Neural Contractive Dynamical Systems

Hadi Beik Mohammadi, Søren Hauberg, Georgios Arvanitidis, Nadia Figueroa, Gerhard Neumann, Leonel Rozo

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Keywords: learning from demonstration, dynamical systems, contraction theory

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TL;DR: The paper introduces the Neural Contractive Dynamical System (NCDS), providing a flexible and stable approach for learning contractive dynamics, and extends it to high-dimensional systems with obstacle avoidance capabilities.

Abstract: Stability guarantees are crucial when ensuring that 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 \emph{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.

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Primary Area: applications to robotics, autonomy, planning

Submission Number: 5107