## 4 Experiments
### Experimental Results  
#### 4.4.1 Single Frame Experimental Comparison  
All of the above registration methods are required to set parameters, and different application scenarios need to set different parameters. The initial parameters are the default parameters set in PCL, and then the parameters are chosen according to the registration accuracy and time. First, we discuss the transformation epsilon (the maximum allowable difference between two consecutive transformations) and the maximum number of iterations. Furthermore, for the ICP series of algorithms, all filtered point clouds are used for registration. For point-to-plane ICP (PTPLICP, PTPLOMPICP), analyze the number of points using the calculated normal. For GICP, FastGICP, and FastVGICP, discuss the effect of using different numbers of points to calculate the covariance matrix on registration. For the NDT series algorithms, the relationship between voxel side length and registration time, and accuracy is analyzed. Figure 1(a)-f shows the relationship between registration time and registration accuracy when different registration parameters are selected for each registration algorithm. The x-axis represents the registration time, the y-axis is the registration accuracy, and broken lines of different colors correspond to different registration algorithms. The values in the box above the broken line are registration parameter values, corresponding to the points on the broken line. The unselected parameters are represented by yellow boxes, and the parameters in the red box are the final parameters selected by the algorithm. In addition, point cloud registration is an error accumulation process. The frequency of the LiDAR used in the experiment is 10 Hz; that is, 600 frames of data are emitted per minute. To ensure that the error is within tens of centimeters, the _RMSE_ error of a single frame should be retained to three decimal places, so the error level of the _RMSE_ of 0.001 is reasonable. Figure 1(a) shows the relationship between the registration time and the registration accuracy (_RMSE_) of the t transformation epsilon from \(1\times 10^{-10}\) to \(1\times 10^{-1}\). Each registration algorithm is sensitive to the parameter transformation epsilon. The final value of the parameter transformation epsilon is shown in Figure 1(b) It can be seen from Figure 1(c) that as the number of iterations increases, the registration accuracy and registration time increase until convergence. When the maximum number of iterations is 10, all registration algorithms achieve convergence. Figure 1(d) shows the registration effect of the point-to-plane ICP algorithm when calculating normals with different points. PTPLICP and PTPLOMPICP achieve the best registration effect when calculating normals with 40 points. The number of points used by GICP, FastGICP, and FastVGICP to calculate the covariance matrix ranges from 10 to 100 intervals of 10. The covariance matrix is calculated with 40, 100, and 80 points, respectively. Registration accuracy is considered first, and then the registration time. After many experiments, we set the NDT series algorithm voxel side length range to 1.0 to 1.9 interval 0.1. It can be seen from Figure 1(f) that the registration effect of the NDT series algorithms changes obviously with the voxel side length. The voxel side lengths of NDT, NDTOMP1, and NDTOMP7 are 1.4, 1.8, and 1.8. After configuring the parameters, the final registration results are shown in Figure 3. ICP and LMICP have the highest registration accuracy, but the speed is relatively slow, especially in LMICP. The registration speed of FastVGICP and NDTOMP1 is faster (less than 40 ms), but the accuracy is significantly lower than that of ICP. It can be seen from Figure 2a,c that ICP, LMICP, and NDT are more sensitive to parameters, especially ICP and LMICP, and that other registration performance changes are relatively small with parameters. Compared with GICP, FastGICP and FastVGICP have better stability (Figure 2e).