リーマン多様体とリー群上の曲線誘導力学システム
Curve-Induced Dynamical Systems on Riemannian Manifolds and Lie Groups
ロボットの動作生成のため、リーマン多様体やリー群上で曲線に沿って安定に収束する力学システムを構築する新しいフレームワークを提案し、安定性解析と実験で有効性を示した。
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著者: Saray Bakker, Martin Schonger, Tobias Löw, Javier Alonso-Mora, Sylvain Calinon
分類: cs.RO, cs.SY, eess.SY
原文アブストラクト
Deploying robots in household environments requires safe, adaptable, and interpretable behaviors that respect the geometric structure of tasks. Often represented on Lie groups and Riemannian manifolds, this includes poses on SE(3) or symmetric positive definite matrices encoding stiffness or damping matrices. In this context, dynamical system-based approaches offer a natural framework for generating such behavior, providing stability and convergence while remaining responsive to changes in the environment. We introduce Curve-induced Dynamical systems on Smooth Manifolds (CDSM), a real-time framework for constructing dynamical systems directly on Riemannian manifolds and Lie groups. The proposed approach constructs a nominal curve on the manifold, and generates a dynamical system which combines a tangential component that drives motion along the curve and a normal component that attracts the state toward the curve. We provide a stability analysis of the resulting dynamical system and validate the method quantitatively. On an S2 benchmark, CDSM demonstrates improved trajectory accuracy, reduced path deviation, and faster generation and query times compared to state-of-the-art methods. Finally, we demonstrate the practical applicability of the framework on both a robotic manipulator, where poses on SE(3) and damping matrices on SPD(n) are adapted online, and a mobile manipulator.
