Goal-Conditioned Neural ODEs with Guaranteed Safety and Stability for Learning-Based All-Pairs Motion Planning

2026-04-03

AI Summary

This work addresses the full-pair motion planning problem for arbitrary initial and target states by proposing a goal-conditioned neural ordinary differential equation (ODE) model based on bi-Lipschitz diffeomorphisms. It is the first to integrate bi-Lipschitz neural networks with neural ODEs, constructing a smooth vector field that simultaneously ensures trajectory safety—via forward invariance of safe sets—and global exponential stability. The approach provides provable guarantees on convergence rates, tracking error bounds, and control magnitude limits. Trained in a demonstration-driven manner, the model demonstrates effectiveness in 2D corridor navigation tasks, offering both theoretical assurance and practical feasibility for end-to-end learning-based motion planning.

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.

Problem

• motion planning
• safety
• stability
• goal-conditioned
• neural ODEs

Innovation

• Goal-Conditioned Neural ODEs
• Bi-Lipschitz Diffeomorphism
• Safety Guarantee
• Global Exponential Stability
• All-Pairs Motion Planning