{"id":101,"date":"2021-11-21T11:20:33","date_gmt":"2021-11-21T11:20:33","guid":{"rendered":"http:\/\/47.103.123.166\/?p=101"},"modified":"2021-11-21T12:33:49","modified_gmt":"2021-11-21T12:33:49","slug":"%e8%bf%90%e5%8a%a8%e8%a7%84%e5%88%92%e5%ad%a6%e4%b9%a0%e7%ac%94%e8%ae%b03-dubins-curve","status":"publish","type":"post","link":"http:\/\/47.103.123.166\/?p=101","title":{"rendered":"\u8fd0\u52a8\u89c4\u5212\u5b66\u4e60\u7b14\u8bb03\u2014\u2014Dubins Curve"},"content":{"rendered":"

\u5b9e\u9645\u95ee\u9898<\/h1>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

Dubins\u66f2\u7ebf\u57fa\u7840<\/h1>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\u95ee\u9898\u5173\u952e<\/h1>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

CSC\u578b<\/h1>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

CCC\u578b<\/h1>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"<\/p>\n

Dubins\u66f2\u7ebf\u7684\u4e00\u4e9b\u8ba8\u8bba<\/h1>\n

\"\u5728\u8fd9\u91cc\u63d2\u5165\u56fe\u7247\u63cf\u8ff0\"
\n\u4e0b\u9762\u662f\u5199\u7684\u4e00\u6bb5MATLAB\u4ee3\u7801\uff0c\u53ea\u662f\u7b80\u5355\u5b9e\u73b0\uff0c\u6ca1\u6709\u8003\u8651\u6700\u4f18\u3002
\n1\u3001CSC<\/p>\n

%Dubins Curve CSC\u578b\n%\u76ee\u6807\u5b9a\u4e49\n    %\u5b9a\u4e49\u8d77\u7ec8\u70b9[x y dir]\n    I=[1 1 7*pi\/4];\n    G=[6 8 3*pi\/4];\n    %\u5b9a\u4e49\u6216\u8ba1\u7b97\u8f6c\u5f2f\u534a\u5f84\n    ri=1;\n    rg=2;\n    %\u7ec4\u5408\n    k=-1;    % 1:RSX,-1:LSX\n    i=-1;   % 1:XSR,-1:XSL\n    j=i*k;  % 1:RSR\/LSL, -1:RSL\/LSR\n%\u8ba1\u7b97\u9996\u5c3e\u5706\u5fc3\u5750\u6807\n    xi=I(1,1)-ri*k*cos(I(1,3));\n    yi=I(1,2)+ri*k*sin(I(1,3));  \n    xg=G(1,1)-rg*i*cos(G(1,3));\n    yg=G(1,2)+rg*i*sin(G(1,3));\n%\u8ba1\u7b97\u6cd5\u5411\u91cf\n    %\u9996\u5c3e\u5706\u5706\u5fc3\u4e4b\u95f4\u7684\u5411\u91cfV1\n    v1x=xg-xi;              %\u5411\u91cf\u5750\u6807x\n    v1y=yg-yi;              %\u5411\u91cf\u5750\u6807y\n    D=sqrt(v1x*v1x+v1y*v1y);%\u5411\u91cf\u6a21\u957f \n    v1x=v1x\/D;              %\u5355\u4f4d\u5316\n    v1y=v1y\/D;\n    %\u8ba1\u7b97\u6cd5\u5411\u91cfn\n    c=(j*ri-rg)\/D;            %\u5b9a\u4e49\u4e2d\u95f4\u91cf\n    nx=v1x*c-i*v1y*sqrt(1-c*c);\n    ny=v1y*c+i*v1x*sqrt(1-c*c);\n%\u8ba1\u7b97\u5207\u70b9\n    xit=xi+j*ri*nx;\n    yit=yi+j*ri*ny;\n    xgt=xg+rg*nx;\n    ygt=yg+rg*ny;\n%\u7ed8\u56fe\n    %\u521d\u59cb\u65b9\u5411\n    xiDir=[I(1,1)-ri*cos(I(1,3)-pi\/2),I(1,1)];\n    yiDir=[I(1,2)+ri*sin(I(1,3)-pi\/2),I(1,2)];\n    xgDir=[G(1,1)-rg*cos(G(1,3)-pi\/2),G(1,1)];\n    ygDir=[G(1,2)+rg*sin(G(1,3)-pi\/2),G(1,2)];\n    %\u5207\u7ebf\n    xxx=[xit xgt];\n    yyy=[yit ygt];\n    %\u9996\u5c3e\u5706\n    t=0:0.01:2*pi;\n    %t=I(1,3)-pi\/2:0.01:3*pi\/2-atan(ny\/nx);\n    xxi=xi+ri*sin(t);\n    yyi=yi+ri*cos(t);\n    %t=-pi\/2-atan(ny\/nx):0.01:G(1,3)-pi\/2;\n    xxg=xg+rg*sin(t);\n    yyg=yg+rg*cos(t);\n    %\u6cd5\u5411\u91cf\n    nxi=[xi xi+ri*nx];\n    nyi=[yi yi+ri*ny];\n    nxg=[xg xg+rg*nx];\n    nyg=[yg yg+rg*ny];\n    %\u7ed8\u56fe\n    plot(I(1,1),I(1,2), 'go' ,G(1,1),G(1,2),'go',...      %\u521d\u59cb\u4f4d\u7f6e\n            xiDir,yiDir,'-g',xgDir,ygDir,'-g',...       %\u521d\u59cb\u65b9\u5411\n            xi,yi,'k*',xg,yg,'k*',...                   %\u5706\u5fc3\n            xxi,yyi,'-r',xxg,yyg,'-r',...               %\u9996\u5c3e\u5706\n            nxi,nyi,'-b',nxg,nyg,'-b',...               %\u6cd5\u5411\u91cf\n            xxx,yyy,'-ro')                              %\u5207\u7ebf\n    axis([-3 15 -3 15])<\/code><\/pre>\n
2\u3001CCC<\/p>\n
%Dubins Curve CCC\u578b\n\n%\u76ee\u6807\u5b9a\u4e49\n    %\u5b9a\u4e49\u8d77\u7ec8\u70b9[x y dir] \n    I=[1 1 7*pi\/4];\n    G=[4 5 3*pi\/4];\n    %\u5b9a\u4e49\u6216\u8ba1\u7b97\u8f6c\u5f2f\u534a\u5f84\n    ri=1;\n    rg=1;\n    rmid=4;\n    %\u7ec4\u5408\n    i=1;    % 1:RLR  -1:LRL\n\n%\u4e09\u5706\u5fc3\u76f8\u5173\u91cf\n    %\u8ba1\u7b97\u9996\u5c3e\u5706\u5fc3\u5750\u6807\u53ca\u5176\u8fde\u7ebf\u5411\u91cfV12\n    xi=I(1,1)-ri*i*cos(I(1,3));\n    yi=I(1,2)+ri*i*sin(I(1,3));\n    xg=G(1,1)-rg*i*cos(G(1,3));\n    yg=G(1,2)+rg*i*sin(G(1,3));\n\n    V12=[xg-xi,yg-yi];\n    angleV12=atan(V12(1,2)\/V12(1,1));\n\n    %\u8ba1\u7b97\u4e2d\u95f4\u5706\u5750\u6807\u53ca\u4e09\u5706\u5fc3\u8fde\u7ebf\u5411\u91cfV13\u3001V32\n    d12=sqrt((xg-xi)^2+(yg-yi)^2);\n    rmid=max([rmid (d12-ri-rg)*0.5]);\n    d13=ri+rmid;\n    d32=rmid+rg;\n    angleP213=acos((d12^2+d13^2-d32^2)\/(2*d12*d13));\n\n    xmid=xi+d13*cos(angleV12-angleP213);\n    ymid=yi+d13*sin(angleV12-angleP213);\n\n    V13=[xmid-xi,ymid-yi];\n    V32=[xg-xmid,yg-ymid];\n\n    V13=V13\/d13;    %\u5355\u4f4d\u5316\n    V32=V32\/d32;\n\n%\u8ba1\u7b97\u5207\u70b9\u5750\u6807\n    xt1=xi+ri*V13(1,1);\n    yt1=yi+ri*V13(1,2);\n    xt2=xmid+rmid*V32(1,1);\n    yt2=ymid+rmid*V32(1,2);\n\n%\u7ed8\u56fe\n    %\u521d\u59cb\u65b9\u5411\n    xiDir=[I(1,1)-ri*cos(I(1,3)-pi\/2),I(1,1)];\n    yiDir=[I(1,2)+ri*sin(I(1,3)-pi\/2),I(1,2)];\n    xgDir=[G(1,1)-rg*cos(G(1,3)-pi\/2),G(1,1)];\n    ygDir=[G(1,2)+rg*sin(G(1,3)-pi\/2),G(1,2)];\n    %\u9996\u5c3e\u5706\n    t=0:0.01:2*pi;\n    xxi=xi+ri*sin(t);\n    yyi=yi+ri*cos(t);\n    xxg=xg+rg*sin(t);\n    yyg=yg+rg*cos(t);\n    xxmid=xmid+rmid*sin(t);\n    yymid=ymid+rmid*cos(t);\n    %\u7ed8\u56fe\n    plot(I(1,1),I(1,2),'go',G(1,1),G(1,2),'go',...          %\u521d\u59cb\u4f4d\u7f6e\n            xiDir,yiDir,'-g',xgDir,ygDir,'-g',...           %\u521d\u59cb\u65b9\u5411\n            xi,yi,'k*',xg,yg,'k*',xmid,ymid,'k*',...        %\u5706\u5fc3\n            xt1,yt1,'bo',xt2,yt2,'bo',...                   %\u5207\u70b9\n            xxi,yyi,'-r',xxg,yyg,'-r',xxmid,yymid,'-r')     %\u4e09\u5706\n    axis([-3 15 -3 15])<\/code><\/pre>\n
\u53c2\u8003\u6587\u732e<\/h1>\n
1\u3001http:\/\/planning.cs.uiuc.edu\/node821.html<\/a><\/a>
\n2\u3001http:\/\/www.banbeichadexiaojiubei.com\/index.php\/2020\/03\/15\/\u81ea\u52a8\u9a7e\u9a76\u8fd0\u52a8\u89c4\u5212-dubins\u66f2\u7ebf<\/a><\/a>
\n3\u3001https:\/\/gieseanw.files.wordpress.com\/2012\/10\/dubins.pdf<\/a><\/a> <\/p>\n","protected":false},"excerpt":{"rendered":"
\u5b9e\u9645\u95ee\u9898 Dubins\u66f2\u7ebf\u57fa\u7840 \u95ee\u9898\u5173\u952e CSC\u578b CCC\u578b Dubins\u66f2\u7ebf\u7684\u4e00\u4e9b\u8ba8\u8bba \u4e0b\u9762\u662f\u5199\u7684\u4e00\u6bb5MATLAB\u4ee3\u7801\uff0c\u53ea\u662f\u7b80\u5355\u5b9e\u73b0\uff0c\u6ca1\u6709\u8003\u8651\u6700\u4f18\u3002 1\u3001CSC %Dubins Curve CSC\u578b %\u76ee\u6807\u5b9a\u4e49 %\u5b9a\u4e49\u8d77\u7ec8\u70b9[x y dir] I=[1 1 7*pi\/4]; G=[6 8 3*pi\/4]; %\u5b9a\u4e49\u6216\u8ba1\u7b97\u8f6c\u5f2f\u534a\u5f84 ri=1; rg=2; %\u7ec4\u5408 k=-1; % 1:RSX,-1:LSX i=-1; % 1:XSR,-1:XSL j=i*k; % 1:RSR\/LSL, -1:RSL\/LSR %\u8ba1\u7b97\u9996\u5c3e\u5706\u5fc3\u5750\u6807 xi=I(1,1)-ri*k*cos(I(1,3)); yi=I(1,2)+ri*k*sin(I(1,3)); xg=G(1,1)-rg*i*cos(G(1,3)); yg=G(1,2)+rg*i*sin(G(1,3)); %\u8ba1\u7b97\u6cd5\u5411\u91cf %\u9996\u5c3e\u5706\u5706\u5fc3\u4e4b\u95f4\u7684\u5411\u91cfV1 v1x=xg-xi; %\u5411\u91cf\u5750\u6807x v1y=yg-yi; %\u5411\u91cf\u5750\u6807y D=sqrt(v1x*v1x+v1y*v1y);%\u5411\u91cf\u6a21\u957f v1x=v1x\/D; %\u5355\u4f4d\u5316 v1y=v1y\/D; %\u8ba1\u7b97\u6cd5\u5411\u91cfn c=(j*ri-rg)\/D; %\u5b9a\u4e49\u4e2d\u95f4\u91cf nx=v1x*c-i*v1y*sqrt(1-c*c); ny=v1y*c+i*v1x*sqrt(1-c*c); […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[2],"tags":[],"_links":{"self":[{"href":"http:\/\/47.103.123.166\/index.php?rest_route=\/wp\/v2\/posts\/101"}],"collection":[{"href":"http:\/\/47.103.123.166\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/47.103.123.166\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/47.103.123.166\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/47.103.123.166\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=101"}],"version-history":[{"count":21,"href":"http:\/\/47.103.123.166\/index.php?rest_route=\/wp\/v2\/posts\/101\/revisions"}],"predecessor-version":[{"id":133,"href":"http:\/\/47.103.123.166\/index.php?rest_route=\/wp\/v2\/posts\/101\/revisions\/133"}],"wp:attachment":[{"href":"http:\/\/47.103.123.166\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=101"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/47.103.123.166\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=101"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/47.103.123.166\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=101"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}