移動機器人gazebo模擬(5)—規劃演算法A*
參考部落格:
導航實際流程為:
進行全域性路徑規劃,在進行區域性路徑規劃,然後釋出速度
全域性路徑規劃在makePlan函式中,該函式中呼叫了planner_的makePlan和empty介面。planner_為繼承於BaseGlobalPlanner的例項,由pluginlib通過具體類的名字進行裝載。
之後,呼叫tc_的setPlan介面,對區域性路徑規劃器進行全域性路徑設定,然後,呼叫tc_的isReached介面進行判斷,然後呼叫tc_的computeVelocityCommands介面,進行速度計算,然後進行速度下發。
tc_為繼承於BaseLocalPlanner的例項,也是由pluginlinb通過具體類的名字進行裝載。
planner_在初始化時候,被塞入了planner_costmap_ros_
tc_在初始化時,被塞入了controller_costmap_ros_
在global planner的包中,註冊了外掛:global planner::GlobalPlanner
程式碼閱讀:
global_planne
1、plan_node.cpp
plan_node.cpp是全域性規劃程式碼的入口(程式碼註釋都是自己理解然後新增,也許會有錯誤)
#include <global_planner/planner_core.h>
#include <navfn/MakeNavPlan.h>
#include <boost/shared_ptr.hpp>
#include <costmap_2d/costmap_2d_ros.h>
namespace cm = costmap_2d;
namespace rm = geometry_msgs;
using std::vector;
using rm::PoseStamped;
using std::string;
using cm::Costmap2D;
using cm::Costmap2DROS;
namespace global_planner {
class PlannerWithCostmap : public GlobalPlanner {
public:
PlannerWithCostmap(string name, Costmap2DROS* cmap);
bool makePlanService(navfn::MakeNavPlan::Request& req, navfn::MakeNavPlan::Response& resp);
private:
void poseCallback(const rm::PoseStamped::ConstPtr& goal);
Costmap2DROS* cmap_;
ros::ServiceServer make_plan_service_;
ros::Subscriber pose_sub_;
};
//Publish a path for visualization purposes
bool PlannerWithCostmap::makePlanService(navfn::MakeNavPlan::Request& req, navfn::MakeNavPlan::Response& resp) {
vector<PoseStamped> path;
req.start.header.frame_id = "/map";
req.goal.header.frame_id = "/map";
bool success = makePlan (req.start, req.goal, path);
resp.plan_found = success;
if (success) {
resp.path = path;
}
return true;
}
void PlannerWithCostmap::poseCallback(const rm::PoseStamped::ConstPtr& goal) {
tf::Stamped<tf::Pose> global_pose;
cmap_->getRobotPose(global_pose);//獲取機器人起始位姿
vector<PoseStamped> path;
rm::PoseStamped start;
start.header.stamp = global_pose.stamp_;
start.header.frame_id = global_pose.frame_id_;
start.pose.position.x = global_pose.getOrigin().x();
start.pose.position.y = global_pose.getOrigin().y();
start.pose.position.z = global_pose.getOrigin().z();
start.pose.orientation.x = global_pose.getRotation().x();
start.pose.orientation.y = global_pose.getRotation().y();
start.pose.orientation.z = global_pose.getRotation().z();
start.pose.orientation.w = global_pose.getRotation().w();
makePlan (start, *goal, path);//路徑規劃
}
PlannerWithCostmap::PlannerWithCostmap(string name, Costmap2DROS* cmap) :
GlobalPlanner(name, cmap->getCostmap(), cmap->getGlobalFrameID()) {
ros::NodeHandle private_nh("~");
cmap_ = cmap;
make_plan_service_ = private_nh.advertiseService("make_plan", &PlannerWithCostmap::makePlanService, this);
pose_sub_ = private_nh.subscribe<rm::PoseStamped>("goal", 1, &PlannerWithCostmap::poseCallback, this);
}
} // namespace
int main(int argc, char** argv) {
ros::init(argc, argv, "global_planner");
//設定tf監聽時間間隔
tf::TransformListener tf(ros::Duration(10));
//costmap_2d::Costmap2D 類是儲存和訪問2D代價地圖的的基本資料結構,下面程式碼作用是初始化
costmap_2d::Costmap2DROS lcr("costmap", tf);
//兩個執行緒:1、提供planservice 2、訂閱goal,當得到goal則啟動makeplan
global_planner::PlannerWithCostmap pppp("planner", &lcr);
ros::spin();
return 0;
}
接下來分析makeplan函式
2、makeplan
GlobalPlanner::makePlan類的使用介面有多種,例如:
bool GlobalPlanner::makePlan(const geometry_msgs::PoseStamped& start, const geometry_msgs::PoseStamped& goal,
std::vector<geometry_msgs::PoseStamped>& plan) {
return makePlan(start, goal, default_tolerance_, plan);
}
bool GlobalPlanner::makePlan(const geometry_msgs::PoseStamped& start, const geometry_msgs::PoseStamped& goal,
double tolerance, std::vector<geometry_msgs::PoseStamped>& plan){.....}
但最終程式的主體是:
bool GlobalPlanner::makePlan(const geometry_msgs::PoseStamped& start, const geometry_msgs::PoseStamped& goal,
double tolerance, std::vector<geometry_msgs::PoseStamped>& plan) {
boost::mutex::scoped_lock lock(mutex_);//給執行緒加鎖直到被銷燬
if (!initialized_) {
ROS_ERROR(
"This planner has not been initialized yet, but it is being used, please call initialize() before use");
return false;
}
//clear the plan, just in case
plan.clear();
ros::NodeHandle n;
std::string global_frame = frame_id_;
//until tf can handle transforming things that are way in the past... we'll require the goal to be in our global frame
if (tf::resolve(tf_prefix_, goal.header.frame_id) != tf::resolve(tf_prefix_, global_frame)) {
ROS_ERROR(
"The goal pose passed to this planner must be in the %s frame. It is instead in the %s frame.", tf::resolve(tf_prefix_, global_frame).c_str(), tf::resolve(tf_prefix_, goal.header.frame_id).c_str());
return false;
}
if (tf::resolve(tf_prefix_, start.header.frame_id) != tf::resolve(tf_prefix_, global_frame)) {
ROS_ERROR(
"The start pose passed to this planner must be in the %s frame. It is instead in the %s frame.", tf::resolve(tf_prefix_, global_frame).c_str(), tf::resolve(tf_prefix_, start.header.frame_id).c_str());
return false;
}
//記錄開始位姿
double wx = start.pose.position.x;
double wy = start.pose.position.y;
unsigned int start_x_i, start_y_i, goal_x_i, goal_y_i;//map
double start_x, start_y, goal_x, goal_y;
//下面將世界座標系下的start和goal轉化為map形式
if (!costmap_->worldToMap(wx, wy, start_x_i, start_y_i)) {
ROS_WARN(
"The robot's start position is off the global costmap. Planning will always fail, are you sure the robot has been properly localized?");
return false;
}
if(old_navfn_behavior_){
start_x = start_x_i;
start_y = start_y_i;
}else{
worldToMap(wx, wy, start_x, start_y);
}
wx = goal.pose.position.x;
wy = goal.pose.position.y;
if (!costmap_->worldToMap(wx, wy, goal_x_i, goal_y_i)) {
ROS_WARN_THROTTLE(1.0,
"The goal sent to the global planner is off the global costmap. Planning will always fail to this goal.");
return false;
}
if(old_navfn_behavior_){
goal_x = goal_x_i;
goal_y = goal_y_i;
}else{
worldToMap(wx, wy, goal_x, goal_y);
}
//clear the starting cell within the costmap because we know it can't be an obstacle
tf::Stamped<tf::Pose> start_pose;
tf::poseStampedMsgToTF(start, start_pose);//map下資訊轉化為tf類的資料
clearRobotCell(start_pose, start_x_i, start_y_i);//清除開始點,因為開始位置不可能是障礙
//計算costmap的xsize和ysize,賦值給nx ,ny
int nx = costmap_->getSizeInCellsX(), ny = costmap_->getSizeInCellsY();
//make sure to resize the underlying array that Navfn uses,(分配空間,大小和costmap一樣大)
p_calc_->setSize(nx, ny);
planner_->setSize(nx, ny);
path_maker_->setSize(nx, ny);
potential_array_ = new float[nx * ny];
//呼叫以下函式將costmap的四個邊的全部cell都設定為LETHAL_OBSTACLE(佔用)
outlineMap(costmap_->getCharMap(), nx, ny, costmap_2d::LETHAL_OBSTACLE);
//計算potential
bool found_legal = planner_->calculatePotentials(costmap_->getCharMap(), start_x, start_y, goal_x, goal_y,
nx * ny * 2, potential_array_);
if(!old_navfn_behavior_)
planner_->clearEndpoint(costmap_->getCharMap(), potential_array_, goal_x_i, goal_y_i, 2);
if(publish_potential_)
publishPotential(potential_array_);
if (found_legal) {
//extract the plan
if (getPlanFromPotential(start_x, start_y, goal_x, goal_y, goal, plan)) {
//make sure the goal we push on has the same timestamp as the rest of the plan
geometry_msgs::PoseStamped goal_copy = goal;
goal_copy.header.stamp = ros::Time::now();
plan.push_back(goal_copy);
} else {
ROS_ERROR("Failed to get a plan from potential when a legal potential was found. This shouldn't happen.");
}
}else{
ROS_ERROR("Failed to get a plan.");
}
// add orientations if needed
orientation_filter_->processPath(start, plan);
//publish the plan for visualization purposes
publishPlan(plan);
delete potential_array_;
return !plan.empty();
}
值得注意的是,在GlobalPlanner::initialize()這個初始化函式中有一段程式碼,決定了使用A*還是D*亦或是其他演算法計算:
bool use_quadratic;
private_nh.param("use_quadratic", use_quadratic, true);
if (use_quadratic)
p_calc_ = new QuadraticCalculator(cx, cy);
else
p_calc_ = new PotentialCalculator(cx, cy);
bool use_dijkstra;
private_nh.param("use_dijkstra", use_dijkstra, true);
if (use_dijkstra)
{
DijkstraExpansion* de = new DijkstraExpansion(p_calc_, cx, cy);
if(!old_navfn_behavior_)
de->setPreciseStart(true);
planner_ = de;
}
else
planner_ = new AStarExpansion(p_calc_, cx, cy);//決定使用的演算法
bool use_grid_path;
private_nh.param("use_grid_path", use_grid_path, false);
if (use_grid_path)
path_maker_ = new GridPath(p_calc_);
else
path_maker_ = new GradientPath(p_calc_);
從makeplan程式碼中分析,最關鍵的語句有兩句:
1、計算potential
bool found_legal = planner_->calculatePotentials(costmap_->getCharMap(), start_x, start_y, goal_x, goal_y,
nx * ny * 2, potential_array_);
這裡的planner_的定義由GlobalPlanner::initialize()中的引數決定(程式見上)
2、提取plan
if (getPlanFromPotential(start_x, start_y, goal_x, goal_y, goal, plan)) {
//make sure the goal we push on has the same timestamp as the rest of the plan
geometry_msgs::PoseStamped goal_copy = goal;
goal_copy.header.stamp = ros::Time::now();
plan.push_back(goal_copy);
}
astar.cpp檔案
計算potential時,假設 引數檔案中 use_dijkstra = fause ,那麼使用的就是astar演算法,即
planner_ = new AStarExpansion(p_calc_, cx, cy)
因此首先需要分析astar.cpp內的函式:這篇部落格這部分寫的不錯點選開啟連結
輸入引數 為指向概率地圖的指標 其實位置地座標 目標座標 一個指向大小為nx*ny的陣列
bool AStarExpansion::calculatePotentials(unsigned char* costs, double start_x, double start_y, double end_x, double end_y,
int cycles, float* potential) {
queue_.clear();
int start_i = toIndex(start_x, start_y);
queue_.push_back(Index(start_i, 0));//push the start point into OPEN queue_
std::fill(potential, potential + ns_, POT_HIGH); //initial all the potential as very large value 1e10
potential[start_i] = 0;//set start_i為0
int goal_i = toIndex(end_x, end_y);
int cycle = 0;
while (queue_.size() > 0 && cycle < cycles) {
Index top = queue_[0];//get the Index with lowest cost (set to current)
std::pop_heap(queue_.begin(), queue_.end(), greater1());//build the heap sort
queue_.pop_back();//remove the Index with mini cost (remove from OPEN)
int i = top.i;//target node the Index's i from (i,cost)
if (i == goal_i)
return true;
//for each neighbour node (*) of the current node(0),
// + * + i-nx
// * 0 * i-1, 0 , i+1
// + * + i+nx
add(costs, potential, potential[i], i + 1, end_x, end_y);
add(costs, potential, potential[i], i - 1, end_x, end_y);
add(costs, potential, potential[i], i + nx_, end_x, end_y);
add(costs, potential, potential[i], i - nx_, end_x, end_y);
cycle++;
}
return false;
}
//接下來add函式的定義
/*f(n)=g(n)+h(n)
其中, f(n) 是從初始狀態經由狀態n到目標狀態的代價估計,g(n) 是在狀態空間中從初始狀態到狀態n的實際代價,
h(n) 是從狀態n到目標狀態的最佳路徑的估計代價。
(對於路徑搜尋問題,狀態就是圖中的節點,代價就是距離)*/
void AStarExpansion::add(unsigned char* costs, float* potential, float prev_potential, int next_i, int end_x,
int end_y) {
if (next_i < 0 || next_i >= ns_)
return;
if (potential[next_i] < POT_HIGH)//it means the potential cell has been explored
return;
if(costs[next_i]>=lethal_cost_ && !(unknown_ && costs[next_i]==costmap_2d::NO_INFORMATION))//it means this cell is obstaclereturn;
return;
//計算next_i的potential值,calculatePotential函式返回next_i周圍的節點到next_i的最小值
potential[next_i] = p_calc_->calculatePotential(potential, costs[next_i] + neutral_cost_, next_i, prev_potential);
int x = next_i % nx_, y = next_i / nx_;//x mean column ,y means row
float distance = abs(end_x - x) + abs(end_y - y);//calculate h(n)
queue_.push_back(Index(next_i, potential[next_i] + distance * neutral_cost_));
std::push_heap(queue_.begin(), queue_.end(), greater1());
}
} //end namespace global_planner
3、A*演算法程式碼總結:
1、bool AStarExpansion::calculatePotentials(unsigned char* costs, double start_x, double start_y, double end_x, double end_y, int cycles, float* potential)
輸入引數:* costs 即: costmap_->getCharMap()
start_x,start_y 起始點
end_x,end_y 目標點
cycles 即:nx * ny * 2
*potential 用於儲存代價,陣列大小為nx * ny
首先 start_x,start_y,end_x,end_y轉化為 start_i,end_i;
將start_i加入到open 中
queue_.push_back(Index(start_i, 0)); //Index包括 i 和 cost ,程式碼將cost清零
進入迴圈,迴圈條件:堆的size大於0 且 迴圈次數小於 2*nx*ny
迴圈中先定義 Index top = queue_[0]; 即取最小堆的根,包含序號i,代價 cost
然後通過 std::pop_heap(queue_.begin(), queue_.end(), greater1()); queue_.pop_back(); 將樹根放到末端並刪除
取i=top.i, 計算代價地圖中要到達目標點 該點(i)的鄰點 所消耗代價的最小值
接下來分析如何計算:
2、void AStarExpansion::add(unsigned char* costs, float* potential, float prev_potential, int next_i, int end_x,
int end_y)代價計算:f(n)=g(n)+h(n)
呼叫形式是: add(costs, potential, potential[i], i + 1, end_x, end_y);
add(costs, potential, potential[i], i - 1, end_x, end_y);add(costs, potential, potential[i], i + nx_, end_x, end_y);
add(costs, potential, potential[i], i - nx_, end_x, end_y);
輸入引數: costs地圖 potential陣列 當前i點的potential值 鄰點的代號 目標點的行、列資訊
先計算start_i到 鄰點(i+1,i-1,i+nx,i-nx) 的最小代價g(n),使用函式:
potential[next_i] = p_calc_->calculatePotential(potential, costs[next_i] + neutral_cost_, next_i, prev_potential);
然後計算 鄰點(i+1,i-1,i+nx,i-nx) 到目標點的估值代價h (n),與前面的最小代價g(n)相加,並放到樹根
queue_.push_back(Index(next_i, potential[next_i] + distance * neutral_cost_));
std::push_heap(queue_.begin(), queue_.end(), greater1());
3、 calculatePotential函式
virtual float calculatePotential(float* potential, unsigned char cost, int n, float prev_potential=-1){
if(prev_potential < 0){
// get min of neighbors
float min_h = std::min( potential[n - 1], potential[n + 1] ),
min_v = std::min( potential[n - nx_], potential[n + nx_]);
prev_potential = std::min(min_h, min_v);
}
return prev_potential + cost;
}