Juggling on a bouncing ball apparatus via hybrid control

A novel solution to the problem of controlling a one degree-of-freedom ball juggling system that explicitly models friction is proposed. A hybrid controller is designed to steer the ball to track a specific reference trajectory. The juggling system consists of a nearly-smooth vertical shaft with a piston-actuated bouncing ball. The hybrid controller is capable of tracking a periodic reference trajectory. A practical (finite-time) tracking property is established using hybrid systems theory, while juggling experiments are presented to validate the hybrid control algorithm. Key to these experimental results are: 1) the use of a filtered zero-crossing impact detection algorithm; 2) a Savitzky-Golay filter for smooth piston position and velocity; 3) a custom external PID controller; and 4) the estimation of the apparatus parameters via system ID methods.