Juggling a Devil-Stick: Hybrid Orbit Stabilization Using the Impulse Controlled Poincaré Map

The control design for juggling a devil-stick between two symmetric configurations is proposed. Impulsive forces are applied to the devil-stick at the two configurations; and impulse of the force and its point of application are modeled as the control inputs. The dynamics of the devil-stick is described by a single return Poincare map and it is shown that the control objective of juggling can be achieved by stabilizing a hybrid orbit. The impulse controlled Poincare map (ICPM) approach, recently proposed for stabilization of continuous-time orbits of underactuated systems, is extended to achieve asymptotic stabilization of the hybrid orbit. The applicability of the ICPM approach to devil-stick juggling is demonstrated through numerical simulations.