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

TL;DR

This paper introduces FB-NTFields, a neural field method that improves large-scale motion planning by representing cost-to-go functions through latent space distances, enabling scalable and coherent planning in complex environments.

Contribution

The paper proposes FB-NTFields, a novel neural representation that captures spatial connectivity for motion planning, overcoming limitations of existing domain decomposition methods.

Findings

FB-NTFields outperform existing PiNMPs in synthetic and real-world scenarios.

The method enables efficient navigation of indoor environments by a quadruped robot.

Latent space distance computation ensures global spatial coherence in planning.

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.