Citation: Sun, N.; Qiu, Q.; Fan, Z.; Li,
T.; Ji, C.; Feng, Q.; Zhao, C. Intrinsic
Calibration of Multi-Beam LiDARs
for Agricultural Robots. Remote Sens.
2022, 14, 4846. https://doi.org/
10.3390/rs14194846
Academic Editors: Luis A. Ruiz, M.
Jamal Deen, Subhas Mukhopadhyay,
Yangquan Chen, Simone Morais,
Nunzio Cennamo and Junseop Lee
Received: 19 July 2022
Accepted: 26 September 2022
Published: 28 September 2022
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Article
Intrinsic Calibration of Multi-Beam LiDARs for
Agricultural Robots
Na Sun
1,2,†
, Quan Qiu
3,†
, Zhengqiang Fan
2,4
, Tao Li
2
, Chao Ji
5
, Qingchun Feng
2
and Chunjiang Zhao
1,2,
*
1
College of Engineering and Technology, Southwest University, Chongqing 400715, China
2
Intelligent Equipment Research Center, Beijing Academy of Agriculture and Forestry Sciences,
Beijing 100097, China
3
Academy of Artificial Intelligence, Beijing Institute of Petrochemical Technology, Beijing 102617, China
4
College of Mechanical and Electronic Engineering, Northwest A&F University, Xianyang 712100, China
5
Institute of Mechanical Equipment, Xinjiang Academy of Agricultural and Reclamation Science,
Shihezi 832000, China
* Correspondence: zhaocj@nercita.org.cn
† These authors contributed equally to this work.
Abstract:
With the advantages of high measurement accuracy and wide detection range, LiDARs
have been widely used in information perception research to develop agricultural robots. However,
the internal configuration of the laser transmitter layout changes with increasing sensor working
duration, which makes it difficult to obtain accurate measurement with calibration files based on
factory settings. To solve this problem, we investigate the intrinsic calibration of multi-beam laser
sensors. Specifically, we calibrate the five intrinsic parameters of LiDAR with a nonlinear optimization
strategy based on static planar models, which include measured distance, rotation angle, pitch angle,
horizontal distance, and vertical distance. Firstly, we establish a mathematical model based on
the physical structure of LiDAR. Secondly, we calibrate the internal parameters according to the
mathematical model and evaluate the measurement accuracy after calibration. Here, we illustrate the
parameter calibration with three steps: planar model estimation, objective function construction, and
nonlinear optimization. We also introduce the ranging accuracy evaluation metrics, including the
standard deviation of the distance from the laser scanning points to the planar models and the 3
σ
criterion. Finally, the experimental results show that the ranging error of calibrated sensors can be
maintained within 3 cm, which verifies the effectiveness of the laser intrinsic calibration.
Keywords:
three-dimensional; LiDAR; intrinsic calibration; nonlinear optimization; agricultural robot
1. Introduction
Light Detection and Ranging (LiDAR) sensors, cameras, and other information per-
ception sensors are essential components in current robotics and automation systems [
1
,
2
].
The performance of such systems highly depends on the quality of intrinsic and extrinsic
calibration parameters for these sensors [
3
–
6
]. Accurate intrinsic parameters can ensure
that the data obtained by the sensors are meaningful and valid. Currently, the intrinsic
calibration techniques of cameras are relatively mature and many open-source packages are
available [
7
,
8
]. However, the intrinsic calibration of LiDAR needs further investigation due
to its complex manufacturing process. Typically, LiDAR is subjected to rigorous internal
calibration before leaving the factory with initial parameter values. As the service time
of LiDARs increases, the initial parameters may not maintain their optimal values due to
changes caused by shock in the internal mechanical parts of the sensor. Especially in the
agriculture field, rough farmland will exacerbate the loosening of internal components of
LiDARs mounted on ground vehicles.
At present, LiDARs have a wide range of applications in the agricultural field. Some
common LiDAR-based research hotpots include 3D reconstruction [
9
,
10
], crop phenotyp-
ing [
11
], and yield estimation [
12
], etc. For these applications, the observed objects (such
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