Stability and Variability in Skilled Rhythmic Action—A Dynamical Analysis of Rhythmic Ball Bouncing

The task of rhythmically bouncing a ball in the air serves as a model system that addresses many fundamental questions of coordination and perceptual control of actions. The task is simplified such that ball and racket movements are constrained to the vertical direction and the ball cannot be lost. As such, a discrete nonlinear model for the kinematics of periodic racket motions and ballistic ball flight between ball-racket contacts was formulated which permitted a set of analyses and predictions. Most centrally, linear stability analysis predicts that the racket trajectory should be decelerating prior to ball contact in order to guarantee dynamically stable performance. Such solutions imply that small perturbations need not be explicitly corrected for and therefore provide a computationally efficient solution. Four quantitative predictions were derived from a deterministic and a stochastic version of the model and were experimentally tested. Results support that human actors sense and make use of the stability properties of task. However, when single larger perturbations arise, human actors are able to adjust their racket trajectory to correct for errors and maintain a stable bouncing pattern.