Title: Neural Navigation Functions for Zero-Shot Generalizable Motion Planning

Abstract: This paper presents Neural Navigation Functions (Neural-NF), a reactive navigation system learned through data that enables zero-shot transfer to previously unseen environmental geometries. By embedding data-driven adaptation into a structured elliptic planner, Neural-NF ensures that while the navigation objective is learned, the fundamental planner structure remains intact by design. The approach maps intrinsic features derived from the Laplacian to local partial differential equation (PDE) coefficients; solving the resulting boundary value problem yields a globally consistent value function for each target domain. Due to its construction, any admissible learned model guarantees a collision-free policy with monotonic descent and a global minimum at the goal. Furthermore, this framework allows for a linearly-solvable optimal-control interpretation regardless of the specific parameter settings. Experimental results demonstrate that Neural-NF achieves robust zero-shot transfer across varied geometries, surpassing learned planners that directly predict value functions by a factor of up to 5.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC