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.

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。 但是,它们的表达性受到只定位的量度以及测量和几何之间的密切联系的限制。最近关于里曼尼运动政策(RMPs)的工作表明,取消这些限制的结果是强大的设计工具,但以理论保障为代价。在这项工作中,我们将古典机械系统推广到我们所谓的几何结构结构,这些结构的表达性和理论使得能够设计在实际中超过RMP的系统。几何结构严格概括形成新行为物理学的古典机械,先将其概括到芬斯勒的几何形图案,然后明确将其弯曲,以塑造其行为。我们开发了结构理论理论理论理论,并展示了一系列受控实验,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(我们目前的控制设计中最先进的技术)方面提高了性能。