Abstract-This paper introduces a stabilization problem for an elementary impact control system in the plane. The rich dynamical properties of the wedge billiard, combined to the relevance of the associated stabilization problem for feedback control issues in legged robotics make it a valuable benchmark for energy-based stabilization of impact control systems.

The paper addresses the stabilization of periodic orbits in a wedge billiard with actuated edges. It is shown how the rich dynamical properties of the open-loop dynamics, e.g. ergodicity properties and KAM curves, can be exploited to design robust stabilizing feedbacks with large basins of attraction.

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