Optimal eye and head movement control using q-parametrization

Sanath Darshana Kahagalage, Eugenio Aulisa, Bijoy K. Ghosh

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

2 Scopus citations


Human eye and head movements can be looked at, as a rotational dynamics on the space SO(3) with constraints that have to do with the axis of rotation. Eye movements satisfy Listing's constraint, wherein the axis vector is restricted to a fixed plane called the Listing's plane. On the other hand, head movements satisfy Donders' constraint, wherein the axis vector, after a suitable scaling, is assumed to lie in a surface called Donders' surface. Various descriptions of the Donders' surface are in the literature and in this paper we assume that the surface originates from the Fick gimbal. Assuming boundary values on the states, optimal movement trajectories are constructed where the goal is to transfer the state between an initial to a final value while minimizing a quadratic cost function on the energy of the, externally applied, control torques. Using Newton-Euler formulation of the dynamical system, in this paper we introduce a new q-parametrization to synthesize the optimal control.

Original languageEnglish
Title of host publication19th IFAC World Congress IFAC 2014, Proceedings
EditorsEdward Boje, Xiaohua Xia
PublisherIFAC Secretariat
Number of pages6
ISBN (Electronic)9783902823625
StatePublished - 2014
Event19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014 - Cape Town, South Africa
Duration: Aug 24 2014Aug 29 2014

Publication series

NameIFAC Proceedings Volumes (IFAC-PapersOnline)
ISSN (Print)1474-6670


Conference19th IFAC World Congress on International Federation of Automatic Control, IFAC 2014
Country/TerritorySouth Africa
CityCape Town


  • Donders' law
  • Listing's law
  • Optimal Control
  • Quaternions
  • Rigid body dynamics


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