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.

我们提出了一种新的方法来学习神经收缩动力系统，使得我们的神经网络结构确保收缩从而实现全局稳定性。为了有效地应用于高维动力系统，我们开发了一种变分自编码器的变体，它学习低维潜在表示空间中的动力学，并在解码后保持收缩稳定性。此外，我们进一步将我们的方法扩展到旋转李群上学习具有避障能力的收缩系统。经验证明，我们的方法比当前的最先进方法更准确地编码了所需的动力学，并提供了更强的稳定性保证。