A Spatiotemporal Calibration Algorithm for IMU–LiDAR Navigation System Based on Similarity of Motion Trajectories

The fusion of light detection and ranging (LiDAR) and inertial measurement unit (IMU) sensing information can effectively improve the environment modeling and localization accuracy of navigation systems. To realize the spatiotemporal unification of data collected by the IMU and the LiDAR, a two-step spatiotemporal calibration method combining coarse and fine is proposed. The method mainly includes two aspects: (1) Modeling continuous-time trajectories of IMU attitude motion using B-spline basis functions; the motion of the LiDAR is estimated by using the normal distributions transform (NDT) point cloud registration algorithm, taking the Hausdorff distance between the local trajectories as the cost function and combining it with the hand–eye calibration method to solve the initial value of the spatiotemporal relationship between the two sensors’ coordinate systems, and then using the measurement data of the IMU to correct the LiDAR distortion. (2) According to the IMU preintegration, and the point, line, and plane features of the lidar point cloud, the corresponding nonlinear optimization objective function is constructed. Combined with the corrected LiDAR data and the initial value of the spatiotemporal calibration of the coordinate systems, the target is optimized under the nonlinear graph optimization framework. The rationality, accuracy, and robustness of the proposed algorithm are verified by simulation analysis and actual test experiments. The results show that the accuracy of the proposed algorithm in the spatial coordinate system relationship calibration was better than 0.08° (3δ) and 5 mm (3δ), respectively, and the time deviation calibration accuracy was better than 0.1 ms and had strong environmental adaptability. This can meet the high-precision calibration requirements of multisensor spatiotemporal parameters of field robot navigation systems.