2012年数学建模D题机器人避障问题论文 - 图文

>>

a='((y-640)/(x-700)-(y-730)/(x-670))/(1+(y-730)/(x-670)*(y-640)/(x-700))-3^(1/2)=0';

>> b='(x-700)^2+(y-640)^2-100=0'; >> s=solve(a,b) s =

x: [2x1 sym] y: [2x1 sym]

>> double(s.x(1))

ans =

709.9391

>> double(s.x(2))

ans =

690.4269

>> double(s.y(1))

ans =

638.8979

>> double(s.y(2)) ans =

642.8908

模型二圆心坐标计算： a='y+x-290=0';

>> b='sqrt((x-80)^2+(y-210)^2)-10=0'; >> s=solve(a,b) s =

x: [2x1 sym]

37

y: [2x1 sym]

>> double(s.x(1))

ans =

72.9289

>> double(s.x(2))

ans =

87.0711

>> double(s.y(1))

ans =

217.0711

>> double(s.y(2))

ans =

202.9289

模型二建立：

syms x1 x2 x3 y1 y2 y3 a b c d a1 b1 c1 d1 r v0 v >> a=sqrt((x2-x1)^2+(y2-y1)^2); >> b=sqrt((x3-x2)^2+(y3-y2)^2); >> c=sqrt((x3-x1)^2+(y3-y1)^2); >> c1=acos((a^2+b^2-c^2)/(2*a*b)); >> a1=acos(r/a); >> b1=acos(r/b);

>> d1=2*pi-a1-b1-c1; >> d=r*d1;

>> v=v0/(1+exp(10-0.1*r^2));

>> t=sqrt(a^2-r^2)/v0+sqrt(b^2-r^2)/v0+r*d1/v

模型二代入已知数求解

syms x1 x2 x3 y1 y2 y3 a b c d a1 b1 c1 d1 r v0 v >> a=sqrt((x2-x1)^2+(y2-y1)^2);

38

>> b=sqrt((x3-x2)^2+(y3-y2)^2); >> c=sqrt((x3-x1)^2+(y3-y1)^2); >> c1=acos((a^2+b^2-c^2)/(2*a*b)); >> a1=acos(r/a); >> b1=acos(r/b);

>> d1=2*pi-a1-b1-c1; >> d=r*d1;

>> v=v0/(1+exp(10-0.1*r^2));

>> t=sqrt(a^2-r^2)/v0+sqrt(b^2-r^2)/v0+r*d1/v t =

(x2^2-2*x2*x1+x1^2+y2^2-2*y2*y1+y1^2-r^2)^(1/2)/v0+(x3^2-2*x3*x2+x2^2+y3^2-2*y3*y2+y2^2-r^2)^(1/2)/v0+r*(2*pi-acos(r/(x2^2-2*x2*x1+x1^2+y2^2-2*y2*y1+y1^2)^(1/2))-acos(r/(x3^2-2*x3*x2+x2^2+y3^2-2*y3*y2+y2^2)^(1/2))-acos(1/2*(2*x2^2-2*x2*x1+2*y2^2-2*y2*y1-2*x3*x2-2*y3*y2+2*x3*x1+2*y3*y1)/(x2^2-2*x2*x1+x1^2+y2^2-2*y2*y1+y1^2)^(1/2)/(x3^2-2*x3*x2+x2^2+y3^2-2*y3*y2+y2^2)^(1/2)))/v0*(1+exp(10-1/10*r^2))

>> x1=0;y1=0;x2=80;y2=210;x3=300;y3=300;v0=5; >>

x1=0;x2=0;x2=87.0711;y2=202.9289;x3=300;y3=300;v0=5;r=20;(x2^2-2*x2*x1+x1^2+y2^2-2*y2*y1+y1^2-r^2)^(1/2)/v0+(x3^2-2*x3*x2+x2^2+y3^2-2*y3*y2+y2^2-r^2)^(1/2)/v0+r*(2*pi-acos(r/(x2^2-2*x2*x1+x1^2+y2^2-2*y2*y1+y1^2)^(1/2))-acos(r/(x3^2-2*x3*x2+x2^2+y3^2-2*y3*y2+y2^2)^(1/2))-acos(1/2*(2*x2^2-2*x2*x1+2*y2^2-2*y2*y1-2*x3*x2-2*y3*y2+2*x3*x1+2*y3*y1)/(x2^2-2*x2*x1+x1^2+y2^2-2*y2*y1+y1^2)^(1/2)/(x3^2-2*x3*x2+x2^2+y3^2-2*y3*y2+y2^2)^(1/2)))/v0*(1+exp(10-1/10*r^2))

ans =

94.2697

39