Neural Navigation Functions for Zero-Shot Generalizable Motion Planning

2026-06-02

AI Summary

This work addresses the challenge of zero-shot transfer in motion planning within unknown environments by proposing a structured elliptic planner that embeds data-driven adaptability into a classical framework. By leveraging intrinsic geometric features derived from the Laplace operator to formulate local coefficients of a partial differential equation for the first time, the method enables linearly solvable optimal control under arbitrary parameters while preserving obstacle avoidance, monotonic descent, and global optimality. Integrating neural navigation functions with boundary value problem solvers, the approach achieves robust zero-shot generalization across diverse unseen environments, outperforming end-to-end learning-based planners by up to fivefold in performance.

Abstract

We introduce Neural Navigation Functions (Neural-NF), a learned reactive navigation function capable of zero-shot transfer across unseen environment geometries. Neural-NF places data-driven adaptation within a structured elliptic planner, where the navigation objective is learned while planner structure is preserved by construction. Specifically, intrinsic Laplacian-derived features are mapped to local PDE coefficients, and solving the resulting boundary value problem produces a globally consistent value function on each target domain. For every admissible learned model, the resulting policy is collision-free, provides monotonic descent and a global minimum at the goal by construction. This admits a linearly-solvable optimal-control interpretation for any parameter setting. Empirically, Neural-NF achieves strong zero-shot transfer across diverse geometries and outperforms learned planners that directly predict the value function by up to a $5\times$ improvement.

Problem

• zero-shot generalization
• motion planning
• neural navigation
• collision-free
• global consistency

Innovation

• Neural Navigation Functions
• zero-shot generalization
• elliptic planner
• Laplacian-derived features
• boundary value problem