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

• URL: http://arxiv.org/abs/2604.13204v1
• Date: Tue, 14 Apr 2026 18:26:22 GMT
• Title: Weakly-supervised Learning for Physics-informed Neural Motion Planning via Sparse Roadmap
• Abstract summary: We propose a weakly-supervised framework that combines weak supervision from sparse roadmaps with physics-informed PDE regularization.<n> Experiments on 18 Gibson environments and real robotic platforms show that H-NTFields substantially improves robustness over prior physics-informed methods.
• Score: 26.000609838439754
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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