Actively tracking 'passive' stability in a ball bouncing task.

Abstract

This study investigates the control involved in a task where subjects rhythmically bounce a ball with a hand-held racket as regularly as possible to a prescribed amplitude. Stability analyses of a kinematic model of the ball-racket system revealed that dynamically stable solutions exist if the racket hits the ball in its decelerating upward movement phase. Such solutions are resistant to small perturbations obviating explicit error corrections. Previous studies reported that subjects' performance was consistent with this 'passive' stability. However, some 'active' control is needed to attune to this passive stability. The present study investigates this control by confronting subjects with perturbations where stable behavior cannot be maintained solely from passive stability. Six subjects performed rhythmic ball bouncing in a virtual reality set-up with and without perturbations. In the perturbation trials the coefficient of restitution of the ball-racket contact was changed at every fifth contact leading to unexpected ball amplitudes. The perturbations were compensated for within 2-3 bouncing cycles such that ball amplitudes decreased to initial values. Passive stability was reestablished as indicated by negative racket acceleration. Results revealed that an adjustment of the racket period ensured that the impacts occurred at a phase associated with passive stability. These findings were implemented in a model consisting of a neural oscillator that drives a mechanical actuator (forearm holding the racket) to bounce the ball. Following the perturbation, the oscillator's period is adjusted based on the perceived ball velocity after impact. Simulation results reproduced the major aspects of the experimental results.