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Cerebellar learning of internal models for reaching and grasping: adaptive control in the presence of delays

As a synthesis of a legacy of cerebellar models, we have developed a new general cerebellar module incorporating all major cell types and connections. It has two key features: 1. reciprocal connections between cerebellar nuclear cells and the inferior olive result in a stable learning system driving the cerebellum to mirror sensory input to the olive; and 2. synaptic eligibility effects a time-shift between training and input signals so that the cerebellar circuit becomes a predictor. We then show how the same module could perform different tasks where the cerebellum has been implicated, namely prism adaptation; inverse dynamics learning for accurate execution of movements; and state estimation and timing for on-line trajectory planning. Replicating experiments by Martin et al. (1996b), we show how observed behavior such as the prism after-effect and transfer between overand underarm throwing could be generated and contrast the acquisition of a new skill with simple adaptation to a novel condition. For adaptive control of movements, we argue that with trajectory deviations detected at the spinal cord level, eligibility traces in the cerebellum can solve the temporal mismatch problem of delayed error signals. We demonstrate that the cerebellar module implements a nonlinear predictive regulator by learning part of the inverse dynamics of the plant and spinal circuit. Addressing the coordination problem, we embedded the cerebellar module in a control theoretic model (Hoff and Arbib, 1993) for the kinematics of hand transport and preshape during reach and grasp. A critical part of the model was a state predictor unit, needed to compensate for long efferent and afferent delays. We show that our cerebellum module, by virtue of its structure and connectivity in the motor system, is uniquely suited to learn this function.