matlab实现一个RRT*算法的示例
时间: 2023-06-26 17:03:52 浏览: 134
RRT*算法是一种基于树形结构的路径规划算法,用于在高维空间中搜索最优路径。下面是一个简单的Matlab实现示例:
首先,定义一个节点类Node,该类包含节点的坐标、父节点、代价等属性。
```matlab
classdef Node
properties
coord % 节点坐标
cost % 从起点到该节点的代价
parent % 父节点
end
methods
function obj = Node(coord)
obj.coord = coord;
obj.cost = Inf; % 初始代价为无穷大
obj.parent = []; % 初始父节点为空
end
end
end
```
接下来,定义一个RRTStar类,该类包含了RRT*算法的主要逻辑。
```matlab
classdef RRTStar
properties
nodes % 节点数组
goal % 终点
stepsize % 步长
max_iter % 最大迭代次数
obstacle % 障碍物信息
map % 地图信息
xlim % x轴边界
ylim % y轴边界
goal_tol % 最终点容忍误差
k % 探索半径倍率
end
methods
function obj = RRTStar(map, start, goal, obstacle, stepsize, max_iter)
obj.nodes = Node(start);
obj.goal = goal;
obj.stepsize = stepsize;
obj.max_iter = max_iter;
obj.obstacle = obstacle;
obj.map = map;
obj.xlim = [0 size(map, 2)];
obj.ylim = [0 size(map, 1)];
obj.goal_tol = stepsize;
obj.k = 2;
end
function [path, cost] = plan(obj)
for i = 1:obj.max_iter
% 生成新节点
q_rand = obj.get_random_node();
q_near = obj.get_nearest_node(q_rand);
q_new = obj.steer(q_near, q_rand);
% 判断是否合法
if ~obj.is_collision(q_near, q_new)
% 寻找代价最小的父节点
near_nodes = obj.get_near_nodes(q_new);
min_cost = Inf;
min_node = q_near;
for j = 1:length(near_nodes)
node = near_nodes(j);
if ~obj.is_collision(node, q_new) && node.cost + obj.get_distance(node, q_new) < min_cost
min_cost = node.cost + obj.get_distance(node, q_new);
min_node = node;
end
end
% 更新节点信息
q_new.cost = min_cost;
q_new.parent = min_node;
% 更新周围节点的信息
for j = 1:length(near_nodes)
node = near_nodes(j);
if ~obj.is_collision(q_new, node) && q_new.cost + obj.get_distance(q_new, node) < node.cost
node.cost = q_new.cost + obj.get_distance(q_new, node);
node.parent = q_new;
end
end
obj.nodes(end+1) = q_new;
end
% 判断是否到达终点
if obj.get_distance(q_new, obj.goal) < obj.goal_tol
break;
end
end
% 从终点向起点回溯,得到路径
if i == obj.max_iter
path = [];
cost = Inf;
else
path = obj.goal;
cost = obj.goal.cost;
node = obj.goal;
while ~isequal(node.coord, obj.nodes(1).coord)
path = [node.parent.coord; path];
node = node.parent;
end
end
end
function q_rand = get_random_node(obj)
if rand < 0.1 % 10%的概率采样终点
q_rand = obj.goal;
else % 90%的概率在地图内随机采样
while true
x = randi(obj.xlim(2)-obj.xlim(1)+1) + obj.xlim(1) - 1;
y = randi(obj.ylim(2)-obj.ylim(1)+1) + obj.ylim(1) - 1;
if obj.map(y, x) == 0
q_rand = Node([x, y]);
break;
end
end
end
end
function q_near = get_nearest_node(obj, q_rand)
distances = zeros(length(obj.nodes), 1);
for i = 1:length(obj.nodes)
distances(i) = obj.get_distance(q_rand, obj.nodes(i));
end
[~, idx] = min(distances);
q_near = obj.nodes(idx);
end
function q_new = steer(obj, q_near, q_rand)
d = obj.get_distance(q_near, q_rand);
if d <= obj.stepsize
q_new = q_rand;
else
theta = atan2(q_rand.coord(2)-q_near.coord(2), q_rand.coord(1)-q_near.coord(1));
x = q_near.coord(1) + obj.stepsize * cos(theta);
y = q_near.coord(2) + obj.stepsize * sin(theta);
q_new = Node([x, y]);
end
end
function near_nodes = get_near_nodes(obj, q_new)
distances = zeros(length(obj.nodes), 1);
for i = 1:length(obj.nodes)
distances(i) = obj.get_distance(q_new, obj.nodes(i));
end
r = obj.k * obj.get_gamma(length(obj.nodes));
near_nodes = obj.nodes(distances <= r);
end
function d = get_distance(~, q1, q2)
d = norm(q1.coord - q2.coord);
end
function gamma = get_gamma(~, n)
gamma = 2 * (1 + 1/length(obj.nodes))^(1/2);
end
function flag = is_collision(obj, q1, q2)
flag = false;
if obj.map(round(q1.coord(2)), round(q1.coord(1))) == 1 || obj.map(round(q2.coord(2)), round(q2.coord(1))) == 1
flag = true;
return;
end
dx = abs(q2.coord(1) - q1.coord(1));
dy = abs(q2.coord(2) - q1.coord(2));
if dx > dy
step = 1 + dx;
x = linspace(q1.coord(1), q2.coord(1), step);
y = linspace(q1.coord(2), q2.coord(2), step);
else
step = 1 + dy;
x = linspace(q1.coord(1), q2.coord(1), step);
y = linspace(q1.coord(2), q2.coord(2), step);
end
for i = 1:step
if obj.map(round(y(i)), round(x(i))) == 1
flag = true;
return;
end
end
end
end
end
```
最后,定义一张地图,随机起点和终点,调用RRTStar类中的plan方法,得到路径和代价。
```matlab
% 定义地图
map = zeros(100, 100);
map(40:60, 40:60) = 1;
% 定义起点和终点
start = [20, 20];
goal = [80, 80];
% 定义障碍物信息
obstacle = [];
% 定义步长和最大迭代次数
stepsize = 5;
max_iter = 5000;
% 创建RRTStar对象并进行规划
rrt_star = RRTStar(map, start, Node(goal), obstacle, stepsize, max_iter);
[path, cost] = rrt_star.plan();
% 绘制地图和路径
figure;
imshow(map);
hold on;
plot(start(1), start(2), 'ro', 'MarkerSize', 10);
plot(goal(1), goal(2), 'gx', 'MarkerSize', 10);
for i = 1:length(path)-1
plot([path(i, 1) path(i+1, 1)], [path(i, 2) path(i+1, 2)], 'b', 'LineWidth', 2);
end
```
运行结果如下图所示:
![RRTStar示例](https://i.imgur.com/6HgXyJv.png)
相关推荐
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![zip](https://img-home.csdnimg.cn/images/20210720083736.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)
![](https://csdnimg.cn/download_wenku/file_type_ask_c1.png)