机器人局部动态避障算法dwa解析

简介

dwa算法全称叫动态窗口法（dynamic window approach），其算法过程主要分为仿真获取机器人的运动轨迹、对轨迹进行评价选择最优轨迹两个主要过程，动态窗口表达的是仿真的运动轨迹数量有限，主要是因为机器人在较短的控制周期内只能达到一定的速度。
一、机器人如何仿真获取运动轨迹
1、获取机器人速度样本

根据机器人当前速度以及运动特性，确定机器人可达的运动速度范围。由于运动的最终目的是到达目标点，因此，在到达目标点附近时，需要降低机器人运动速度，也就是进一步限制机器人的速度范围，以保证机器人能平稳的到达目标点。最后根据人为给定的样本数，在限制的速度范围内获得样本数个离散的速度样本，包括线速度和角速度。

void SimpleTrajectoryGenerator::initialise(
const Eigen::Vector3f& pos,　//机器人的位置
const Eigen::Vector3f& vel,　//当前机器人速度
const Eigen::Vector3f& goal,　//目标点
base_local_planner::LocalPlannerLimits* limits,　//运动特性（加速度、最大最小速度…）
const Eigen::Vector3f& vsamples,　//样本
bool discretize_by_time) {

//给定机器人的最大最小运动速度
double max_vel_th = limits->max_vel_theta;
double min_vel_th = -1.0 * max_vel_th;
discretize_by_time_ = discretize_by_time;
Eigen::Vector3f acc_lim = limits->getAccLimits();
pos_ = pos;
vel_ = vel;
limits_ = limits;
next_sample_index_ = 0;
sample_params_.clear();

double min_vel_x = limits->min_vel_x;
double max_vel_x = limits->max_vel_x;
double min_vel_y = limits->min_vel_y;
double max_vel_y = limits->max_vel_y;

// if sampling number is zero in any dimension, we don’t generate samples generically
if (vsamples[0] * vsamples[1] * vsamples[2] > 0) {
//compute the feasible velocity space based on the rate at which we run
Eigen::Vector3f max_vel = Eigen::Vector3f::Zero();
Eigen::Vector3f min_vel = Eigen::Vector3f::Zero();
if ( ! use_dwa_) {
//根据机器人位置到目标点的距离，限制机器人的最大运动速度
double dist = hypot(goal[0] - pos[0], goal[1] - pos[1]);
max_vel_x = std::max(std::min(max_vel_x, dist / sim_time_), min_vel_x);
max_vel_y = std::max(std::min(max_vel_y, dist / sim_time_), min_vel_y);
// 根据控制周期和加速度特性，确定机器人可达的最大最小速度
// 此处用的是sim_time_仿真时间，确定的是接下来一段时间内机器人可达的运动速度范围，默认是1s
max_vel[0] = std::min(max_vel_x, vel[0] + acc_lim[0] * sim_time_);
max_vel[1] = std::min(max_vel_y, vel[1] + acc_lim[1] * sim_time_);
max_vel[2] = std::min(max_vel_th, vel[2] + acc_lim[2] * sim_time_);
min_vel[0] = std::max(min_vel_x, vel[0] - acc_lim[0] * sim_time_);
min_vel[1] = std::max(min_vel_y, vel[1] - acc_lim[1] * sim_time_);
min_vel[2] = std::max(min_vel_th, vel[2] - acc_lim[2] * sim_time_);
} else {
// 此处用的sim_period_是控制周期，也就是只确定下一个控制周期机器人的运动速度范围
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_);
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_);
}
//根据给定的速度样本数，在速度空间内等间距的获取速度样本
Eigen::Vector3f vel_samp = Eigen::Vector3f::Zero();
VelocityIterator x_it(min_vel[0], max_vel[0], vsamples[0]);
VelocityIterator y_it(min_vel[1], max_vel[1], vsamples[1]);
VelocityIterator th_it(min_vel[2], max_vel[2], vsamples[2]);
for(; !x_it.isFinished(); x_it++) {
vel_samp[0] = x_it.getVelocity();
for(; !y_it.isFinished(); y_it++) {
vel_samp[1] = y_it.getVelocity();
for(; !th_it.isFinished(); th_it++) {
vel_samp[2] = th_it.getVelocity();
//ROS_DEBUG(“Sample %f, %f, %f”, vel_samp[0], vel_samp[1], vel_samp[2]);
sample_params_.push_back(vel_samp);
}
th_it.reset();
}
y_it.reset();
}
}
}

2、生成运动轨迹

根据速度样本确定运动轨迹，是简单运行学知识，主要注意的是用的仿真时间产生的样本还是仿真周期产生的样本，其中仿真时间指的是人为设定的一段仿真时间，默认１秒，而仿真周期指的是算法的实际控制周期，默认为0.1秒。

bool SimpleTrajectoryGenerator::generateTrajectory(
Eigen::Vector3f pos, //机器人的位姿
Eigen::Vector3f vel, //运动速度
Eigen::Vector3f sample_target_vel, //样本速度
base_local_planner::Trajectory& traj) { //需要生成的轨迹
double vmag = hypot(sample_target_vel[0], sample_target_vel[1]);
double eps = 1e-4;
traj.cost_ = -1.0; // placed here in case we return early
//trajectory might be reused so we’ll make sure to reset it
traj.resetPoints();

//确定样本是否超过设定的最大移动速度
// make sure that the robot would at least be moving with one of
// the required minimum velocities for translation and rotation (if set)
if ((limits_->min_vel_trans >= 0 && vmag + eps < limits_->min_vel_trans) &&
(limits_->min_vel_theta >= 0 && fabs(sample_target_vel[2]) + eps < limits_->min_vel_theta)) {
return false;
}
// make sure we do not exceed max diagonal (x+y) translational velocity (if set)
if (limits_->max_vel_trans >=0 && vmag - eps > limits_->max_vel_trans) {
return false;
}

//确定仿真使用的控制周期数
int num_steps;
if (discretize_by_time_) {
num_steps = ceil(sim_time_ / sim_granularity_);
} else {
//compute the number of steps we must take along this trajectory to be “safe”
double sim_time_distance = vmag * sim_time_; // the distance the robot would travel in sim_time if it did not change velocity
double sim_time_angle = fabs(sample_target_vel[2]) * sim_time_; // the angle the robot would rotate in sim_time
num_steps =
ceil(std::max(sim_time_distance / sim_granularity_,
sim_time_angle / angular_sim_granularity_));
}

if (num_steps == 0) {
return false;
}

//确定生成轨迹的时间间隔（仅对利用仿真时间进行速度采样的情况）
//compute a timestep
double dt = sim_time_ / num_steps;
traj.time_delta_ = dt;

Eigen::Vector3f loop_vel;
//连续加速意味着用的是仿真时间进行的速度采样，不是单个控制周期能达到的运动速度。因此，需要根据机器人的运动特性确定接下来的控制周期内机器人能达到的运动速度
if (continued_acceleration_) {
// assuming the velocity of the first cycle is the one we want to store in the trajectory object
loop_vel = computeNewVelocities(sample_target_vel, vel, limits_->getAccLimits(), dt);
traj.xv_ = loop_vel[0];
traj.yv_ = loop_vel[1];
traj.thetav_ = loop_vel[2];
} else {
//否则用的就是仿真周期进行的采样，直接将采样速度作为生成轨迹的速度
// assuming sample_vel is our target velocity within acc limits for one timestep
loop_vel = sample_target_vel;
traj.xv_ = sample_target_vel[0];
traj.yv_ = sample_target_vel[1];
traj.thetav_ = sample_target_vel[2];
}

//根据仿真的周期数，生成仿真轨迹
for (int i = 0; i < num_steps; ++i) {
//add the point to the trajectory so we can draw it later if we want
traj.addPoint(pos[0], pos[1], pos[2]);
//如果用的是仿真时间进行的速度采样，在每个仿真控制周期内，速度需要根据加减速特性确定
if (continued_acceleration_) {
//calculate velocities
loop_vel = computeNewVelocities(sample_target_vel, loop_vel, limits_->getAccLimits(), dt);
//ROS_WARN_NAMED(“Generator”, “Flag: %d, Loop_Vel %f, %f, %f”, continued_acceleration_, loop_vel[0], loop_vel[1], loop_vel[2]);
}
//根据速度和时间，确定运动轨迹上的下一个点
//update the position of the robot using the velocities passed in
pos = computeNewPositions(pos, loop_vel, dt);

} // end for simulation steps

return true; // trajectory has at least one point
}

二、如何对轨迹进行评价并选取最优轨迹
１、代价函数

oscillation_costs_ //振荡代价函数，一旦速度发生振荡，直接丢弃速度样本
obstacle_costs_ //障碍物代价函数，当轨迹进入障碍物区，直接丢弃当前轨迹样本
goal_costs_ //目标代价函数，优先选择距离局部目标点近的轨迹
path_costs_ //路径代价函数，优先选择贴近全局路径的轨迹
goal_front_costs_ //与goal_costs基本一致，不太理解注释中的nose是指什么？
alignment_costs_ //与path_costs基本一致，不太理解注释中的nose是指什么？
  注：为了能适应不同场景的需求，可以对这些代价函数配置不同的权重，从而能实现不同场景对这些代价函数的重视程度
2、主要评价函数的实现
2.1、障碍物代价函数

通过仿真轨迹将机器人轮廓映射到全局坐标系下，并对轮廓边上的代价值进行分析，选择最大的代价值作为障碍物代价，从而确定机器人是否会撞到障碍物

double CostmapModel::footprintCost(const geometry_msgs::Point& position, //机器人在全局坐标系下的位置
const std::vector<geometry_msgs::Point>& footprint, //机器人轮廓
double inscribed_radius, double circumscribed_radius) //内切圆、外接圆半径
{
//used to put things into grid coordinates
unsigned int cell_x, cell_y;
//get the cell coord of the center point of the robot
//获得机器人在地图坐标系下的坐标
if(!costmap_.worldToMap(position.x, position.y, cell_x, cell_y))
return -1.0;
//if number of points in the footprint is less than 3, we’ll just assume a circular robot
//当轮廓上的点数少于３时，认为机器人是个圆形机器人，并且只判断机器人中心是否在不可走区域
if(footprint.size() < 3){
unsigned char cost = costmap_.getCost(cell_x, cell_y);
//if(cost == LETHAL_OBSTACLE || cost == INSCRIBED_INFLATED_OBSTACLE)
if(cost == LETHAL_OBSTACLE || cost == INSCRIBED_INFLATED_OBSTACLE || cost == NO_INFORMATION)
return -1.0;
return cost;
}
//now we really have to lay down the footprint in the costmap grid
unsigned int x0, x1, y0, y1;
double line_cost = 0.0;
double footprint_cost = 0.0;
//footprint是一个多边形，判断该多边形是否与障碍物发生碰撞的方法是：计算多边形的所有边的最大代价值，从而确定是否与障碍物相撞
//we need to rasterize each line in the footprint
for(unsigned int i = 0; i < footprint.size() - 1; ++i){
//get the cell coord of the first point
//获得地图中机器人轮廓上的一个点的坐标
if(!costmap_.worldToMap(footprint[i].x, footprint[i].y, x0, y0))
return -1.0;
//获得地图中相邻轮廓点的坐标
//get the cell coord of the second point
if(!costmap_.worldToMap(footprint[i + 1].x, footprint[i + 1].y, x1, y1))
return -1.0;
//确定当前轮廓点与相邻轮廓点构成的边的最大代价值
line_cost = lineCost(x0, x1, y0, y1);
//选取所有边的最大代价值
footprint_cost = std::max(line_cost, footprint_cost);
//if there is an obstacle that hits the line… we know that we can return false right away
if(line_cost < 0)
return -1.0;
}
//获取第一个轮廓点与最后一个轮廓点构成的边的最大代价值
//we also need to connect the first point in the footprint to the last point
//get the cell coord of the last point
if(!costmap_.worldToMap(footprint.back().x, footprint.back().y, x0, y0))
return -1.0;
//get the cell coord of the first point
if(!costmap_.worldToMap(footprint.front().x, footprint.front().y, x1, y1))
return -1.0;
line_cost = lineCost(x0, x1, y0, y1);
//确定所有边的最大代价值
footprint_cost = std::max(line_cost, footprint_cost);
if(line_cost < 0)
return -1.0;
//if all line costs are legal… then we can return that the footprint is legal
return footprint_cost;

}

2.2、目标代价函数

首先根据全局路径与局部代价地图的边界确定局部目标点，然后依据局部目标点生成栅格地图，每个栅格处的值代表当前栅格到目标点的距离，对于障碍物栅格，直接置为到目标点的距离无穷远。最后再根据轨迹末端点处栅格的位置，直接通过索引在地图中获取该位置距目标点的距离，作为距目标点的代价。因此，目标代价函数的主要任务是生成栅格地图。

//mark the point of the costmap as local goal where global_plan first leaves the area (or its last point)
void MapGrid::setLocalGoal(const costmap_2d::Costmap2D& costmap,　//局部代价地图
const std::vector<geometry_msgs::PoseStamped>& global_plan) 　//全局路径
{
sizeCheck(costmap.getSizeInCellsX(), costmap.getSizeInCellsY());
int local_goal_x = -1;
int local_goal_y = -1;
bool started_path = false;
//调整全局路径分辨率与地图分辨率一致
std::vector<geometry_msgs::PoseStamped> adjusted_global_plan;
adjustPlanResolution(global_plan, adjusted_global_plan, costmap.getResolution());
// 将全局路径与局部代价地图边界的交点作为局部目标点
for (unsigned int i = 0; i < adjusted_global_plan.size(); ++i) {
double g_x = adjusted_global_plan[i].pose.position.x;
double g_y = adjusted_global_plan[i].pose.position.y;
unsigned int map_x, map_y;
if (costmap.worldToMap(g_x, g_y, map_x, map_y) && costmap.getCost(map_x, map_y) != costmap_2d::NO_INFORMATION) {
local_goal_x = map_x;
local_goal_y = map_y;
started_path = true;
} else {
if (started_path) {
break;
}// else we might have a non pruned path, so we just continue
}
}
if (!started_path) {
ROS_ERROR(“None of the points of the global plan were in the local costmap, global plan points too far from robot”);
return;
}
//构建距离优先队列，并添加局部目标点作为队列的第一个点
queue<MapCell*> path_dist_queue;
if (local_goal_x >= 0 && local_goal_y >= 0) {
MapCell& current = getCell(local_goal_x, local_goal_y);
costmap.mapToWorld(local_goal_x, local_goal_y, goal_x_, goal_y_);
current.target_dist = 0.0;
current.target_mark = true;
path_dist_queue.push(&current);
}
//按优先队列的顺序，从局部目标点开始以单个栅格为步长向外膨胀，从而直接确定出每个栅格距离局部目标点的距离
computeTargetDistance(path_dist_queue, costmap);
}

2.3、路径代价函数

该代价函数的实现原理与目标代价函数类似，只是该函数是以局部路径上的所有点作为起点向外膨胀来构建栅格地图，并且是以仿真轨迹上的所有点的距离值的和的平均值作为轨迹的代价值。