Generalizable Motion Planning via Operator Learning

TL;DR

This paper introduces a neural operator for motion planning that accurately predicts value functions across resolutions, enabling efficient planning and heuristic acceleration in complex environments.

Contribution

We propose a novel neural operator-based value function predictor that generalizes across resolutions and integrates into motion planning, improving accuracy and efficiency.

Findings

Achieves 16x resolution accuracy on 2D city dataset

Outperforms state-of-the-art neural predictors on 3D scenes

Reduces nodes visited by 30% using the PNO heuristic

Abstract

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 $16\times$ 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 $\epsilon$-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 ($A^\ast$, $RRT^\ast$).