用matlab写一个rrt算法

好的，关于您的问题，我可以回答。RRT算法（Rapidly-exploring Random Tree）是一种基于树形结构生成路径的算法，可以用于路径规划，机器人导航等领域。如果您正在使用Matlab进行编程，可以尝试使用Matlab Robotics Toolbox中提供的RRT实现算法。您可以查阅相关文档和示例以获取更详细的信息。希望能对您有所帮助。

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rrt matlab算法,rrt算法matlab代码

以下是基于 RRT（Rapidly-exploring Random Tree）算法的 Matlab 代码，用于构建机器人路径规划：

clear all; close all; clc

% Environment and robot parameters
xMin = 0;
xMax = 10;
yMin = 0;
yMax = 10;
obs = [4 4 1; 6 6 1];

robotLength = 0.5;
robotWidth = 0.5;

% Start and goal positions
startPos = [1,1];
goalPos = [9,9];

% RRT parameters
maxNodes = 5000;
stepSize = 0.5;

nodes(1).x = startPos(1);
nodes(1).y = startPos(2);
nodes(1).parent = 0;

for i = 2:maxNodes
    x = rand*(xMax-xMin) + xMin;
    y = rand*(yMax-yMin) + yMin;
    node = [x,y];
    
    % Check if node is inside an obstacle
    insideObs = 0;
    for j = 1:size(obs,1)
        if sqrt((node(1)-obs(j,1))^2 + (node(2)-obs(j,2))^2) < obs(j,3)
            insideObs = 1;
            break;
        end
    end
    
    if insideObs == 1
        continue;
    end
    
    % Find the nearest node
    dist = inf;
    nearestNode = 0;
    for j = 1:length(nodes)
        d = sqrt((node(1)-nodes(j).x)^2 + (node(2)-nodes(j).y)^2);
        if d < dist
            dist = d;
            nearestNode = j;
        end
    end
    
    % Check if there is a direct path between the nearest node and the new node
    theta = atan2(node(2)-nodes(nearestNode).y, node(1)-nodes(nearestNode).x);
    xTest = nodes(nearestNode).x + stepSize*cos(theta);
    yTest = nodes(nearestNode).y + stepSize*sin(theta);
    if sqrt((xTest-node(1))^2 + (yTest-node(2))^2) > stepSize
        continue;
    end
    
    % Check if the direct path is inside an obstacle
    insideObs = 0;
    for j = 1:size(obs,1)
        if sqrt((xTest-obs(j,1))^2 + (yTest-obs(j,2))^2) < obs(j,3)
            insideObs = 1;
            break;
        end
    end
    
    if insideObs == 1
        continue;
    end
    
    % Add the new node to the tree
    nodes(end+1).x = xTest;
    nodes(end).y = yTest;
    nodes(end).parent = nearestNode;
    
    % Check if the goal has been reached
    if sqrt((nodes(end).x-goalPos(1))^2 + (nodes(end).y-goalPos(2))^2) < stepSize
        break;
    end
end

% Plot the obstacles
figure(1)
hold on
axis([xMin xMax yMin yMax])
for i = 1:size(obs,1)
    rectangle('Position',[obs(i,1)-obs(i,3), obs(i,2)-obs(i,3), 2*obs(i,3), 2*obs(i,3)], 'Curvature', [1,1], 'FaceColor', 'r')
end

% Plot the tree
for i = 2:length(nodes)
    x = [nodes(i).x, nodes(nodes(i).parent).x];
    y = [nodes(i).y, nodes(nodes(i).parent).y];
    plot(x,y,'k')
end

% Find the path from start to goal
path = [nodes(end).x, nodes(end).y];
while nodes(end).parent ~= 0
    endNode = nodes(end);
    path = [endNode.x, endNode.y; path];
    endNode = nodes(endNode.parent);
end
path = [startPos; path];

% Plot the path
plot(path(:,1), path(:,2), 'b', 'LineWidth', 2)

这段代码会生成一个基于 RRT 算法的路径规划过程，其中包括环境参数、机器人参数、起始位置、目标位置和 RRT 参数。代码将生成一个随机树，以搜索从起始位置到目标位置的路径。最终，该代码会绘制出路径和环境。

matlab实现一个RRT*算法的示例

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。

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。

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。

% 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：