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Noisy optimal control strategies for modelling saccades Jones, Garrett L.


Eye movements have for a while provided us a closer view into how the brain commands the body. Particularly interesting are saccades: fast and accurate eye movements that allow us to scan our visual surroundings. One observation is that motor commands issued by the brain are corrupted by a signal-dependent noise. Moreover, the variance of the signal scales linearly with the control signal squared. It is assumed that such uncertainty in the dynamics introduces a probability distribution of the eye that the brain accounts for during motion planning. We propose a framework for computing the optimal control law for arbitrary dynamical systems, subject to noise, and where the cost function depends on a statistical distribution of the eye’s position. A key contribution of this framework is estimating the endpoint distribution of the plant using Monte Carlo sampling, which is done efficiently using commodity graphics hardware in parallel. We then describe a modified form of gradient descent for computing the optimal control law for an objective function prone to stochastic effects. We compare our approach to other methods, such as downhill simplex and Covariance-Matrix-Adaptation, which are considered “gradient-free” approaches to optimization. We finally conclude with several examples that show the framework successfully controlling saccades for different plant models of the oculomotor system: this includes a 3D torque-based model of the eye, and a a nonlinear model of the muscle actuator that drives the eye.

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