E(2)-Equivariant Graph Planning for Navigation

TL;DR

This paper introduces an E(2)-equivariant graph neural network approach for robot navigation that leverages Euclidean symmetry to improve training efficiency, stability, and generalization across diverse environments.

Contribution

It develops an equivariant message passing network for value iteration in navigation and a learnable equivariant layer for multi-camera input, addressing unstructured environments.

Findings

Enhanced training efficiency and stability.

Improved generalization across environments.

Effective handling of multi-camera inputs.

Abstract

Learning for robot navigation presents a critical and challenging task. The scarcity and costliness of real-world datasets necessitate efficient learning approaches. In this letter, we exploit Euclidean symmetry in planning for 2D navigation, which originates from Euclidean transformations between reference frames and enables parameter sharing. To address the challenges of unstructured environments, we formulate the navigation problem as planning on a geometric graph and develop an equivariant message passing network to perform value iteration. Furthermore, to handle multi-camera input, we propose a learnable equivariant layer to lift features to a desired space. We conduct comprehensive evaluations across five diverse tasks encompassing structured and unstructured environments, along with maps of known and unknown, given point goals or semantic goals. Our experiments confirm the substantial benefits on training efficiency, stability, and generalization. More details can be found at the project website: https://lhy.xyz/e2-planning/.