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In human-robot interactions, eye movements play an important role innon-verbal communication. However, controlling the motions of a robotic eyethat display similar performance as the human oculomotor system is still amajor challenge. In this paper, we study how to control a realistic model ofthe human eye with a cable-driven actuation system that mimics the six degreesof freedom of the extra-ocular muscles. The biomimetic design introduces novelchallenges to address, most notably the need to control the pretension on eachindividual muscle to prevent the loss of tension during motion, that would leadto cable slack and lack of control. We built a robotic prototype and developeda nonlinear simulator and two controllers. In the first approach, we linearizedthe nonlinear model, using a local derivative technique, and designedlinear-quadratic optimal controllers to optimize a cost function that accountsfor accuracy, energy expenditure, and movement duration. The second method usesa recurrent neural network that learns the nonlinear system dynamics fromsample trajectories of the system, and a non-linear trajectory optimizationsolver that minimizes a similar cost function. We focused on the generation ofrapid saccadic eye movements with fully unconstrained kinematics, and thegeneration of control signals for the six cables that simultaneously satisfiedseveral dynamic optimization criteria. The model faithfully mimics thethree-dimensional rotational kinematics and dynamics observed for humansaccades. Our experimental results indicate that while both methods yieldedsimilar results, the nonlinear method is more flexible for future improvementsto the model, for which the calculations of the linearized model'sposition-dependent pretensions and local derivatives become particularlytedious.

Emergence of human oculomotor behavior from optimal control of a cable-driven biomimetic robotic eye