Feedback Linearization of the Human Head Rotation Dynamics using Tait-Bryan Parameterization

Bhagya Athukorallage, Bijoy K. Ghosh

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

Abstract

Using the well-known Tait-Bryan (TB) Parameterization, we revisit the human head pointing control problem as a constrained dynamics on SO(3) from the point of view of a nonlinear multi input multi output (MIMO) system. The constraint, proposed by Donders, is that for every human head rotating away from its primary pointing direction, the rotational vectors are restricted to lie on a surface called the Donders'surface. This paper assumes that the Donders' surface is described by a quadratic equation on the coordinates of the rotation vector. The inputs to the MIMO system are three external torques provided by muscles rotating the head. The three output signals are chosen as follows. Two of the signals are coordinates of the frontal pointing direction. The third signal measures deviation of the state vector from the Donders' surface. Thus we have a 3 × 3 square system and recent results have shown that this system is feedback linearizable on a suitable neighborhood N of the state space. In this paper, we estimate a lower bound on the size of N by computing distance between the Donders' and the associated Singularity surface, using the TB parameterization. The computed distance function is compared with a similarly computed distance function using Novelia and O'Reilly parametrization. Our surprising result, on the location of the singular points, suggests an advantage of using the TB parameterization for this class of feedback linearization.

Original languageEnglish
Title of host publication2018 IEEE 14th International Conference on Control and Automation, ICCA 2018
PublisherIEEE Computer Society
Pages447-452
Number of pages6
ISBN (Print)9781538660898
DOIs
StatePublished - Aug 21 2018
Event14th IEEE International Conference on Control and Automation, ICCA 2018 - Anchorage, United States
Duration: Jun 12 2018Jun 15 2018

Publication series

NameIEEE International Conference on Control and Automation, ICCA
Volume2018-June
ISSN (Print)1948-3449
ISSN (Electronic)1948-3457

Conference

Conference14th IEEE International Conference on Control and Automation, ICCA 2018
CountryUnited States
CityAnchorage
Period06/12/1806/15/18

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