# Learning Complex Motion Plans using Neural ODEs with Safety and Stability Guarantees

arXiv: https://arxiv.org/abs/2308.00186 · HTML: https://mlsanity.com/paper/2308.00186/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2023.

## Built on by (most cited first, 8 of 8)

- [Elastic Motion Policy: An Adaptive Dynamical System for Robust and Efficient One-Shot Imitation Learning](https://mlsanity.com/paper/2503.08029/) (2025)
- [Formal Safety Verification and Refinement for Generative Motion Planners via Certified Local Stabilization](https://mlsanity.com/paper/2509.19688/) (2025)
- [KoopMotion: Learning Almost Divergence Free Koopman Flow Fields for Motion Planning](https://mlsanity.com/paper/2509.09074/) (2025)
- [A context-adaptive policy framework for robust and reactive robotic manipulation via uncertainty-aware imitation learning](https://mlsanity.com/paper/2410.24035/) (2024)
- [Stable Robot Motions on Manifolds: Learning Lyapunov-Constrained Neural Manifold ODEs](https://mlsanity.com/paper/2510.05707/) (2025)
- [A Robust Task-Level Control Architecture for Learned Dynamical Systems](https://mlsanity.com/paper/2511.09790/) (2025)
- [Learning from Demonstration via Spatiotemporal Tubes for Unknown Euler-Lagrange Systems](https://mlsanity.com/paper/2607.00534/) (2026)
- [Long-Time Trajectory Approximation via SA-NODEs: Model Predictive and Floquet Strategies](https://mlsanity.com/paper/2608.10738/) (2026)

## Abstract (arXiv)

We propose a Dynamical System (DS) approach to learn complex, possibly periodic motion plans from kinesthetic demonstrations using Neural Ordinary Differential Equations (NODE). To ensure reactivity and robustness to disturbances, we propose a novel approach that selects a target point at each time step for the robot to follow, by combining tools from control theory and the target trajectory generated by the learned NODE. A correction term to the NODE model is computed online by solving a quadratic program that guarantees stability and safety using control Lyapunov functions and control barrier functions, respectively. Our approach outperforms baseline DS learning techniques on the LASA handwriting dataset and complex periodic trajectories. It is also validated on the Franka Emika robot arm to produce stable motions for wiping and stirring tasks that do not have a single attractor, while being robust to perturbations and safe around humans and obstacles.