dijkstra算法栅格图路径规划matlab代码
时间: 2023-09-08 15:10:27 浏览: 174
下面是Dijkstra算法在栅格图路径规划的MATLAB代码实现:
```matlab
function path = Dijkstra(grid, start, goal)
% 栅格图路径规划的Dijkstra算法实现
% 输入参数:
% grid:栅格地图
% start:起点坐标
% goal:终点坐标
% 返回值:
% path:从起点到终点的路径
% 初始化
[row, col] = size(grid); % 获取栅格地图的行列数
start_index = sub2ind([row, col], start(1), start(2)); % 将起点坐标转换为线性索引
goal_index = sub2ind([row, col], goal(1), goal(2)); % 将终点坐标转换为线性索引
dist = inf(row * col, 1); % 初始化起点到每个点的距离为无穷大
prev = zeros(row * col, 1); % 初始化每个点的前驱为0
visited = false(row * col, 1); % 初始化每个点为未访问
dist(start_index) = 0; % 起点到起点的距离为0
% 计算每个点的邻居
neighbours = [-1, 0; 1, 0; 0, -1; 0, 1; -1, -1; -1, 1; 1, -1; 1, 1]; % 8个邻居的相对坐标
neighbours_cost = [1; 1; 1; 1; sqrt(2); sqrt(2); sqrt(2); sqrt(2)]; % 8个邻居的代价
neighbours_index = repmat((1:(row * col))', 1, 8) + repmat(neighbours * [col; 1], row * col, 1); % 计算8个邻居的线性索引
neighbours_index = neighbours_index(all(neighbours_index > 0 & neighbours_index <= row * col, 2), :); % 过滤越界的邻居
% Dijkstra算法主循环
while true
% 选择未访问中距离最小的点
[~, current] = min(dist(~visited));
if isempty(current) || current == goal_index
break;
end
% 标记选中点为已访问
visited(current) = true;
% 更新所有邻居的距离
for i = 1:size(neighbours_index, 2)
neighbour = neighbours_index(current, i);
if ~visited(neighbour) && grid(neighbour) ~= -1
alt = dist(current) + neighbours_cost(i) * grid(neighbour);
if alt < dist(neighbour)
dist(neighbour) = alt;
prev(neighbour) = current;
end
end
end
end
% 没有找到终点,返回空路径
if prev(goal_index) == 0
path = [];
return;
end
% 从终点反向遍历路径
path = goal_index;
while path(1) ~= start_index
path = [prev(path(1)); path];
end
% 将线性索引转换为坐标
[path_row, path_col] = ind2sub([row, col], path);
path = [path_row, path_col];
```
该函数的输入参数包括栅格地图、起点坐标和终点坐标,返回值为从起点到终点的路径。栅格地图中的-1表示障碍物,0表示自由空间,1表示半自由空间。函数的实现过程与Dijkstra算法的一般实现类似,不同之处在于计算每个点的邻居时需要考虑8个方向。在计算邻居的代价时,对角线方向的代价为sqrt(2),其他方向的代价为1。