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

2026-04-14

AI Summary

This work addresses the challenge that existing physics-informed neural motion planning methods often converge to local minima and fail to ensure global consistency in high-dimensional, complex environments. To overcome this limitation, the authors propose Hierarchical Neural Time Fields (H-NTFields), which, for the first time, incorporate sparse roadmap priors as weak supervision into physics-informed neural networks. By integrating Eikonal equation constraints with PDE-based regularization, H-NTFields simultaneously preserve local geometric accuracy and capture global topological structure. The method enforces upper and lower bounds on travel time, substantially enhancing planning robustness and global consistency in multi-room settings. Extensive experiments across 18 Gibson scenes and real-world robotic platforms demonstrate its superiority over current physics-informed approaches, while supporting efficient amortized inference.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs

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.

Problem

• motion planning
• physics-informed learning
• weakly-supervised learning
• global consistency
• local minima

Innovation

• Weakly-supervised learning
• Physics-informed neural networks
• Neural motion planning
• Sparse roadmap
• Eikonal equation