Abstract
In complex real-life motor skills such as unconstrained throwing, performance depends on how accurate is on average the outcome of noisy, high-dimensional, and redundant actions. What characteristics of the action distribution relate to performance and how different individuals select specific action distributions are key questions in motor control. Previous computational approaches have highlighted that variability along the directions of first order derivatives of the action-to-outcome mapping affects performance the most, that different mean actions may be associated to regions of the actions space with different sensitivity to noise, and that action covariation in addition to noise magnitude matters. However, a method to relate individual high-dimensional action distribution and performance is still missing. Here we introduce a de-composition of performance into a small set of indicators that compactly and directly characterize the key performance-related features of the distribution of high-dimensional redundant actions. Central to the method is the observation that, if performance is quantified as a mean score, the Hessian (second order derivatives) of the action-to-score mapping and its geometric relationship with the action covariance determines the noise sensitivity of the action distribution. Thus, we approximate mean score as the sum of the score of the mean action and a tolerance-variability index which depends on both Hessian and covariance matrices. Such index can be expressed as the product of three terms capturing overall noise magnitude, overall noise sensitivity, and alignment of the most variable and most noise sensitive directions. We apply this method to the analysis of unconstrained throwing actions by non-expert participants and show that our de-composition allows to compactly characterize inter-individual differences in throwing strategies with different but also with similar performance.
Author summary Why do people differ in their performance of complex motor skills? In many real-life motor tasks achieving a goal requires selecting an appropriate high-dimensional action out of infinitely many goal-equivalent actions. Because of sensorimotor noise, we are unable to execute the exact same action twice and our performance depends on how accurate we are on average. Thus, to understand why people perform differently we need to characterize how their action distribution relates to their mean task score. While better performance is often associated to smaller variability around a more accurate mean action, performance also depends on the relationship between the directions of highest variability in action space and the directions in which action variability affects the most the outcome of the action. However, characterizing such geometric relationship when actions are high dimensional is challenging. In this work we introduce a method that allows to characterize the key performance-related features of the distribution of high-dimensional actions by a small set of indicators. We can then compare such indicators in different people performing a complex task (such as unconstrained throwing) and directly characterize the most skilled ones but also identify different strategies that distinguish people with similar performance.
