A*算法用matlab实现
时间: 2023-05-19 22:03:23 浏览: 123
可以使用以下代码实现A*算法:
function [path, cost] = A_star(start, goal, map)
% start: 起点坐标
% goal: 终点坐标
% map: 地图矩阵,1表示障碍物,0表示可通行
% path: 路径,每一行是一个坐标点
% cost: 路径的总代价
% 初始化起点和终点节点
start_node = Node(start, 0, heuristic(start, goal));
goal_node = Node(goal, Inf, 0);
% 初始化open和closed列表
open_list = [start_node];
closed_list = [];
while ~isempty(open_list)
% 从open列表中选取f值最小的节点
[current_node, idx] = min([open_list.f]);
current_node = open_list(idx);
% 如果当前节点是终点节点,返回路径和代价
if current_node == goal_node
path = get_path(current_node);
cost = current_node.g;
return;
end
% 将当前节点从open列表中删除,并加入closed列表
open_list(idx) = [];
closed_list = [closed_list, current_node];
% 扩展当前节点的邻居节点
neighbors = get_neighbors(current_node, map);
for i = 1:length(neighbors)
neighbor = neighbors(i);
% 如果邻居节点已经在closed列表中,跳过
if ismember(neighbor, closed_list)
continue;
end
% 计算邻居节点的代价
tentative_g = current_node.g + distance(current_node, neighbor);
% 如果邻居节点不在open列表中,或者新的代价更小,更新邻居节点
idx = find([open_list == neighbor]);
if isempty(idx) || tentative_g < open_list(idx).g
neighbor.g = tentative_g;
neighbor.h = heuristic(neighbor.pos, goal);
neighbor.f = neighbor.g + neighbor.h;
neighbor.parent = current_node;
if isempty(idx)
open_list = [open_list, neighbor];
else
open_list(idx) = neighbor;
end
end
end
end
% 如果open列表为空,表示无法到达终点
path = [];
cost = Inf;
end
function neighbors = get_neighbors(node, map)
% 获取当前节点的邻居节点
x = node.pos(1);
y = node.pos(2);
[n, m] = size(map);
% 邻居节点的坐标偏移量
offsets = [-1, 0; 0, -1; 1, 0; 0, 1];
neighbors = [];
for i = 1:size(offsets, 1)
nx = x + offsets(i, 1);
ny = y + offsets(i, 2);
% 如果邻居节点越界或者是障碍物,跳过
if nx < 1 || nx > n || ny < 1 || ny > m || map(nx, ny) == 1
continue;
end
% 创建邻居节点
neighbor = Node([nx, ny], Inf, Inf);
neighbors = [neighbors, neighbor];
end
end
function path = get_path(node)
% 获取路径
path = [];
while ~isempty(node)
path = [node.pos; path];
node = node.parent;
end
end
function d = distance(node1, node2)
% 计算两个节点之间的距离
d = norm(node1.pos - node2.pos);
end
function h = heuristic(pos1, pos2)
% 计算启发式函数值
h = norm(pos1 - pos2);
end
classdef Node
% 节点类
properties
pos % 坐标
g % 起点到该节点的代价
h % 该节点到终点的启发式函数值
f % 代价函数值
parent % 父节点
end
methods
function obj = Node(pos, g, h)
obj.pos = pos;
obj.g = g;
obj.h = h;
obj.f = g + h;
obj.parent = [];
end
end
end