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

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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>S</mi><mi>E</mi><mo>(</mo><mn>3</mn><mo>)</mo></mrow></semantics></math></inline-formula> 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.