The Dynamical Analysis of Inter-Trial Fluctuations Near Goal Equivalent Manifolds

Abstract

Using the concept of task manifolds, a number of data analysis methods have been used to explain how redundancy influences the structure of variability observed during repeated motor performance. Here we describe investigations that integrate the task manifold perspective with the analysis of Inter-Trial task dynamics. Goal equivalent manifolds (GEMs), together with optimal control ideas, are used to formulate simple models that serve as experimentally testable hypotheses on how Inter-Trial fluctuations are generated and regulated. In an experimental context, these phenomenological models allow us to show how error-correcting control is spatiotemporally organized around a given GEM. To illustrate our approach, we apply it to study the variability observed in a virtual shuffleboard task. The geometric stability properties of the Inter-Trial dynamics near the GEM are extracted from fluctuation time series data. We find that subjects exhibit strong control of fluctuations in an eigendirection transverse to the GEM, whereas they only weakly control fluctuations in an eigendirection nearly, but not exactly, tangent to it. We demonstrate that our dynamical analysis is robust under coordinate transformations, and discuss how our results support a generalized interpretation of the minimum intervention principle that suggests the involvement of competing costs in addition to goal-level error minimization.