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

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 t...

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Bibliographic Details
Published in:Automatica (Oxford) 2014-02, Vol.50 (2), p.519-529
Main Authors: Wijayasinghe, Indika, Ruths, Justin, Büttner, Ulrich, Ghosh, Bijoy K., Glasauer, Stefan, Kremmyda, Olympia, Li, Jr-Shin
Format: Article
Language:English
Subjects:
Applied sciences
Classical mechanics
Computer science
control theory
systems
Construction costs
Control theory. Systems
Donders’ surface
Euler Lagrange’s equation
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Head movement
Human
Mathematical models
Optimal control
Parametrization
Physics
Potential control
Quadratic forms
Solid dynamics (ballistics, collision, multibody system, stabilization...)
Solid mechanics
Tait–Bryan parametrization
Trajectories
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Summary: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.
ISSN:0005-1098
1873-2836
DOI:10.1016/j.automatica.2013.11.017