Passive Stability and Active Control in a Rhythmic Task

Abstract

Rhythmically bouncing a ball with a racket is a task that affords passively stable solutions as demonstrated by stability analyses of a mathematical model of the task. Passive stability implies that no active control is needed as errors die out without requiring corrective actions. Empirical results from human performance demonstrated that actors indeed exploit this passive dynamics in steady-state performance, thereby reducing computational demands of the task. The present study investigated the response to perturbations of different magnitudes designed on the basis of the model's basin of attraction. Humans performed the task in a virtual reality set-up with a haptic interface. Relaxation times of the performance errors showed significantly faster returns than predicted from the purely passive model, indicative of active error corrections. Systematic adaptations in the racket trajectories were a monotonic function of the perturbation magnitudes, indicating that active control was applied in proportion to the perturbation. These results did not indicate any sensitivity to the boundary of stability. Yet the influence of passive dynamics was also seen: the pattern of relaxation times in the major performance variable ball height was consistent with qualitative predictions derived from the basin of attraction and racket accelerations at contact were generally negative signaling use of passive stability. These findings suggest that the fast return back to steady state was assisted by passive properties of the task. It was concluded that actors used a blend of active and passive control for all sizes of perturbations.