at least assume that you want to sample one value... so we're going to set vx_samples to 1 instead");
      vx_samp = 1;
      config.vx_samples = vx_samp;
    }
 
    if(vy_samp <= 0){
      ROS_WARN("You've specified that you don't want any samples in the y dimension. We'll at least assume that you want to sample one value... so we're going to set vy_samples to 1 instead");
      vy_samp = 1;
      config.vy_samples = vy_samp;
    }
 
    if(vth_samp <= 0){
      ROS_WARN("You've specified that you don't want any samples in the th dimension. We'll at least assume that you want to sample one value... so we're going to set vth_samples to 1 instead");
      vth_samp = 1;
      config.vth_samples = vth_samp;
    }
 
    vsamples_[0] = vx_samp;
    vsamples_[1] = vy_samp;
    vsamples_[2] = vth_samp;
 
    penalize_negative_x_ = config.penalize_negative_x;
  }

  DWAPlanner::DWAPlanner(std::string name, costmap_2d::Costmap2DROS* costmap_ros) : costmap_ros_(NULL), world_model_(NULL), dsrv_(ros::NodeHandle("~/" + name)), setup_(false), penalize_negative_x_(true) {
    costmap_ros_ = costmap_ros;
    costmap_ros_->getCostmapCopy(costmap_);

    map_ = base_local_planner::MapGrid(costmap_.getSizeInCellsX(), costmap_.getSizeInCellsY(), 
        costmap_.getResolution(), costmap_.getOriginX(), costmap_.getOriginY());
    front_map_ = base_local_planner::MapGrid(costmap_.getSizeInCellsX(), costmap_.getSizeInCellsY(), 
        costmap_.getResolution(), costmap_.getOriginX(), costmap_.getOriginY());
    ros::NodeHandle pn("~/" + name);

    double acc_lim_x, acc_lim_y, acc_lim_th;
    pn.param("acc_lim_x", acc_lim_x, 2.5);
    pn.param("acc_lim_y", acc_lim_y, 2.5);
    pn.param("acc_lim_th", acc_lim_th, 3.2);

    //Assuming this planner is being run within the navigation stack, we can
    //just do an upward search for the frequency at which its being run. This
    //also allows the frequency to be overwritten locally.
    std::string controller_frequency_param_name;
    if(!pn.searchParam("controller_frequency", controller_frequency_param_name))
      sim_period_ = 0.05;
    else
    {
      double controller_frequency = 0;
      pn.param(controller_frequency_param_name, controller_frequency, 20.0);
      if(controller_frequency > 0)
        sim_period_ = 1.0 / controller_frequency;
      else
      {
        ROS_WARN("A controller_frequency less than 0 has been set. Ignoring the parameter, assuming a rate of 20Hz");
        sim_period_ = 0.05;
      }
    }
    ROS_INFO("Sim period is set to %.2f", sim_period_);

    acc_lim_[0] = acc_lim_x;
    acc_lim_[1] = acc_lim_y;
    acc_lim_[2] = acc_lim_th;

    dynamic_reconfigure::Server<DWAPlannerConfig>::CallbackType cb = boost::bind(&DWAPlanner::reconfigureCB, this, _1, _2);
    dsrv_.setCallback(cb);

    footprint_spec_ = costmap_ros_->getRobotFootprint();

    world_model_ = new base_local_planner::CostmapModel(costmap_);

    prev_stationary_pos_ = Eigen::Vector3f::Zero();
    resetOscillationFlags();

    map_viz_.initialize(name, &costmap_, boost::bind(&DWAPlanner::getCellCosts, this, _1, _2, _3, _4, _5, _6));
  }

  bool DWAPlanner::getCellCosts(int cx, int cy, float &path_cost, float &goal_cost, float &occ_cost, float &total_cost) {
    base_local_planner::MapCell cell = map_(cx, cy);
    if (cell.within_robot) {
        return false;
    }
    occ_cost = costmap_.getCost(cx, cy);
    if (cell.path_dist >= map_.map_.size() || cell.goal_dist >= map_.map_.size() || occ_cost >= costmap_2d::INSCRIBED_INFLATED_OBSTACLE) {
        return false;
    }
    path_cost = cell.path_dist;
    goal_cost = cell.goal_dist;

    double resolution = costmap_.getResolution();
    total_cost = pdist_scale_ * resolution * path_cost + gdist_scale_ * resolution * goal_cost + occdist_scale_ * occ_cost;
    return true;
  }

  Eigen::Vector3f DWAPlanner::computeNewPositions(const Eigen::Vector3f& pos, 
      const Eigen::Vector3f& vel, double dt){
    Eigen::Vector3f new_pos = Eigen::Vector3f::Zero();
    new_pos[0] = pos[0] + (vel[0] * cos(pos[2]) + vel[1] * cos(M_PI_2 + pos[2])) * dt;
    new_pos[1] = pos[1] + (vel[0] * sin(pos[2]) + vel[1] * sin(M_PI_2 + pos[2])) * dt;
    new_pos[2] = pos[2] + vel[2] * dt;
    return new_pos;
  }
  
  void DWAPlanner::selectBestTrajectory(base_local_planner::Trajectory* &best, base_local_planner::Trajectory* &comp){
    //check if the comp trajectory is better than the current best and, if so, swap them
    bool best_valid = best->cost_ >= 0.0;
    bool best_forward = best->xv_ >= 0.0;
    bool comp_valid = comp->cost_ >= 0.0;
    bool comp_forward = comp->xv_ >= 0.0;

    //if we don't have a valid trajecotry... then do nothing
    if(!comp_valid)
      return;

    if(penalize_negative_x_ && best_valid && best_forward && !comp_forward)
      return;


    if(comp_valid && ((comp->cost_ < best->cost_ || !best_valid) || (penalize_negative_x_ && comp_forward && !best_forward))){
      base_local_planner::Trajectory* swap = best;
      best = comp;
      comp = swap;
    }
  }

  bool DWAPlanner::oscillationCheck(const Eigen::Vector3f& vel){
    if(forward_pos_only_ && vel[0] < 0.0)
      return true;

    if(forward_neg_only_ && vel[0] > 0.0)
      return true;

    if(strafe_pos_only_ && vel[1] < 0.0)
      return true;

    if(strafe_neg_only_ && vel[1] > 0.0)
      return true;

    if(rot_pos_only_ && vel[2] < 0.0)
      return true;

    if(rot_neg_only_ && vel[2] > 0.0)
      return true;

    return false;
  }

  base_local_planner::Trajectory DWAPlanner::computeTrajectories(const Eigen::Vector3f& pos, const Eigen::Vector3f& vel){
    tf::Stamped<tf::Pose> robot_pose_tf;
    geometry_msgs::PoseStamped robot_pose;

    //compute the distance between the robot and the last point on the global_plan
    costmap_ros_->getRobotPose(robot_pose_tf);
    tf::poseStampedTFToMsg(robot_pose_tf, robot_pose);

    double sq_dist = squareDist(robot_pose, global_plan_.back());

    bool two_point_scoring = true;
    if(sq_dist < forward_point_distance_ * forward_point_distance_)
      two_point_scoring = false;

    //compute the feasible velocity space based on the rate at which we run
    Eigen::Vector3f max_vel = Eigen::Vector3f::Zero();
    max_vel[0] = std::min(max_vel_x_, vel[0] + acc_lim_[0] * sim_period_);
    max_vel[1] = std::min(max_vel_y_, vel[1] + acc_lim_[1] * sim_period_);
    max_vel[2] = std::min(max_vel_th_, vel[2] + acc_lim_[2] * sim_period_);

    Eigen::Vector3f min_vel = Eigen::Vector3f::Zero();
    min_vel[0] = std::max(min_vel_x_, vel[0] - acc_lim_[0] * sim_period_);
    min_vel[1] = std::max(min_vel_y_, vel[1] - acc_lim_[1] * sim_period_);
    min_vel[2] = std::max(min_vel_th_, vel[2] - acc_lim_[2] * sim_period_);

    Eigen::Vector3f dv = Eigen::Vector3f::Zero();
    //we want to sample the velocity space regularly
    for(unsigned int i = 0; i < 3; ++i){
      dv[i] = (max_vel[i] - min_vel[i]) / (std::max(1.0, double(vsamples_[i]) - 1));
    }

    //keep track of the best trajectory seen so far... we'll re-use two memeber vars for efficiency
    base_local_planner::Trajectory* best_traj = &traj_one_;
    best_traj->cost_ = -1.0;

    base_local_planner::Trajectory* comp_traj = &traj_two_;
    comp_traj->cost_ = -1.0;

    Eigen::Vector3f vel_samp = Eigen::Vector3f::Zero();

    //ROS_ERROR("x(%.2f, %.2f), y(%.2f, %.2f), th(%.2f, %.2f)", min_vel[0], max_vel[0], min_vel[1], max_vel[1], min_vel[2], max_vel[2]);
    //ROS_ERROR("x(%.2f, %.2f), y(%.2f, %.2f), th(%.2f, %.2f)", min_vel_x_, max_vel_x_, min_vel_y_, max_vel_y_, min_vel_th_, max_vel_th_);
    //ROS_ERROR("dv %.2f %.2f %.2f", dv[0], dv[1], dv[2]);

    for(VelocityIterator x_it(min_vel[0], max_vel[0], dv[0]); !x_it.isFinished(); x_it++){
      vel_samp[0] = x_it.getVelocity();
      for(VelocityIterator y_it(min_vel[1], max_vel[1], dv[1]); !y_it.isFinished(); y_it++){
        vel_samp[1] = y_it.getVelocity();
        for(VelocityIterator th_it(min_vel[2], max_vel[2], dv[2]); !th_it.isFinished(); th_it++){
          vel_samp[2] = th_it.getVelocity();
          generateTrajectory(pos, vel_samp, *comp_traj, two_point_scoring);
          selectBestTrajectory(best_traj, comp_traj);
        }
      }
    }

    ROS_DEBUG_NAMED("oscillation_flags", "forward_pos_only: %d, forward_neg_only: %d, strafe_pos_only: %d, strafe_neg_only: %d, rot_pos_only: %d, rot_neg_only: %d",
        forward_pos_only_, forward_neg_only_, strafe_pos_only_, strafe_neg_only_, rot_pos_only_, rot_neg_only_);

    //ok... now we have our best trajectory
    if(best_traj->cost_ >= 0){
      //we want to check if we need to set any oscillation flags
      if(setOscillationFlags(best_traj)){
        prev_stationary_pos_ = pos;
      }

      //if we've got restrictions... check if we can reset any oscillation flags
      if(forward_pos_only_ || forward_neg_only_ 
          || strafe_pos_only_ || strafe_neg_only_
          || rot_pos_only_ || rot_neg_only_){
        resetOscillationFlagsIfPossible(pos, prev_stationary_pos_);
      }
    }

    //TODO: Think about whether we want to try to do things like back up when a valid trajectory is not found

    return *best_traj;

  }

  void DWAPlanner::resetOscillationFlagsIfPossible(const Eigen::Vector3f& pos, const Eigen::Vector3f& prev){
    double x_diff = pos[0] - prev[0];
    double y_diff = pos[1] - prev[1];
    double sq_dist = x_diff * x_diff + y_diff * y_diff;

    //if we've moved far enough... we can reset our flags
    if(sq_dist > oscillation_reset_dist_ * oscillation_reset_dist_){
      resetOscillationFlags();
    }
  }

  void DWAPlanner::resetOscillationFlags(){
    strafe_pos_only_ = false;
    strafe_neg_only_ = false;
    strafing_pos_ = false;
    strafing_neg_ = false;

    rot_pos_only_ = false;
    rot_neg_only_ = false;
    rotating_pos_ = false;
    rotating_neg_ = false;

    forward_pos_only_ = false;
    forward_neg_only_ = false;
    forward_pos_ = false;
    forward_neg_ = false;
  }
  
  bool DWAPlanner::setOscillationFlags(base_local_planner::Trajectory* t){
    bool flag_set = false;
    //set oscillation flags for moving forward and backward
    if(t->xv_ < 0.0){
      if(forward_pos_){
        forward_neg_only_ = true;
        flag_set = true;
      }
      forward_pos_ = false;
      forward_neg_ = true;
    }
    if(t->xv_ > 0.0){
      if(forward_neg_){
        forward_pos_only_ = true;
        flag_set = true;
      }
      forward_neg_ = false;
      forward_pos_ = true;
    }

    //we'll only set flags for strafing and rotating when we're not moving forward at all
    if(fabs(t->xv_) <= min_vel_trans_){
      //check negative strafe
      if(t->yv_ < 0){
        if(strafing_pos_){
          strafe_neg_only_ = true;
          flag_set = true;
        }
        strafing_pos_ = false;
        strafing_neg_ = true;
      }

      //check positive strafe
      if(t->yv_ > 0){
        if(strafing_neg_){
          strafe_pos_only_ = true;
          flag_set = true;
        }
        strafing_neg_ = false;
        strafing_pos_ = true;
      }

      //check negative rotation
      if(t->thetav_ < 0){
        if(rotating_pos_){
          rot_neg_only_ = true;
          flag_set = true;
        }
        rotating_pos_ = false;
        rotating_neg_ = true;
      }

      //check positive rotation
      if(t->thetav_ > 0){
        if(rotating_neg_){
          rot_pos_only_ = true;
          flag_set = true;
        }
        rotating_neg_ = false;
        rotating_pos_ = true;
      }
    }
    return flag_set;
  }

  double DWAPlanner::footprintCost(const Eigen::Vector3f& pos, double scale){
    double cos_th = cos(pos[2]);
    double sin_th = sin(pos[2]);

    std::vector<geometry_msgs::Point> scaled_oriented_footprint;
    for(unsigned int i  = 0; i < footprint_spec_.size(); ++i){
      geometry_msgs::Point new_pt;
      new_pt.x = pos[0] + (scale * footprint_spec_[i].x * cos_th - scale * footprint_spec_[i].y * sin_th);
      new_pt.y = pos[1] + (scale * footprint_spec_[i].x * sin_th + scale * footprint_spec_[i].y * cos_th);
      scaled_oriented_footprint.push_back(new_pt);
    }

    geometry_msgs::Point robot_position;
    robot_position.x = pos[0];
    robot_position.y = pos[1];

    //check if the footprint is legal
    double footprint_cost = world_model_->footprintCost(robot_position, scaled_oriented_footprint, costmap_.getInscribedRadius(), costmap_.getCircumscribedRadius());

    return footprint_cost;
  }

  void DWAPlanner::generateTrajectory(Eigen::Vector3f pos, const Eigen::Vector3f& vel, base_local_planner::Trajectory& traj, bool two_point_scoring){
    //ROS_ERROR("%.2f, %.2f, %.2f - %.2f %.2f", vel[0], vel[1], vel[2], sim_time_, sim_granularity_);
    double impossible_cost = map_.map_.size();

    double vmag = sqrt(vel[0] * vel[0] + vel[1] * vel[1]);
    double eps = 1e-4;

    //make sure that the robot is at least moving with one of the required velocities
    if((vmag + eps < min_vel_trans_ && fabs(vel[2]) + eps < min_rot_vel_) ||
        vmag - eps > max_vel_trans_ ||
        oscillationCheck(vel)){
      traj.cost_ = -1.0;
      return;
    }

    //compute the number of steps we must take along this trajectory to be "safe"
    int num_steps = ceil(std::max((vmag * sim_time_) / sim_granularity_, fabs(vel[2]) / sim_granularity_));

    //compute a timestep
    double dt = sim_time_ / num_steps;
    double time = 0.0;

    //initialize the costs for the trajectory
    double path_dist = 0.0;
    double goal_dist = 0.0;
    double occ_cost = 0.0;

    //we'll also be scoring a point infront of the robot
    double front_path_dist = 0.0;
    double front_goal_dist = 0.0;

    //create a potential trajectory... it might be reused so we'll make sure to reset it
    traj.resetPoints();
    traj.xv_ = vel[0];
    traj.yv_ = vel[1];
    traj.thetav_ = vel[2];
    traj.cost_ = -1.0;

    //if we're not actualy going to simulate... we may as well just return now
    if(num_steps == 0){
      traj.cost_ = -1.0;
      return;
    }

    //we want to check against the absolute value of the velocities for collisions later
    Eigen::Vector3f abs_vel = vel.array().abs();

    //simulate the trajectory and check for collisions, updating costs along the way
    for(int i = 0; i < num_steps; ++i){
      //get the mapp coordinates of a point
      unsigned int cell_x, cell_y;

      //we won't allow trajectories that go off the map... shouldn't happen that often anyways
      if(!costmap_.worldToMap(pos[0], pos[1], cell_x, cell_y)){
        //we're off the map
        traj.cost_ = -1.0;
        return;
      }

      double front_x = pos[0] + forward_point_distance_ * cos(pos[2]);
      double front_y = pos[1] + forward_point_distance_ * sin(pos[2]);

      unsigned int front_cell_x, front_cell_y;
      //we won't allow trajectories that go off the map... shouldn't happen that often anyways
      if(!costmap_.worldToMap(front_x, front_y, front_cell_x, front_cell_y)){
        //we're off the map
        traj.cost_ = -1.0;
        return;
      }


      //if we're over a certain speed threshold, we'll scale the robot's
      //footprint to make it either slow down or stay further from walls
      double scale = 1.0;
      if(vmag > scaling_speed_){
        //scale up to the max scaling factor linearly... this could be changed later
        double ratio = (vmag - scaling_speed_) / (max_vel_trans_ - scaling_speed_);
        scale = max_scaling_factor_ * ratio + 1.0;
      }

      //we want to find the cost of the footprint
      double footprint_cost = footprintCost(pos, scale);

      //if the footprint hits an obstacle... we'll check if we can stop before we hit it... given the time to get there
      if(footprint_cost < 0){
        traj.cost_ = -1.0;
        return;

        /* TODO: I'm not convinced this code is working properly
        //we want to compute the max allowable speeds to be able to stop
        //to be safe... we'll make sure we can stop some time before we actually hit
        Eigen::Vector3f max_vel = getMaxSpeedToStopInTime(time - stop_time_buffer_);

        //check if we can stop in time
        if(abs_vel[0] < max_vel[0] && abs_vel[1] < max_vel[1] && abs_vel[2] < max_vel[2]){
          //if we can, then we'll just break out of the loop here.. no point in checking future points
          break;
        }
        else{
          //if we can't... then this trajectory is invalid
          traj.cost_ = -1.0;
          return;
        }
        */
      }

      //compute the costs for this point on the trajectory
      occ_cost = std::max(std::max(occ_cost, footprint_cost), double(costmap_.getCost(cell_x, cell_y)));
      path_dist = map_(cell_x, cell_y).path_dist;
      goal_dist = map_(cell_x, cell_y).goal_dist;

      front_path_dist = front_map_(front_cell_x, front_cell_y).path_dist;
      front_goal_dist = front_map_(front_cell_x, front_cell_y).goal_dist;

      //if a point on this trajectory has no clear path to the goal... it is invalid
      if(impossible_cost <= goal_dist || impossible_cost <= path_dist){
        traj.cost_ = -2.0; //-2.0 means that we were blocked because propagation failed
        return;
      }

      //add the point to the trajectory so we can draw it later if we want
      traj.addPoint(pos[0], pos[1], pos[2]);

      //update the position of the robot using the velocities passed in
      pos = computeNewPositions(pos, vel, dt);
      time += dt;
    }

    double resolution = costmap_.getResolution();
    //if we're not at the last point in the plan, then we can just score 
    if(two_point_scoring)
      traj.cost_ = pdist_scale_ * resolution * ((front_path_dist + path_dist) / 2.0) + gdist_scale_ * resolution * ((front_goal_dist + goal_dist) / 2.0) + occdist_scale_ * occ_cost;
    else
      traj.cost_ = pdist_scale_ * resolution * path_dist + gdist_scale_ * resolution * goal_dist + occdist_scale_ * occ_cost;
    //ROS_ERROR("%.2f, %.2f, %.2f, %.2f", vel[0], vel[1], vel[2], traj.cost_);
  }

  bool DWAPlanner::checkTrajectory(const Eigen::Vector3f& pos, const Eigen::Vector3f& vel){
    resetOscillationFlags();
    base_local_planner::Trajectory t;
    generateTrajectory(pos, vel, t, false);

    //if the trajectory is a legal one... the check passes
    if(t.cost_ >= 0)
      return true;

    //otherwise the check fails
    return false;
  }

  void DWAPlanner::updatePlan(const std::vector<geometry_msgs::PoseStamped>& new_plan){
    global_plan_.resize(new_plan.size());
    for(unsigned int i = 0; i < new_plan.size(); ++i){
      global_plan_[i] = new_plan[i];
    }
  }

  //given the current state of the robot, find a good trajectory
  base_local_planner::Trajectory DWAPlanner::findBestPath(tf::Stamped<tf::Pose> global_pose, tf::Stamped<tf::Pose> global_vel, 
      tf::Stamped<tf::Pose>& drive_velocities){

    //make sure that our configuration doesn't change mid-run
    boost::mutex::scoped_lock l(configuration_mutex_);

    //make sure to get an updated copy of the costmap before computing trajectories
    costmap_ros_->getCostmapCopy(costmap_);

    Eigen::Vector3f pos(global_pose.getOrigin().getX(), global_pose.getOrigin().getY(), tf::getYaw(global_pose.getRotation()));
    Eigen::Vector3f vel(global_vel.getOrigin().getX(), global_vel.getOrigin().getY(), tf::getYaw(global_vel.getRotation()));

    //reset the map for new operations
    map_.resetPathDist();
    front_map_.resetPathDist();

    //make sure that we update our path based on the global plan and compute costs
    map_.setPathCells(costmap_, global_plan_);

    std::vector<geometry_msgs::PoseStamped> front_global_plan = global_plan_;
    front_global_plan.back().pose.position.x = front_global_plan.back().pose.position.x + forward_point_distance_ * cos(tf::getYaw(front_global_plan.back().pose.orientation));
    front_global_plan.back().pose.position.y = front_global_plan.back().pose.position.y + forward_point_distance_ * sin(tf::getYaw(front_global_plan.back().pose.orientation));
    front_map_.setPathCells(costmap_, front_global_plan);
    ROS_DEBUG_NAMED("dwa_local_planner", "Path/Goal distance computed");

    //rollout trajectories and find the minimum cost one
    base_local_planner::Trajectory best = computeTrajectories(pos, vel);
    ROS_DEBUG_NAMED("dwa_local_planner", "Trajectories created");

    //if we don't have a legal trajectory, we'll just command zero
    if(best.cost_ < 0){
      drive_velocities.setIdentity();
    }
    else{
      btVector3 start(best.xv_, best.yv_, 0);
      drive_velocities.setOrigin(start);
      btMatrix3x3 matrix;
      matrix.setRotation(tf::createQuaternionFromYaw(best.thetav_));
      drive_velocities.setBasis(matrix);
    }

    //we'll publish the visualization of the costs to rviz before returning our best trajectory
    map_viz_.publishCostCloud();

    return best;
  }
};

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dwa_local_planner
Author(s): Eitan Marder-Eppstein
autogenerated on Fri Mar 1 16:11:01 2013