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Empty sym: 0-by-1

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What does it mean and why am I geting this? is there anyway to fix it?
%inverse kinematic given:[−320,30,−320] with respected to base frame
H=[0 0 1 -320;
0 -1 0 30;
1 0 0 -320;
0 0 0 1;]
t1 = 0; d1 = th1_; a1 = 0; alpha1 = 0;
t2 = th2_+pi; d2 = 0; a2 = L; alpha2 = 0;
t3 = th3_-pi/2;d3 = 0; a3 = L; alpha3= -pi/2;
t31 = 0; d31 =L; a31 = 0; alpha31 = 0;
t4 = 0;d4 = L+th4_;a4 =-L; alpha4 = pi;
t5 = th5_+pi;d5 = 0;a5 = L; alpha5 = pi/2;
t51 = pi/2; d51= L; a51 = 0; alpha51 = pi/2;
t52 = 0; d52 = L; a52 =0; alpha52 = 0;
t6 = th6_;d6 = L;a6 = 0; alpha6 = 0;
A_1_ = inTransMat(a_1,alpha_1,d_1,t_1);
A0_ = inTransMat(a0,alpha0,d0,t0);
%setting frame 0 as shown
A1 = inTransMat(a1,alpha1,d1,t1);
A2_ = inTransMat(a2,alpha2,d2,t2);
A3_ = inTransMat(a3,alpha3,d3,t3);
A31_= inTransMat (a31,alpha31,d31,t31);
A4_ = inTransMat(a4,alpha4,d4,t4);
A5_= inTransMat(a5,alpha5,d5,t5);
A51_= inTransMat (a51,alpha51,d51,t51);
A52_= inTransMat (a52,alpha52,d52,t52);
A6_= inTransMat(a6,alpha6,d6,t6);
T_ = A_1*A0*A1*A2_*A3_*A31*A4_*A5_*A51_*A52_*A6
T01_ = A_1*A0*A1;
T02_ = A_1*A0*A1*A2_;
T03_ = A_1*A0*A1*A2_*A3_*A31;
T04_ = A_1*A0*A1*A2_*A3_*A31*A4_;
T05_ = A_1*A0*A1*A2_*A3_*A4_*A5*A51_*A52_;
T_06= vpa(T_,2)
%alegrabi approach
eqn1= T_06(1,1)==H(1,1);
eqn2= T_06(1,2)==H(1,2);
eqn3= T_06(1,3)==H(1,3);
eqn4= T_06(1,4)==H(1,4);
eqn5= T_06(2,1)==H(2,1);
eqn6= T_06(2,2)==H(2,2);
eqn7= T_06(2,3)==H(2,3);
eqn8= T_06(2,4)==H(2,4);
eqn9= T_06(3,1)==H(3,2);
eqn10= T_06(3,2)==H(3,2);
eqn11= T_06(3,3)==H(3,3);
eqn12= T_06(3,4)==H(3,4);
sol = solve([eqn1, eqn2, eqn3,eqn4,eqn5,eqn6,eqn7,eqn8,eqn9,eqn10,eqn11,eqn12], [th1_, th2_, th3_, th4_,th5_,th6_]);
th1sol= sol.th1_
th2sol= sol.th2_
th3sol= sol.th3_
th4sol= sol.th4_
th5sol= sol.th5_
th6sol= sol.th6_
function IT = inTransMat(a,b,c,d)
IT = [cos(d) -sin(d)*cos(b) sin(d)*sin(b) a*cos(d); sin(d) cos(d)*cos(b) -cos(d)*sin(b) a*sin(d); 0 sin(b) cos(b) c; 0 0 0 1];
function T = TransMat(a,b,c,d)
T = [cos(d) -sin(d)*cos(b) sin(d)*sin(b) a*cos(d); sin(d) cos(d)*cos(b) -cos(d)*sin(b) a*sin(d); 0 sin(b) cos(b) c; 0 0 0 1];

  1 Comment

Surya Talluri
Surya Talluri on 10 Aug 2020
I understand that th1_, th2_, th3_, th4_, th5_, th6_, L are symbols. Can you give more information about any other symbols that you have defined and what is the value of a_1 in equation defined for A_1_?

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Accepted Answer

Walter Roberson
Walter Roberson on 10 Aug 2020
t6 = th6_;d6 = L;a6 = 0; alpha6 = 0;
so t6 uses th6_
A6_= inTransMat(a6,alpha6,d6,t6);
and A6_ uses t6, so A6_ uses th6_
T_ = A_1*A0*A1*A2_*A3_*A31*A4_*A5_*A51_*A52_*A6
but that uses A6 not A6_ so T_ does not uses th6_ . None of the other equations do either. So when you construct the vector of formulas to be solved for [th1_, th2_, th3_, th4_,th5_,th6_] then none of them involve th6_
You are also trying to solve 12 equations for 6 variables. That is not going to work unless each missing variable th*_ happens to be a vector of length 2.
In order to get your code to run I had to define
syms th1_ th2_ th3_ th4_ th5_ th6_ L
syms a0 a_1 a31
syms A0 A_1 A1 A2_ A3_ A31 A4_ A5_ A51_ A52_ A5 A6
syms alpha0 alpha_1
syms d0 d_1
syms t0 t_1
Variables with lower-case names, variables with or without trailing underscore... it sure is a mess to read and be sure that the formula is correct, not accidentally referring to the wrong version of a variable.


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