编写一个路径规划A星算法代码matlab
时间: 2024-05-09 10:15:59 浏览: 115
以下是一个简单的 MATLAB 实现 A*(A-star)算法的示例代码:
```matlab
function [path, closed] = AStar(start, goal, map)
% A*算法的 MATLAB 实现
% 输入参数:
% start:起点的坐标
% goal:终点的坐标
% map:地图,0 表示可以通行,1 表示障碍物
% 返回值:
% path:路径,返回一个 n*2 的矩阵,n 表示路径节点数,第一列是 x 坐标,第二列是 y 坐标
% closed:经过的节点,返回一个 m*2 的矩阵,m 表示经过的节点数,第一列是 x 坐标,第二列是 y 坐标
% 初始化起点和终点节点
start_node.x = start(1);
start_node.y = start(2);
goal_node.x = goal(1);
goal_node.y = goal(2);
% 初始化 open 和 closed 列表
open = [start_node];
closed = [];
% 初始化节点的代价和父节点
for i = 1:size(map,1)
for j = 1:size(map,2)
node(i,j).f = Inf;
node(i,j).g = Inf;
node(i,j).h = Inf;
node(i,j).parent = [];
node(i,j).x = i;
node(i,j).y = j;
node(i,j).visited = false;
node(i,j).obstacle = map(i,j);
end
end
% 设置起点的代价
node(start_node.x, start_node.y).f = 0;
node(start_node.x, start_node.y).g = 0;
node(start_node.x, start_node.y).h = heuristic(start_node, goal_node);
% 开始搜索
while ~isempty(open)
% 找到 F 值最小的节点
[min_f, idx] = min([open.f]);
current = open(idx);
% 如果当前节点是终点,则搜索完成
if current.x == goal_node.x && current.y == goal_node.y
path = getPath(current);
return;
end
% 将当前节点从 open 列表中删除,并添加到 closed 列表中
open(idx) = [];
closed = [closed; current];
% 扩展当前节点的邻居节点
neighbors = getNeighbors(current, node);
for i = 1:length(neighbors)
neighbor = neighbors(i);
% 如果邻居节点已经在 closed 列表中,则跳过
if neighbor.visited
continue;
end
% 如果邻居节点没有被访问过,则更新其代价和父节点
if ~neighbor.visited
neighbor.g = current.g + distance(current, neighbor);
neighbor.h = heuristic(neighbor, goal_node);
neighbor.f = neighbor.g + neighbor.h;
neighbor.parent = current;
neighbor.visited = true;
open(end+1) = neighbor;
end
end
end
% 如果搜索完成后仍未找到终点,则返回空路径
path = [];
end
% 计算两个节点之间的距离
function dist = distance(node1, node2)
dist = sqrt((node1.x - node2.x)^2 + (node1.y - node2.y)^2);
end
% 计算节点到终点的启发式估价函数
function h = heuristic(node, goal)
h = sqrt((node.x - goal.x)^2 + (node.y - goal.y)^2);
end
% 获取从起点到当前节点的路径
function path = getPath(node)
path = [node.x node.y];
while ~isempty(node.parent)
node = node.parent;
path = [node.x node.y; path];
end
end
% 获取当前节点的邻居
function neighbors = getNeighbors(node, graph)
[x, y] = meshgrid(-1:1,-1:1);
x = x + node.x;
y = y + node.y;
valid = x >= 1 & y >= 1 & x <= size(graph,1) & y <= size(graph,2);
x = x(valid);
y = y(valid);
neighbors = [graph(x + (y-1)*size(graph,1))];
neighbors = neighbors(~[neighbors.obstacle] & ~[neighbors.visited]);
end
```
以上代码中,我们使用了以下几个函数:
- `AStar(start, goal, map)`:A* 算法的主函数,输入起点、终点和地图,返回路径和经过的节点。
- `distance(node1, node2)`:计算两个节点之间的距离。
- `heuristic(node, goal)`:计算节点到终点的启发式估价函数。
- `getPath(node)`:获取从起点到当前节点的路径。
- `getNeighbors(node, graph)`:获取当前节点的邻居。
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