2012年数学建模D题机器人避障问题论文 - 图文

L3= sqrt(a^2-r^2)+ r*d1+ sqrt((x3-x2)^2+(y3-y2)^2)+ r*d2+ sqrt(b^2-r^2) L3 =

305.6100

>> syms a b c x1 x2 x3 y1 y2 y3 a1 b1 c1 d1 r L1 x1=610;y1=360;x2=500;y2=200;x3=455;y3=150;r=10; a=sqrt((x2-x1)^2+(y2-y1)^2); b=sqrt((x3-x2)^2+(y3-y2)^2); c=sqrt((x3-x1)^2+(y3-y1)^2); a1=acos((b^2+a^2-c^2)/(2*b*a)); b1=acos(r/b); c1=acos(r/a); d1=2*pi-a1-b1-c1;

L1=sqrt(b^2-r^2)+sqrt(a^2-r^2)+r*d1 L1 =

236.7405

syms a b c x1 x2 x3 y1 y2 y3 a1 b1 c1 d1 r L1 x1=455;y1=150;x2=410;y2=100;x3=0;y3=0;r=10; a=sqrt((x2-x1)^2+(y2-y1)^2); b=sqrt((x3-x2)^2+(y3-y2)^2); c=sqrt((x3-x1)^2+(y3-y1)^2); a1=acos((b^2+a^2-c^2)/(2*b*a)); b1=acos(r/b); c1=acos(r/a); d1=2*pi-a1-b1-c1;

L1=sqrt(b^2-r^2)+sqrt(a^2-r^2)+r*d1 L1 =

496.1377

路径O→A→B→C→O的第二条：

syms a b c x1 x2 x3 y1 y2 y3 a1 b1 c1 d1 r L1 x1=0;y1=0;x2=80;y2=210;x3=190;y3=255;r=10; a=sqrt((x2-x1)^2+(y2-y1)^2); b=sqrt((x3-x2)^2+(y3-y2)^2); c=sqrt((x3-x1)^2+(y3-y1)^2); a1=acos((b^2+a^2-c^2)/(2*b*a)); b1=acos(r/b); c1=acos(r/a);

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d1=2*pi-a1-b1-c1;

L1=sqrt(b^2-r^2)+sqrt(a^2-r^2)+r*d1 L1 =

352.3992

>> Syms x1 x2 x3 x4 y1 y2 y3 y4 a b c d f g h m n a1 a2 b1 b2 d1 d2 L3 x1=190;y1=255;x2=300;y2=300;x3=220;y3=530;x4=185;y4=565;r=10; a=sqrt((x2-x1)^2+(y2-y1)^2); g=sqrt(a^2-r^2); b1=acos(r/a);

f=sqrt((x3-x2)^2+(y3-y2)^2); c=sqrt((x3-x1)^2+(y3-y1)^2); a1=acos((a^2+f^2-c^2)/(2*a*f)); d1=2*pi-a1-b1-pi/2; m=r*d1;

b=sqrt((x4-x3)^2+(y4-y3)^2); d=sqrt((x4-x2)^2+(y4-y2)^2); a2=acos((f^2+b^2-d^2)/(2*f*b)); b2=acos(r/b);

d2=2*pi-a2-b2-pi/2; n=r*d2;

h=sqrt(b^2-r^2);

L3= sqrt(a^2-r^2)+ r*d1+ sqrt((x3-x2)^2+(y3-y2)^2)+ r*d2+ sqrt(b^2-r^2) L3 =

432.9754

Syms x1 x2 x3 x4 y1 y2 y3 y4 a b c d f g h m n a1 a2 b1 b2 d1 d2 L3 x1=185;y1=565;x2=150;y2=600;x3=100;y3=700;x4=167.5;y4=695;r=10; a=sqrt((x2-x1)^2+(y2-y1)^2); g=sqrt(a^2-r^2); b1=acos(r/a);

f=sqrt((x3-x2)^2+(y3-y2)^2); c=sqrt((x3-x1)^2+(y3-y1)^2); a1=acos((a^2+f^2-c^2)/(2*a*f)); d1=2*pi-a1-b1-pi/2; m=r*d1;

b=sqrt((x4-x3)^2+(y4-y3)^2); d=sqrt((x4-x2)^2+(y4-y2)^2); a2=acos((f^2+b^2-d^2)/(2*f*b)); b2=acos(r/b);

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d2=2*pi-a2-b2-pi/2; n=r*d2;

h=sqrt(b^2-r^2);

L3= sqrt(a^2-r^2)+ r*d1+ sqrt((x3-x2)^2+(y3-y2)^2)+ r*d2+ sqrt(b^2-r^2) L3 =

255.0408

Syms x1 x2 x3 x4 y1 y2 y3 y4 a b c d f g h m n a1 a2 b1 b2 d1 d2 L3 x1=167.5;y1=695;x2=235;y2=690;x3=500;y3=600;x4=570;y4=560;r=10; a=sqrt((x2-x1)^2+(y2-y1)^2); g=sqrt(a^2-r^2); b1=acos(r/a);

f=sqrt((x3-x2)^2+(y3-y2)^2); c=sqrt((x3-x1)^2+(y3-y1)^2); a1=acos((a^2+f^2-c^2)/(2*a*f)); d1=2*pi-a1-b1-pi/2; m=r*d1;

b=sqrt((x4-x3)^2+(y4-y3)^2); d=sqrt((x4-x2)^2+(y4-y2)^2); a2=acos((f^2+b^2-d^2)/(2*f*b)); b2=acos(r/b);

d2=2*pi-a2-b2-pi/2; n=r*d2;

h=sqrt(b^2-r^2);

L3= sqrt(a^2-r^2)+ r*d1+ sqrt((x3-x2)^2+(y3-y2)^2)+ r*d2+ sqrt(b^2-r^2) L3 =

433.9867

>> Syms x1 x2 x3 x4 y1 y2 y3 y4 a b c d f g h m n a1 a2 b1 b2 d1 d2 L3 x1=570;y1=560;x2=640;y2=520;x3=720;y3=520;x4=730;y4=560;r=10; a=sqrt((x2-x1)^2+(y2-y1)^2); g=sqrt(a^2-r^2); b1=acos(r/a);

f=sqrt((x3-x2)^2+(y3-y2)^2); c=sqrt((x3-x1)^2+(y3-y1)^2); a1=acos((a^2+f^2-c^2)/(2*a*f)); d1=2*pi-a1-b1-pi/2; m=r*d1;

b=sqrt((x4-x3)^2+(y4-y3)^2);

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d=sqrt((x4-x2)^2+(y4-y2)^2); a2=acos((f^2+b^2-d^2)/(2*f*b)); b2=acos(r/b);

d2=2*pi-a2-b2-pi/2; n=r*d2;

h=sqrt(b^2-r^2);

L3= sqrt(a^2-r^2)+ r*d1+ sqrt((x3-x2)^2+(y3-y2)^2)+ r*d2+ sqrt(b^2-r^2) L3 =

222.1430

syms a b c x1 x2 x3 y1 y2 y3 a1 b1 c1 d1 r L1 x1=730;y1=560;x2=720;y2=600;x3=700;y3=640;r=10; a=sqrt((x2-x1)^2+(y2-y1)^2); b=sqrt((x3-x2)^2+(y3-y2)^2); c=sqrt((x3-x1)^2+(y3-y1)^2); a1=acos((b^2+a^2-c^2)/(2*b*a)); b1=acos(r/b); c1=acos(r/a); d1=2*pi-a1-b1-c1;

L1=sqrt(b^2-r^2)+sqrt(a^2-r^2)+r*d1 L1 =

90.4806

Syms x1 x2 x3 x4 y1 y2 y3 y4 a b c d f g h m n a1 a2 b1 b2 d1 d2 L3 x1=700;y1=640;x2=720;y2=600;x3=720;y3=520;x4=610;y4=360;r=10; a=sqrt((x2-x1)^2+(y2-y1)^2); g=sqrt(a^2-r^2); b1=acos(r/a);

f=sqrt((x3-x2)^2+(y3-y2)^2); c=sqrt((x3-x1)^2+(y3-y1)^2); a1=acos((a^2+f^2-c^2)/(2*a*f)); d1=2*pi-a1-b1-pi/2; m=r*d1;

b=sqrt((x4-x3)^2+(y4-y3)^2); d=sqrt((x4-x2)^2+(y4-y2)^2); a2=acos((f^2+b^2-d^2)/(2*f*b)); b2=acos(r/b);

d2=2*pi-a2-b2-pi/2; n=r*d2;

h=sqrt(b^2-r^2);

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