Learning a Flexible Neural Energy Function with a Unique Minimum for Globally Stable and Accurate Demonstration Learning

Learning a stable autonomous dynamic system (ADS) encoding human motion rules has been shown as an effective way for demonstration learning. However, the stability guarantee may sacrifice the demonstration learning accuracy. This article solves the issue by learning a stability certificate, represented by a neural energy function, on the demonstration set. We propose a polarlike space analysis approach to derive parameter constraints to guaran- tee the unique-minimum property of the neural energy function, which is essential for it to be a cogent stability certificate. Then, the neural energy function is learned to capture the demonstra- tion preferences via constrained optimization algorithms. With the learned neural energy function, a globally asymptotically stable ADS with predefined position constraint is further formulated. We also quantitatively analyze the generalization ability of the learned ADS by utilizing the substantial flexibility of the neural energy function. The effectiveness of the proposed approach is validated on the LASA dataset and two representative robotic experiments.