測定誘導束構造による環境制約下のダイナミクス学習
Learning Dynamics under Environmental Constraints via Measurement-Induced Bundle Structures
センサー測定と環境制約をファイバー束構造で統合し、測定に適応する制御バリア関数とNeural ODEを組み合わせて、制約を満たしながら未知の連続時間ダイナミクスを学習する幾何学的フレームワークを提案した。
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著者: Dongzhe Zheng, Wenjie Mei
分類: cs.RO, cs.LG, cs.SY, eess.SY
原文アブストラクト
Learning unknown dynamics under environmental (or external) constraints is fundamental to many fields (e.g., modern robotics), particularly challenging when constraint information is only locally available and uncertain. Existing approaches requiring global constraints or using probabilistic filtering fail to fully exploit the geometric structure inherent in local measurements (by using, e.g., sensors) and constraints. This paper presents a geometric framework unifying measurements, constraints, and dynamics learning through a fiber bundle structure over the state space. This naturally induced geometric structure enables measurement-aware Control Barrier Functions that adapt to local sensing (or measurement) conditions. By integrating Neural ODEs, our framework learns continuous-time dynamics while preserving geometric constraints, with theoretical guarantees of learning convergence and constraint satisfaction dependent on sensing quality. The geometric framework not only enables efficient dynamics learning but also suggests promising directions for integration with reinforcement learning approaches. Extensive simulations demonstrate significant improvements in both learning efficiency and constraint satisfaction over traditional methods, especially under limited and uncertain sensing conditions.
