Inverse Kinematics - Algebraic approach - 6 DOF robotic arm, ERROR: Atan2: Inputs must be real.

Hey guys, read a lot about this error but I guess the root cause of this issue is the calculation itself. And I don't know how to move forward...

I am calculating theta1, theta3 and then theta2: a2=10; a3=8.5; d3=5; d4=5.5;

 %
%
%Theta1
theta1=atan2(py,px)-atan2(d3,sqrt(px*px +py*py-d3*d3));
K=(px*px+py*py+pz*pz-a2*a2-a3*a3-d3*d3-d4*d4)/(2*a2);

 %
%
%Theta3
theta3=atan2(a3,d4)-atan2(K,-sqrt(a3*a3+d4*d4-K*K));

By using my variables (DH parameters), all positive values in that case, i'm getting the error: Error using atan2: inputs must be real.

This data will lead for a solution for K=995.0281 Changing the inputs to 1, 0.85, 0.5, 0.55 does not make any difference, although: K=1.0063e+04

I am new to the world of MATLAB and assistance is appreciated! Cheers

[Birdman]

Can you provide all necessary variables? Also your DH parameters.

[Uede Max]

FYI: changed the variables (if compared to above), no solution.

    %DH= [0.9659    0.2588         0  108.6072;
               0         0   -1.0000         0;
          -0.2588    0.9659         0  174.2076;
               0         0         0    1.0000];
%
a1=0;               px=DH(1,4);   
a2=8.2;             py=DH(2,4);
a3=9.3;             pz=DH(3,4);            
a4=14;
a6=3;
d1=4.7;
d3=0;
d4=0;
d5=0;
%

Thanks Birdman!

[Birdman]

What do you expect theta3 to be?

[Uede Max]

Theta1=0°, Theta3=45°

Answer 1

[Birdman]

The problem arises from the statement

sqrt(a3*a3+d4*d4-K*K)

because the argument is negative which is

-6.5598e+06

and which will end up a complex number.

Therefore, you might want to look at that part again. Maybe there is some kind of miscalculation.

If you change theta3 calculation to the following, you get pi/4.

theta3=atan2(a3,d4)-atan2(K,sqrt(abs(a3*a3+d4*d4-K*K)));

[Uede Max]

Thanks! Formula seems to be alright, though. Too bad, need to re-think the approach.

thank you!

[Birdman]

You are welcome. Maybe you need to reconsider the forward kinematic model.