Error Correction and the Structure of Inter-Trial Fluctuations in a Redundant Movement Task

Abstract

We study inter-trial movement fluctuations exhibited by human participants during the repeated execution of a virtual shuffleboard task. Focusing on skilled performance, theoretical analysis of a previously-developed general model of inter-trial error correction is used to predict the temporal and geometric structure of variability near a goal equivalent manifold (GEM). The theory also predicts that the goal-level error scales linearly with intrinsic body-level noise via the total body-goal sensitivity, a new derived quantity that illustrates how task performance arises from the interaction of active error correction and passive sensitivity properties along the GEM. Linear models estimated from observed fluctuations, together with a novel application of bootstrapping to the estimation of dynamical and correlation properties of the inter-trial dynamics, are used to experimentally confirm all predictions, thus validating our model. In addition, we show that, unlike “static” variability analyses, our dynamical approach yields results that are independent of the coordinates used to measure task execution and, in so doing, provides a new set of task coordinates that are intrinsic to the error-regulation process itself.

Increased gait variability may not imply impaired stride-to-stride control of walking in healthy older adults

“…α = ½ indicates uncorrelated data: all deviations are equally likely to be followed by deviations in either direction. Consistent with our computational control model results [21, 22, 24, 25], we interpret statistical persistence ( α > ½) to indicate variables that are weakly regulated. Variables that are tightly regulated are expected to exhibit either uncorrelated or anti-persistent fluctuations ( α ≤ ~½).…”

“…Therefore, it is important to better understand where gait variability comes from and what factors contribute to that variability [22]. In particular, there is a need to distinguish between variability that arises simply from changes in neuromotor noise [10–13] from that which may arise from changes in how people regulate their stride variables (e.g., L , T , etc.)…”

“…To quantify how deviations in stride variables are regulated from each stride to the next, we need analytical tools that directly quantify the degree and direction of stride-to-stride changes in each variable [22, 25]. Here, we computed scaling exponents, α , using Detrended Fluctuation Analysis (DFA) [25, 30] (see Fig.…”

“…Complicating this question is equifinality [19–22]: for most real tasks, there exists an infinite number of movement solutions that equally satisfy the task goal. Thus, certain control actions may reduce variability of some variables, while simultaneously increasing variability of others.…”

“…We then analyze not only the magnitude of the variability observed, but also quantify the degree to which fluctuations about the GEM on any given stride are directly corrected for on subsequent strides [24, 25]. This fundamentally dynamical analysis of movement fluctuations near the GEM yields a quantification of the “strength” of motor regulation (i.e., control) that is independent of the amount of variability present in the data [21, 22]. Our models of stride-to-stride fluctuation dynamics were validated experimentally [24, 25] and our overall theoretical predictions replicated in at least three independent studies [26–28].…”