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Motor Adaptation as a Greedy Optimization of Error and Effort

¹Mechanical and Aerospace Engineering Department and ²Biomedical Engineering Department, University of California, Irvine, California; and ³Automatic Control Department, Universitat Politècnica de Catalunya, Barcelona, Spain

Submitted 12 October 2006; accepted in final form 24 March 2007

Motor adaptation to a novel dynamic environment is primarily thought of as a process in which the nervous system learns to anticipate the environmental forces to eliminate kinematic error. Here we show that motor adaptation can more generally be modeled as a process in which the motor system greedily minimizes a cost function that is the weighted sum of kinematic error and effort. The learning dynamics predicted by this minimization process are a linear, auto-regressive equation with only one state, which has been identified previously as providing a good fit to data from force-field-type experiments. Thus we provide a new theoretical result that shows how these previously identified learning dynamics can be viewed as arising from an optimization of error and effort. We also show that the coefficients of the learning dynamics must fall within a specific range for the optimization model to be valid and verify with experimental data from walking in a force field that they indeed fall in this range. Finally, we attempted to falsify the model by performing experiments in two conditions (repeated exposure to a force field, exposure to force fields of different strengths) for which the single-state, auto-regressive equation might be expected to not fit the data well. We found however that the equation adequately captured the pattern of errors and thus conclude that motor adaptation to a force field can be approximated as an optimization of effort and error for a range of experimental conditions.

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