Generating Stable Propeller Motions for Devil Stick

The theory for motion planning and feedback stabilization of periodic orbits has regained a large interest during the last couple of years, with applications in, for instance, biped locomotion. The analysis of zero-dynamics after partial feedback linearization has been one means. More recently, the introduction of virtual holonomic constraints has offered also the design tools for these type of systems. The devil stick is a juggling device. We concentrate here on a particular propeller-like juggling motion where the periodic rotational motion of the center stick is induced by the contact force from a one-hand stick. The control design for a stabilized periodic orbit of the devil stick is based on virtual holonomic constraints for hybrid systems