在MATLAB中实现一个智能小车的路径规划系统，我们可以采用多种方法，包括基于图的搜索算法（如A算法）、基于采样的方法（如RRT - Rapidly-exploring Random Trees）、或者更复杂的基于优化的方法（如模型预测控制MPC）。这里，我将以AI算法为例，展示如何在MATLAB中实现一个简单的路径规划系统。
步骤 1: 准备环境
首先，我们需要定义小车的运行环境，这通常是一个二维的网格图。每个网格可以是可通行的或不可通行的。
% 创建一个简单的网格图 |
|
gridSize = 50; |
|
grid = zeros(gridSize); |
|
% 设置障碍 |
|
grid(10:15, 10:15) = 1; |
|
grid(30:35, 30:35) = 1; |
|
% 显示网格 |
|
figure; |
|
imagesc(grid); |
|
colormap([1 1 1; 0 0 0]); % 白色为可行走，黑色为障碍 |
|
axis equal; |
|
axis image; |
|
grid on; |
|
hold on; |
步骤 2: 实现AI算法
AI算法是一种启发式搜索算法，它结合了最好优先搜索和Dijkstra算法的优点。我们需要定义启发式函数（如曼哈顿距离或欧几里得距离）来评估节点到终点的距离。
function [path, cost] = astar(start, goal, grid) |
|
% 初始化 |
|
openSet = containers.Map('KeyType', 'any', 'ValueType', 'any'); |
|
openSet(num2str(start)) = struct('f', 0, 'g', 0, 'parent', [], 'x', start(1), 'y', start(2)); |
|
closedSet = containers.Map('KeyType', 'any', 'ValueType', 'logical', 'DefaultValue', false); |
|
% 启发式函数（曼哈顿距离） |
|
heuristic = @(x1, y1, x2, y2) abs(x1 - x2) + abs(y1 - y2); |
|
% 主循环 |
|
while ~isempty(openSet) |
|
% 查找F值最小的节点 |
|
[~, currentIdx] = min(arrayfun(@(k) openSet(k).f, keys(openSet))); |
|
current = openSet(num2str(currentIdx)); |
|
% 如果到达目标 |
|
if current.x == goal(1) && current.y == goal(2) |
|
path = backtrack(current, goal); |
|
return; |
|
end |
|
% 扩展节点 |
|
[x, y] = ndgrid(current.x-1:current.x+1, current.y-1:current.y+1); |
|
x = x(:); |
|
y = y(:); |
|
validMoves = (x >= 1 & x <= size(grid, 1) & y >= 1 & y <= size(grid, 2) & grid(x, y) == 0); |
|
for i = validMoves |
|
neighbor = [x(i), y(i)]; |
|
tentativeGScore = current.g + 1; |
|
if ~closedSet(num2str(neighbor)) || tentativeGScore < openSet(num2str(neighbor)).g |
|
openSet(num2str(neighbor)) = struct(... |
|
'f', tentativeGScore + heuristic(neighbor(1), neighbor(2), goal(1), goal(2)), ... |
|
'g', tentativeGScore, ... |
|
'parent', currentIdx, ... |
|
'x', neighbor(1), ... |
|
'y', neighbor(2)); |
|
end |
|
end |
|
% 移除当前节点 |
|
closedSet(num2str(currentIdx)) = true; |
|
remove(openSet, num2str(currentIdx)); |
|
end |
|
% 如果找不到路径 |
|
path = []; |
|
cost = inf; |
|
end |
|
function path = backtrack(current, goal) |
|
if isempty(current.parent) |
|
path = [goal;]; |
|
else |
|
path = backtrack(openSet(num2str(current.parent)), goal); |
|
path = [current.x, current.y; path]; |
|
end |
|
end |
步骤 3: 调用AI算法并显示路径
start = [1, 1]; |
|
goal = [45, 45]; |
|
[path, cost] = astar(start, goal, grid); |
|
% 绘制 |