Geometry and control of human eye movements

Ashoka D. Polpitiya, Wijesuriya P. Dayawansa, Clyde F. Martin, Bijoy K. Ghosh

Research output: Contribution to journalArticlepeer-review

47 Scopus citations


In this paper, we study the human oculomotor system as a simple mechanical control system. It is a well known physiological fact that all eye movements obey Listing's law, which states that eye orientations form a subset consisting of rotation matrices for which the axes are orthogonal to the normal gaze direction. First, we discuss the geometry of this restricted configuration space (referred to as the Listing space). Then we formulate the system as a simple mechanical control system with a holonomic constraint. We propose a realistic model with musculotendon complexes and address the question of controlling the gaze. As an example, an optimal energy control problem is formulated and numerically solved.

Original languageEnglish
Pages (from-to)170-180
Number of pages11
JournalIEEE Transactions on Automatic Control
Issue number2
StatePublished - Feb 2007


  • Eye movements
  • Geodesics
  • Hill model
  • Listing's law
  • Simple mechanical control systems


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