【路径规划】基于matlab GUI A_star算法最短路径规划【含Matlab源码 633期】

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二、A_star算法简介

1 A Star算法及其应用现状
进行搜索任务时提取的有助于简化搜索过程的信息被称为启发信息.启发信息经过文字提炼和公式化后转变为启发函数.启发函数可以表示自起始顶点至目标顶点间的估算距离, 也可以表示自起始顶点至目标顶点间的估算时间等.描述不同的情境、解决不同的问题所采用的启发函数各不相同.我们默认将启发函数命名为H (n) .以启发函数为策略支持的搜索方式我们称之为启发型搜索算法.在救援机器人的路径规划中, A Star算法能结合搜索任务中的环境情况, 缩小搜索范围, 提高搜索效率, 使搜索过程更具方向性、智能性, 所以A Star算法能较好地应用于机器人路径规划相关领域.

2 A Star算法流程
承接2.1节, A Star算法的启发函数是用来估算起始点到目标点的距离, 从而缩小搜索范围, 提高搜索效率.A Star算法的数学公式为:F (n) =G (n) +H (n) , 其中F (n) 是从起始点经由节点n到目标点的估计函数, G (n) 表示从起点移动到方格n的实际移动代价, H (n) 表示从方格n移动到目标点的估算移动代价.

如图2所示, 将要搜寻的区域划分成了正方形的格子, 每个格子的状态分为可通过(walkable) 和不可通过 (unwalkable) .取每个可通过方块的代价值为1, 且可以沿对角移动 (估值不考虑对角移动) .其搜索路径流程如下:

图2 A Star算法路径规划
Step1:定义名为open和closed的两个列表;open列表用于存放所有被考虑来寻找路径的方块, closed列表用于存放不会再考虑的方块;
Step2:A为起点, B为目标点, 从起点A开始, 并将起点A放入open列表中, closed列表初始化为空;
Step3:查看与A相邻的方格n (n称为A的子点, A称为n的父点) , 可通过的方格加入到open列表中, 计算它们的F, G和H值.将A从open移除加入到closed列表中;
Step4:判断open列表是否为空, 如果是, 表示搜索失败, 如果不是, 执行下一步骤;
Step5:将n从open列表移除加入到closed列表中, 判断n是否为目标顶点B, 如果是, 表示搜索成功, 算法运行结束;
Step6:如果不是, 则扩展搜索n的子顶点:
a.如果子顶点是不可通过或在close列表中, 忽略它.
b.子顶点如果不在open列表中, 则加入open列表, 并且把当前方格设置为它的父亲, 记录该方格的F, G和H值.
Step7:跳转到步骤Step4;
Step8:循环结束, 保存路径.从终点开始, 每个方格沿着父节点移动直至起点, 即是最优路径.A Star算法流程图如图3所示.

图3 A Star算法流程

三、部分源代码

function varargout = A_GUI(varargin)
% A_GUI MATLAB code for A_GUI.fig
%      A_GUI, by itself, creates a new A_GUI or raises the existing
%      singleton*.
%
%      H = A_GUI returns the handle to a new A_GUI or the handle to
%      the existing singleton*.
%
%      A_GUI('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in A_GUI.M with the given input arguments.
%
%      A_GUI('Property','Value',...) creates a new A_GUI or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before A_GUI_OpeningFcn gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to A_GUI_OpeningFcn via varargin.
%
%      *See GUI Options on GUIDE's Tools menu.  Choose "GUI allows only one
%      instance to run (singleton)".
%
% See also: GUIDE, GUIDATA, GUIHANDLES% Edit the above text to modify the response to help A_GUI% Last Modified by GUIDE v2.5 21-Oct-2018 17:10:48% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...'gui_Singleton',  gui_Singleton, ...'gui_OpeningFcn', @A_GUI_OpeningFcn, ...'gui_OutputFcn',  @A_GUI_OutputFcn, ...'gui_LayoutFcn',  [] , ...'gui_Callback',   []);
if nargin && ischar(varargin{1})gui_State.gui_Callback = str2func(varargin{1});
endif nargout[varargout{1:nargout}] = gui_mainfcn(gui_State, varargin{:});
elsegui_mainfcn(gui_State, varargin{:});
end
% End initialization code - DO NOT EDIT% --- Executes just before A_GUI is made visible.
function A_GUI_OpeningFcn(hObject, eventdata, handles, varargin)
% This function has no output args, see OutputFcn.
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)
% varargin   command line arguments to A_GUI (see VARARGIN)% Choose default command line output for A_GUI
handles.output = hObject;% Update handles structure
guidata(hObject, handles);% UIWAIT makes A_GUI wait for user response (see UIRESUME)
% uiwait(handles.figure1);% --- Outputs from this function are returned to the command line.
function varargout = A_GUI_OutputFcn(hObject, eventdata, handles)
% varargout  cell array for returning output args (see VARARGOUT);
% hObject    handle to figure
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)% Get default command line output from handles structure
varargout{1} = handles.output;% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton1 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)% set up color map for display 生成彩色地图
global cmap;
global map;
global n_r;
global n_c;
global state;cmap = [1 1 1; ...% 1 -白色-无障碍0 0 0; ...% 2 -黑色-有障碍0 0.8 0; ...% 3 -绿色-已搜索0 0.4 0; ...% 4 -粉色-正在搜索0 1 1; ...% 5 -浅蓝色-起始点1 1 0; ...% 6 -黄色-目标点0 0 1];   % 7 -蓝色-最终路径
colormap(cmap);
%生成随机地图
map = zeros(n_r,n_c);
randmap = rand(n_r,n_c);
for i = 2:(sub2ind(size(randmap),n_r,n_c)-1)if (randmap(i) >= 0.75)map(i) = 2;end
endmap(1, 1) = 5; % start_coords 起点坐标
map(n_r, n_c) = 6; % dest_coords 终点坐标
image(1.5,1.5,map);
grid on;
axis image;
set(handles.text5,'string','随机地图生成完毕');% --- Executes on button press in pushbutton2.
function pushbutton2_Callback(hObject, eventdata, handles)
% hObject    handle to pushbutton2 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    structure with handles and user data (see GUIDATA)%搜索最佳路径
global n_r;
global n_c;
global cmap;
global map;
global state;nrows = n_r;
ncols = n_c;
start_node = sub2ind(size(map), 1, 1);
%sub2ind()函数将矩阵中的某个元素的线性序号计算出来
%线性索引号例子：2*2矩阵[1 3;中，1是第一个，5是第二个
%                       5 7]  ，3是第三个，7是第四个
%（matlab是列优先，不是我们通常习惯的行优先）
dest_node = sub2ind(size(map), n_r, n_c);
% Initialize distance array 初始化距离数组
distanceFromStart = Inf(nrows,ncols);
distanceFromStart(start_node) = 0 ;[X, Y] = meshgrid (1:ncols, 1:nrows);
H = abs(Y - n_r) + abs(X - n_c);
f = Inf(nrows,ncols);
f(start_node) = H(start_node); % For each grid cell this array holds the index of its parent 对于每个网格单元，该数组都保存其父单元的索引
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; %网格axis image; %显示坐标drawnow; %刷新屏幕% Find the node with the minimum distance 找到距离最短的节点
%   [min_dist, current] = min(distanceFromStart(:));
[~, current] = min(f(:)); [min_dist, ~] = min(distanceFromStart(:));if ((current == dest_node) || isinf(min_dist)) %TF = isinf(A) 　返回一个和A尺寸一样的数组， 如果A中某个元素是inf  (无穷)， 则对应TF中元素是1， 否则TF中对应元素是0。 break; end; %搜索中心的索引坐标：current,%搜索中心与起始点的路程：min_dist% 这两个值后面会用。map(current) = 3;
%   distanceFromStart(current) = Inf;
f(current) = Inf; [i, j] = ind2sub(size(distanceFromStart), current); %索引号变为坐标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);  %返回outRangetest中大于0的元素的相对应的线性索引值。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)); % pause(0.02); end end end end
% %%if (isinf(distanceFromStart(dest_node))) %route = [];disp('路径搜索失败');set(handles.text5,'string','路径搜索失败');else %提取路线坐标set(handles.text5,'string','路径搜索成功');route = [dest_node];while (parent(route(1)) ~= 0) route(1);parent(route(1))route = [parent(route(1)), route] ;end

四、运行结果

五、matlab版本及参考文献

1 matlab版本
2014a

2 参考文献
[1] 包子阳,余继周,杨杉.智能优化算法及其MATLAB实例（第2版）[M].电子工业出版社，2016.
[2]张岩,吴水根.MATLAB优化算法源代码[M].清华大学出版社，2017.
[3]钱程,许映秋,谈英姿.A Star算法在RoboCup救援仿真中路径规划的应用[J].指挥与控制学报. 2017,3(03)