I Solved inverse velocity (joint velocity) at velocity level problem. So, I have actual orientation of the manipulator. Now I wanted to get the desired orientation from angular velocity that I used to solve inverse kinematics. So I can calculate the orientation error. $$ \boldsymbol{V} = \begin{vmatrix} 0 \\ 0 \\ 0 \\ \hline 10 \cos(2 \pi t) \\ 10 \sin(2 \pi t) \\ 5 \cos(2 \pi t) \end{vmatrix} $$ is a velocity profile used to solve joint velocity.

  • $\begingroup$ Are the non zero components the angular or the linear part of the velocity twist? Are you using Ray or Axis coordinates for your twists? $\endgroup$ Commented Apr 15, 2020 at 18:10
  • $\begingroup$ The twist is in axis order. $$ \boldsymbol{V} = \begin{vmatrix} \boldsymbol {v}\\ \hline \boldsymbol{\omega} \end{vmatrix} $$ . This velocity is regarded as the velocity profile of moving plate given to solve inverse rate kinematics. Thanks $\endgroup$
    – Jae H
    Commented Apr 16, 2020 at 9:22

1 Answer 1


Although this is quite late, I believe this question should get an answer. The solution for this problem is: If one has no other information but the angular velocity and needs to get the Euler angles, using the relation of quaternion derivative and angular velocity is the best option I found. Then, the quaternion derivative can be integrated numerically to get the Euler angles. Integration of quaternion derivative perfectly satisfies the property of special orthogonal group S0(3).

Let me know if otherwise.


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