用RRT*算法写一个无人机三维空间的路径规划MATLAB程序

以下是一个基于RRT*算法的无人机三维空间路径规划MATLAB程序的示例：

% 定义起始点和目标点
start_pos = [0, 0, 0];
goal_pos = [10, 10, 10];

% 定义空间边界和障碍物
xlim = [0, 20];
ylim = [0, 20];
zlim = [0, 20];
obstacles = [5, 5, 5, 2;
             10, 10, 10, 3;
             15, 15, 15, 4];

% 定义RRT*算法参数
delta_q = 1;
max_iter = 1000;
goal_bias = 0.2;
rrt_star_step_size = 0.1;

% 初始化RRT*树
tree.vertices = start_pos;
tree.edges = [];

% 开始迭代
for i = 1:max_iter
    % 随机采样一个点
    if rand() < goal_bias
        q_rand = goal_pos;
    else
        q_rand = [randrange(xlim), randrange(ylim), randrange(zlim)];
    end
    
    % 寻找树中距离q_rand最近的节点
    [q_near, q_near_idx] = nearest_neighbor(q_rand, tree.vertices);
    
    % 在q_near和q_rand之间插入一个新节点q_new
    q_new = new_state(q_near, q_rand, delta_q);
    
    % 如果q_new不与障碍物相撞，则将其加入树中
    if ~collision(q_near, q_new, obstacles, rrt_star_step_size)
        % 对所有与q_new距离小于rrt_star_step_size的节点进行更新
        [near_indices, near_dists] = near_neighbors(q_new, tree.vertices, rrt_star_step_size);
        q_min = q_near;
        c_min = cost(q_near) + dist(q_near, q_new);
        for j = 1:length(near_indices)
            q_near_j = tree.vertices(near_indices(j), :);
            c_near_j = cost(q_near_j) + near_dists(j);
            if ~collision(q_near_j, q_new, obstacles, rrt_star_step_size) && c_near_j < c_min
                q_min = q_near_j;
                c_min = c_near_j;
            end
        end
        
        % 更新q_new的父节点和代价
        tree.vertices = [tree.vertices; q_new];
        tree.edges = [tree.edges; q_min, q_new];
        cost_from_start = cost(q_min) + dist(q_min, q_new);
        cost_to_goal = dist(q_new, goal_pos);
        tree.costs = [tree.costs; cost_from_start, cost_to_goal];
        tree.parents = [tree.parents; q_near_idx];
        
        % 如果q_new与目标点的距离小于rrt_star_step_size，则路径规划完成
        if dist(q_new, goal_pos) < rrt_star_step_size
            path = [q_new];
            parent_idx = length(tree.parents);
            while parent_idx > 0
                path = [tree.vertices(parent_idx, :); path];
                parent_idx = tree.parents(parent_idx);
            end
            break;
        end
    end
end

% 绘制结果
figure;
hold on;
plot3(start_pos(1), start_pos(2), start_pos(3), 'go', 'MarkerSize', 10, 'LineWidth', 2);
plot3(goal_pos(1), goal_pos(2), goal_pos(3), 'ro', 'MarkerSize', 10, 'LineWidth', 2);
for i = 1:size(obstacles, 1)
    draw_sphere(obstacles(i, 1:3), obstacles(i, 4));
end
for i = 1:size(tree.edges, 1)
    plot3(tree.edges(i, [1, 4]), tree.edges(i, [2, 5]), tree.edges(i, [3, 6]), '-b', 'LineWidth', 1);
end
plot3(path(:, 1), path(:, 2), path(:, 3), '-r', 'LineWidth', 2);
axis equal;
view(-30, 30);

% 辅助函数
function r = randrange(lim)
    r = lim(1) + rand() * (lim(2) - lim(1));
end

function [q_near, q_near_idx] = nearest_neighbor(q, vertices)
    [dists, idx] = pdist2(vertices, q, 'euclidean', 'Smallest', 1);
    q_near = vertices(idx, :);
    q_near_idx = idx(1);
end

function q_new = new_state(q_near, q_rand, delta_q)
    direction = (q_rand - q_near) / norm(q_rand - q_near);
    q_new = q_near + delta_q * direction;
end

function c = cost(q)
    global tree;
    idx = find(all(tree.vertices == q, 2));
    c = tree.costs(idx, 1);
end

function d = dist(q1, q2)
    d = norm(q1 - q2);
end

function [indices, dists] = near_neighbors(q, vertices, r)
    [dists, indices] = pdist2(vertices, q, 'euclidean', 'Smallest', inf);
    indices = indices(dists <= r);
    dists = dists(dists <= r);
end

function c = collision(q1, q2, obstacles, step_size)
    for i = 1:size(obstacles, 1)
        c = sphere_collision(q1, q2, obstacles(i, 1:3), obstacles(i, 4), step_size);
        if c
            return;
        end
    end
    c = false;
end

function c = sphere_collision(q1, q2, c, r, step_size)
    d = q2 - q1;
    n = ceil(norm(d) / step_size);
    for i = 0:n
        q = q1 + i * step_size * d / norm(d);
        if norm(q - c) < r
            c = true;
            return;
        end
    end
    c = false;
end

function draw_sphere(c, r)
    [x, y, z] = sphere();
    x = x * r + c(1);
    y = y * r + c(2);
    z = z * r + c(3);
    surf(x, y, z, 'FaceColor', [0.5, 0.5, 0.5], 'EdgeColor', 'none', 'FaceAlpha', 0.5);
end

这个程序使用了一些辅助函数，例如nearest_neighbor函数用于寻找距离某个点最近的树节点，new_state函数用于在树中插入一个新节点，collision函数用于检查节点之间是否存在障碍物等等。在运行程序之前，需要将这些辅助函数定义在程序之前或保存在单独的文件中。