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

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 th...

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Bibliographic Details
Published in:IEEE robotics and automation letters 2022-04, Vol.7 (2), p.3202-3209
Main Authors: Van Wyk, Karl, Xie, Mandy, Li, Anqi, Rana, Muhammad Asif, Babich, Buck, Peele, Bryan, Wan, Qian, Akinola, Iretiayo, Sundaralingam, Balakumar, Fox, Dieter, Boots, Byron, Ratliff, Nathan D.
Format: Article
Language:English
Subjects:
Bending
Classical mechanics
Control systems design
Controllers
Damping
Dynamics
Fabrics
Geometry
Mathematical models
Measurement
Mechanical systems
Mechanics
Optimization and Optimal Control
Stability
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Summary: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.
ISSN:2377-3766
2377-3766
DOI:10.1109/LRA.2022.3143311