双向RRT※算法MATLAB

您好！双向RRT（Rapidly-exploring Random Tree）算法是一种用于路径规划的算法，它通过两个随机生成的树（一棵从起点开始，另一棵从终点开始）来搜索可行路径。下面是一个使用MATLAB实现双向RRT算法的示例代码：

function [path, tree] = bidirectionalRRT(start, goal, obstacles, mapSize, maxIter, stepSize)
    % 初始化树的节点
    tree.start.pos = start;
    tree.start.parent = 0;
    tree.goal.pos = goal;
    tree.goal.parent = 0;
    
    % 迭代搜索
    for i = 1:maxIter
        % 在起点树上随机采样一个点
        if rand < 0.5
            randPos = rand(1, 2) .* mapSize;
            [nearestNode, ~] = nearestNeighbor(tree.start, randPos);
            newNode.pos = steer(nearestNode.pos, randPos, stepSize);
            newNode.parent = nearestNode;
            
            % 检查新节点是否与障碍物相交
            if ~collisionCheck(newNode.pos, nearestNode.pos, obstacles)
                tree.start = addNode(tree.start, newNode);
                tree.start = rewire(tree.start, newNode, stepSize);
                
                % 检查新节点是否与终点树的节点相交
                [goalNode, dist] = nearestNeighbor(tree.goal, newNode.pos);
                if ~collisionCheck(newNode.pos, goalNode.pos, obstacles)
                    path = getPath(tree.start, newNode);
                    path = [path; flip(getPath(tree.goal, goalNode))];
                    return;
                end
            end
        else
            % 在终点树上随机采样一个点，过程与起点树相似
            randPos = rand(1, 2) .* mapSize;
            [nearestNode, ~] = nearestNeighbor(tree.goal, randPos);
            newNode.pos = steer(nearestNode.pos, randPos, stepSize);
            newNode.parent = nearestNode;
            
            if ~collisionCheck(newNode.pos, nearestNode.pos, obstacles)
                tree.goal = addNode(tree.goal, newNode);
                tree.goal = rewire(tree.goal, newNode, stepSize);
                
                [startNode, dist] = nearestNeighbor(tree.start, newNode.pos);
                if ~collisionCheck(newNode.pos, startNode.pos, obstacles)
                    path = getPath(tree.start, startNode);
                    path = [path; flip(getPath(tree.goal, newNode))];
                    return;
                end
            end
        end
    end
    
    path = [];
    tree = [];
end

function [nearestNode, minDist] = nearestNeighbor(tree, pos)
    nearestNode = tree;
    minDist = norm(pos - tree.pos);
    
    % 寻找最近的节点
    queue = tree;
    while ~isempty(queue)
        node = queue(1);
        queue(1) = [];
        
        dist = norm(pos - node.pos);
        if dist < minDist
            minDist = dist;
            nearestNode = node;
        end
        
        queue = [queue node.children];
    end
end

function newPos = steer(fromPos, toPos, stepSize)
    direction = toPos - fromPos;
    distance = norm(direction);
    if distance <= stepSize
        newPos = toPos;
    else
        newPos = fromPos + direction / distance * stepSize;
    end
end

function tree = addNode(tree, newNode)
    newNode.children = [];
    tree.children = [tree.children newNode];
end

function tree = rewire(tree, newNode, maxDist)
    queue = newNode.children;
    while ~isempty(queue)
        node = queue(1);
        queue(1) = [];
        
        dist = norm(newNode.pos - node.pos);
        if dist <= maxDist
            node.parent = newNode;
            queue = [queue node.children];
        end
    end
end

function collides = collisionCheck(pos1, pos2, obstacles)
    collides = false;
    for i = 1:size(obstacles, 1)
        if lineSegmentIntersectsPolygon(pos1, pos2, obstacles{i})
            collides = true;
            return;
        end
    end
end

function intersects = lineSegmentIntersectsPolygon(pos1, pos2, polygon)
    intersects = false;
    for i = 1:size(polygon, 1)
        pos3 = polygon(i, :);
        pos4 = polygon(mod(i, size(polygon, 1)) + 1, :);
        
        if lineSegmentsIntersect(pos1, pos2, pos3, pos4)
            intersects = true;
            return;
        end
    end
end

function intersects = lineSegmentsIntersect(pos1, pos2, pos3, pos4)
    intersects = false;
    
    p1 = pos1';
    p2 = pos2';
    q1 = pos3';
    q2 = pos4';
    
    r = p2 - p1;
    s = q2 - q1;
    
    uNumerator = cross(q1 - p1, r);
    denominator = cross(r, s);
    
    if denominator == 0
        if uNumerator == 0
            intersects = true;
        end
        return;
    end
    
    u = uNumerator / denominator;
    t = cross(q1 - p1, s) / denominator;
    
    if t >= 0 && t <= 1 && u >= 0 && u <= 1
        intersects = true;
    end
end

function path = getPath(tree, node)
    path = [];
    while node.parent ~= 0
        path = [path; node.pos];
        node = node.parent;
    end
    path = [path; tree.start.pos];
end

这段代码实现了双向RRT算法，其中`start`和`goal`表示起点和终点的坐标，`obstacles`表示障碍物的坐标，`mapSize`表示地图的尺寸，`maxIter`表示最大迭代次数，`stepSize`表示每次扩展的步长。函数返回的`path`是搜索到的路径，`tree`是搜索得到的树。

请注意，这只是一个简单的实现示例，您可能需要根据自己的具体需求进行适当的修改和优化。希望对您有帮助！