Potential and optimal control of human head movement using Tait-Bryan parametrization

Indika Wijayasinghe, Justin Ruths, Ulrich Büttner, Bijoy K. Ghosh, Stefan Glasauer, Olympia Kremmyda, Jr Shin Li

Research output: Contribution to journalArticlepeer-review

21 Scopus citations


Human head movement can be looked at, as a rotational dynamics on the space SO(3) with constraints that have to do with the axis of rotation. Typically the axis vector, after a suitable scaling, is assumed to lie in a surface called Donders' surface. Various descriptions of Donders' surface are in the literature and in this paper we assume that the surface is described by a quadratic form. We propose a Tait-Bryan parametrization of SO(3), that is new in the head movement literature, and describe Donders' constraint in these parameters. Assuming that the head is a perfect sphere with its mass distributed uniformly and rotating about its own center, head movement models are constructed using classical mechanics. A new potential control method is described to regulate the head to a desired final orientation. Optimal head movement trajectories are constructed using a pseudospectral method, where the goal is to minimize a quadratic cost function on the energy of the applied control torques. The model trajectories are compared with measured trajectories of human head movement.

Original languageEnglish
Pages (from-to)519-529
Number of pages11
Issue number2
StatePublished - Feb 2014


  • Donders' surface
  • Euler Lagrange's equation
  • Head movement
  • Optimal control
  • Potential control
  • Tait-Bryan parametrization


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