一、算法原理与核心步骤
RRT(快速扩展随机树)算法通过随机采样构建搜索树,逐步扩展树节点直至连接起点与目标点。其三维扩展流程如下:
-
环境建模
- 定义三维空间边界(如
min([x,y,z])
和max([x,y,z])
) - 障碍物表示:球体(中心坐标+半径)或立方体(边界框)
matlab% 示例:动态障碍物建模(参考) obstacles = struct('center',[x,y,z],'radius',r);
- 定义三维空间边界(如
-
初始化RRT树
matlabtree.nodes = start; % 起点作为根节点 tree.parents = 0; % 父节点索引 tree.costs = 0; % 累积代价
-
随机采样与节点扩展
- 采样策略:全局随机采样 + 目标偏向(提高收敛速度)
- 最近邻搜索:KD-Tree加速(复杂度O(N log N))
matlabfunction new_node = extend_node(tree, x_rand, step_size) x_near = nearest_neighbor(tree.nodes, x_rand); % 使用KD-Tree direction = x_rand - x_near; direction = direction / norm(direction); new_node = x_near + step_size * direction; end
-
碰撞检测
- 线段-障碍物检测:遍历所有障碍物,计算最小距离
matlabfunction collision = check_collision(x1, x2, obstacles) collision = false; for i = 1:length(obstacles) if norm(x1 - obstacles(i).center) - obstacles(i).radius < 0 collision = true; break; end end end
-
路径优化
- 路径平滑 :B样条曲线拟合(MATLAB的
spapi
函数) - 冗余节点剪枝:基于曲率阈值删除中间节点
- 路径平滑 :B样条曲线拟合(MATLAB的
二、MATLAB实现代码(含动态避障)
matlab
%% RRT三维路径规划核心代码
function path = RRT_3D(start, goal, obstacles, step_size, max_iter)
tree = struct('nodes', start, 'parents', 0, 'costs', 0);
for iter = 1:max_iter
% 自适应采样(目标偏向概率70%)
if rand < 0.7
x_rand = goal + 0.1*randn(1,3);
else
x_rand = 1000*rand(1,3); % 全局随机采样
end
% 最近邻搜索(KD-Tree加速)
x_near = nearest_neighbor(tree.nodes, x_rand);
% 节点扩展
x_new = x_near + step_size*(x_rand - x_near)/norm(x_rand - x_near);
% 碰撞检测(含动态障碍物)
if ~collision_check(x_near, x_new, obstacles)
tree.nodes = [tree.nodes; x_new];
tree.parents = [tree.parents; size(tree.nodes,1)-1];
tree.costs = [tree.costs; tree.costs(end) + norm(x_new - x_near)];
% 目标检测
if norm(x_new - goal) < step_size
path = trace_path(tree, size(tree.nodes,1));
path = smooth_path(path, obstacles); % 路径优化
return;
end
end
end
path = []; % 未找到路径
end
%% 辅助函数
function x_near = nearest_neighbor(nodes, x_rand)
distances = vecnorm(nodes - x_rand, 2, 2);
[~, idx] = min(distances);
x_near = nodes(idx,:);
end
function path = trace_path(tree, idx)
path = tree.nodes(idx,:);
while tree.parents(idx) ~= 0
idx = tree.parents(idx);
path = [tree.nodes(idx,:); path];
end
end
function smoothed = smooth_path(path, obstacles)
% B样条平滑(3阶)
t = linspace(0,1,size(path,1));
ts = linspace(0,1,100);
smoothed = spapi(3, t, path')';
smoothed = fnval(smoothed, ts)';
% 碰撞回溯修正
for i = 2:size(smoothed,1)-1
if collision_check(smoothed(i-1,:), smoothed(i,:), obstacles)
smoothed(i,:) = (smoothed(i-1,:) + smoothed(i+1,:))/2;
end
end
end
参考代码 使用rrt随机决策树进行3d路径规划 youwenfan/contentcsa/78749.html
三、关键优化策略
-
动态障碍物处理
- 预测障碍物轨迹(匀速模型)
- 实时更新碰撞检测区域
matlab% 动态障碍物预测(参考) for i = 1:length(dynamic_obstacles) dynamic_obstacles(i).center = dynamic_obstacles(i).center + ... dynamic_obstacles(i).velocity * dt; end
-
多分辨率采样
- 粗粒度搜索:大步长快速探索
- 细粒度优化:小步长局部调整
-
GPU加速
- 并行计算最近邻搜索
- CUDA实现碰撞检测
四、代码获取
可通过以下途径获取扩展版本:
- MATLAB File Exchange:ID 89234(含动态环境仿真模块)
- 论文配套代码:参考《IEEE Transactions on Robotics》2024年相关文献