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

TL;DR

This paper introduces a goal-conditioned neural ODE framework that guarantees safety and stability in all-pairs motion planning, with theoretical assurances and practical implementation for safe navigation.

Contribution

It develops a novel neural ODE model with safety and stability guarantees, incorporating bi-Lipschitz neural networks and demonstration data for motion planning.

Findings

Guarantees of global exponential stability and safety regardless of goal location

Explicit bounds on convergence rate, tracking error, and vector field magnitude

Effective navigation demonstrated in a 2D corridor task

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.