# Generalizable Motion Planning via Operator Learning

arXiv: https://arxiv.org/abs/2410.17547 · HTML: https://mlsanity.com/paper/2410.17547/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Oct 2024.

## Built on by (most cited first, 7 of 7)

- [A Survey of Agentic Reasoning for Large Language Models: Towards Recursively Self-Improving and Collective Agents](https://mlsanity.com/paper/2601.12538/) (2026)
- [Learning PDE Solvers with Physics and Data: A Unifying View of Physics-Informed Neural Networks and Neural Operators](https://mlsanity.com/paper/2601.14517/) (2026)
- [U-Mind: A Unified Framework for Real-Time Multimodal Interaction with Audiovisual Generation](https://mlsanity.com/paper/2602.23739/) (2026)
- [Mollified Value Learning](https://mlsanity.com/paper/2602.23280/) (2026)
- [Neural Operators for Design-Space Surrogate Modeling of Tendon-Actuated Continuum Robots](https://mlsanity.com/paper/2605.19104/) (2026)
- [Neural Navigation Functions for Zero-Shot Generalizable Motion Planning](https://mlsanity.com/paper/2606.03756/) (2026)
- [Terminal Symmetry as a Carrier of Asymmetric Process Knowledge: Statewise Refinement for Anytime Verified Construction](https://mlsanity.com/paper/2608.11318/) (2026)

## Abstract (arXiv)

In this work, we introduce a planning neural operator (PNO) for predicting the value function of a motion planning problem. We recast value function approximation as learning a single operator from the cost function space to the value function space, which is defined by an Eikonal partial differential equation (PDE). Therefore, our PNO model, despite being trained with a finite number of samples at coarse resolution, inherits the zero-shot super-resolution property of neural operators. We demonstrate accurate value function approximation at 16× the training resolution on the MovingAI lab's 2D city dataset, compare with state-of-the-art neural value function predictors on 3D scenes from the iGibson building dataset and showcase optimal planning with 4-DOF robotic manipulators. Lastly, we investigate employing the value function output of PNO as a heuristic function to accelerate motion planning. We show theoretically that the PNO heuristic is ε-consistent by introducing an inductive bias layer that guarantees our value functions satisfy the triangle inequality. With our heuristic, we achieve a 30% decrease in nodes visited while obtaining near optimal path lengths on the MovingAI lab 2D city dataset, compared to classical planning methods (A^ast, RRT^ast).