请给matlab一个完整的三维A*算法,且障碍物可移动
时间: 2023-06-24 08:09:28 浏览: 91
基于Matlab的无人机三维路径规划A*算法
以下是一个基本的 MATLAB 三维 A* 算法实现,其中障碍物可移动:
```matlab
function [path, closedList] = Astar3D(map, start, goal)
% map: 3D地图,0表示自由空间,1表示障碍物
% start: 起点坐标,格式为[x,y,z]
% goal: 终点坐标,格式为[x,y,z]
% path: 返回路径,格式为一个nx3的矩阵,每一行表示路径上的一个节点
% closedList: 返回搜索过程中的关闭列表,格式为一个nx4的矩阵,
% 每一行表示一个节点的坐标和它的f值
% 初始化起点和终点节点
startNode = Node(start, 0, 0, 0);
goalNode = Node(goal, 0, 0, 0);
% 初始化开放列表和关闭列表
openList = [startNode];
closedList = [];
while ~isempty(openList)
% 选取f值最小的节点进行扩展
currentNode = openList(1);
currentIndex = 1;
for i = 1:length(openList)
if openList(i).f < currentNode.f
currentNode = openList(i);
currentIndex = i;
end
end
% 如果当前节点是终点,则返回路径
if isequal(currentNode.position, goalNode.position)
path = [];
while ~isequal(currentNode.position, startNode.position)
path = [currentNode.position; path];
currentNode = currentNode.parent;
end
path = [startNode.position; path];
return;
end
% 从开放列表中移除当前节点,并将其加入关闭列表
openList(currentIndex) = [];
closedList = [closedList; currentNode];
% 扩展当前节点的邻居节点
neighbors = getNeighbors(map, currentNode);
for i = 1:length(neighbors)
neighbor = neighbors(i);
% 如果邻居节点已经在关闭列表中,则忽略
if any(isequal(neighbor.position, closedList.position, 'rows'))
continue;
end
% 计算邻居节点的g值和f值
tentativeGCost = currentNode.g + neighbor.cost;
if ~any(isequal(neighbor.position, openList.position, 'rows'))
openList = [openList; neighbor];
elseif tentativeGCost >= neighbor.g
continue;
end
neighbor.parent = currentNode;
neighbor.g = tentativeGCost;
neighbor.h = heuristic(neighbor.position, goalNode.position);
neighbor.f = neighbor.g + neighbor.h;
end
end
% 如果开放列表为空且没有找到路径,则返回空
path = [];
end
function neighbors = getNeighbors(map, node)
% 获取邻居节点
x = node.position(1);
y = node.position(2);
z = node.position(3);
deltas = [-1,0,0; 1,0,0; 0,-1,0; 0,1,0; 0,0,-1; 0,0,1];
neighbors = [];
for i = 1:size(deltas,1)
dx = deltas(i,1);
dy = deltas(i,2);
dz = deltas(i,3);
if x+dx>0 && x+dx<=size(map,1) && y+dy>0 && y+dy<=size(map,2) && z+dz>0 && z+dz<=size(map,3)
if map(x+dx, y+dy, z+dz) == 0
neighbors = [neighbors; Node([x+dx,y+dy,z+dz],0,0,0)];
end
end
end
% 计算邻居节点的代价
for i = 1:length(neighbors)
neighbors(i).cost = norm(neighbors(i).position - node.position);
end
end
function h = heuristic(position, goal)
% 计算启发式估价函数
h = norm(position - goal);
end
classdef Node
% 表示一个节点
properties
position % 节点的坐标,格式为[x,y,z]
parent % 父节点
g % 节点到起点的代价
h % 节点到终点的启发式估价
f % 节点的f值
cost % 节点的代价
end
methods
function obj = Node(position, g, h, f)
obj.position = position;
obj.g = g;
obj.h = h;
obj.f = f;
end
end
end
```
在这个实现中,我们定义了 `Node` 类来表示搜索过程中的节点,其中包括节点的位置、父节点、g 值、h 值、f 值和代价。我们还定义了 `getNeighbors` 函数来获取当前节点的邻居节点,并计算它们的代价。启发式估价函数使用欧几里得距离。
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