Realistic 3D human saccades generated by a 6-DOF biomimetic robotic eye under optimal control

We recently developed a biomimetic robotic eye with six independent tendons, each controlled by their own rotatory motor, and with insertions on the eye ball that faithfully mimic the biomechanics of the human eye. We constructed an accurate physical computational model of this system, and learned to control its nonlinear dynamics by optimising a cost that penalised saccade inaccuracy, movement duration, and total energy expenditure of the motors. To speed up the calculations, the physical simulator was approximated by a recurrent neural network (NARX). We showed that the system can produce realistic eye movements that closely resemble human saccades in all directions: their nonlinear main-sequence dynamics (amplitude-peak eye velocity and duration relationships), cross-coupling of the horizontal and vertical movement components leading to approximately straight saccade trajectories, and the 3D kinematics that restrict 3D eye orientations to a plane (Listing's law). Interestingly, the control algorithm had organised the motors into appropriate agonist-antagonist muscle pairs, and the motor signals for the eye resembled the well-known pulse-step characteristics that have been reported for monkey motoneuronal activity. We here fully analyse the eye-movement properties produced by the computational model across the entire oculomotor range and the underlying control signals. We argue that our system may shed new light on the neural control signals and their couplings within the final neural pathways of the primate oculomotor system, and that an optimal control principle may account for a wide variety of oculomotor behaviours. The generated data are publicly available at https://data.ru.nl/collections/di/dcn/DSC_626870_0003_600.