# Calibration of a Rotating or Revolving Platform with a LiDAR Sensor
## 5 Conclusions and Future Work  
In this work, we introduced a novel calibration method to optimize the extrinsic parameters of rotating or revolving multi-beam LiDARs. It is inspired by the work of [PERSON] et al. [16] to exploit redundancies in the LiDAR measurements, and on the decoupling of pose components by [PERSON] et al. [7]. This enabled us to deduce a theoretical method which allows the separate optimization of orientation and translation. The method was also tested with an exemplary sensor platform by [PERSON] et al. [6]. Revolving LiDARs theoretically come up with problems like the different view points of the redundant surface information. Therefore, the SWAP platform [6] with its revolving Velodyne VLP-16 was used in our experiments. Our experiments indicated that the proposed method works, with restriction under the expected circumstances. Decoupling the LiDAR's orientation from its translational shift relative to the carrier center allows a precise optimization of the five degrees of freedom pose in two steps, as long as a target pair can be detected by the LiDAR at a time and the sensor carrier orientation can be measured e.g., by a rotation encoder. The calibration quality unfortunately strongly depends on the accuracy of the target detection, which correlates with the target distance. However, the experiments showed that the targets have to be as far away as possible and the resolution of the search grid needs to be relatively high, in order to achieve the optimal results. In particular, the latter can get inconvenient because it leads to longer calibration runtimes. This, however, could still be tractable, since the calibration process usually is not a time-critical application. Nevertheless, the decoupling and separate optimization was the focus of this work and performed well, and thus the proposed method is a promising approach with potential for further improvements. For future improvements, the target center issues probably can be addressed by using bigger spheres. Maybe the estimation accuracy for the sphere centers could also be increased if a better  
Figure 9: The plot shows the runtime behavior of the grid search with respect to the grid resolution. The curve in the graph is an approximation to the grid search durations in Table 1.  
reflecting material is used for the calibration targets. This has to be tested in further experiments. Another approach to tackle center estimation errors could be to decrease the individual influence of each inaccuracy. It is possible that using more spheres could reduce the influence of each single one and thus also the influence of the error each one contributes to the sum of residuals. This possibility makes it worthwhile to test the calibration with additional target pairs placed around the platform--especially because the angle between the target pairs was shown to have less effect on the calibration quality. Moreover, for future applications, the sphere fitting method should be generalized. At the moment, our implementation is restricted to multi-beam LiDARs because a single scanline on a sphere has two equivalent fitting solutions. This can not actually be fixed, but maybe the right solution can be parameterized, e.g., by configuring if a certain scanline to be left or right of the sphere's center point w.r.t. the LiDAR. This has to be implemented and tested. Unfortunately, it is out of the scope of this work to decide if there are optimization algorithms that are better suited to the proposed problems i.e., more sophisticated global optimizers able to handle saddle regions. This also remains a topic for further research. Furthermore, the restriction to LiDARs perceiving two calibration targets at a time could be slightly weakened by enabling a calibration, using another already calibrated sensor on the same platform. The alignment of the sphere centers detected by the calibrated LiDAR with the center points estimated by the uncalibrated sensor could also converge to optimized extrinsic parameters. However, this has to be implemented and tested.