# Calibration of a Rotating or Revolving Platform with a LiDAR Sensor
## 4 Evaluation
### Experiments  
The error caused by mistransformation in a point cloud is difficult to isolate, since there are different possible sources for errors. For example, there are errors caused by LiDAR noise or caused by the discrete measurement of the rotation encoder, resulting from angles which are actually between two encoder steps. Neither the source nor the respective portion of the sensory error can be distinguished from the residual error remaining after calibration. Furthermore, another problem prevents the direct analysis of the actual remaining transformation error. The data used during the calibration process are estimated sphere centers. These estimations are themselves erroneous and prevent the calculating the exact pose. Therefore, the quality measure described in Section 4.1 is applied to the uncalibrated LiDAR measurements and to all calibration results with the different target arrangements, parameter grid resolutions, and initial pose guesses. Rating the outcomes of the calibration in different conditions allows a reasoning about the method's behavior. During all experiments, the Velodyne VLP-16 of the SWAP platform [6] was calibrated. This is a suitable sensing platform since the mounted Velodyne is a revolving multi-beam LiDAR. The platform was placed in the hall of a building on our campus, i.e., in an environment with many planar surfaces that are not too close to the platform (ca. 5 m away). This is important, since errors caused by the orientation of the LiDAR increase with the distance of the sampled surface data. Moreover, the walls and floor, contained in the excerpt of the hall used to rate the calibration quality, have different orientations to ensure all dimensions of the sensor orientation are reflected by the orientation of the planar surfaces. The excerpt is depicted in Figure 6. Additionally, two objects, a cube (ca. 0.4 m side length) and a cylinder (ca. 0.4 m diameter and height), were placed in the scene to provide additional surface data and show concurrence of the redundant LiDAR measurements. The experiments can be split into two phases. The first phase records the calibration targets within the different arrangements discussed earlier and calibrates the extrinsic parameters using different configuration sets. The second phase takes the resulting LiDAR poses from the first phase and applies them to the platform configuration to record the environment, i.e., the building on our campus, in operation-mode. Finally, the proposed quality measure is applied to the record, in order to compare several calibration results. In the first phase, the spherical calibration targets were placed around the LiDAR platform and were recorded in calibration mode. This means that the platform drives to several previously configured angles in sequence, from which the spheres can be scanned by the mounted Velodyne VLP-16 LiDAR to estimate their center points. These scans were recorded and passed to the calibration software, which optimizes the kinematic chain as explained earlier. We performed several calibration runs under different circumstances. First, the target arrangements were changed, i.e., the targets were placed at different distances of 2.0 m, 3.0 m, 3.5 m and 4.0 m from the sensor platform. This allows us to estimate how the sensitivity changes with the distance, as mentioned in Section 3.2. Furthermore, we, in addition, expected, that it is more beneficial to have a 90\({}^{\circ}\) angle between the \(\overline{d}\)-pairs. Therefore, the target pairs were additionally placed in a \(\omega\approx 90^{\circ}\) and a \(\omega^{\prime}\approx 45^{\circ}\) angle from each other (see Figure 5). In addition to the physical variations during the experiments, calibration parameters were also changed. The resolution of the search grid, used to find the global optimal orientation parameters, was configured to a 0.005 step size in each dimension, to test a low resolution grid. To study a significantly higher resolution, the step size was also set to 0.00025 in yaw, pitch and roll.