  In human-robot interactions, eye movements play an important role in
non-verbal communication. However, controlling the motions of a robotic eye
that display similar performance as the human oculomotor system is still a
major challenge. In this paper, we study how to control a realistic model of
the human eye with a cable-driven actuation system that mimics the six degrees
of freedom of the extra-ocular muscles. The biomimetic design introduces novel
challenges to address, most notably the need to control the pretension on each
individual muscle to prevent the loss of tension during motion, that would lead
to cable slack and lack of control. We built a robotic prototype and developed
a nonlinear simulator and two controllers. In the first approach, we linearized
the nonlinear model, using a local derivative technique, and designed
linear-quadratic optimal controllers to optimize a cost function that accounts
for accuracy, energy expenditure, and movement duration. The second method uses
a recurrent neural network that learns the nonlinear system dynamics from
sample trajectories of the system, and a non-linear trajectory optimization
solver that minimizes a similar cost function. We focused on the generation of
rapid saccadic eye movements with fully unconstrained kinematics, and the
generation of control signals for the six cables that simultaneously satisfied
several dynamic optimization criteria. The model faithfully mimics the
three-dimensional rotational kinematics and dynamics observed for human
saccades. Our experimental results indicate that while both methods yielded
similar results, the nonlinear method is more flexible for future improvements
to the model, for which the calculations of the linearized model's
position-dependent pretensions and local derivatives become particularly
tedious.
