Neural Navigation Functions for Zero-Shot Generalizable Motion 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× improvement.
Diffusion-based motion planners have demonstrated strong performance in generating diverse and high-quality robot trajectories in cluttered environments with multiple feasible solutions. However, existing approaches typically operate on fixed-length waypoint sequences, making the learned model resolution-dependent, thereby preventing zero-shot generalization across resolutions. In this work, we propose Function-Space Diffusion for Motion Planning (FSD-MP), a diffusion-based motion planner that models trajectories as continuous functions and performs diffusion directly in function space, achieving discretization-invariant trajectory generation. We define a mode-wise forward process in the spectral domain, driven by Gaussian noise with a Matérn-type covariance, and parameterize the reverse process with a boundary-compatible Discrete Sine Transform-based Fourier Neural Operator (DST-FNO) that preserves start-goal constraints across resolutions. We evaluate FSD-MP on 2D point robot and 7-DoF Franka manipulator planning benchmarks. Our method achieves competitive planning performance at the training resolution and generalizes zero-shot across resolutions up to 16× higher, preserving consistent planning behavior without retraining. These results demonstrate that function-space diffusion provides an effective framework for discretization-invariant motion planning.
Recent progress in visual navigation has largely been driven by scale: end-to-end policies with hundreds of millions of parameters trained on billions of frames or large-scale simulated data. We ask how much of this scale a single task family actually requires, and what structure can substitute for it. We propose a decomposed navigation model in which operations with known closed-form structure, such as projective geometry, occupancy, and coordinate transforms, are computed analytically and serve as interfaces between three small learned modules: an egress predictor that grounds the episode goal as a local subgoal in the current view, a navigation predictor that estimates a goal-conditioned posterior over where trajectories travel, and an endpoint-pinned residual diffusion generator that samples trajectory shapes from this posterior. The system trains only 0.58M out of a total of 22.7M parameters, on 44k frames in under one GPU-hour, yet approaches the performance of state-of-the-art models on navigation tasks across 6060 point-goal episodes and 60 environments, while having 233x fewer trainable parameters, the lowest collision rate among all evaluated methods, and 50 Hz inference speed. The decomposition further transfers to no-goal exploration by retraining only the 123k-parameter egress head, and its failure modes under sensor corruption are transparent and analytically correctable.
Autonomous navigation in unknown environments requires a robot to efficiently reach a predefined goal while exploring without prior maps. Although progress has been made in this area, most existing works still rely on traditional planning methods with hand-crafted rules, while learning-based methods often suffer from limited environmental memory and challenges in simulation-to-real (sim-to-real) transfer. To overcome these limitations, we propose a Contextual-memory Oriented Reinforcement-learning (CORE) planner for robot navigation in unknown environments. The proposed CORE planner effectively combines the core advantages of traditional and learning-based methods. Specifically, our method uses a sparse visibility graph for structured environment representation, reducing the computational overhead of dense grid maps, and employs a Transformer network to achieve a holistic environmental understanding, thereby significantly improving navigation efficiency. Moreover, we introduce a visibility graph-based graph sparsification method and a contextual memory mechanism, which alleviates local optima and enhances computational performance in large-scale scenes. Finally, our approach achieves zero-shot sim-to-real transfer after training solely on image-based environments, requiring no fine-tuning. Experimental results show that CORE Planner consistently outperforms state-of-the-art methods, including the traditional FAR Planner and all learning-based baselines, across representative environments, reducing travel distance by 13% over traditional FAR Planner and by up to 48% relative to learning-based baselines, with larger gains observed in more complex environments. In real-world scenarios, CORE successfully navigates without human intervention, showcasing zero-shot sim-to-real transfer. Code is available at https://github.com/BBD00/core_planner.