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(:));
[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 0; ...% 2 - black - obstacle 
               1 0 0; ...% 3 - red = visited 
               0 0 1; ...% 4 - blue - on list 
               0 1 0; ...% 5 - green - start 
               1 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