Weakly-supervised Learning for Physics-informed Neural Motion Planning via Sparse Roadmap

TL;DR

This paper introduces Hierarchical Neural Time Fields, a weakly-supervised approach combining sparse roadmaps and physics-informed PDEs to improve motion planning in complex environments.

Contribution

It presents a novel hierarchical framework that leverages sparse roadmaps and PDE regularization to enhance scalability and robustness in neural motion planning.

Findings

H-NTFields outperform prior physics-informed methods in complex environments.

The approach enables fast amortized inference with continuous value representation.

Experiments demonstrate robustness on Gibson environments and real robots.

Abstract

The motion planning problem requires finding a collision-free path between start and goal configurations in high-dimensional, cluttered spaces. Recent learning-based methods offer promising solutions, with self-supervised physics-informed approaches such as Neural Time Fields (NTFields) solving the Eikonal equation to learn value functions without expert demonstrations. However, existing physics-informed methods struggle to scale in complex, multi-room environments, where simply increasing the number of samples cannot resolve local minima or guarantee global consistency. We propose Hierarchical Neural Time Fields (H-NTFields), a weakly-supervised framework that combines weak supervision from sparse roadmaps with physics-informed PDE regularization. The roadmap provides global topological anchors through upper and lower bounds on travel times, while PDE losses enforce local geometric fidelity and obstacle-aware propagation. Experiments on 18 Gibson environments and real robotic platforms show that H-NTFields substantially improves robustness over prior physics-informed methods, while enabling fast amortized inference through a continuous value representation.