Classical mechanical systems are central to controller design in energy shaping methods of geometric control. However, their expressivity is limited by position-only metrics and the intimate link between metric and geometry. Recent work on Riemannian Motion Policies (RMPs) has shown that shedding these restrictions results in powerful design tools, but at the expense of theoretical guarantees. In this work, we generalize classical mechanics to what we call geometric fabrics, whose expressivity and theory enable the design of systems that outperform RMPs in practice. Geometric fabrics strictly generalize classical mechanics forming a new physics of behavior by first generalizing them to Finsler geometries and then explicitly bending them to shape their behavior. We develop the theory of fabrics and present both a collection of controlled experiments examining their theoretical properties and a set of robot system experiments showing improved performance over a well-engineered and hardened implementation of RMPs, our current state-of-the-art in controller design.

中文翻译：

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几何结构：概括经典力学以捕捉行为物理学

在几何控制的能量塑造方法中，经典机械系统是控制器设计的核心。然而，它们的表现力受到仅位置度量以及度量和几何之间的密切联系的限制。最近关于黎曼运动策略 (RMP) 的工作表明，摆脱这些限制会产生强大的设计工具，但会牺牲理论保证。在这项工作中，我们将经典力学推广到我们所说的几何结构，其表现力和理论使系统设计能够在实践中胜过 RMP。几何结构严格概括经典力学，形成一种新的行为物理学，首先将它们概括为 Finsler 几何，然后明确地弯曲它们以塑造它们的行为。