A Geometric Approach to Head/Eye Control
In this paper, we study control problems that can be directly applied to controlling the rotational motion of eye and head. We model eye and head as a sphere, or ellipsoid, rotating about its center, or about its south pole, where the axes of rotation are physiologically constrained, as was proposed...
Published in: | IEEE Access |
---|---|
Main Authors: | , , |
Format: | Article in Journal/Newspaper |
Language: | English |
Published: |
IEEE
2014
|
Subjects: | |
Online Access: | https://doi.org/10.1109/ACCESS.2014.2315523 https://doaj.org/article/24f26d85aa9442ec8fd82615533919c0 |
id |
ftdoajarticles:oai:doaj.org/article:24f26d85aa9442ec8fd82615533919c0 |
---|---|
record_format |
openpolar |
spelling |
ftdoajarticles:oai:doaj.org/article:24f26d85aa9442ec8fd82615533919c0 2023-05-15T18:22:50+02:00 A Geometric Approach to Head/Eye Control Bijoy K. Ghosh Indika B. Wijayasinghe Sanath D. Kahagalage 2014-01-01T00:00:00Z https://doi.org/10.1109/ACCESS.2014.2315523 https://doaj.org/article/24f26d85aa9442ec8fd82615533919c0 EN eng IEEE https://ieeexplore.ieee.org/document/6782433/ https://doaj.org/toc/2169-3536 2169-3536 doi:10.1109/ACCESS.2014.2315523 https://doaj.org/article/24f26d85aa9442ec8fd82615533919c0 IEEE Access, Vol 2, Pp 316-332 (2014) Electrical engineering. Electronics. Nuclear engineering TK1-9971 article 2014 ftdoajarticles https://doi.org/10.1109/ACCESS.2014.2315523 2022-12-31T15:32:37Z In this paper, we study control problems that can be directly applied to controlling the rotational motion of eye and head. We model eye and head as a sphere, or ellipsoid, rotating about its center, or about its south pole, where the axes of rotation are physiologically constrained, as was proposed originally by Listing and Donders. The Donders' constraint is either derived from Fick gimbals or from observed rotation data of adult human head. The movement dynamics is derived on SO(3) or on a suitable submanifold of SO(3) after describing a Lagrangian. Using two forms of parametrization, the axis-angle and Tait-Bryan, the motion dynamics is described as an Euler-Lagrange's equation, which is written together with an externally applied control torque. Using the control system, so obtained, we propose a class of optimal control problem that minimizes the norm of the applied external torque vector. Our control objective is to point the eye or head, toward a stationary point target, also called the regulation problem. The optimal control problem has also been analyzed by writing the dynamical system as a Newton-Euler's equation using angular velocity as part of the state variables. In this approach, explicit parametrization of SO(3) is not required. Finally, in the appendix, we describe a recently introduced potential control problem to address the regulation problem. Article in Journal/Newspaper South pole Directory of Open Access Journals: DOAJ Articles South Pole Tait ENVELOPE(-58.000,-58.000,-64.350,-64.350) IEEE Access 2 316 332 |
institution |
Open Polar |
collection |
Directory of Open Access Journals: DOAJ Articles |
op_collection_id |
ftdoajarticles |
language |
English |
topic |
Electrical engineering. Electronics. Nuclear engineering TK1-9971 |
spellingShingle |
Electrical engineering. Electronics. Nuclear engineering TK1-9971 Bijoy K. Ghosh Indika B. Wijayasinghe Sanath D. Kahagalage A Geometric Approach to Head/Eye Control |
topic_facet |
Electrical engineering. Electronics. Nuclear engineering TK1-9971 |
description |
In this paper, we study control problems that can be directly applied to controlling the rotational motion of eye and head. We model eye and head as a sphere, or ellipsoid, rotating about its center, or about its south pole, where the axes of rotation are physiologically constrained, as was proposed originally by Listing and Donders. The Donders' constraint is either derived from Fick gimbals or from observed rotation data of adult human head. The movement dynamics is derived on SO(3) or on a suitable submanifold of SO(3) after describing a Lagrangian. Using two forms of parametrization, the axis-angle and Tait-Bryan, the motion dynamics is described as an Euler-Lagrange's equation, which is written together with an externally applied control torque. Using the control system, so obtained, we propose a class of optimal control problem that minimizes the norm of the applied external torque vector. Our control objective is to point the eye or head, toward a stationary point target, also called the regulation problem. The optimal control problem has also been analyzed by writing the dynamical system as a Newton-Euler's equation using angular velocity as part of the state variables. In this approach, explicit parametrization of SO(3) is not required. Finally, in the appendix, we describe a recently introduced potential control problem to address the regulation problem. |
format |
Article in Journal/Newspaper |
author |
Bijoy K. Ghosh Indika B. Wijayasinghe Sanath D. Kahagalage |
author_facet |
Bijoy K. Ghosh Indika B. Wijayasinghe Sanath D. Kahagalage |
author_sort |
Bijoy K. Ghosh |
title |
A Geometric Approach to Head/Eye Control |
title_short |
A Geometric Approach to Head/Eye Control |
title_full |
A Geometric Approach to Head/Eye Control |
title_fullStr |
A Geometric Approach to Head/Eye Control |
title_full_unstemmed |
A Geometric Approach to Head/Eye Control |
title_sort |
geometric approach to head/eye control |
publisher |
IEEE |
publishDate |
2014 |
url |
https://doi.org/10.1109/ACCESS.2014.2315523 https://doaj.org/article/24f26d85aa9442ec8fd82615533919c0 |
long_lat |
ENVELOPE(-58.000,-58.000,-64.350,-64.350) |
geographic |
South Pole Tait |
geographic_facet |
South Pole Tait |
genre |
South pole |
genre_facet |
South pole |
op_source |
IEEE Access, Vol 2, Pp 316-332 (2014) |
op_relation |
https://ieeexplore.ieee.org/document/6782433/ https://doaj.org/toc/2169-3536 2169-3536 doi:10.1109/ACCESS.2014.2315523 https://doaj.org/article/24f26d85aa9442ec8fd82615533919c0 |
op_doi |
https://doi.org/10.1109/ACCESS.2014.2315523 |
container_title |
IEEE Access |
container_volume |
2 |
container_start_page |
316 |
op_container_end_page |
332 |
_version_ |
1766202252541820928 |