Lyapunov stability analysis of rigid body systems with multiple contacts by sums-of-squares programming

Péter L. Várkonyi

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arXiv · 2209.13908

Lyapunov stability analysis of rigid body systems with multiple contacts by sums-of-squares programming

Péter L. Várkonyi

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Abstract

Reliable quasi-static object manuipulation and robotic locomotion require verification of the stability of equilibria under rigid contacts and friction. In a recent paper, M. Posa, M. Tobenkin, and R. Tedrake demonstrated that sums-of-squares (SOS) programming can be used to verify Lyapunov stability via Lyapunov's direct method. This test was successfully applied to several simple problems with a single point contact. At the same time it has been found that this method is too conservative for several multi-contact systems. In this paper, an extension of Lyapunov's direct method is proposed, which makes use of several Lyapunov functions, and which allows \emph{temporary} increase of those Lyapunov function along a motion trajectory. The proposed method remains compatible with SOS programming techniques. The improved stability test is successfully applied to a rigid body with 2 point contacts, for which the exact conditions of Lyapunov stability are unknown.

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Péter L. Várkonyi. 2022-09-28. Lyapunov stability analysis of rigid body systems with multiple contacts by sums-of-squares programming. https://arxiv.org/abs/2209.13908

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