表1 PUMA560机器人的连杆参数
| 关节i |
|
|
|
|
变化范围/(o) |
| 1 |
90 |
0 |
0 |
0 |
-160~160 |
| 2 |
0 |
-90 |
0 |
149.09 |
-225~45 |
| 3 |
-90 |
0 |
431.8 |
0 |
-45~225 |
| 4 |
0 |
-90 |
20.32 |
443.07 |
-110~170 |
| 5 |
0 |
90 |
0 |
0 |
-100~100 |
| 6 |
0 |
-90 |
0 |
0 |
-266~266 |
正解源码
DEG = pi/180;
cta1=-70.4385
cta2=182.6918
cta3=-90.0000
cta4=-82.4708
cta5=-19.7387
cta6=-97.9933
T01=[cosd(cta1),-sind(cta1),0,0;
sind(cta1), cosd(cta1),0,0;
0,0,1,0;
0,0,0,1];
T02=T01*[cosd(cta2),-sind(cta2),0,0;
0,0,1, 149.09;
-sind(cta2),-cosd(cta2),0,0;
0,0,0,1] ;
T03=T02*[cosd(cta3),-sind(cta3),0,431.8;
sind(cta3), cosd(cta3),0,0;
0,0,1,0;
0,0,0,1];
T04=T03*[cosd(cta4),-sind(cta4),0,20.32;
0,0,1,433.07;
-sind(cta4),-cosd(cta4),0,0;
0,0,0,1];
T05=T04*[cosd(cta5),-sind(cta5),0,0;
0,0,-1,0;
sind(cta5), cosd(cta5), 0,0;
0,0,0,1];
T06=T05*[cosd(cta6),-sind(cta6),0,0;
0,0,1,0;
-sind(cta6),-cosd(cta6),0,0;
0,0,0,1];
O=T06*[0;0;0;1];
=====================================================
逆解源码
fid = fopen('inverseout.txt','w');%逆解的保存文件
%赋初值
T06 =[0.0000 1.0000 0.0000 -149.0900;
0.0000 -0.0000 1.0000 864.8700;
1.0000 0 -0.0000 20.3200;
0 0 0 1.0000] ;
a0=0; a1=0; a2=431.8; a3=20.32; a4=0; a5=0;
d1=0; d2=149.09; d3=0; d4=433.07; d5=0; d6=0;
n_x=T06(1); n_y=T06(2); n_z=T06(3);
o_x=T06(5); o_y=T06(6); o_z=T06(7);
a_x=T06(9); a_y=T06(10); a_z=T06(11);
p_x=T06(13); p_y=T06(14); p_z=T06(15);
disp(['八组解分别是：']);
for i=1:2
for j=1:2
for k=1:2
%求解theta1(为弧度)
sqr1=[sqrt(p_x^2+p_y^2-d2^2),-sqrt(p_x^2+p_y^2-d2^2)];
ta1=atan2(p_y,p_x)-atan2(d2,sqr1(i));
%求解theta3（弧度表示）
k1=(p_x^2+p_y^2+p_z^2-a2^2-a3^2-d2^2-d4^2)/(2*a2);
sqr3=[sqrt(a3^2+d4^2-k1^2),-sqrt(a3^2+d4^2-k1^2) ];
ta3=atan2(a3,d4)-atan2(k1,sqr3(j));
fs23=-((a3+a2*cos(ta3))*p_z)+(cos(ta1)*p_x+sin(ta1)*p_y)*(a2*sin(ta3)-d4);
sc23=(-d4+a2*sin(ta3))*p_z+(cos(ta1)*p_x+sin(ta1)*p_y)*(a2*cos(ta3)+a3);
ta23=atan2( fs23,sc23);
%求解theta2 （弧度表示）
ta2=ta23-ta3;
%求解theta4 （弧度表示）
fs4=[ -a_x*sin(ta1)+a_y*cos(ta1),a_x*sin(ta1)-a_y*cos(ta1)];
sc4=[ -a_x*cos(ta1)*cos(ta23)-a_y*sin(ta1)*cos(ta23)+a_z*sin(ta23),
a_x*cos(ta1)*cos(ta23)+a_y*sin(ta1)*cos(ta23)-a_z*sin(ta23)];
fprintf(fid,'%d,',sc4(1,1));
fprintf(fid,'\t');
fprintf(fid,'%d,',sc4(2,1));
fprintf(fid,'\t');
fprintf(fid,'%d,',fs4(1,1));
fprintf(fid,'\t');
fprintf(fid,'%d,',fs4(1,2));
fprintf(fid,'\t');
fprintf(fid,'\n');
ta4=atan2(fs4(k),sc4(k));
%求解theta5 （弧度表示）
fs5=-a_x*(cos(ta1)*cos(ta23)*cos(ta4)+sin(ta1)*sin(ta4))...
-a_y*(sin(ta1)*cos(ta23)*cos(ta4)-cos(ta1)*sin(ta4))...
+a_z*(sin(ta23)*cos(ta4));
sc5=a_x*(-cos(ta1)*sin(ta23))+a_y*(-sin(ta1)*sin(ta23))+a_z*(-cos(ta23));
ta5=atan2(fs5,sc5);
%求解theta6 （弧度表示）
fs6=-n_x*(cos(ta1)*cos(ta23)*sin(ta4)-sin(ta1)*cos(ta4))...
-n_y*(sin(ta1)*cos(ta23)*sin(ta4)+cos(ta1)*cos(ta4))...
+n_z*(sin(ta23)*sin(ta4));
sc6= n_x*(cos(ta1)*cos(ta23)*cos(ta4)+sin(ta1)*sin(ta4))*cos(ta5)...
-n_x*cos(ta1)*sin(ta23)*sin(ta5)...
+n_y*(sin(ta1)*cos(ta23)*cos(ta4)+cos(ta1)*sin(ta4))*cos(ta5)...
-n_y*sin(ta1)*sin(ta23)*sin(ta5)...
-n_z*(sin(ta23)*cos(ta4)*cos(ta5)+cos(ta23)*sin(ta5));
ta6=atan2(fs6,sc6);
%save
%将其化为角度
Theta=[ta1 ta2 ta3 ta4 ta5 ta6]./pi*180
end
end
end
关于C++版本的运动学正解和逆解的代码，可以在以下链接下载
https://download.csdn.net/download/kobesdu/12099712