TY - JOUR
T1 - Dynamics of human head and eye rotations under donders' constraint
AU - Ghosh, Bijoy K.
AU - Wijayasinghe, Indika B.
N1 - Funding Information:
Manuscript received February 07, 2011; revised June 16, 2011; accepted September 26, 2011. Date of publication February 03, 2012; date of current version September 21, 2012. This work was supported in part by the National Science Foundation under Grant 0523983. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation. Recommended by Associate Editor Z. Qu.
PY - 2012
Y1 - 2012
N2 - The rotation of human head and the eye are modeled as a perfect sphere with the rotation actuated by external torques. For the head movement, the axis of rotation is constrained by a law proposed in the 19th century by Donders. For the saccadic eye movement, Donders' Law is restricted to a law that goes by the name of Listing's Law. In this paper, head movement and saccadic eye movement are modeled using principles from classical mechanics and the associated Euler Lagrange's equations (EL) are analyzed. Geodesic curves are obtained in the space of allowed orientations for the head and the eye and projections of these curves on the space \rm S 2 of pointing directions of the eye/head are shown. A potential function and a damping term has been added to the geodesic dynamics from EL and the resulting head and eye trajectories settle down smoothly towards the unique point of minimum potential. The minimum point can be altered to regulate the end point of the trajectories (potential control). Throughout the paper, the restricted dynamics of the eye and the head movement have been compared with the unrestricted rotational dynamics on SO(3) and the corresponding EL equations have been analyzed. A version of the Donders' Theorem, on the possible head orientations for a specific head direction, has been stated and proved in AppendixI. In the case of eye movement, Donders' Theorem restricts to the well known Listing's Theorem. In AppendixII , a constraint on the angular velocity and the angular acceleration vectors is derived for the head movement satisfying Donders' constraint. A statement of this constraint that goes by the name half angle rule, has been derived.
AB - The rotation of human head and the eye are modeled as a perfect sphere with the rotation actuated by external torques. For the head movement, the axis of rotation is constrained by a law proposed in the 19th century by Donders. For the saccadic eye movement, Donders' Law is restricted to a law that goes by the name of Listing's Law. In this paper, head movement and saccadic eye movement are modeled using principles from classical mechanics and the associated Euler Lagrange's equations (EL) are analyzed. Geodesic curves are obtained in the space of allowed orientations for the head and the eye and projections of these curves on the space \rm S 2 of pointing directions of the eye/head are shown. A potential function and a damping term has been added to the geodesic dynamics from EL and the resulting head and eye trajectories settle down smoothly towards the unique point of minimum potential. The minimum point can be altered to regulate the end point of the trajectories (potential control). Throughout the paper, the restricted dynamics of the eye and the head movement have been compared with the unrestricted rotational dynamics on SO(3) and the corresponding EL equations have been analyzed. A version of the Donders' Theorem, on the possible head orientations for a specific head direction, has been stated and proved in AppendixI. In the case of eye movement, Donders' Theorem restricts to the well known Listing's Theorem. In AppendixII , a constraint on the angular velocity and the angular acceleration vectors is derived for the head movement satisfying Donders' constraint. A statement of this constraint that goes by the name half angle rule, has been derived.
KW - Donders' law
KW - Euler Lagrange equation
KW - Listing's Law
KW - Riemannian Metric
KW - eye/head movement
KW - geodesics
KW - half angle rule
KW - potential control
UR - http://www.scopus.com/inward/record.url?scp=84866941203&partnerID=8YFLogxK
U2 - 10.1109/TAC.2012.2186183
DO - 10.1109/TAC.2012.2186183
M3 - Article
AN - SCOPUS:84866941203
VL - 57
SP - 2478
EP - 2489
JO - IEEE Transactions on Automatic Control
JF - IEEE Transactions on Automatic Control
SN - 0018-9286
IS - 10
M1 - 6144709
ER -