Learning a flexible neural energy function with a unique minimum for globally stable and accurate demonstration learning

Jin, Zhehao; Si, Weiyong; Liu, Andong; Zhang, Wen An; Yu, Li; Yang, Chenguang

Abstract

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 guarantee 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 demonstration 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.

• Journal Article Type: Article
• Acceptance Date: Aug 3, 2023
• Online Publication Date: Aug 22, 2023
• Deposit Date: Sep 9, 2023
• Publicly Available Date: Aug 23, 2025
• Journal: IEEE Transactions on Robotics
• Print ISSN: 1552-3098
• Electronic ISSN: 1941-0468
• Publisher: Institute of Electrical and Electronics Engineers
• Peer Reviewed: Peer Reviewed
• DOI: https://doi.org/10.1109/tro.2023.3303011
• Keywords: Electrical and Electronic Engineering, Computer Science Applications, Control and Systems Engineering
• Public URL: https://uwe-repository.worktribe.com/output/11086298