A threedimensional (3D) laser scanner with characteristics such as acquiring huge point cloud data and noncontact measurement has revolutionized the surveying and mapping industry. Nonetheless, how to guarantee the 3D laser scanner precision remains the critical factor that determines the excellence of 3D laser scanners. Hence, this study proposes a 3D laser scanner error analysis and calibrationmethodbased DH model, applies the DH model method in the robot area to the 3D laser scanner coordinate for calculating the point cloud data and creatively derive the error model, comprehensively analyzes six external parameters and seven inner structure parameters that affect point cloud coordinator error, and designs two calibration platforms for inner structure parameters. To validate the proposed method, we used SOKKIA total station and BLSSPE 3D laser scanner to attain the center coordinate of the testing target sphere and then evaluate the external parameters and modify the point coordinate. Based on modifying the point coordinate, comparing the point coordinate that considered the inner structure parameters with the point coordinate that did not consider the inner structure parameters, the experiment revealed that the BLSSPE 3D laser scanner’s precision enhanced after considering the inner structure parameters, demonstrating that the error analysis and calibration method was correct and feasible.
Threedimensional (3D) laser scanning technology [
While using a 3D laser scanner, the precision and index of the instrument have strict requirements, and how to ensure the precision of the 3D laser scanner that can fulfill the actual use of requirements is imperative. Currently, many scientific research institutions are researching the theory and technology of 3D laser scanning and have made some achievements. A study [
In recent years, some scholars started using the selfchecking calibration method to validate the system error of 3D laser scanners. A study [
Starting from the working principle and instrument structure of a 360° laser scanner developed by SureStar Technology Co., Ltd., a study [
The error analysis of the 3D laser scanner primarily analyzed the impact of the external influence factors on the measurement error, using the method of mathematical modeling, selfcalibration, or combination calibration method for system calibration—all these methods [
The fundamental principle of the 3D laser scanner is that, first, a drive scanner is used to rotate in the axial direction by the axial motor and the axial rotation angle
The point coordinates in the coordinate system of the 3D laser scanner.
Distance
D–H modeling method is a standard method to represent robots and model robot motions. Assumedly, the robot comprises a series of joints and linkages, which could be sliding or rotating and can be placed in any order and any plane. First, a reference coordinate system is assigned to each joint. Then, the steps for the transformation from one joint to the next are determined. Second, all transformations from the base to the first joint and then from the first joint to the second joint until to the last joint are combined to obtain the total transformation matrix of the robot. Figure
The schematic diagram of the DH modeling method.
The 3D laser scanning principle presents the formula of how to calculate the coordinates of spatial point clouds. The formula is derived on the basis of the simplified model, which only considers the measurement distance S, axial scanning angle
The following definitions are given to fulfill the DH model establishment principle:
Point
Point
Point
Point
Point
Point
The measuring distance of the laser ranging module is assumed as
Figure
The inner structure of the 3D laser scanner and coordinate system for the DH model.
Table
DH model parameters.
Number 





1 




2 




3 




The homogeneous coordinate transformation matrix between coordinate system {
We assume any point
The DH model real parameters.
Number 





1  0  0  − 
−180° 
2  − 

0  0 
3  0  0  − 

The coordinate of point
The coordinate of point
The 3D laser scanner point cloud calculation formula contains two types of parameters. One is the transformation parameter of the scanner coordinate system and the external coordinate system, which is called the external orientation parameter and comprises three translation parameters
According to formula (
The external orientation parameter contains three translation parameters
The result using the abovementioned equation minus the equation below is
Based on the characteristics of the orthogonal matrix and formula (
Based on formula (
The distance parameter calibration platform of the inner structure.
In this study, we designed the internal angle parameter calibration platform, including highprecision linear guide, highprecision clamping tool, and calibration coordinate paper (as shown in Figure
The angle parameter calibration platform of the inner structure.
The internal angle parameters
Calculating the fitting line parameter using the leastsquare method.
Number 









1  0.058  0.081  0.071  0.072  0.078  0.035  0.068  0.080 
2  0.065  0.079  0.073  0.074  
3  0.067  0.082  0.074  0.072  
4  0.069  0.078  0.077  0.073  
5  0.073  0.082  0.080  0.075 
We used a mine 3D laser scanner named BLSSPE to calculate external orientation parameters; six standard test target balls were set up in the laboratory, the entire laboratory scene was scanned with the 3D laser scanner to extract the cloud data of test target ballpoints, and the central coordinates of the target ball were fitted with the software of the 3D laser scanner (as shown in Figure
Scanning the test target sphere using the 3D laser scanner.
Scanning the test target sphere using the total station.
Table
The real coordinate of the test target.
Target ball  Measured value of the total station (m)  Measured value of the 3D laser scanner (m)  








1  7.181  5.083  14.408  5.008  6.054  3.052 
2  7.198  4.738  14.406  4.675  6.047  3.738 
3  8.025  3.850  13.936  3.664  6.037  3.858 
4  7.294  3.896  13.560  3.556  5.884  3.057 
5  7.483  2.679  12.375  1.869  5.465  3.039 
6  8.852  4.598  13.232  3.995  4.931  4.395 
Using the coordinate values of the first four targets and then using formulas (
Using the calculated external orientation parameters, the scan coordinates of the other two target balls were converted to the coordinate system of the total station, and the difference between them is calculated (Table
The difference between real and transformed coordinates.
Target ball  Measured value of the total station (m)  Correction coordinate (m)  Difference of coordinate (m)  











5  7.483  2.679  12.375  7.441  2.715  9.317  0.042  −0.037  0.018 
6  8.852  4.598  13.232  8.903  4.643  13.200  −0.051  −0.045  0.032 
The error in each direction is as follows：
The mean square error of measurement points is as follows:
By evaluating the external directional parameters and combining the internal parameters determined by the calibration platform of the 3D laser scanner, the coordinates of the standard test target ball center obtained by the 3D laser scanner can be converted into the coordinate system of the total station, and the difference between the measured coordinates and the corrected coordinates can be calculated (Table
The difference between real coordinates and transformed coordinates using the inner parameter.
Target ball  Measured value of the total station (m)  Correction coordinate (m)  Difference in coordinate (m)  











5  7.483  2.679  12.375  7.491  2.669  12.358  −0.008  0.009  0.016 
6  8.852  4.598  13.232  8.842  4.603  13.217  0.010  −0.005  0.015 
The error in each direction is as follows:
The mean square error of measurement points is as follows：
Table
Comparison of position accuracy.
Name  Error before correction (mm)  Error after correction (mm)  Improved accuracy (%) 

Error of 
47  9  80.9 
Error of 
41  7  82.9 
Error of 
25  16  36 
Accuracy  67  20  70.1 
After the correction of the instrument system error, the errors in all directions of the test point were improved compared with those before the correction. Meanwhile, the error in the point position was increased from 67 mm before correction to 20 mm, and the accuracy was increased by approximately 70.1%.
To ensure that the accuracy of the 3D laser scanner fulfills the requirements, this study innovatively uses the DH modeling method in the robotics field to derive the error model of the 3D laser scanner, along with a detailed analysis of the six external orientation parameters and seven internal structure parameters. All these parameters are involved in the coordinate conversion error of the device, machining error, electrical installation error, and tooling error. In addition, this study integrally analyzes the error sources and whether the concrete measurement results are correct; experiments revealed that the DH error model and calibration method proposed could enhance the instrument’s accuracy significantly. Of note, the method proposed in this study analyzes most error sources, but does not consider the environmental temperature, air pressure, reflectivity, and other factors. How to integrate these factors to further enhance the accuracy of the system would be the next research direction.
The data that support the findings of this study are available from the corresponding author upon reasonable request.
The authors declare that they have no conflicts of interest.
This work was financially supported by the National Key Research and Development Program of China (grant nos. 2018YFE0121000 and 2020YFE0202800).