## 5 Experiments  
### Effectiveness Test  
#### 5.1.1 Data of Experiments  
According to the method described in Figure 7, a total of 70 point clouds were collected, which can be divided into 2 groups, one is without attitude correction, and the other is with attitude correction. In each group, 7 modes of the prototype were tested respectively, and 5 point clouds were collected in each mode.  
First, we show the data qualitatively. In Figure 8, the top views of these 70 3D point clouds are listed, which can show the attitude of the 3D point cloud. The red 3D point cloud was obtained without attitude correction (that is, point cloud \(\mathbf{C}_{O^{\prime}}\)), and the blue 3D point cloud was obtained with attitude correction (that is, point cloud \(\mathbf{C}_{O}\)).  
It can be found from Figure 8 that the attitudes of the 3D point clouds without correction (which are red) are uncertain. This uncertainty exists not only between different modes, but also between different 3D point clouds in the same mode. In comparison, the attitudes of the 3D point clouds with correction (which are blue) are roughly constant. Inthe following, the attitudes of 3D point clouds will be showed quantitatively by the curves of data.  
Figure 8: _Cont._  
In order to highlight the strip blank area and strip overlap area of each 3D point cloud, we marked them by a thick orange line. It is the position of the motor shaft when a 3D scanning starts. For the 3D point clouds with attitude correction, although their attitudes are roughly the same, the positions of the thick orange lines relative to the 3D point clouds are not the same. As mentioned above, the thick orange line shows the position of the motor shaft when a rotating 2D lidar starts a 3D scan, that is, the position of the \(Y\)'-axis in the coordinate frame \(O\)'. Since this position is not constant for each 3D scan, the position of thick orange line relative to the 3D point cloud is different for different 3D point clouds.  
Next, we show the data quantitatively. We calculated the angle \(\varphi_{\text{error}}\) of each 3D point cloud in Figure 8 through Equations (12)-(14). It is worth noting that \(f(\varphi_{\text{error}})=0\) in Formula (14) is under ideal conditions. During data processing, we calculated the \(\varphi_{\text{error}}\) that minimizes \(f(\varphi_{\text{error}})\) as the result.  
The values of angle \(\varphi_{\text{error}}\) of 70 3D point clouds are shown in Figure 9. We used a line chart to make it more intuitive. The horizontal axis is the number of the mode, that is, mode 1 to mode 7 of the prototype. The vertical axis is the value of angle \(\varphi_{\text{error}}\), its units are degrees. Looking down on a 3D point cloud, if the offset is clockwise relative to the correct attitude, \(\varphi_{\text{error}}\) is positive, while a counterclockwise offset relative to the correct attitude, indicates negative error. The red line corresponds to the 3D point clouds without attitude correction, and the blue line corresponds to the 3D point clouds with attitude correction. For each line, it is divided into 7 segments by 7 modes, and there are 5 sampling points in each mode, which corresponding to 5 3D point clouds collected in this mode.  
Figure 8: Top views of 70 3D point clouds.  
For the values of angle \(\varphi_{\text{error}}\) of the 5 sampling points in each mode, we calculated the maximum, average and minimum values respectively, as shown in Figure 10.  
Through the above experimental data, we can know the following points.