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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