【路径规划】基于matlab A_star算法机器人动态避障路径规划【含Matlab源码 1033期】

一、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

二、部分源代码

function varargout = Astar(varargin)
% ASTAR MATLAB code for Astar.fig
%      ASTAR, by itself, creates a new ASTAR or raises the existing
%      singleton*.
%
%      H = ASTAR returns the handle to a new ASTAR or the handle to
%      the existing singleton*.
%
%      ASTAR('CALLBACK',hObject,eventData,handles,...) calls the local
%      function named CALLBACK in ASTAR.M with the given input arguments.
%
%      ASTAR('Property','Value',...) creates a new ASTAR or raises the
%      existing singleton*.  Starting from the left, property value pairs are
%      applied to the GUI before Astar_OpeningFcn gets called.  An
%      unrecognized property name or invalid value makes property application
%      stop.  All inputs are passed to Astar_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 Astar% Last Modified by GUIDE v2.5 30-Oct-2020 10:58:46% Begin initialization code - DO NOT EDIT
gui_Singleton = 1;
gui_State = struct('gui_Name',       mfilename, ...'gui_Singleton',  gui_Singleton, ...'gui_OpeningFcn', @Astar_OpeningFcn, ...'gui_OutputFcn',  @Astar_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 Astar is made visible.
function Astar_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 Astar (see VARARGIN)% Choose default command line output for Astar
handles.output = hObject;% Update handles structure
guidata(hObject, handles);% UIWAIT makes Astar wait for user response (see UIRESUME)
% uiwait(handles.figure1);% --- Outputs from this function are returned to the command line.
function varargout = Astar_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 during object creation, after setting all properties.
function axes1_CreateFcn(hObject, eventdata, handles)
%%%%%%%%%%%%%%%%%%%%%%%%%%初始化参数%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Xo=[0 0];%起点位置
longth=1;%步长
J=2000;%循环迭代次数
Xj=Xo;%j=1循环初始，将车的起始坐标赋给Xj
MAX_X=100;
MAX_Y=100;
%This array stores the coordinates of the map and the
%Objects in each coordinate
MAP=2*(ones(MAX_X,MAX_Y));
% Obtain Obstacle, Target and Robot Position
% Initialize the MAP with input values
% Obstacle=-1,Target = 0,Robot=1,Space=2
j=0;
x_val = 1;
y_val = 1;
axis([-20 120 -20 120])
axis equal;
hold on;
axis off;
%set(gcf,'color','y')
%title ('A*算法路径规划');
fill([-20,120,120,-20],[-20 -20 120 120],'y')
fill([95,120,120,95],[-20 -20 10 10],'w')
text(100,5,'Notes:','FontSize',12)
plot(101,-5,'sb','markerfacecolor','b');
text(101,-5,'  Robot','FontSize',12);
plot(101,-15,'om','markerfacecolor','m');
text(101,-15,'  Ball','FontSize',12);
plot(1,1,'bs')
car=plot(1,1,'sb','markerfacecolor','b');
%car_name=text(0,0,'  ','FontSize',12);
object=plot(0,100,'om','markerfacecolor','m');
%object_name=text(0,100,'  Ball','FontSize',12);
but=1;
text(-4,-4,'  Start','FontSize',12);
n=0;%Number of Obstacles
% BEGIN Interactive Obstacle, Target, Start Location selection
xTarget=0;%X Coordinate of the Target
yTarget=100;%Y Coordinate of the Target
m_Target=[xTarget,yTarget];
%object=plot(1,100,'om','markerfacecolor','m');
%object_name=text(1,100,'  Ball','FontSize',12);
%选择小车起点位置
xval=1;
yval=1;
xStart=xval;
yStart=yval;
MAP(xval,yval)=1;
%car=plot(1,1,'bs','markerfacecolor','b');
%car_name=text(1,1,' ','FontSize',12);
% hObject    handle to axes1 (see GCBO)
% eventdata  reserved - to be defined in a future version of MATLAB
% handles    empty - handles not created until after all CreateFcns called% Hint: place code in OpeningFcn to populate axes1% --- Executes on button press in pushbutton1.
function pushbutton1_Callback(hObject, eventdata, handles)
%main
Xo=[0 0];%起点位置
longth=1;%步长
J=2000;%循环迭代次数
Xj=Xo;%j=1循环初始，将车的起始坐标赋给Xj
%DEFINE THE 2-D MAP ARRAY
MAX_X=100;
MAX_Y=100;
%MAX_VAL=100;
%This array stores the coordinates of the map and the
%Objects in each coordinate
MAP=2*(ones(MAX_X,MAX_Y));
% Obtain Obstacle, Target and Robot Position
% Initialize the MAP with input values
% Obstacle=-1,Target = 0,Robot=1,Space=2
j=0;
x_val = 1;
y_val = 1;
axis([-20 120 -20 120])
%grid on;
%hold on;
axis equal;
hold on;
axis off;
%set(gcf,'color','y')
%title ('A*算法路径规划');
fill([-20,120,120,-20],[-20 -20 120 120],'y')
fill([95,120,120,95],[-20 -20 10 10],'w')
text(100,5,'Notes:','FontSize',12)
plot(101,-5,'sb','markerfacecolor','b');
text(101,-5,'  Robot','FontSize',12);
plot(101,-15,'om','markerfacecolor','m');
text(101,-15,'  Ball','FontSize',12);
plot(1,1,'bs')
car=plot(1,1,'sb','markerfacecolor','b');
%car_name=text(0,0,'  ','FontSize',12);
object=plot(0,100,'om','markerfacecolor','m');
%object_name=text(0,100,'  Ball','FontSize',12);
but=1;
text(-4,-4,'  Start','FontSize',12);
n=0;%Number of Obstacles
% BEGIN Interactive Obstacle, Target, Start Location selection
xTarget=0;%X Coordinate of the Target
yTarget=100;%Y Coordinate of the Target
m_Target=[xTarget,yTarget];
%object=plot(1,100,'om','markerfacecolor','m');
%object_name=text(1,100,'  Ball','FontSize',12);
%选择小车起点位置
xval=1;
yval=1;
xStart=xval;
yStart=yval;
MAP(xval,yval)=1;
while but == 1[xval,yval,but] = ginput(1);if but==1xval=floor(xval);yval=floor(yval);MAP(xval,yval)=-1;%Put on the closed list as well%plot(xval,yval,'ro','markerfacecolor','r','MarkerSize',10);Theta=0:pi/20:pi;xx =xval+cos(Theta)*3;yy= yval+sin(Theta)*3;fill(xx,yy,'w')Theta=pi:pi/20:2*pi;xx =xval+cos(Theta)*3;yy= yval+sin(Theta)*3;fill(xx,yy,'k')end
end%End of While loop

三、运行结果

四、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)