## 6 Discussion  
After completing the validation of each aspect in the calibration process, this section evaluates the individual results and puts them into relation with each other. The order of such follows the order of the previous Section 5. The first paragraph covers the theoretical validation of the reference points and the moving head. The second paragraph focuses on the calibration algorithm and the aspect of using [PERSON]'s method. The third and final paragraph discusses the results of the practical validation. Capturing the **reference points** with a laser tracker adequately functioned in this case, delivering valid and usable results. This method can be applied to most large-structure workpieces or work areas if no CAD data is available, or if the expected data accuracy is insufficient. The described **point distortion** posed significant issues and was a limiting factor for the accuracy when jogging the light spot to the reference points. An unclear but potentially significant amount of uncertainty was rendered at this stage, owing to the difficulty in determining the exact spot center. In all probability, this outweighed the other error sources discussed. In the validation of the **movement control**, it was shown that the step granularity of the control input allows for precise movement inputs. Similarly, the results of the qualitative and laser-tracker-based pose repeatability experiment indicated that the moving head used in this paper is capable of achieving a precise **mechanical accuracy** in practice as well. It  
Figure 13: Lower (\(e_{l}\)) and upper (\(e_{u}\)) measured point position errors of a light spot at a given reference point \(P_{u}\). should be noted, however, that mechanical and control accuracy vary for different devices and application scenarios. For example, at greater distances between the moving head and the workpiece, small angular errors have a larger effect. Obtaining meaningful measures for the **algorithmic accuracy** proved challenging due to both the nature of iterative algorithms and the non-trivial surface of the respective workpiece. The proposed point position error metric only offered limited relevance and predicted a low overall accuracy. Furthermore, a discrepancy between the two steps of the algorithm were discovered, where a suboptimal result of the first step can perpetuate a high error in the second step. Currently, no feedback from the second to the first algorithm step is in place to counteract such effects. The distribution of the reference points embodies a direct influence on the accuracy of the result components if certain input characteristics outweigh others. None of these aforementioned effects can be attributed to the use of **[PERSON]'s method** for the calibration; however, in the current implementation, the control authority over the results is limited. While [PERSON]'s method converged to a result reliably, it was not necessarily the correct or desired result, attributable to multiple local minima that can occur in the multidimensional function equations. The calculation speed of the calibration algorithm increases significantly with an increased point count \(N\) since the number of function equations scales with \(O(N^{2})\), leading to larger Jacobian matrices and more substitution steps. Further information regarding relevant performance metrics can be found in Appendix C.3. While improved solving algorithms exist that are less susceptible to local minima and offer higher performance, they embody increased complexity for the implementation. Overall, [PERSON]'s method offered an adequate compromise between performance and complexity and was sufficient for the proof-of-concept. The **practical validation** was able to demonstrate a higher-than-predicted point position accuracy, revealing a discrepancy between the algorithmic accuracy analysis and the real-world example. It was shown that the proposed method is applicable to large-structure workpieces with non-trivial surfaces (as intended) with reasonable accuracy.