论文标题
部分可观测时空混沌系统的无模型预测
Lyapunov stability analysis of rigid body systems with multiple contacts by sums-of-squares programming
论文作者
论文摘要
可靠的准静态对象的构造和机器人运动需要在刚性接触和摩擦下验证平衡的稳定性。在最近的一篇论文中，M。Posa，M。Tobenkin和R. Tedrake证明，可以使用Lyapunov的直接方法来验证Lyapunov稳定性。该测试成功地应用于单点接触的几个简单问题。同时，已经发现该方法对于多个多接触系统来说太保守了。在本文中，提出了Lyapunov的直接方法的扩展，该方法利用了几种Lyapunov函数，并允许\ emph {临时}沿运动轨迹增加这些Lyapunov函数。所提出的方法与SOS编程技术保持兼容。改进的稳定性测试成功地应用于具有2分触点的刚体，为此，Lyapunov稳定性的确切条件尚不清楚。
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.
