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.

翻译：在确保全自主机器人不会采取不良或潜在危险行为时，稳定性保障至关重要。然而，从数据中学习的动力系统难以提供全局稳定性保证，尤其是当学习到的动力学由神经网络主导时。我们提出了一种学习神经收缩动力系统的新方法，其中我们的神经架构能够确保收缩性，进而实现全局稳定性。为高效地将该方法扩展到高维动力系统，我们开发了一种变分自编码器的改进版本，该模型在低维潜在表示空间中学习动力学，同时在解码后保持收缩稳定性。我们进一步将方法扩展至旋转李群上的收缩系统学习，以处理完整位姿的末端执行器动态运动。最终成果是首个兼具高灵活性与收缩稳定性保证的学习架构，并能实现避障功能。实验表明，与当前仅能提供较弱稳定性保证的最先进方法相比，我们的方法能更精确地编码所需动力学。