I'm working on a kinematic estimation algorithm, and am trying to come up with the right terminology.

I'm using the Product-of-Exponentials formulation for kinematic chains (and ignoring position for now):

$R = e^{\omega_1 \theta_1}e^{\omega_2 \theta_2}...e^{\omega_n \theta_n}R_0$

$R \in SO(3)$: orientation of end effector
$\theta_{1..n}$: joint coordinates
$\omega_{1..n} \in so(3)$: joint screw axes

Forward Kinematics: Solve for $R$ given $\omega_{1..n}, \theta_{1..n}$
Inverse Kinematics: Solve for $\theta_{1..n}$ given $R, \omega_{1..n}$
?___?: Solve for $\omega_{1..n}$ given $R, \theta_{1..n}$

My question is, what phrase fills that blank? I've been using the PoE formula for so long that I am starting to forget the DH paradigm but I'd imagine there's an equivalent with DH params too.

The literature I'm comparing against calls this "system identification" but I think that's because they're treating it like a dynamical system...I am treating it like a standard robot kinematics problem.

Is there an agreed-upon term for this process?

  • 1
    $\begingroup$ \omega is the so(3) matrix and \theta is the joint coordinate? Shouldn't there be an SO(3) matrix on the end, the orientation when all \theta are zero? $\endgroup$ Commented Apr 27, 2019 at 22:14
  • $\begingroup$ @PeterCorke correct, I had omitted for brevity, just edited for clarity ;) $\endgroup$ Commented Apr 28, 2019 at 2:26

1 Answer 1


Try looking for terms like robot calibration, robot kinematic calibration or kinematic calibration. Have a look at Chapter 6 of [1].

[1] Springer Handbook of Robotics, Eds: B.Siciliano, O.Khatib, 2016

  • $\begingroup$ Great! That seems like the right direction. I'll look into that chapter when I can get my hands on a copy. And I'm sure you get this all the time but a sincere thank you for all the work you put into that toolbox. Cheers! $\endgroup$ Commented Apr 28, 2019 at 2:34

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