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 stability 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 while maintaining stability. 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.
翻译:古典机械系统是控制能源构造方法几何控制方法的设计的核心。然而,它们的表达性受到只定位的计量标准以及测量和几何之间的密切联系的限制。最近有关里曼尼运动政策(RMPs)的工作表明,取消这些限制的结果是强大的设计工具,但牺牲理论稳定性保障。在这项工作中,我们把古典机械系统推广到我们所谓的几何结构,这些结构的表达性和理论使得能够设计出在实际中超过RMP的系统。几何结构严格地概括了形成新行为物理学的古典机械,首先将其归纳为Finsler的几何体,然后明确将其弯曲,以形成其行为,同时保持稳定性。我们开发了结构理论理论理论,并展示了一套受控实验,以及一系列机器人系统实验,表明在精密设计和更硬化地实施RMP系统方面,我们目前的控制器设计中最先进的技术,其性能有所改善。