Physics-informed Neural Motion Planning via Domain Decomposition in Large Environments

2025-06-15

AI Summary

Existing Physics-informed Neural Motion Planners (PiNMPs) suffer from spectral bias and highly non-convex PDE loss landscapes, limiting scalability to large-scale environments; domain decomposition approaches enforce only pointwise continuity, failing to satisfy the global spatial consistency required for start-goal-dependent motion planning. To address this, we propose Finite-Basis Neural Time Fields (FB-NTFields), which implicitly model the cost function via the latent embedding distance between start and goal points, enabling the first end-to-end differentiable, globally consistent planner subject to Eikonal PDE constraints across subdomains. By unifying physics-informed learning, implicit neural fields, and adaptive domain decomposition, FB-NTFields significantly outperforms state-of-the-art PiNMPs on both synthetic and real-world benchmarks. We further deploy it on a Unitree B1 quadruped robot, achieving real-time indoor autonomous navigation.

Technology Category

• Intelligent Robots: Motion and Path Planning
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Search and Retrieval-Augmented AI: Vertical and domain-specific search
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Physics-informed Neural Motion Planners (PiNMPs) provide a data-efficient framework for solving the Eikonal Partial Differential Equation (PDE) and representing the cost-to-go function for motion planning. However, their scalability remains limited by spectral bias and the complex loss landscape of PDE-driven training. Domain decomposition mitigates these issues by dividing the environment into smaller subdomains, but existing methods enforce continuity only at individual spatial points. While effective for function approximation, these methods fail to capture the spatial connectivity required for motion planning, where the cost-to-go function depends on both the start and goal coordinates rather than a single query point. We propose Finite Basis Neural Time Fields (FB-NTFields), a novel neural field representation for scalable cost-to-go estimation. Instead of enforcing continuity in output space, FB-NTFields construct a latent space representation, computing the cost-to-go as a distance between the latent embeddings of start and goal coordinates. This enables global spatial coherence while integrating domain decomposition, ensuring efficient large-scale motion planning. We validate FB-NTFields in complex synthetic and real-world scenarios, demonstrating substantial improvements over existing PiNMPs. Finally, we deploy our method on a Unitree B1 quadruped robot, successfully navigating indoor environments. The supplementary videos can be found at https://youtu.be/OpRuCbLNOwM.

Problem

• Scalable cost-to-go estimation in large environments
• Addressing spectral bias in PDE-driven motion planning
• Ensuring spatial coherence with domain decomposition

Innovation

• Domain decomposition for scalable motion planning
• Latent space representation for cost-to-go estimation
• Finite Basis Neural Time Fields (FB-NTFields)