dijkstra法栅格地图路径规划matlab
时间: 2023-08-31 21:09:23 浏览: 206
Dijkstra算法是一种常用的最短路径算法,可以用于栅格地图路径规划。下面是一个简单的MATLAB代码实现,用于在给定的栅格地图中寻找起点到终点的最短路径。
```matlab
function [path, cost] = dijkstra(map, start, goal)
% DIJKSTRA Find the shortest path in a grid map using Dijkstra's algorithm
% [path, cost] = DIJKSTRA(map, start, goal) returns the shortest path
% between the start and goal points in the given map using Dijkstra's
% algorithm. The input map is a binary matrix where 0 represents an
% obstacle and 1 represents an open space. The input start and goal are
% vectors containing the row and column indices of the start and goal
% points, respectively. The output path is a matrix where each row
% represents a point on the path in the form [row, col]. The output cost
% is the total cost of the path.
% Initialize variables
[nrows, ncols] = size(map);
start_node = sub2ind([nrows ncols], start(1), start(2));
goal_node = sub2ind([nrows ncols], goal(1), goal(2));
cost = inf(nrows, ncols);
parent = zeros(nrows, ncols);
visited = false(nrows, ncols);
% Set the cost of the starting node to 0 and add it to the heap
cost(start_node) = 0;
heap = [start_node];
% Loop until the heap is empty or the goal node is visited
while ~isempty(heap)
% Get the node with the lowest cost
curr_node = heap(1);
heap(1) = [];
visited(curr_node) = true;
% Check if the goal node is reached
if curr_node == goal_node
break
end
% Get the neighbors of the current node
[row, col] = ind2sub([nrows ncols], curr_node);
neighbors = [];
if row > 1
neighbors = [neighbors; sub2ind([nrows ncols], row-1, col)];
end
if row < nrows
neighbors = [neighbors; sub2ind([nrows ncols], row+1, col)];
end
if col > 1
neighbors = [neighbors; sub2ind([nrows ncols], row, col-1)];
end
if col < ncols
neighbors = [neighbors; sub2ind([nrows ncols], row, col+1)];
end
% Loop through the neighbors and update their costs
for i = 1:length(neighbors)
neighbor = neighbors(i);
if visited(neighbor) || map(neighbor) == 0
continue
end
new_cost = cost(curr_node) + 1;
if new_cost < cost(neighbor)
cost(neighbor) = new_cost;
parent(neighbor) = curr_node;
heap = [heap neighbor];
end
end
% Reorder the heap based on the new costs
[~, idx] = sort(cost(heap));
heap = heap(idx);
end
% Reconstruct the path
path = [];
curr_node = goal_node;
while curr_node ~= start_node
path = [path; ind2sub([nrows ncols], curr_node)];
curr_node = parent(curr_node);
end
path = [path; ind2sub([nrows ncols], start_node)];
path = flipud(path);
cost = cost(goal_node);
end
```
该代码实现了Dijkstra算法的基本步骤,包括初始化变量、设置起点和终点、计算代价、更新代价等。在函数的最后,使用 parent 矩阵从终点到起点重构最短路径。你可以将地图作为二进制矩阵输入,并提供起点和终点的坐标作为输入来使用此函数。
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