【Abstract】In this talk, our goal is to study control problems on human binoculomotor system as a simple mechanical control system, extending our earlier studies on monocular system. We assume that during the eye movement, each eye separately obeys a suitable form of Donders' law which states that, moving away from the primary gaze direction, eye orientations lie in a subset consisting of rotation matrices for which the axes are restricted to a suitable Donders' surface. When head is fixed, this surface is usually the Listing's plane. Additionally we assume that the gaze direction vectors, of the two eyes, remain coplanar during the entire time of the eye movement. This is equivalent to asking that the eyes are always fixated in the visual space. We define a restricted configuration space for the two eye system as a subset of SO(3) X SO(3) and describe a binocular system as a simple mechanical control system. A Riemannian metric has been introduced and the corresponding Euler Lagrange dynamics is written out. Two special cases of the Donders' surface is detailed in this paper. The first one is when the Donders' surface is the Listing's plane. The second one is when the Donders' surface for each of the two eyes are derived from Fick Gimbal. We have displayed the geodesic curves for binocular eye movements satisfying the Fick Gimbal. Optimal trajectory plots are subject of future research.
【Brief CV】Bijoy received his Ph.D. degree in Engineering Sciences from the Decision and Control Group of the Division of Applied Sciences, Harvard University, Cambridge, MA, in 1983. From 1983 to 2007 Bijoy was with the Department of Electrical and Systems Engineering, Washington University, St. Louis, MO, USA, where he was a Professor and Director of the Center for BioCybernetics and Intelligent Systems. Currently he is the Dick and Martha Brooks Regents Professor of Mathematics and Statistics at Texas Tech University, Lubbock, TX, USA. He received the D. P. Eckmann award in 1988 from the American Automatic Control Council, the Japan Society for the Promotion of Sciences Invitation Fellowship in 1997, the Chinese Academy of Sciences Invitation Fellowship in 2016, the Distinguished Visiting Professorship to visit IIT Kharagpur, India in 2016. He became a Fellow of the IEEE in 2000 and a Fellow of the International Federation on Automatic Control in 2014. Bijoy had held visiting positions at Tokyo Institute of Technology, Osaka University and Tokyo Denki University, Japan, University of Padova in Italy, Royal Institute of Technology and Institut Mittag-Leffler, Stockholm, Sweden, Yale University, USA, Technical University of Munich, Germany, Chinese Academy of Sciences, China and Indian Institute of Technology, Kharagpur, India. Bijoy's current research interests are in BioMechanics, Cyberphysical Systems and Control Problems in Rehabilitation Engineering.