Targetless IMU-LiDAR extrinsic calibration methods are gaining significant attention as the importance of the IMU-LiDAR fusion system increases. Notably, existing calibration methods derive calibration parameters under the assumption that the methods require full motion in all axes. When IMU and LiDAR are mounted on a ground robot the motion of which is restricted to planar motion, existing calibration methods are likely to exhibit degraded performance. To address this issue, we present GRIL-Calib: a novel targetless Ground Robot IMU-LiDAR Calibration method. Our proposed method leverages ground information to compensate for the lack of unrestricted full motion. First, we propose LiDAR Odometry (LO) using ground plane residuals to enhance calibration accuracy. Second, we propose the Ground Plane Motion (GPM) constraint and incorporate it into the optimization for calibration, enabling the determination of full 6-DoF extrinsic parameters, including theoretically unobservable direction. Finally, unlike baseline methods, we formulate the calibration not as sequential two optimizations but as a single optimization (SO) problem, solving all calibration parameters simultaneously and improving accuracy. We validate our \textit{GRIL-Calib} by applying it to three public real-world datasets and comparing its performance with that of existing state-of-the-art methods in terms of accuracy and robustness. Our code is available at https://github.com/Taeyoung96/GRIL-Calib.

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