# Safe and Stable Neural Network Dynamical Systems for Robot Motion Planning

arXiv: https://arxiv.org/abs/2511.20593 · HTML: https://mlsanity.com/paper/2511.20593/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Nov 2025.

## Built on by (most cited first, 1 of 1)

- [Learning from Demonstration via Spatiotemporal Tubes for Unknown Euler-Lagrange Systems](https://mlsanity.com/paper/2607.00534/) (2026)

## Abstract (arXiv)

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 S2-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, S2-NNDS leverages neural networks to capture complex robot motions, providing probabilistic guarantees through split conformal prediction in learned certificates. Experimental results in various 2D and 3D datasets -- including LASA handwriting and demonstrations recorded kinesthetically from the Franka Emika Panda robot -- validate the effectiveness of S2-NNDS in learning robust, safe, and stable motions from potentially unsafe demonstrations. The source code, supplementary material and experiment videos can be accessed via https://github.com/allemmbinn/S2NNDS