CDS Lecture Series

Friday, May 9, 2003, 2:00 p.m.

Rodolphe Sepulchre
Department of Electrical Engineering and Computer Science
University of Liege

Juggling dynamics and a billiard control problem

Juggling serves as a remarkable benchmark for cross-disciplinary studies of complex animal tasks that involve rhythm and coordination. The task is complex enough to retain central issues and simple enough to allow for mathematical analysis. Often precursors of hopping or walking robots, impressive juggling machines have been built during the last decade. Yet the theoretical understanding of their dynamical behavior has remain limited.

This talk will introduce a stabilization problem for periodic orbits in a wedge billiard, the simplest mathematical model of a planar juggler. Starting with the rich dynamical behavior of the uncontrolled wedge billiard, we will illustrate the derivation of stabilizing control laws of some unstable periodic orbits. We will also discuss the minimal feedback information needed to achieve stabilization of these impact control systems and some related open issues.

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