Nathan Sitkoff

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A model of cerebellar learning for control of arm movements using muscle synergies

by James Houk and Nathan Sitkoff

… Intelligence in Robotics …, 1997

Biological control systems have long been studied as possible inspiration for the construction of... more Biological control systems have long been studied as possible inspiration for the construction of robotic controllers. The cerebellum is known to be involved in the production and learning of smooth, coordinated movements. In this paper, we present a model of cerebellar control of a muscle-actuated, two-link, planar arm. The model learns in a trial-and-error fashion to generate the appropriate sequence of motor signals that accurately bring the arm to a speci ed target. The motor signals produced by the cerebellum are speci ed in muscle synergy space. When the cerebellum fails to bring the arm to the target, an extra-cerebellar module performs low-quality corrective movements, from which the cerebellum updates its program. In learning to perform the task, the cerebellum constructs an implicit inverse model of the plant. This model uses a combination of delayed sensory signals and recentlygenerated motor commands to compute the new output motor signal.

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Cerebellar Learning for Control of a Two-Link Arm in Muscle Space

by James Houk and Nathan Sitkoff

cs.cmu.edu

Biological control systems have long been studied as possible inspiration for the construction of... more

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Implementing a genetic algorithm on a parallel custom computing machine

Proceedings IEEE Symposium on FPGAs for Custom Computing Machines, 1995

Genetic algorithms (GAS) are a currently popular method for nonlinear optimization that can be us... more

Kettner, R. E. et al. Prediction of complex two-dimensional trajectories by a cerebellar model of smooth pursuit eye movement. J. Neurophysiol. 77, 2115-2130

by James Houk, Barry Peterson, and Nathan Sitkoff

Journal of Neurophysiology

frequency, the eye soon locks onto the target so that Houk, B. W. Peterson, and A. G. Barto. Pred... more frequency, the eye soon locks onto the target so that Houk, B. W. Peterson, and A. G. Barto. Prediction of complex there is little or no lag, and sometimes even a slight lead, two-dimensional trajectories by a cerebellar model of smooth purbetween eye and target. This has been shown during tracking suit eye movement. J. Neurophysiol. 77: 2115Neurophysiol. 77: -2130Neurophysiol. 77: , 1997. A of a variety of periodic stimuli, including sine and square neural network model based on the anatomy and physiology of the waves in one dimension (Bahill and McDonald 1983; Dallos cerebellum is presented that can generate both simple and complex and Jones 1963; Kowler and Steinman 1979; Lisberger et predictive pursuit, while also responding in a feedback mode to al. 1981; Pola and Wyatt 1980) and circular and rhomboid visual perturbations from an ongoing trajectory. The model allows trajectories in two dimensions (Collewijn and Tamminga the prediction of complex movements by adding two features that Deno et al. 1995; Leung and Kettner 1997). This are not present in other pursuit models: an array of inputs distributed over a range of physiologically justified delays, and a novel, tracking behavior is considered predictive because visual biologically plausible learning rule that generated changes in synsignals are processed by the smooth pursuit system with aptic strengths in response to retinal slip errors that arrive after considerable delays that have been estimated at Ç100 ms long delays. To directly test the model, its output was compared (Becker and Fuchs 1984; Carl and Gellman 1986; Fuchs with the behavior of monkeys tracking the same trajectories. There 1967; Leung and Kettner 1997; Lisberger and Westbrook was a close correspondence between model and monkey perfor-1985; Robinson 1965). One would expect tracking to lag mance. Complex target trajectories were created by summing two by similar delays during smooth pursuit if the eye were or three sinusoidal components of different frequencies along horicontrolled exclusively by a simple negative feedback system zontal and/or vertical axes. Both the model and the monkeys were able to track these complex sum-of-sines trajectories with small based on visual input. phase delays that averaged 8 and 20 ms in magnitude, respectively.

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Prediction of complex two-dimensional trajectories by a cerebellar model of smooth pursuit eye movement

by James Houk and Nathan Sitkoff

Journal of neurophysiology, 1997

A neural network model based on the anatomy and physiology of the cerebellum is presented that ca... more A neural network model based on the anatomy and physiology of the cerebellum is presented that can generate both simple and complex predictive pursuit, while also responding in a feedback mode to visual perturbations from an ongoing trajectory. The model allows the prediction of complex movements by adding two features that are not present in other pursuit models: an array of inputs distributed over a range of physiologically justified delays, and a novel, biologically plausible learning rule that generated changes in synaptic strengths in response to retinal slip errors that arrive after long delays. To directly test the model, its output was compared with the behavior of monkeys tracking the same trajectories. There was a close correspondence between model and monkey performance. Complex target trajectories were created by summing two or three sinusoidal components of different frequencies along horizontal and/or vertical axes. Both the model and the monkeys were able to track the...

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A Cerebellar Model of Timing and Prediction in the Control of Reaching

by James Houk and Nathan Sitkoff

Neural Computation, 1999

A simplified model of the cerebellum was developed to explore its potential for adaptive, predict... more A simplified model of the cerebellum was developed to explore its potential for adaptive, predictive control based on delayed feedback information. An abstract representation of a single Purkinje cell with multistable properties was interfaced, via a formalized premotor network, with a simulated single degree-of-freedom limb. The limb actuator was a nonlinear spring-mass system based on the nonlinear velocity dependence of the stretch reflex. By including realistic mossy fiber signals, as well as realistic conduction delays in afferent and efferent pathways, the model allowed the investigation of timing and predictive processes relevant to cerebellar involvement in the control of movement. The model regulates movement by learning to react in an anticipatory fashion to sensory feedback. Learning depends on training information generated from corrective movements and uses a temporally-asymmetric form of plasticity for the parallel fiber synapses on Purkinje cells.

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A Computational Model of Cerebellar Learning for Limb Control

by James Houk and Nathan Sitkoff

We present a model of cerebellar learning for control of limb movements. The model learns to gene... more We present a model of cerebellar learning for control of limb movements. The model learns to generate relatively smooth and direct arm movements, while not assuming (as some models do) a high-level input that speci es a preplanned trajectory. The model controls a simulated two-joint arm, which is actuated by a set of six muscles. Control of the arm is shared by a learning cerebellar module and a hard-wired extra-cerebellar (EC) system. The cerebellar module consists of a group of independent submodules, referred to as Adjustable Pattern Generators (APGs). Each APG is made up of a set of Purkinje cells and a single cerebellar nuclear cell. Activation of an APG's nuclear cell drives a muscle synergy (a subset of the muscles). The EC system is responsible for producing low-quality corrective movements in situations where the cerebellar module is unable to bring the arm to the speci ed target. Via proprioceptive inputs, the modeled inferior olive assesses directional errors in cerebellar-generated movements by observing subsequent corrective movements produced by the EC system.

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