rrt算法matlab

RRT (Rapidly-exploring Random Tree) 是一种用于路径规划的算法。在 MATLAB 中实现 RRT 算法可以通过以下步骤进行：

1. 定义问题空间：首先，你需要定义问题的状态空间和可行域。状态空间是指机器人或物体可能存在的位置和方向的集合。可行域则是指机器人或物体可以在其中移动的区域。

2. 初始化树：创建一个包含起始状态（节点）的树。起始状态是指机器人或物体的初始位置。

3. 随机采样：随机在问题空间中采样一个点作为目标状态。

4. 最近邻搜索：从树中找到与目标状态最近的节点。

5. 扩展树：从最近邻节点向目标状态方向扩展一条新的边，并创建一个新的节点。

6. 碰撞检测：检测新产生的边是否与障碍物碰撞。如果没有碰撞，则将新节点添加到树中。

7. 迭代：重复步骤3-6，直到达到终止条件（例如，达到目标状态或超过最大迭代次数）。

8. 路径回溯：从目标状态回溯树，找到一条从起始状态到目标状态的路径。

9. 可视化路径：将路径可视化以进行验证和展示。

这是一个简单的 RRT 算法的实现步骤。你可以根据具体的问题进行修改和扩展。

相关问题

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。

rrt算法 matlab代码

以下是RRT算法的MATLAB实现：

% RRT algorithm
% Written by Yifan Hou, 2018

% Define the map boundaries
map = [0 100; 0 100];

% Define the start and goal positions
start_pos = [10 10];
goal_pos = [90 90];

% Define the step size
step_size = 5;

% Define the maximum number of iterations
max_iter = 1000;

% Define the maximum distance to connect to the tree
max_dist = 10;

% Define the radius of the goal region
goal_radius = 2;

% Initialize the tree with the start position
tree = [start_pos 0];

% Initialize the list of explored nodes
explored = [];

% Run the RRT algorithm
for i = 1:max_iter
    
    % Generate a random point in the map
    random_point = [randi(map(1,:), 1) randi(map(2,:), 1)];
    
    % Find the nearest node in the tree
    [nearest_node, nearest_dist] = nearestNode(random_point, tree);
    
    % Calculate the new node in the direction of the random point
    new_node = steer(nearest_node, random_point, step_size);
    
    % Check if the new node is within the map boundaries
    if checkBounds(new_node, map)
        
        % Check if the new node is collision-free
        if checkCollision(nearest_node, new_node, map)
            
            % Add the new node to the tree
            tree = [tree; new_node nearest_node];
            
            % Check if the new node is within the goal region
            if norm(new_node - goal_pos) <= goal_radius
                
                % Add the goal node to the tree
                tree = [tree; goal_pos size(tree, 1)];
                
                % Trace the path from the goal node to the start node
                path = tracePath(tree);
                
                % Plot the final path
                plotPath(path, explored, map);
                
                break;
            end
            
            % Add the new node to the list of explored nodes
            explored = [explored; new_node];
            
            % Connect the new node to the tree if it is within the maximum
            % distance
            if nearest_dist <= max_dist
                tree = [tree; new_node size(tree, 1)];
            end
            
        end
    end
    
end

其中，nearestNode函数用于查找离给定点最近的树节点，steer函数用于从最近的节点朝着随机点方向延伸一定长度，checkBounds函数用于检查点是否在地图边界内，checkCollision函数用于检查两个点之间的路径是否与障碍物相交，tracePath函数用于从终点向根节点遍历树，plotPath函数用于绘制路径和探索节点。这些函数在代码中并未给出，需要根据实际情况自行实现。