用RRT*算法写一个无人机三维空间的避障路径规划MATLAB程序

好的，以下是一个基本的无人机三维空间的避障路径规划MATLAB程序。

首先，我们需要定义一个类来表示无人机。这个类包括位置、速度、加速度等属性，以及一些方法来更新这些属性。这里我们假设无人机可以以任意姿态飞行，因此我们需要使用四元数来表示无人机的方向。

classdef UAV
    properties
        position % 当前位置 [x, y, z]
        velocity % 当前速度 [vx, vy, vz]
        acceleration % 当前加速度 [ax, ay, az]
        orientation % 当前方向 [qw, qx, qy, qz]
        max_speed % 最大飞行速度
        max_acceleration % 最大加速度
    end
    
    methods
        function obj = UAV(position, velocity, acceleration, orientation, max_speed, max_acceleration)
            obj.position = position;
            obj.velocity = velocity;
            obj.acceleration = acceleration;
            obj.orientation = orientation;
            obj.max_speed = max_speed;
            obj.max_acceleration = max_acceleration;
        end
        
        function obj = update(obj, dt)
            % 根据当前速度和加速度更新位置和速度
            obj.position = obj.position + obj.velocity * dt + 0.5 * obj.acceleration * dt^2;
            obj.velocity = obj.velocity + obj.acceleration * dt;
        end
        
        function obj = set_acceleration(obj, acceleration)
            % 设置加速度，但不允许超过最大加速度
            obj.acceleration = acceleration;
            if norm(obj.acceleration) > obj.max_acceleration
                obj.acceleration = obj.max_acceleration * obj.acceleration / norm(obj.acceleration);
            end
        end
        
        function obj = set_orientation(obj, orientation)
            % 设置方向，但要保证四元数的模为1
            obj.orientation = orientation / norm(orientation);
        end
        
        function obj = set_velocity(obj, velocity)
            % 设置速度，但不允许超过最大速度
            obj.velocity = velocity;
            if norm(obj.velocity) > obj.max_speed
                obj.velocity = obj.max_speed * obj.velocity / norm(obj.velocity);
            end
        end
    end
end

接下来，我们需要定义一个类来表示障碍物。这个类包括位置、大小等属性，以及一些方法来检查无人机是否与障碍物相交。

classdef Obstacle
    properties
        position % 障碍物中心位置 [x, y, z]
        size % 障碍物大小 [dx, dy, dz]
    end
    
    methods
        function obj = Obstacle(position, size)
            obj.position = position;
            obj.size = size;
        end
        
        function is_colliding = check_collision(obj, uav)
            % 检查无人机是否与障碍物相交
            p = uav.position;
            r = max(uav.size) / 2;
            q = obj.position;
            s = obj.size / 2;
            is_colliding = (abs(p(1) - q(1)) <= r + s(1)) && ...
                           (abs(p(2) - q(2)) <= r + s(2)) && ...
                           (abs(p(3) - q(3)) <= r + s(3));
        end
    end
end

然后，我们需要定义一个函数来生成一组随机目标点。这个函数会在三维空间中随机生成一些点，并检查这些点是否与障碍物相交。如果某个点与障碍物相交，则重新生成一个新的点。

function goals = generate_goals(num_goals, obstacles, xmin, xmax, ymin, ymax, zmin, zmax)
    goals = zeros(num_goals, 3);
    for i = 1:num_goals
        while true
            x = xmin + rand() * (xmax - xmin);
            y = ymin + rand() * (ymax - ymin);
            z = zmin + rand() * (zmax - zmin);
            is_colliding = false;
            for j = 1:length(obstacles)
                if obstacles(j).check_collision(UAV([x, y, z], [0, 0, 0], [0, 0, 0], [1, 0, 0, 0], 0, 0))
                    is_colliding = true;
                    break;
                end
            end
            if ~is_colliding
                goals(i, :) = [x, y, z];
                break;
            end
        end
    end
end

接下来，我们需要实现 RRT* 算法。这是一个基于 RRT 算法的路径规划算法，可以在具有复杂障碍物的三维空间中寻找无人机的安全路径。具体来说，算法会在空间中生成一棵随机生长的树，该树的根节点是无人机的起始位置，每个节点代表一个无人机所在的位置，每个节点的子节点是通过一些随机样本和反向链来生成的。在树生长过程中，算法会使用代价函数来评估每个节点和路径的优劣，以便找到一条在避开障碍物的同时尽可能直接到达目标位置的路径。

function path = RRT_star(start_position, goal_positions, obstacles, xmin, xmax, ymin, ymax, zmin, zmax, max_iter, goal_tolerance)
    % 参数定义
    step_size = 1; % 每一步的最大距离
    num_goals = size(goal_positions, 1);
    num_obstacles = length(obstacles);
    tree = struct('position', {}, 'parent', {}, 'cost', {}, 'children', {}); % 树的结构体
    tree(1).position = start_position;
    tree(1).parent = 0;
    tree(1).cost = 0;
    tree(1).children = [];
    nearest_node = 1;
    
    % 定义代价函数
    function cost = compute_cost(uav)
        cost = norm(uav.position - start_position);
    end
    
    % 定义近邻查找函数
    function [nearest_node, min_dist] = find_nearest_node(position)
        nearest_node = 0;
        min_dist = inf;
        for i = 1:length(tree)
            dist = norm(tree(i).position - position);
            if dist < min_dist
                nearest_node = i;
                min_dist = dist;
            end
        end
    end
    
    % 定义插入节点函数
    function new_node = insert_node(parent_node, position)
        uav = UAV(position, [0, 0, 0], [0, 0, 0], [1, 0, 0, 0], 0, 0);
        uav.set_velocity(step_size * (position - tree(parent_node).position) / norm(position - tree(parent_node).position));
        if norm(uav.velocity) > uav.max_speed
            uav.set_velocity(uav.max_speed * uav.velocity / norm(uav.velocity));
        end
        uav.set_acceleration(zeros(1, 3));
        uav.set_orientation([1, 0, 0, 0]);
        is_colliding = false;
        for i = 1:num_obstacles
            if obstacles(i).check_collision(uav)
                is_colliding = true;
                break;
            end
        end
        if is_colliding
            new_node = 0;
        else
            new_node = length(tree) + 1;
            tree(new_node).position = position;
            tree(new_node).parent = parent_node;
            tree(new_node).cost = tree(parent_node).cost + norm(position - tree(parent_node).position);
            tree(new_node).children = [];
            tree(parent_node).children(end+1) = new_node;
        end
    end
    
    % 迭代生成树
    for iter = 1:max_iter
        % 生成随机目标点
        if mod(iter, 10) == 0
            goal_index = randi(num_goals);
            goal_position = goal_positions(goal_index, :);
        else
            goal_position = start_position;
        end
        
        % 查找最近节点
        [nearest_node, min_dist] = find_nearest_node(goal_position);
        if nearest_node == 0
            continue;
        end
        
        % 插入新节点
        new_position = tree(nearest_node).position + step_size * (goal_position - tree(nearest_node).position) / min_dist;
        new_node = insert_node(nearest_node, new_position);
        if new_node == 0
            continue;
        end
        
        % 更新近邻节点
        for i = 1:length(tree)
            if i == new_node || norm(tree(i).position - new_position) > step_size
                continue;
            end
            uav = UAV(tree(i).position, [0, 0, 0], [0, 0, 0], [1, 0, 0, 0], 0, 0);
            uav.set_velocity(step_size * (new_position - tree(i).position) / norm(new_position - tree(i).position));
            if norm(uav.velocity) > uav.max_speed
                uav.set_velocity(uav.max_speed * uav.velocity / norm(uav.velocity));
            end
            uav.set_acceleration(zeros(1, 3));
            uav.set_orientation([1, 0, 0, 0]);
            is_colliding = false;
            for j = 1:num_obstacles
                if obstacles(j).check_collision(uav)
                    is_colliding = true;
                    break;
                end
            end
            if ~is_colliding
                cost = tree(new_node).cost + norm(tree(i).position - new_position);
                if tree(i).parent == 0 || cost < tree(i).cost
                    tree(i).parent = new_node;
                    tree(i).cost = cost;
                end
            end
        end
        
        % 检查是否到达目标点
        if norm(new_position - goal_position) <= goal_tolerance
            break;
        end
    end
    
    % 生成最优路径
    if nearest_node ~= 0
        path = [tree(nearest_node).position];
        while tree(nearest_node).parent ~= 0
            nearest_node = tree(nearest_node).parent;
            path = [tree(nearest_node).position; path];
        end
    else
        path = [];
    end
end

最后，我们可以使用上述函数来进行路径规划：

% 定义起始点、目标点、障碍物等参数
start_position = [0, 0, 0];
goal_positions = generate_goals(10, obstacles, xmin, xmax, ymin, ymax, zmin, zmax);
obstacles = [Obstacle([5, 5, 5], [2, 2, 2]), Obstacle([-5, -5, -5], [2, 2, 2])];
xmin = -10;
xmax = 10;
ymin = -10;
ymax = 10;
zmin = -10;
zmax = 10;
max_iter = 1000;
goal_tolerance = 1;

% 进行路径规划
path = RRT_star(start_position, goal_positions, obstacles, xmin, xmax, ymin, ymax, zmin, zmax, max_iter, goal_tolerance);

% 绘制路径和障碍物
figure;
hold on;
for i = 1:length(obstacles)
    draw_obstacle(obstacles(i));
end
plot3(path(:, 1), path(:, 2), path(:, 3), 'LineWidth',2);
plot3(goal_positions(:, 1), goal_positions(:, 2), goal_positions(:, 3), 'ro', 'MarkerSize', 10);
plot3(start_position(1), start_position(2), start_position(3), 'go', 'MarkerSize', 10);
axis equal;
xlabel('X');
ylabel('Y');
zlabel('Z');

% 定义绘制障碍物的函数
function draw_obstacle(obstacle)
    x = obstacle.position(1) + [-1, -1, 1, 1, -1, -1, 1, 1] * obstacle.size(1) / 2;
    y = obstacle.position(2) + [-1, 1, 1, -1, -1, 1, 1, -1] * obstacle.size(2) / 2;
    z = obstacle.position(3) + [-1, -1, -1, -1, 1, 1, 1, 1] * obstacle.size(3) / 2;
    patch(x, y, z, 'r');
end