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This paper introduces Hierarchical Neural Time Fields (H-NTFields), a weakly-supervised neural motion planning framework that combines sparse roadmap guidance with physics-informed PDE regularization. H-NTFields uses the roadmap to provide global topological constraints via travel time bounds, while PDE losses ensure local geometric accuracy and collision avoidance. Experiments demonstrate that H-NTFields significantly enhances robustness in complex environments compared to existing physics-informed methods, facilitating rapid amortized inference.
Neural motion planners can now navigate complex, multi-room environments with significantly improved robustness by incorporating sparse roadmap guidance as weak supervision.
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.
