Equi-RO: A 4D mmWave Radar Odometry via Equivariant Networks

TL;DR

This paper presents Equi-RO, a 4D mmWave radar odometry framework that leverages invariant Doppler features and SO(3)/SE(3) equivariant neural networks within a graph-based point representation. By compensating Doppler velocities and constructing a graph with carefully designed feature sets, Equi-RO decouples ego-motion from object motion and achieves robust frame-to-frame registration even under large rotations. The method demonstrates consistent improvements over state-of-the-art baselines on the NTU4DRadLM open dataset and shows strong generalization on a self-collected dataset, with notable performance in high-dynamic scenarios. The results highlight the value of combining invariant/equivariant feature design with graph-based aggregation for radar-based perception in autonomous systems, and point toward future multi-modal fusion and further on-board optimization for real-time deployment.

Abstract

Autonomous vehicles and robots rely on accurate odometry estimation in GPS-denied environments. While LiDARs and cameras struggle under extreme weather, 4D mmWave radar emerges as a robust alternative with all-weather operability and velocity measurement. In this paper, we introduce Equi-RO, an equivariant network-based framework for 4D radar odometry. Our algorithm pre-processes Doppler velocity into invariant node and edge features in the graph, and employs separate networks for equivariant and invariant feature processing. A graph-based architecture enhances feature aggregation in sparse radar data, improving inter-frame correspondence. Experiments on an open-source dataset and a self-collected dataset show Equi-RO outperforms state-of-the-art algorithms in accuracy and robustness. Overall, our method achieves 10.7% and 13.4% relative improvements in translation and rotation accuracy, respectively, compared to the best baseline on the open-source dataset.

Figures (10)

• Figure 1: Our Equi-RO method incorporates Doppler velocity compensation and graph construction to preserve noise-resilient and rotation-robust features. The derived equivariant and invariant features are fed into an equivariant Graph Neural Network (GNN)-based framework for consistent and generalizable point cloud registration, yielding more accurate odometry results, especially in large rotations. Trajectory comparison on a partial segment of the loop3 split from the NTU4DRadLM dataset zhang2023ntu4dradlm, where both methods are initialized to the ground truth at the segment's start, comparing against zhang20234dradarslam.
• Figure 2: Overview of the Equi-RO algorithm. Doppler velocity is used to derive invariant node and edge features, which are combined with node and edge features within a unified graph-based network framework to robustly estimate the relative transformation $(\bm{R}, \bm{t})$ between two consecutive radar frames.
• Figure 3: Illustrations of (left) node and (right) edge velocity compensation. The yellow arrow in the left figure indicates the compensated node velocity, which remains SO(3)-invariant. The yellow arrow in the right figure is the compensated edge velocity when the two nodes share the same absolute velocity, which is SE(3)-invariant.
• Figure 4: Test vehicle equipped with a 4D radar for the self-collected dataset.
• Figure 5: Projection of adjacent point clouds onto the corresponding images from loop3 split, where point colors represent compensated node velocities and white circles denote selected keypoints used for matching.