Researching | Automatic Calibration of LiDAR External Parameters

Laser & Optoelectronics Progress, Volume. 60, Issue 22, 2215006(2023)

Automatic Calibration of LiDAR External Parameters

Zikai Gong¹, Yanhui Xi¹, and Dayong Shen^2、*

Author Affiliations

¹School of Electrical and Information Engineering, Changsha University of Science and Technology, Changsha 410114, Hunan, China

²College of Systems Engineering, National University of Defense Technology, Changsha 410003, Hunan, China

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Figures&Tables (21)

References (22)

Paper Information

Figures & Tables(21)

Fig. 1. Calibration process

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Fig. 2. Normal vector diagram of point cloud

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Fig. 3. Flow chart of normal vector calculation

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Fig. 4. Gazebo simulation environment

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Fig. 5. The relative position of the coordinate system

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Fig. 6. The number of point clouds screened by the normal vector

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Fig. 7. Box plot of corner data. (a) x coordinate; (b) y coordinate; (c) z coordinate

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Fig. 8. Original point cloud. (a) Front view; (b) side view

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Fig. 9. Fitting plane

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Fig. 10. Radar point cloud before calibration

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Fig. 11. Point cloud after calibration

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Fig. 12. Experimental environment

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Fig. 13. Calibration objects

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Fig. 14. Point cloud contrast

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Fig. 15. Box point cloud segmentation

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Table 1. Calibration results of Gazebo simulation for attitude 1

Table 1. Calibration results of Gazebo simulation for attitude 1

The method of calculating corner points	$θ_{y a w}$ /（°）	$θ_{r o l l}$ /（°）	$θ_{p i t c h}$ /（°）	$x$ /m	$y$ /m	$z$ /m
RANSAC	-0.003	26.9759	0.028	0.0616	-0.008000	-1.570000
Harris	-0.020	26.7023	1.456	0.0600	-0.001770	-1.780000
This article（not optimized）	-0.001	28.6338	0.064	0.0168	-0.000911	-1.588630
This article（after optimized）	-0.001	28.5579	0.044	0.0016	-4.85778×10^-6	-1.502084

Table 2. Calibration error of attitude 1 (take absolute value)

Table 2. Calibration error of attitude 1 (take absolute value)

The method of calculating corner points	$Δ θ_{y a w}$ /（°）	$Δ θ_{r o l l}$ /（°）	$Δ θ_{p i t c h}$ /（°）	$Δ x$ /m	$Δ y$ /m	$Δ z$ /m
RANSAC	0.003	1.672	0.028	0.0617	0.008000	0.070000
Harris	0.020	1.946	1.456	0.0600	0.001770	0.280000
This article（not optimized）	0.001	0.014	0.064	0.0168	0.000911	0.088630
This article（after optimized）	-0.001	0.090	0.044	0.0016	-4.85778×10^-6	0.002084

Table 3. Calibration error of attitude 2 (take absolute value)

Table 3. Calibration error of attitude 2 (take absolute value)

The method of calculating corner points	$Δ θ_{y a w}$ /（°）	$Δ θ_{r o l l}$ /（°）	$Δ θ_{p i t c h}$ /（°）	$Δ x$ /m	$Δ y$ /m	$Δ z$ /m
This article（not optimized）	0.022195	0.295	0.702000	0.08881	0.0102056	0.092043
This article（after optimized）	0.002149	0.020	0.066043	0.00032	0.0004232	0.001755

Table 4. Calibration results of Gazebo simulation

Table 4. Calibration results of Gazebo simulation

The method of calculating corner points	$Δ θ_{y a w}$ /（°）	$Δ θ_{r o l l}$ /（°）	$Δ θ_{p i t c h}$ /（°）	$Δ x$ /m	$Δ y$ /m	$Δ z$ /m
RANSAC	6.6922	0.8642	6.7870	0.04	2.08089	-0.0167
Harris	3.542	3.734	7.6853	0.0296175	2.075231	-0.0192522
This article（not optimized）	6.032	0.519	5.85625	0.035	2.0720	-0.04478
This article（after optimized）	5.79515	0.0913	5.6750	0.027	2.0305	0.0035

Table 5. Calibration error (take absolute value)

Table 5. Calibration error (take absolute value)

The method of calculating corner points	$Δ θ_{y a w}$ /（°）	$Δ θ_{r o l l}$ /（°）	$Δ θ_{p i t c h}$ /（°）	$Δ x$ /m	$Δ y$ /m	$Δ z$ /m
RANSAC	0.9626	0.8642	1.0574	0.04	0.08089	0.0167
Harris	2.1876	3.734	1.9557	0.0296175	0.075231	-0.0192522
This article（not optimized）	0.3024	0.519	0.12665	0.035	0.0720	-0.04478
This article（after optimized）	0.0655	0.0913	0.0546	0.027	0.0305	0.0035

Table 6. Calibration results

Table 6. Calibration results

Plane No.	Ideal plane normal vector	Calibrated point cloud plane normal vector	Angle /（°）
Plane 1	（0，0，1）	（-0.0164003，-0.0093987，0.999821）	0.02
Plane 2	（1，0，0）	（0.999905，-0.0137898，-0.000619757）	0.0127
Plane 3	（0，1，0）	（0.00956443，0.999605，-0.0264231）	0.0184

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Zikai Gong, Yanhui Xi, Dayong Shen. Automatic Calibration of LiDAR External Parameters[J]. Laser & Optoelectronics Progress, 2023, 60(22): 2215006

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Paper Information

Category: Machine Vision

Received: Feb. 9, 2023

Accepted: Apr. 3, 2023

Published Online: Nov. 24, 2023

The Author Email: Shen Dayong (dayong.shen@nudt.edu.cn)

DOI:10.3788/LOP230605

Topics

laser devices and laser physics

Lasers and Laser Optics

laser manufacturing

Instrumentation, Measurement and Metrology