Geometric Fabrics: Generalizing Classical Mechanics to Capture the Physics of Behavior

Abstract

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.

Autotuning Symbolic Optimization Fabrics for Trajectory Generation

“…In the following, we explain the individual parameters that we exposed symbolically. The form of the individual terms is adapted from [3], [4], [11] but written in a symbolic form. a) Basic inertia: The final tree of fabrics is equipped with a basic inertia metric that indicates how reactive the entire motion is.…”

“…Constant damping is sufficient to achieve the theoretical properties that are needed for trajectory generation. However, [3], [11], [23] proposed enhanced damping under the name of speedcontrol.…”

“…it determines the desired speed of motion. For a detailed discussion on speed control with optimization fabrics, we refer to previous works on optimization fabrics [3], [11].…”

“…As the structure of the resulting trajectory generation methods remains unchanged across all time steps, it can be composed before runtime, thus saving computational costs during executing. Optimization fabrics, but also their predecessor Riemannian Motion Policies (RMPs), have shown impressive results for several manipulator applications, including dynamic and crowded environments [3]- [5]. However, despite their Fig.…”

“…In this section, we very briefly introduce the concepts required for trajectory generation with optimization fabrics. For a more in-depth introduction to optimization fabrics and its foundations in differential geometry, the reader is referred to [3], [5], [11].…”