Safe and Stable Neural Network Dynamical Systems for Robot Motion Planning

2025-11-25

AI Summary

Addressing the challenge of learning safe and stable robotic motions from unsafe demonstrations in environments with dense dynamic obstacles, this paper proposes the S²-NNDS framework. It is the first to jointly learn a neural dynamical system (NDS), a neural Lyapunov function, and a neural barrier function, while incorporating split conformal prediction to provide probabilistic guarantees on both safety and asymptotic stability. The method models nonlinear dynamics end-to-end and explicitly encodes theoretical stability and safety constraints as differentiable loss terms, enabling quantification of model uncertainty. Evaluated on the LASA handwriting and Franka Panda multi-task datasets (2D and 3D), S²-NNDS achieves significant improvements in motion safety, Lyapunov-based stability, and trajectory expressiveness over state-of-the-art imitation-learning approaches.

Technology Category

• Natural Language Processing: Safety and Robustness
• Intelligent Robots: Learning & Optimization for ROB
• Machine Learning: Neuro-Symbolic Learning

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Security and Privacy: Security and privacy of machine learning and AI applications

Abstract

Learning safe and stable robot motions from demonstrations remains a challenge, especially in complex, nonlinear tasks involving dynamic, obstacle-rich environments. In this paper, we propose Safe and Stable Neural Network Dynamical Systems S$^2$-NNDS, a learning-from-demonstration framework that simultaneously learns expressive neural dynamical systems alongside neural Lyapunov stability and barrier safety certificates. Unlike traditional approaches with restrictive polynomial parameterizations, S$^2$-NNDS leverages neural networks to capture complex robot motions providing probabilistic guarantees through split conformal prediction in learned certificates. Experimental results on various 2D and 3D datasets -- including LASA handwriting and demonstrations recorded kinesthetically from the Franka Emika Panda robot -- validate S$^2$-NNDS effectiveness in learning robust, safe, and stable motions from potentially unsafe demonstrations.

Problem

• Learning safe robot motions from demonstrations in complex environments
• Ensuring stability and safety in nonlinear dynamical systems
• Providing probabilistic safety guarantees for neural network controllers

Innovation

• Neural networks model complex robot motion dynamics
• Neural Lyapunov functions ensure system stability guarantees
• Conformal prediction provides probabilistic safety certificates