ハイブリッド周期軌道の微分可能不変集合と脚式ロボットへの応用
Differentiable Invariant Sets for Hybrid Limit Cycles with Application to Legged Robots
脚式ロボットの周期歩行軌道の周りに前方不変集合を計算する手法を提案し、その不変集合を最大化する制御器設計を最適化問題として解いた。
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著者: Varun Madabushi, Akash Harapanahalli, Samuel Coogan, Maegan Tucker
分類: eess.SY, cs.RO, cs.SY
原文アブストラクト
For hybrid systems exhibiting periodic behavior, analyzing the invariant set containing the limit cycle is a natural way to study the robustness of the closed-loop system. However, computing these sets can be computationally expensive, especially when applied to contact-rich cyber-physical systems such as legged robots. In this work, we extend existing methods for overapproximating reachable sets of continuous systems using parametric embeddings to compute a forward-invariant set around the nominal trajectory of a simplified model of a bipedal robot. Our three-step approach (i) computes an overapproximating reachable set around the nominal continuous flow, (ii) catalogs intersections with the guard surface, and (iii) passes these intersections through the reset map. If the overapproximated reachable set after one step is a strict subset of the initial set, we formally verify a forward invariant set for this hybrid periodic orbit. We verify this condition on the bipedal walker model numerically using immrax, a JAX-based library for parametric reachable set computation, and use it within a bi-level optimization framework to design a tracking controller that maximizes the size of the invariant set.
