Dijkstra算法—栅格地图最短路径

Posted 2021-05-26 北极星！

 

matlab中sub2ind函数

Dijkstra算法代码示例

主程序

% 基于栅格地图的机器人路径规划算法
% 第2节：Dijkstra算法
clc
clear
close all

%% 栅格界面、场景定义
% 行数和列数
rows = 10;
cols = 20;
[field,cmap] = defColorMap(rows, cols);

% 起点、终点、障碍物区域
startPos = 2;
goalPos = rows*cols-2;
field(startPos) = 4;
field(goalPos) = 5;

%% 算法初始化
% S/U的第一列表示栅格节点-线性索引编号
% 对于S，第二列表示从源节点到本节点已求得的最小距离，不再变更；
% 对于U，第二列表示从源节点到本节点暂时求得的最小距离，可能会变更
U(:,1) = (1: rows*cols)\';
U(:,2) = inf;
S = [startPos, 0];
U(startPos,:) = [];

% 更新起点的邻节点及代价
neighborNodes = getNeighborNodes(rows, cols, startPos, field);
for i = 1:8
    childNode = neighborNodes(i,1);
    
    % 判断该子节点是否存在
    if ~isinf(childNode)
        idx = find(U(:,1) == childNode);
        U(idx,2) = neighborNodes(i,2);
    end
end



% U集合的最优路径集合
for i = 1:rows*cols
    path{i,1} = i;
end
for i = 1:8
    childNode =  neighborNodes(i,1);
    if ~isinf(neighborNodes(i,2))
        path{childNode,2} = [startPos,neighborNodes(i,1)];
    end
end


%% 循环遍历
while ~isempty(U)
    
    % 在U集合找出当前最小距离值的节点,视为父节点，并移除该节点至S集合中
    [dist_min, idx] = min(U(:,2));
    parentNode = U(idx, 1);
    S(end+1,:) = [parentNode, dist_min];
    U(idx,:) = [];
    
    % 获得当前节点的临近子节点
    neighborNodes = getNeighborNodes(rows, cols, parentNode, field);

    % 依次遍历邻近子节点，判断是否在U集合中更新邻节点的距离值
    for i = 1:8
        
        % 需要判断的子节点
        childNode = neighborNodes(i,1);
        cost = neighborNodes(i,2);
        if ~isinf(childNode)  && ~ismember(childNode, S)
            
            % 找出U集合中节点childNode的索引值
            idx_U = find(childNode == U(:,1));            
            
            % 判断是否更新
            if dist_min + cost < U(idx_U, 2)
                U(idx_U, 2) = dist_min + cost;
                
                % 更新最优路径
                path{childNode, 2} = [path{parentNode, 2}, childNode];
            end
        end
    end
end


%% 画栅格界面
% 找出目标最优路径
path_opt = path{goalPos,2};
field(path_opt(2:end-1)) = 6;

% 画栅格图
image(1.5,1.5,field);
grid on;
set(gca,\'gridline\',\'-\',\'gridcolor\',\'k\',\'linewidth\',2,\'GridAlpha\',0.5);
set(gca,\'xtick\',1:cols+1,\'ytick\',1:rows+1);
axis image;

 defColorMap（）函数

function [field,cmap] = defColorMap(rows, cols)
cmap = [1 1 1; ...       % 1-白色-空地
    0 0 0; ...           % 2-黑色-静态障碍
    1 0 0; ...           % 3-红色-动态障碍
    1 1 0;...            % 4-黄色-起始点 
    1 0 1;...            % 5-品红-目标点
    0 1 0; ...           % 6-绿色-到目标点的规划路径   
    0 1 1];              % 7-青色-动态规划的路径

% 构建颜色MAP图
colormap(cmap);

% 定义栅格地图全域，并初始化空白区域
field = ones(rows, cols);

% 障碍物区域
obsRate = 0.3;
obsNum = floor(rows*cols*obsRate);
obsIndex = randi([1,rows*cols],obsNum,1);
field(obsIndex) = 2;

getNeighborNodes（）函数

function neighborNodes = getNeighborNodes(rows, cols, lineIndex, field)
[row, col] = ind2sub([rows,cols], lineIndex);
neighborNodes = inf(8,2);

%% 查找当前父节点临近的周围8个子节点
% 1.左上节点
% neighborNodes有两列，第一列保存邻接点线性索引值，第二列保存到邻接点的花费
if row-1 > 0 && col-1 > 0
    child_node_sub = [row-1, col-1];
    child_node_line = sub2ind([rows,cols], child_node_sub(1), child_node_sub(2));  % 将child_node_sub = [row-1, col-1];变成线性索引值
    neighborNodes(1,1) = child_node_line;
    if field(child_node_sub(1), child_node_sub(2)) ~= 2   % 判断邻接点是不是障碍物节点
        cost = norm(child_node_sub - [row, col]);    % 计算到邻接点的花费（非障碍物邻接点）
        neighborNodes(1,2) = cost;
    end
end

% 2.上节点
if row-1 > 0
    child_node_sub = [row-1, col];
    child_node_line = sub2ind([rows,cols], child_node_sub(1), child_node_sub(2));
    neighborNodes(2,1) = child_node_line;
    if field(child_node_sub(1), child_node_sub(2)) ~= 2
        cost = norm(child_node_sub - [row, col]);
        neighborNodes(2,2) = cost;
    end
end

% 3.右上节点
if row-1 > 0 && col+1 <= cols
    child_node_sub = [row-1, col+1];
    child_node_line = sub2ind([rows,cols], child_node_sub(1), child_node_sub(2));
    neighborNodes(3,1) = child_node_line;
    if field(child_node_sub(1), child_node_sub(2)) ~= 2
        cost = norm(child_node_sub - [row, col]);
        neighborNodes(3,2) = cost;
    end
end

% 4.左节点
if  col-1 > 0
    child_node_sub = [row, col-1];
    child_node_line = sub2ind([rows,cols], child_node_sub(1), child_node_sub(2));
    neighborNodes(4,1) = child_node_line;
    if field(child_node_sub(1), child_node_sub(2)) ~= 2
        cost = norm(child_node_sub - [row, col]);
        neighborNodes(4,2) = cost;
    end
end

% 5.右节点
if  col+1 <= cols
    child_node_sub = [row, col+1];
    child_node_line = sub2ind([rows,cols], child_node_sub(1), child_node_sub(2));
    neighborNodes(5,1) = child_node_line;
    if field(child_node_sub(1), child_node_sub(2)) ~= 2
        cost = norm(child_node_sub - [row, col]);
        neighborNodes(5,2) = cost;
    end
end

% 6.左下节点
if row+1 <= rows && col-1 > 0
    child_node_sub = [row+1, col-1];
    child_node_line = sub2ind([rows,cols], child_node_sub(1), child_node_sub(2));
    neighborNodes(6,1) = child_node_line;
    if field(child_node_sub(1), child_node_sub(2)) ~= 2
        cost = norm(child_node_sub - [row, col]);
        neighborNodes(6,2) = cost;
    end
end

% 7.下节点
if row+1 <= rows
    child_node_sub = [row+1, col];
    child_node_line = sub2ind([rows,cols], child_node_sub(1), child_node_sub(2));
    neighborNodes(7,1) = child_node_line;
    if field(child_node_sub(1), child_node_sub(2)) ~= 2
        cost = norm(child_node_sub - [row, col]);
        neighborNodes(7,2) = cost;
    end
end

% 8.右下节点
if row+1 <= rows && col+1 <= cols
    child_node_sub = [row+1, col+1];
    child_node_line = sub2ind([rows,cols], child_node_sub(1), child_node_sub(2));
    neighborNodes(8,1) = child_node_line;
    if field(child_node_sub(1), child_node_sub(2)) ~= 2
        cost = norm(child_node_sub - [row, col]);
        neighborNodes(8,2) = cost;
    end
end

 

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