Mixed control for perception and action: timing and error correction in rhythmic ball-bouncing

The task of bouncing a ball on a racket was adopted as a model system for investigating the behavioral dynamics of rhythmic movement, specifically how perceptual information modulates the dynamics of action. Two experiments, with sixteen participants each, were carried out to definitively answer the following questions: How are passive stability and active stabilization combined to produce stable behavior? What informational quantities are used to actively regulate the two main components of the action—the timing of racket oscillation and the correction of errors in bounce height? We used a virtual ball-bouncing setup to simultaneously perturb gravity (g) and ball launch velocity (vb) at impact. In Experiment 1, we tested the control of racket timing by varying the ball’s upward half-period tup while holding its peak height hp constant. Conversely, in Experiment 2, we tested error correction by varying hp while holding tup constant. Participants adopted a mixed control mode in which information in the ball’s trajectory is used to actively stabilize behavior on a cycle-by-cycle basis, in order to keep the system within or near the passively stable region. The results reveal how these adjustments are visually controlled: the period of racket oscillation is modulated by the half-period of the ball’s upward flight, and the change in racket velocity from the previous impact (via a change in racket amplitude) is governed by the error to the target.