Hybrid modelling and constrained control of juggling systems

The goal of this article is to review the modelling framework for juggling systems by stressing the particularities of switching dynamics and to design a controller for the systems based on a reformulation of the model predictive control design. The main idea is to catch an impact during the prediction window at the desired level. One of the particularities is the on-line adaptation of the optimisation problem such that the receding prediction window assures the existence of an impact at a certain moment in absolute time. A constraints softening technique will be used to avoid the in-feasibility problems. In a first stage, the basic juggling system which consists of a ball and a juggling robot in one-dimensional case is detailed and subsequently the study is extended to the case of multiple balls juggling with two degrees of freedom. The simulation results demonstrate the performance of the presented approach.