Neural Contractive Dynamical Systems

TL;DR

This paper introduces a neural architecture for learning contractive dynamical systems that guarantees global stability, scales to high dimensions, and extends to rotation groups, enabling safer autonomous robot control.

Contribution

The paper presents a novel neural network design that ensures contraction and stability in learned dynamics, including a scalable variational autoencoder variant and an extension to Lie groups.

Findings

Outperforms state-of-the-art in encoding dynamics accurately

Provides strong global stability guarantees

Enables obstacle avoidance in learned systems

Abstract

Stability guarantees are crucial when ensuring a fully autonomous robot does not take undesirable or potentially harmful actions. Unfortunately, global stability guarantees are hard to provide in dynamical systems learned from data, especially when the learned dynamics are governed by neural networks. We propose a novel methodology to learn neural contractive dynamical systems, where our neural architecture ensures contraction, and hence, global stability. To efficiently scale the method to high-dimensional dynamical systems, we develop a variant of the variational autoencoder that learns dynamics in a low-dimensional latent representation space while retaining contractive stability after decoding. We further extend our approach to learning contractive systems on the Lie group of rotations to account for full-pose end-effector dynamic motions. The result is the first highly flexible learning architecture that provides contractive stability guarantees with capability to perform obstacle avoidance. Empirically, we demonstrate that our approach encodes the desired dynamics more accurately than the current state-of-the-art, which provides less strong stability guarantees.