Goal-Conditioned Neural ODEs with Guaranteed Safety and Stability for Learning-Based All-Pairs Motion Planning
cs.RO, cs.SY, eess.SY
Submitted: 2026-04-03
Updated: 2026-09-21
Code: https://github.com/acfr/Goal-Conditioned-Safe-ODE
License: http://creativecommons.org/licenses/by/4.0/
The gist: This paper presents a learning-based approach for all-pairs motion planning, where the initial and goal states are allowed to be arbitrary points in a safe set.
Terminology
Abstract
This paper presents a learning-based approach for all-pairs motion planning, where the initial and goal states are allowed to be arbitrary points in a safe set. We construct smooth goal-conditioned neural ordinary differential equations (neural ODEs) via bi-Lipschitz diffeomorphisms. Theoretical results show that the proposed model can provide guarantees of global exponential stability and safety (safe set forward invariance) regardless of goal location. Moreover, explicit bounds on convergence rate, tracking error, and vector field magnitude are established. Our approach admits a tractable learning implementation using bi-Lipschitz neural networks and can incorporate demonstration data. We illustrate the effectiveness of the proposed method on a 2D corridor navigation task.
Related papers
- FMT x: An Efficient and Asymptotically Optimal Extension of the Fast Marching Tree for Dynamic Replanning
- MPCFormer: A physics-informed data-driven approach for explainable socially-aware autonomous driving
- RoboLab: A High-Fidelity Simulation Benchmark for Analysis of Task Generalist Policies
- ARC: A Reasoning Recipe for Robot Foundation Models
- HRDexDB: A 4D Dexterous Grasping Dataset Across Human and Multiple Robot Embodiments
- APT: Action Expert Pretraining Improves Instruction Generalization of Vision-Language-Action Policies