Matlab航迹规划仿真—A*算法

1. 初始化参数

主要参数:

地图大小

起始点和目标点坐标

 

clc
clear all
m = 30;n = 30;
Spoint = [3 3];    %起始点坐标
Epoint = [29 22];  %目标点坐标

 

2. 构建地图

-inf表示不可到达的障碍物点

 

%%构建地图
for i = 1:m+2
    if i == 1
        for j = 1:n+2
            Matrix(i,j) = -inf;
        end
    elseif i == m+2
        for j = 1:n+2
            Matrix(i,j) = -inf;
        end
    else
        for j = 1:n+2
            if ((j == 1)|(j == n+2))
                Matrix(i,j) = -inf;
            else
                Matrix(i,j) = inf;
            end
        end
    end
end
%%障碍
for j=2:10
    Matrix(5,j)=-inf;
for j=2:15
     Matrix(24,j)=-inf;
for j=9:24
%for j=6:24
     Matrix(10,j)=-inf;
for j=20:31
    Matrix(15,j)=-inf;
for j=5:20
    Matrix(20,j)=-inf;
for j=18:27
    Matrix(28,j)=-inf;
for i=2:6  
    Matrix(i,18)=-inf;
for i=17:20
      Matrix(i,5)=-inf;
for i=23:25
     Matrix(i,20)=-inf;
for i=13:17
    Matrix(i,13)=-inf;
end
end
end
end
end
end
end
end
end
end
%end


% 显示地图
%subplot(2,2,1);
h1 = plot(Spoint(1),Spoint(2),'gO');
hold on
h2 = plot(Epoint(1),Epoint(2),'rO');

 

3. A*算法搜索路径

 

%%寻路
Matrix(Spoint(1),Spoint(2))=0;
Matrix(Epoint(1),Epoint(2))=inf;
G=Matrix;
F=Matrix;
openlist=Matrix;
closelist=Matrix;
parentx=Matrix;
parenty=Matrix;
openlist(Spoint(1),Spoint(2)) =0;
%closelist(Epoint(1),Epoint(2))=inf;


for i = 1:n+2
    for j = 1:m+2
        k = Matrix(i,j);
        if(k == -inf)
            %subplot(2,2,1);
            h3 = plot(i,j,'k.');
%         elseif(k == inf)  % show green feasible point
%             %subplot(2,2,1);
%             plot(i,j,'gh');
%         else
%             %subplot(2,2,1);
%             plot(i,j,'gh');
        end
        hold on
    end
end
axis([0 m+3 0 n+3]);
%subplot(2,2,1);
plot(Epoint(1),Epoint(2),'b+');
%subplot(2,2,1);
plot(Spoint(1),Spoint(2),'b+');
while(1)
    num=inf;
    for p=1:m+2
        for q=1:n+2
            if(openlist(p,q)==0&&closelist(p,q)~=1)
                Outpoint=[p,q];
                if(F(p,q)>=0&&num>F(p,q))
                    num=F(p,q);
                    Nextpoint=[p,q];
                end
            end
        end
    end
    closelist(Nextpoint(1),Nextpoint(2))=1;
    for i = 1:3
        for j = 1:3
            k = G(Nextpoint(1)-2+i,Nextpoint(2)-2+j);
            if(i==2&&j==2|closelist(Nextpoint(1)-2+i,Nextpoint(2)-2+j)==1)
                continue;
            elseif (k == -inf)
                G(Nextpoint(1)-2+i,Nextpoint(2)-2+j) = G(Nextpoint(1)-2+i,Nextpoint(2)-2+j);
                closelist(Nextpoint(1)-2+i,Nextpoint(2)-2+j)=1;
            elseif (k == inf)
                distance=((i-2)^2+(j-2)^2)^0.5;
                G(Nextpoint(1)-2+i,Nextpoint(2)-2+j)=G(Nextpoint(1),Nextpoint(2))+distance;
                openlist(Nextpoint(1)-2+i,Nextpoint(2)-2+j)=0;
               % H=((Nextpoint(1)-2+i-Epoint(1))^2+(Nextpoint(2)-2+j-Epoint(2))^2)^0.5;%欧几里德距离启发函数
                H_diagonal=min(abs(Nextpoint(1)-2+i-Epoint(1)),abs(Nextpoint(2)-2+j-Epoint(2)));%比较复杂的对角线启发函数
                H_straight=abs(Nextpoint(1)-2+i-Epoint(1))+abs(Nextpoint(2)-2+j-Epoint(2));
                H=sqrt(2)*H_diagonal+(H_straight-2*H_diagonal);




                % H=max(abs(Nextpoint(1)-2+i-Epoint(1)),abs(Nextpoint(2)-2+j-Epoint(2)));%比较简单的对角线函数
                
                F(Nextpoint(1)-2+i,Nextpoint(2)-2+j)=G(Nextpoint(1)-2+i,Nextpoint(2)-2+j)+H;
                parentx(Nextpoint(1)-2+i,Nextpoint(2)-2+j)=Nextpoint(1);
                parenty(Nextpoint(1)-2+i,Nextpoint(2)-2+j)=Nextpoint(2);
            else distance=((i-2)^2+(j-2)^2)^0.5;
                if(k>(distance+G(Nextpoint(1),Nextpoint(2))))
                k=distance+G(Nextpoint(1),Nextpoint(2));
               % H=((Nextpoint(1)-2+i-Epoint(1))^2+(Nextpoint(2)-2+j-Epoint(2))^2)^0.5;  %欧几里德距离启发函数
                H_diagonal=min(abs(Nextpoint(1)-2+i-Epoint(1)),abs(Nextpoint(2)-2+j-Epoint(2)));%比较复杂的对角线启发函数
                H_straight=abs(Nextpoint(1)-2+i-Epoint(1))+abs(Nextpoint(2)-2+j-Epoint(2));
                H=sqrt(2)*10*H_diagonal+10*(H_straight-2*H_diagonal);




                 % H=max(abs(Nextpoint(1)-2+i-Epoint(1)),abs(Nextpoint(2)-2+j-Epoint(2)));%比较简单的对角线函数
                
                F(Nextpoint(1)-2+i,Nextpoint(2)-2+j)=k+H;
                parentx(Nextpoint(1)-2+i,Nextpoint(2)-2+j)=Nextpoint(1);
                parenty(Nextpoint(1)-2+i,Nextpoint(2)-2+j)=Nextpoint(2);
                end
            end
            if(((Nextpoint(1)-2+i)==Epoint(1)&&(Nextpoint(2)-2+j)==Epoint(2))|num==inf)
                 parentx(Epoint(1),Epoint(2))=Nextpoint(1);
                parenty(Epoint(1),Epoint(2))=Nextpoint(2);
                break;
            end
        end
        if(((Nextpoint(1)-2+i)==Epoint(1)&&(Nextpoint(2)-2+j)==Epoint(2))|num==inf)
             parentx(Epoint(1),Epoint(2))=Nextpoint(1);
                parenty(Epoint(1),Epoint(2))=Nextpoint(2);
            break;
        end
    end
    if(((Nextpoint(1)-2+i)==Epoint(1)&&(Nextpoint(2)-2+j)==Epoint(2))|num==inf)
         parentx(Epoint(1),Epoint(2))=Nextpoint(1);
                parenty(Epoint(1),Epoint(2))=Nextpoint(2);
        break;
    end
end
    P=[];
    s=1;
while(1)
    if(num==inf)
        break;
    end
    %subplot(2,2,1);
    h4 = plot(Epoint(1),Epoint(2),'b+');


    P(s,:)=Epoint;
    s=s+1;
%      pause(1);
    xx=Epoint(1);
    Epoint(1)=parentx(Epoint(1),Epoint(2));
    Epoint(2)=parenty(xx,Epoint(2));
    if(parentx(Epoint(1),Epoint(2))==Spoint(1)&&parenty(Epoint(1),Epoint(2))==Spoint(2))
        %subplot(2,2,1);
        plot(Epoint(1),Epoint(2),'b+');
        P(s,:)=Epoint;
        break;
    end
end
P(s+1,:)=Spoint;
legend([h1,h2,h3,h4],'起始点','目标点','障碍物','航迹点');


count=0;
for i=2:12
    for j=2:12
        if(G(i,j)~=inf&&G(i,j)~=-inf)
            count=count+1;
        end
    end
end
count

 

4. 路径优化

 

%将得到的折现曲线拟合成光滑的曲线
P=P';
a=[];
b=[];
a=P(1,:);
b=P(2,:);
figure
%subplot(2,2,3);
plot(a,b);
axis([0,n+3,0,n+3]);


values = spcrv([[a(1) a a(end)];[b(1) b b(end)]],3);
figure
%subplot(2,2,4);
plot(values(1,:),values(2,:),'r');
axis([0,m+3,0,m+3]);

 

5. 效果图

 

A*路径

优化后路径

6. 下载链接

直接复制到matlab即可使用，或者也可以点击下载。

　　审核编辑：汤梓红