Citation: Li, Y.; Yang, S.; Xiu, X.;
Miao, Z. A Spatiotemporal
Calibration Algorithm for
IMU–LiDAR Navigation System
Based on Similarity of Motion
Trajectories. Sensors 2022, 22, 7637.
https://doi.org/10.3390/s22197637
Academic Editors: Luis Payá, Oscar
Reinoso García and Helder
Jesus Araújo
Received: 30 August 2022
Accepted: 4 October 2022
Published: 9 October 2022
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Article
A Spatiotemporal Calibration Algorithm for IMU–LiDAR
Navigation System Based on Similarity of Motion Trajectories
Yunhui Li , Shize Yang, Xianchao Xiu and Zhonghua Miao *
School of Mechatronic Engineering and Automation, Shanghai University, Shanghai 200444, China
* Correspondence: zhhmiao@shu.edu.cn
Abstract:
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’ coor-
dinate 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
◦
(3
δ
) and 5 mm (3
δ
), 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.
Keywords: multisensor fusion; multisensor calibration; factor graph optimization; state estimation
1. Introduction
Multisensor fusion is an important way to aid in the environmental perception and
navigation of robots in complex environments. It can fully use the advantages of different
sensors, and they can then compensate each other, and achieve more accurate and robust
perception and localization performance than that of a single sensor. Therefore, in recent
years, it has received extensive attention, such as in driverless cars, field robots, high-
precision map construction, and target tracking [
1
–
4
]. LiDAR is widely used in robot
navigation due to its high measurement accuracy, insensitivity to light, and good reliability.
Its fusion with the environment-independent IMU can achieve robust perception and
localization in complex environments. The calibration of the spatiotemporal relationship
between sensors is the premise of realizing multisensor information fusion, which mainly
includes the calibration of the spatial transformation relationship between sensor coordinate
systems and the calibration of the time deviation of sensor acquisition data.
To realize the calibration of the multisensor spatial transformation relationship in a
robot navigation system, many methods have emerged in recent years that are mainly
divided into methods based on calibration equipment and self-calibration methods. The
method based on calibration equipment refers to the estimation of spatial transformation
Sensors 2022, 22, 7637. https://doi.org/10.3390/s22197637 https://www.mdpi.com/journal/sensors
