Listing-Consistent Reduced-Order Dynamics and Nonlinear Feedback Control of Eye Movements

This study develops an explicit Listing-consistent reduced-order dynamics and nonlinear feedback control framework for generating biomimetic eye movements. Building on the established relationship between Listing’s Law and the Half-Angle Rule, we give a coordinate-specific necessary-and-sufficient proof for trajectories starting from a compatible orientation within a nonsingular gaze domain. A single holonomic constraint and its velocity relation reduce a spherical-eye model from three rotational degrees of freedom and six states to two rotational degrees of freedom and four states. A fixed-frame torque compatibility condition and an explicit inverse control map convert desired yaw and pitch accelerations into two independent torque components and reconstruct the required torsional component. Human saccade recordings inform representative controller gains, which are held fixed across six trajectory comparisons using measured target displacements. These limited comparisons provide a preliminary qualitative assessment of the framework’s ability to generate saccade-like responses. Torsion is determined by Listing’s Law rather than measured independently.