Fabrics: A Foundationally Stable Medium for Encoding Prior Experience

TL;DR

This paper reformulates the theory of fabrics, a stable medium for encoding prior experience in control systems, making it more general and applicable for policy learning with strong stability properties.

Contribution

It provides a rigorous reformulation of fabrics theory, emphasizing stability and geometric interpretation, to enhance policy synthesis in control systems.

Findings

Fabrics create a stable medium for policy operation.

Geometric fabrics form a path network for system behavior.

Theoretical results guide fabric design for stability and task achievement.

Abstract

Most dynamics functions are not well-aligned to task requirements. Controllers, therefore, often invert the dynamics and reshape it into something more useful. The learning community has found that these controllers, such as Operational Space Control (OSC), can offer important inductive biases for training. However, OSC only captures straight line end-effector motion. There's a lot more behavior we could and should be packing into these systems. Earlier work [15][16][19] developed a theory that generalized these ideas and constructed a broad and flexible class of second-order dynamical systems which was simultaneously expressive enough to capture substantial behavior (such as that listed above), and maintained the types of stability properties that make OSC and controllers like it a good foundation for policy design and learning. This paper, motivated by the empirical success of the types of fabrics used in [20], reformulates the theory of fabrics into a form that's more general and easier to apply to policy learning problems. We focus on the stability properties that make fabrics a good foundation for policy synthesis. Fabrics create a fundamentally stable medium within which a policy can operate; they influence the system's behavior without preventing it from achieving tasks within its constraints. When a fabrics is geometric (path consistent) we can interpret the fabric as forming a road network of paths that the system wants to follow at constant speed absent a forcing policy, giving geometric intuition to its role as a prior. The policy operating over the geometric fabric acts to modulate speed and steers the system from one road to the next as it accomplishes its task. We reformulate the theory of fabrics here rigorously and develop theoretical results characterizing system behavior and illuminating how to design these systems, while also emphasizing intuition throughout.