Geometric Contact Flows: Contactomorphisms for Dynamics and Control

TL;DR

This paper introduces Geometric Contact Flows, a new geometric framework using contactomorphisms to model, predict, and control complex dynamical systems with energy constraints, enhancing robustness and adaptability.

Contribution

It proposes a novel contact geometric framework that encodes stability and energy conservation, enabling robust learning and control of complex dynamical systems.

Findings

Effective modeling of physical dynamics demonstrated

Robust control of robots on interaction tasks achieved

Uncertainty-aware geodesics improve generalization

Abstract

Accurately modeling and predicting complex dynamical systems, particularly those involving force exchange and dissipation, is crucial for applications ranging from fluid dynamics to robotics, but presents significant challenges due to the intricate interplay of geometric constraints and energy transfer. This paper introduces Geometric Contact Flows (GFC), a novel framework leveraging Riemannian and Contact geometry as inductive biases to learn such systems. GCF constructs a latent contact Hamiltonian model encoding desirable properties like stability or energy conservation. An ensemble of contactomorphisms then adapts this model to the target dynamics while preserving these properties. This ensemble allows for uncertainty-aware geodesics that attract the system's behavior toward the data support, enabling robust generalization and adaptation to unseen scenarios. Experiments on learning dynamics for physical systems and for controlling robots on interaction tasks demonstrate the effectiveness of our approach.