# Calibration of a Rotating or Revolving Platform with a LiDAR Sensor
## 2 Related Work
### Targetless Calibration
Once a reference LiDAR is calibrated, other mounted LiDARs can be calibrated to minimize the distance between their fitted planes and the reference planes of the already calibrated sensor. Again, driving is required and the use of 2D-SLAM could cause additional transformation errors. It also requires extra hardware. Furthermore, the error based on the distance between the fitted planes is a good error measure, but assumes relatively large planar surfaces in the environment. In [16], [PERSON] et al. utilize the crispness introduced by [PERSON] [10], and also the redundancy in the observation of a rotating or swiwelling 2D laser range finder, mounted on their sensor platform, after a full rotation of the LRF. Given the case that the surrounding environment is static, the scanner has seen everything twice after a full revolution. Based on this fact, an objective function that represents the crispness of point clouds with this redundancy feature is formulated. To exploit this redundancy, the point cloud is separated into the two similar parts after a whole rotation. The objective function transforms the sample points into a common frame. Different to [10], the GMM of each point's neighbourhood inside the other redundant point set, respectively, is calculated. The quantification is the same as in [10]. A high crispness, depending on the 6-DOF pose parameters of the scanner encodes a low deviation of points in their respective neighbourhood, which, in return, means, that point pairs in the redundant data are close together, or, in other words, represent the same surface patch. In both methods, [PERSON]'s [10] and [PERSON]'s [16], the crispness is optimised using iterative, numerical Newton-like algorithms. However, ambiguities emerge between translation and rotation when the sensors are rotated eccentrically on the platform, i.e., rotated around the center with a radius \(r>0\). Furthermore, there are problems caused by different view angles of the redundant LiDARmeasures. Nevertheless, the exploitation of redundancies in general is an elegant way to determine the scanner's pose. [PERSON] et al. [17] make use of the precise knowledge of the vehicle's pose. They state that sample points on a planar surface of the same or a neighbouring scanline should be close together, if the transformations from navigation frame to the vehicle's baselink and finally to the scanner's frame are known and correct. Due to the fact that the pose is known by several sensors, [PERSON] et al. [17] were able to formulate an objective function which minimizes the Euclidean distance of neighbouring points on planar surfaces. This, however, requires several additional sensors and driving during the calibration process. Moreover, some of the required sensors, such as GPS are not always available. Besides the sensor requirements, there are difficulties exploiting the environments structure to avoid calibration targets. Planar surfaces are mostly found in artificial environments. Some of the proposed methods require driving. This makes them inapplicable in many situations, for example, in stand-alone operation of sensing platforms. Others require additional localization information which are also often not available. Avoiding the use of calibration targets comes with strong assumptions about the agent's environment. This will make recalibration sometimes difficult. Our novel calibration method does not require any additional localization nor does it make any assumptions about the scanner's surroundings during the calibration process. Moreover, the majority of methods either optimize the sensor pose information with respect to other sensors, while our approach optimizes the extrinsic parameters with respect to static construction parts of the platform.