# FFT-Based Scan-Matching for SLAM Applications with Low-Cost Laser Range Finders
## 5 Experiment
### Scan Matching  
For scan matching, two different poses and their corresponding scan data were taken as one set. The ground truth of the poses were given by manual measurement. A series of such data sets of different environments and different conditions were used for the experiments.  
Figure 8 shows an example of the scan-matching results of different steps with our proposed method. As can be seen from Figure 7(b), the approach of estimating the rotation angle through missing data only performs well under certain scenes. After FFT processing, the rough poses were estimated, and they were close enough to the real pose as shown in Figure 7(c). Finally, as can be seen from Figure 7(d), the two scans were matched precisely.  
Figure 6: Experimental facilities, robot platform (**left**), RPLidar-A1 sensor (**right**).  
Figure 7: Typical experimental environments: Office (**a**); Corridor (**b**); and Room (**c**).  
To evaluate the matching success rate under different conditions, the data sets were separated into 3 parts: small pose difference (average translation 0.3 m, rotation 10 deg), middle pose difference (average translation 0.5 m, rotation 20 deg), large pose difference (average translation 0.8 m, rotation 30 deg). The iteration times for matching was limited to 200. If the error of the final aligned poses were smaller than translation 0.1 m and rotation 3 deg, we judge them as successful matchings.  
Another example of matching result via different methods is shown in Figure 9. For the input scans in Figure 9a, the method of ICP finally converged to a wrong result in Figure 9b, while NDT reported a matching fail in Figure 9c. In Figure 9d, the result of FFT is near to the truth, but it still has errors. FFT-ICP1 and FFT-ICP2 give approximate and accurate results here.  
Figure 8: An example of matching result with proposed method. (**a**) The input scan data; (**b**) rotation via the angle estimated by missing data features; (**c**) the matching result with rough posed estimate by FFT; and (**d**) the final result.  
As shown in Figure 10, the success rate of the ICP method decreases very quickly when the difference of poses becomes larger, especially when the rotation angle becomes large. That is because ICP needs the scan points to overlap enough for matching. Although the NDT method performs more robustly than does ICP, it still cannot deal with the large difference of the poses. The FFT-based methods are more robust through large pose changes because they are theoretically unaffected by position changes. The matching fail for FFT-based methods mainly comes from the excessive change of total shape caused by different positions.  
Table 2 shows the average matching accuracy of different methods. Comparatively speaking, our original FFT method has larger errors than the other methods. This is mainly because its processing image is small. The FFT-ICP1 and FFT-ICP2 methods achieve better results because of their coarse-to-fine estimation.  
Figure 10: Results of the matching success rates for different methods.  
Figure 9: Example of matching results via different methods. (**a**) The input scans; (**b**) the result of ICP; (**c**) the result of Normal Distributions Transform (NDT); (**d**) the result of FFT; (**e**) the result of FFT-ICP1 (original); and (**f**) the result of FFT-ICP2 (current paper).