# 5 DOF robot - Velocity Inverse Kinematics

I am modelling an articulated robot arm with 5 degrees-of-freedom from igus (igus Robolink).

I deduced its direct kinematics equations using Denavit-Hartenberg parameters and homogeneous transformation matrices. I also calculated its Jacobian and inverse kinematics problem of position.

Now I am bit stuck with the problem of inverse velocity. Since the Jacobian is a [6x5] matrix and can't be inverted directly, could you tell me any way to invert it, i.e. Pseudo-Inverse matrix? Or is there a better way to solve inverse velocity problems for 5 DOF robots rather than with the Jacobian?

• It might help if you type out all of your equations. – Paul Oct 2 '18 at 20:33
• Already added equations. It is general solution for direct velocity. My point regarding inverse velocity is a way to invert jacobian. – João Sobral Oct 3 '18 at 14:11
• It would be much better if you attach a picture of the robot. Also it might be possible to get velocity inverse kinematics from that of position. – AlFagera Oct 14 '18 at 6:32

• derivation in joint space. If you already solved the inverse problem, and $$q$$ is known, you can just derivate the position signal:
$$\dot q = \frac{d q}{dt}$$
I would prefer the second method. If you want to use the pseudo-inverse you have to check the condition of the matrix. Your pseudo-inverse may become singular. Since you usually have to solve the coordinate transformation of the position signal $$q$$ anyway, this is way more efficient. You need no matrix operations. For a discrete signal (with sample Time $$T$$) you can approximate the velocity signal with:
$$\dot q(i) = \frac{q(i+1) -q(i)}{T}$$