A*算法 (MATLAB) 路径搜索

A* 算法跟 Dijkstra 算法 很像，只是在下一步搜索中心的选择的方法不一样。Dijkstra 算法 没有任何干预，找离起点 “最近”的邻居作为备选点，如果有若干个邻居都是相同距离的话，纯粹就是按照找到的顺序取第一个。A*算法，找与终点最近的邻居，作为下一个搜索中心。(不过，如果若干个邻居与终点的距离一样呢？)

下面的代码是从 Dijkstra 算法 拷贝来的，四个黄色的部分是修改的。

第二个黄色部分: 找与终点最近的邻居作为下一个搜索点。
[~, current] = min(f(:));

f=f(:)什么意思

%将矩阵f的每一列元素堆积起来，成为一个列向量，而这也是MATLAB变量的内部储存方式。例如：

A=[-45 65;87 64;23 54];
B=A(:)
B=

-45
87
23
65
64
23
54

[min_dist, ~] = min(distanceFromStart(:));

在

Dijkstra 算法

里，这部分是：[min_dist, current] = min(distanceFromStart(:));

第三个黄色部分: 排除已经作为搜索点的邻居再次被 min 到的可能性f(current) = Inf; 在

Dijkstra 算法

里，这部分是：distanceFromStart(current) = Inf;

第四个黄色部分是新增加的：就是为了计算每一个邻居与终点的距离权值。只不过这里的距离权值预先计算好了放在H矩阵里，所以直需要从 H 里取值就好了。

所以第一黄色部分：定义f,计算H

[X, Y] = meshgrid (1:ncols, 1:nrows); 

H = abs(Y - 4) + abs(X - 8); 

f = Inf(nrows,ncols); 

f(start_node) = H(start_node); 

H 有很多种计算方法，可以直接算两点距离之类。

%% % set up color map for display
cmap = [1 1 1; ...% 1 - white - clear cell
0 0; ...% 2 - black - obstacle
0 0; ...% 3 - red = visited
0 1; ...% 4 - blue - on list
1 0; ...% 5 - green - start
1 0];% 6 - yellow - destination
colormap(cmap);
map = zeros(10);
% Add an obstacle
map (1:5, 7) = 2;
map(6, 2) = 5; % start_coords
map(4, 8) = 6; % dest_coords
image(1.5,1.5,map);
grid on;
axis image;
%%
nrows = 10;
ncols = 10;
start_node = sub2ind(size(map), 6, 2);
dest_node = sub2ind(size(map), 4, 8);
% Initialize distance array
distanceFromStart = Inf(nrows,ncols);
distanceFromStart(start_node) = 0;

%====================
[X, Y] = meshgrid (1:ncols, 1:nrows);
H = abs(Y - 4) + abs(X - 8);
f = Inf(nrows,ncols);
f(start_node) = H(start_node);
%=======================
% For each grid cell this array holds the index of its parent
parent = zeros(nrows,ncols);
% Main Loop
while true
% Draw current map
map(start_node) = 5;
map(dest_node) = 6;
image(1.5, 1.5, map);
grid on;
axis image;
drawnow;
%====================
% Find the node with the minimum distance
[
~, current] = min(f(:)); [min_dist, ~] =
min(distanceFromStart(:));
%===================
if ((current == dest_node) || isinf(min_dist))
break;
end;

map(current) = 3;
%============
f(current)
=
Inf;
%============
[i, j] = ind2sub(size(distanceFromStart), current);

neighbor = [i-1,j;...
i+1,j;...
i,j+1;...
i,j-1]
outRangetest = (neighbor(:,1)<1) + (neighbor(:,1)>nrows) +...
(neighbor(:,2)<1) + (neighbor(:,2)>ncols )
locate = find(outRangetest>0);
neighbor(locate,:)=[]
neighborIndex = sub2ind(size(map),neighbor(:,1),neighbor(:,2))
for i=1:length(neighborIndex)
if (map(neighborIndex(i))~=2) && (map(neighborIndex(i))~=3 && map(neighborIndex(i))~= 5)
map(neighborIndex(i)) = 4;
if distanceFromStart(neighborIndex(i))> min_dist + 1
distanceFromStart(neighborIndex(i)) = min_dist+1;
parent(neighborIndex(i)) = current;
f(neighborIndex(i))
=
H(neighborIndex(i));
end
end
end
end
%%
if (isinf(distanceFromStart(dest_node)))
route = [];
else
%提取路线坐标
route = [dest_node];
while (parent(route(1)) ~= 0)
route = [parent(route(1)), route];
end
% 动态显示出路线
for k = 2:length(route) - 1
map(route(k)) = 7;
pause(0.1);
image(1.5, 1.5, map);
grid on;
axis image;
end
end