无人机三维路径规划：蚁群、A* 与 RRT* 算法对比及 Matlab 实现

1.3 性能指标定量对比

关键数据解读：

• 能耗对比：改进蚁群算法能耗（64.08 J）低于 A*（72.93 J），因路径平滑减少姿态调整。
• 安全性：A* 在风险路径长度（0.15m）与危险路径长度（0.05m）上最优，因精确栅格碰撞检测。

1.4 环境适应性与场景推荐

1. 静态复杂环境：
   • A*：规则障碍物场景下路径最短，但计算耗时随复杂度飙升。
   • 蚁群算法：栅格建模灵活，适合非结构化地形，但收敛速度慢。
   • RRT*：正态采样改进后，节点数减少 85%，适合大型三维地图。
2. 动态障碍环境：
   • 蚁群算法：引入动态惩罚机制（AS-N），避障路径长度缩短 15%。
   • A*：需融合动态窗口法（DWA）提升实时性。
   • RRT*：实时采样避障成功率 100%。

1.5 总结与展望

• 算法融合趋势：
  • A* + 贝塞尔曲线：解决路径平滑问题。
  • RRT* + 梯度优化：提升初始路径质量。
  • 蚁群 + 动态惩罚机制：增强动态响应。
• 未来方向：轻量化神经网络加速在线规划，强化学习优化多目标权重。

具体应用需结合场景约束（如实时性要求、硬件算力）综合权衡。

2. Matlab 代码实现

下面给出主函数的实现逻辑，用于对比三种算法的运行结果。运行前请确保已添加对应的算法文件夹路径（如 ./ACO3D, ./Astar3D 等）。

% 清除工作区与命令窗口
clc; clear; close all;

% 载入函数路径
addpath(genpath('./ACO3D'))
addpath(genpath('./Astar3D'))
addpath(genpath('./RRT3D'))
addpath(genpath('./Evaluation'))

Algorithm_name = {'ACO', 'Astar', 'RRT'};
map = Makemap3D; % 地图规模在 Makemap3D 函数中设置
source = [10, 10, 1]; % 起点
goal = [450, 400, 50]; % 终点
max_item = 1000; % 最大迭代次数
comparative_data = {}; % 记录需要比较的内容
Global_data = {};
Straight_distance = sqrt(sum((source-goal).^2, 2)); % 直线距离
fprintf('起点到终点的直线距离：%d\n\n', Straight_distance);

Global_data(1,end+1) = {num2str(source)};
Global_data(1,end+1) = {num2str(goal)};
Global_data(1,end+1) = {Straight_distance};

t1 = clock;

%% ********蚁群算法********************************
figure(1)
plot3DMap(map);
text(source(1), source(2), source(3), '起点', 'color', 'r');
text(goal(1), goal(2), goal(3), '终点', 'color', 'r');
scatter3(source(1), source(2), source(3), "filled", "g");
scatter3(goal(1), goal(2), goal(3), "filled", "b");
title('ACO');
popNum = 10; % 蚁群数量
tic
[aco_path, aco_cost, aco_Number_of_searches, aco_Number_of_successful_searches, aco_Number_of_failed_searches] = aco(source, goal, map, popNum);
aco_time = toc;
fprintf('ACO 历时：%0.3f 秒\n', aco_time);
hold on
plot3(aco_path(:,1), aco_path(:,2), aco_path(:,3), 'LineWidth', 2, 'color', 'r');
view(-30, 30);
fprintf('ACO 路径长度：%d \n\n', aco_cost);
[aco_max_turning_angle, aco_turning_num, aco_index] = Max_turning_angle(aco_path, 1);
comparative_data(1,end+1) = {aco_time};
comparative_data(2,end) = {aco_cost};
comparative_data(3,end) = {size(aco_path,1)};
comparative_data(4,end) = {aco_Number_of_searches};
comparative_data(5,end) = {aco_Number_of_successful_searches};
comparative_data(6,end) = {aco_Number_of_successful_searches/aco_Number_of_searches};
comparative_data(7,end) = {aco_max_turning_angle};
comparative_data(8,end) = {aco_turning_num};

%% ************Astar********************************
figure(2)
plot3DMap(map);
text(source(1), source(2), source(3), '起点', 'color', 'r');
text(goal(1), goal(2), goal(3), '终点', 'color', 'r');
scatter3(source(1), source(2), source(3), "filled", "g");
scatter3(goal(1), goal(2), goal(3), "filled", "b");
title('Astar');
tic % 计算运行时间
[astar_path, astar_cost, astar_Number_of_searches, astar_Number_of_successful_searches, astar_Number_of_failed_searches] = Astar_main(source, goal, map, max_item);
astar_time = toc;
fprintf('Astar 历时：%0.3f 秒\n', astar_time);
plot3(astar_path(:,1), astar_path(:,2), astar_path(:,3), 'LineWidth', 2, 'color', 'r');
view(-30, 30);
fprintf('Astar 路径长度：%d\n\n', astar_cost);
[astar_max_turning_angle, astar_turning_num, astar_index] = Max_turning_angle(astar_path, 1);
comparative_data(1,end+1) = {astar_time};
comparative_data(2,end) = {astar_cost};
comparative_data(3,end) = {size(astar_path,1)};
comparative_data(4,end) = {astar_Number_of_searches};
comparative_data(5,end) = {astar_Number_of_successful_searches};
comparative_data(6,end) = {astar_Number_of_successful_searches/astar_Number_of_searches};
comparative_data(7,end) = {astar_max_turning_angle};
comparative_data(8,end) = {astar_turning_num};

%% ****************RRT********************************
figure(3)
plot3DMap(map);
text(source(1), source(2), source(3), '起点', 'color', 'r');
text(goal(1), goal(2), goal(3), '终点', 'color', 'r');
scatter3(source(1), source(2), source(3), "filled", "g");
scatter3(goal(1), goal(2), goal(3), "filled", "b");
title('RRT');
step = 10; % 设置步长
tic
[rrt_path, rrt_cost, rrt_Number_of_searches, rrt_Number_of_successful_searches, rrt_Number_of_failed_searches] = RRT_main(source, goal, map, step);
rrt_time = toc;
fprintf('RRT 历时：%0.3f 秒\n', rrt_time);
plot3(rrt_path(:,1), rrt_path(:,2), rrt_path(:,3), 'LineWidth', 2, 'color', 'r');
view(-30, 30);
fprintf('RRT 路径长度：%d \n\n', rrt_cost);
[rrt_max_turning_angle, rrt_turning_num, rrt_index] = Max_turning_angle(rrt_path, 1);
comparative_data(1,end+1) = {toc};
comparative_data(2,end) = {rrt_cost};
comparative_data(3,end) = {size(rrt_path,1)};
comparative_data(4,end) = {rrt_Number_of_searches};
comparative_data(5,end) = {rrt_Number_of_successful_searches};
comparative_data(6,end) = {rrt_Number_of_successful_searches/rrt_Number_of_searches};
comparative_data(7,end) = {rrt_max_turning_angle};
comparative_data(8,end) = {rrt_turning_num};

%% 打印运行时间
t2 = clock;
fprintf('程序总运行时间：%0.3f 秒\n\n', etime(t2,t1));

% 计算最优项，其中展示表格顺序为 aco、astar、rrt
comparative_data(1,end+1) = {Algorithm_name{Min_value(comparative_data{1,1}, comparative_data{1,2}, comparative_data{1,3})}};
for i = 2:size(comparative_data,1)
    % 求每行的最小值
    comparative_data(i,end) = {Algorithm_name{Min_value(comparative_data{i,1}, comparative_data{i,2}, comparative_data{i,3})}};
end
% 求最大值
comparative_data(6,end) = {Algorithm_name{Max_value(comparative_data{6,1}, comparative_data{6,2}, comparative_data{6,3})}};

% 展示比较结果
Show_Comparative_result(Global_data, comparative_data)

% 三种算法展示到一张图中
figure(4)
plot3DMap(map);
text(source(1), source(2), source(3), '起点', 'color', 'r');
text(goal(1), goal(2), goal(3), '终点', 'color', 'r');
h1 = plot3(aco_path(:,1), aco_path(:,2), aco_path(:,3), 'LineWidth', 2, 'color', 'r');
h2 = plot3(astar_path(:,1), astar_path(:,2), astar_path(:,3), 'LineWidth', 2, 'color', 'k');
h3 = plot3(rrt_path(:,1), rrt_path(:,2), rrt_path(:,3), 'LineWidth', 2, 'color', 'm');
legend([h1,h2,h3], '蚁群', 'A*', 'RRT')

3. 参考文献

[1] 陆璐，孙昱浩，孙启光。基于改进蚁群算法的无人机三维路径规划研究 [J].广东交通职业技术学院学报，2025,24(01):46-51+114.

[2] 温佳霖，梁丰，许雯。基于改进蚁群算法的无人机三维路径规划研究 [J].现代信息科技，2023,7(20):84-87+91.DOI:10.19850/j.cnki.2096-4706.2023.20.018.