Abstract
Variability in motor performance decreases with practice but is never entirely eliminated, due in part to inherent motor noise. The present study develops a method that quantifies how performers can shape their performance to minimize the effects of motor noise on the result of the movement. Adopting a statistical approach on sets of data, the method quantifies three components of variability (tolerance, noise, and covariation) as costs with respect to optimal performance. T-Cost quantifies how much the result could be improved if the location of the data were optimal, N-Cost compares actual results to results with optimal dispersion at the same location, and C-Cost represents how much improvement stands to be gained if the data covaried optimally. The TNC-Cost analysis is applied to examine the learning of a throwing task that participants practiced for 6 or 15 days. Using a virtual set-up, 15 participants threw a pendular projectile in a simulated concentric force field to hit a target. Two variables, angle and velocity at release, fully determined the projectile’s trajectory and thereby the accuracy of the throw. The task is redundant and the successful solutions define a nonlinear manifold. Analysis of experimental results indicated that all three components were present and that all three decreased across practice. Changes in T-Cost were considerable at the beginning of practice; C-Cost and N-Cost diminished more slowly, with N-Cost remaining the highest. These results showed that performance variability can be reduced by three routes: by tuning tolerance, covariation and noise in execution. We speculate that by exploiting T-Cost and C-Cost, participants minimize the effects of inevitable intrinsic noise.
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Notes
The words “result” and “result variable” are used as a general term to designate any measure that quantifies how satisfactorily a task was achieved, such as error, score, difference from target, or even a variability estimate if sets of data were evaluated for their result. In the present study we only consider one such measure: distance to target.
A manifold is a mathematical term from differential geometry generally referring to a collection or set of objects (James and James 1992, 5th ed.). The set of solutions in the skittles task is a smooth differentiable manifold whether or not the execution variables have different units. The interested reader can find definitions at any level of detail in relevant mathematical texts. For example, James and James (1992), 5th ed): “A topological manifold of dimension n is a topological space such that each point has a neighborhood which is homeomorphic to the interior of a sphere in Euclidean space of dimension n.” The term has received many qualifications, including connected or disconnected, compact or noncompact, etc.
The model with the two orthogonal springs is equivalent to one with a single spring rotating around a center pivot. However, both models are approximations as they do not include vertical elevation as is present in the real skittles task.
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Acknowledgments
This research was supported by grants from the National Science Foundation, BCS-0450218, the National Institutes of Health, R01 HD045639, and the Office of Naval Research, N00014-05-1-0844. We would like to express our thanks to Hermann Müller, Tjeerd Dijkstra and Neville Hogan for many insightful discussions and to Kunlin Wei for his help in creating the experimental set-up.
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Cohen, R.G., Sternad, D. Variability in motor learning: relocating, channeling and reducing noise. Exp Brain Res 193, 69–83 (2009). https://doi.org/10.1007/s00221-008-1596-1
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DOI: https://doi.org/10.1007/s00221-008-1596-1