ABSTRACT
Many tasks in robotics and automation require a cyclic exchange of energy between a machine and its environ ment Since most environments are {{underactuatedv — that is, there are more objects to be manipulated than actuated degrees of freedom with which to manipu late them — the exchange must be punctuated by inter mittent repeated contacts. In this paper, we develop the appropriate theoretical setting for framing these prob lems and propose a general method for regulating cou pled cyclic systems. We prove for the first time the local stability of a (slight variant on a) phase regula tion strategy that we have been using with empirical success in the lab for more than a decade. We apply these methods to three examples: juggling two balls, two legged synchronized hopping and two legged running — considering for the first time the analogies between jug gling and running formally.
