A Multi-LiDAR Self-Calibration System Based on Natural Environments and Motion Constraints

Yuxuan Tang, Jie Hu (), Zhiyong Yang, Wencai Xu, Shuaidi He and Bolun Hu
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Yuxuan Tang: Hubei Research Center for New Energy & Intelligent Connected Vehicle, Wuhan University of Technology, Luoshi Road, Wuhan 430070, China
Jie Hu: Hubei Research Center for New Energy & Intelligent Connected Vehicle, Wuhan University of Technology, Luoshi Road, Wuhan 430070, China
Zhiyong Yang: Hubei Agricultural Machinery Institute, Hubei University of Technology, Nanli Road, Wuhan 430068, China
Wencai Xu: Hubei Research Center for New Energy & Intelligent Connected Vehicle, Wuhan University of Technology, Luoshi Road, Wuhan 430070, China
Shuaidi He: Hubei Research Center for New Energy & Intelligent Connected Vehicle, Wuhan University of Technology, Luoshi Road, Wuhan 430070, China
Bolun Hu: Commercial Product R&D Institute, Dongfeng Automobile Co., Ltd., Wuhan 430056, China

Mathematics, 2025, vol. 13, issue 19, 1-18

Abstract: Autonomous commercial vehicles often mount multiple LiDARs to enlarge their field of view, but conventional calibration is labor-intensive and prone to drift during long-term operation. We present an online self-calibration method that combines a ground plane motion constraint with a virtual RGB–D projection, mapping 3D point clouds to 2D feature/depth images to reduce feature extraction cost while preserving 3D structure. Motion consistency across consecutive frames enables a reduced-dimension hand–eye formulation. Within this formulation, the estimation integrates geometric constraints on S E ( 3 ) using Lagrange multiplier aggregation and quasi-Newton refinement. This approach highlights key aspects of identifiability, conditioning, and convergence. An online monitor evaluates plane alignment and LiDAR–INS odometry consistency to detect degradation and trigger recalibration. Tests on a commercial vehicle with six LiDARs and on nuScenes demonstrate accuracy comparable to offline, target-based methods while supporting practical online use. On the vehicle, maximum errors are 6.058 cm (translation) and 4.768° (rotation); on nuScenes, 2.916 cm and 5.386°. The approach streamlines calibration, enables online monitoring, and remains robust in real-world settings.

Keywords: multi-LiDAR calibration; hand–eye; constrained optimization; planar motion; LiDAR odometry; RGB–D projection; RANSAC; BFGS (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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