Safe and Stable Neural Network Dynamical Systems for Robot Motion Planning

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 in various 2D and 3D datasets—including LASA handwriting and demonstrations recorded kinesthetically from the Franka Emika Panda robot—validate the effectiveness of S$^{2}$-NNDS in learning robust, safe, and stable motions from potentially unsafe demonstrations. The source code, supplementary material and experiment videos can be accessed viahttps://github.com/allemmbinn/S2NNDS.