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?

enter image description here

  • $\begingroup$ It might help if you type out all of your equations. $\endgroup$ – Paul Oct 2 '18 at 20:33
  • $\begingroup$ Already added equations. It is general solution for direct velocity. My point regarding inverse velocity is a way to invert jacobian. $\endgroup$ – João Sobral Oct 3 '18 at 14:11
  • $\begingroup$ 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. $\endgroup$ – AlFagera Oct 14 '18 at 6:32

I remember two possibilities:

  • As you already said: inversion of the Jacobi matrix. You can maybe look for Moore-Penrose on this topic.

  • 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}$


You might solve the inverse kinematic problem using the derivation as above. However, I would recommend to solve with Jacobians (Pseudo-inverse matrix). If you are modelling a robot arm, you might have to deal with the classical problems such as collision avoidance or joint-limit problem. One big advantage of the Pseudo-inverse matrix is that you can easily modify it to solve these classical problems.


Your Answer

By clicking "Post Your Answer", you acknowledge that you have read our updated terms of service, privacy policy and cookie policy, and that your continued use of the website is subject to these policies.

Not the answer you're looking for? Browse other questions tagged or ask your own question.