摘要
In this paper,we consider eyes from the human binocular system,that simultaneously gaze on stationary point targets in space,while optimalal skipping from one target to the next,by rotaing their individual gaze drecton.The head is assume fixed on the torso and the rotaing gaze direction of the two eyes are assumed restricted to pass through a point in the visual space.It is further assumed that,individullly the rotations of the two eyes satisfy the well known Listing's law.We formulate and study acombined optimal gaze rotation for the two eyes,by constructing a single Riemanmian metric,on the asociaced parameter space.The goal is to optimally rotate so that the convergent gaze changes between two pre-specified target points in a finite time interval[0,1].The cost function we choose is the total energy,measured by the L2?norm,of the six extenal torques on the binocular system.The torque functions are synthesized by solving an associated*two-point boundary value problem.The paper demonstrates,via simulation,the shape of the optimal gaze trajectory of the focused point of the bin-ocular system.The Euclidean distance between the initial and the final point is compared to the arc:length of the optimal trajectory.The consumed energy.is computed for diferent eye movement chores and discussed in the paper.Via simulation we observe that certain eye movement maneuvers are energy fficicnt and demonstrate that the optimal external torque is a linear function in time.We also explore and conclude that spitting an arbitry opimal eye movement into optimal vergence and version components is not energy fficient although this is how the human oculomotor control seems to operate.Opimal gaze tajectories and opimal extermal torque functions reported in this paper is new.
