歩行ロボットのハイブリッドリミットサイクルにおける吸引領域
Regions of Attraction for Hybrid Limit Cycles of Walking Robots
非線形ハイブリッドリミットサイクルの吸引領域解析手法を、van der Pol振動子や簡略化歩行モデルに適用し、横断面上のLyapunov関数をSOS計画で探索する方法を示した。
著者: Ian R. Manchester, Mark M. Tobenkin, Michael Levashov, Russ Tedrake
分類: math.OC, cs.RO, cs.SY, eess.SY
原文アブストラクト
This paper illustrates the application of recent research in region-of-attraction analysis for nonlinear hybrid limit cycles. Three example systems are analyzed in detail: the van der Pol oscillator, the "rimless wheel", and the "compass gait", the latter two being simplified models of underactuated walking robots. The method used involves decomposition of the dynamics about the target cycle into tangential and transverse components, and a search for a Lyapunov function in the transverse dynamics using sum-of-squares analysis (semidefinite programming). Each example illuminates different aspects of the procedure, including optimization of transversal surfaces, the handling of impact maps, optimization of the Lyapunov function, and orbitally-stabilizing control design.
