Neural Navigation Functions for Zero-Shot Generalizable Motion Planning
Provides a structured learned navigation function for zero-shot generalizable motion planning in robotics, improving over direct value function prediction.
Neural-NF achieves zero-shot transfer across unseen environment geometries for motion planning, outperforming learned planners that directly predict the value function by up to 5x improvement.
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.