Following a moving target with a narrow-view foveal vision system is one of the essential oculomotor behaviors of humans and humanoids. This oculomotor behavior, called "smooth pursuit", requires accurate tracking control which cannot be achieved by a simple visual negative feedback controller due to the significant delays in visual information processing. In this paper, we present a biologically inspired smooth pursuit controller consisting of two cascaded subsystems: one is an inverse model controller for the oculomotor system; and the other is a learning controller for the dynamics of the visual target. The latter learns how to predict the target motion in head coordinates such that the tracking performance can be improved. We investigate our smooth pursuit system in simulations and experiments on a humanoid robot. By using a fast online statistical learning network, our humanoid oculomotor system is able to acquire a high performance smooth pursuit after about 5 seconds of learning despite significant processing delays in the system.
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