A Hybrid Systems Approach to Trajectory Tracking Control for Juggling Systems

From a hybrid systems point of view, we provide
a modeling framework and a trajectory tracking control design
methodology for juggling systems. We present the main ideas
and concepts in a one degree-of-freedom juggler, which consists
of a ball bouncing on an actuated robot. We design a hybrid
control strategy that, with only information of the ball’s state at
impacts, controls the ball to track a reference rhythmic pattern
with arbitrary precision. We extend this hybrid control strategy
to the case of juggling multiple balls with different rhythmic
patterns. Simulation results for juggling of one and three balls
with a single actuated robot are presented.