Neural Navigation Functions for Zero-Shot Generalizable Motion Planning
2026-06-02 • Robotics
RoboticsMachine Learning
AI summaryⓘ
The authors propose Neural Navigation Functions (Neural-NF), a new way for robots or agents to navigate without previous experience in a specific environment. Their method combines learning with a mathematical planner structure to ensure safe and efficient paths to a goal. By using features based on the Laplacian operator and solving certain equations, their approach creates a consistent navigation map that guarantees no collisions and steadily moves toward the goal. Tests show that Neural-NF works well in new environments and is more accurate than other learned navigation methods.
Neural Navigation Functionszero-shot transferreactive navigationelliptic plannerLaplacian operatorpartial differential equation (PDE)boundary value problemvalue functionoptimal controlcollision-free planning
Authors
Benjamin D. Shaffer, Pei-An Hsieh, Brooks Kinch, Nathaniel Trask, M. Ani Hsieh
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.