Dynamic modeling and integrated control framework for an eye-like robot with torsional–positional decoupling and Listing’s law enforcement

This paper introduces a dynamic model of an eye-like robot that incorporates torsional motion, allowing independent control of pupil position and torsion. Based on this model, two complementary controllers are proposed within a quaternion-based single-rotation framework. The Geometrically Optimized Position Controller (GOPC) aligns motion along the optimal convergence axis for fast, stable transitions, while the Neural Network–Based Inverse Dynamics Controller (NNBIDC) learns and replicates the system’s nonlinear dynamics. A torsion-correction algorithm enforces Listing’s law by properly constraining torsional motion. MATLAB simulations confirm the model’s accuracy, showing precise trajectory tracking and physiologically realistic torsion.