Neural Contractive Dynamical Systems
Hadi Beik-Mohammadi Søren Hauberg Georgios Arvanitidis Nadia Figueroa Gerhard Neumann Leonel Rozo
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.