## 3 Experimental Campaign
### Results  
In this chapter, we present the postprocessing of the raw data obtained during the evaluation campaign, as well as the discussion and interpretation of the produced results. The benchmark raw and processed data are shared with the community and can be found in the public Zenodo repository of the project [56]. As illustrated in Figure 13a, we demonstrate how, for each evaluated pose, we can obtain TTool's axis and its GT counterpart. To gauge position accuracy, we measure the Euclidean distance between the start and end points (Figure 19a,b) of the respective computed and GT axes. The mean of these distances is then calculated to provide a current comprehensive indicator of accuracy (Figure 19c). The rotational error is represented by the angle between the same two axes (Figure 19d). Table 1 reports the values from Figure 19c,d. The presented summary reveals a generally coherent and compact distribution of results for both position and rotation error, which is indicative of consistent performance by TTool's pose detector. However, it is noteworthy that the results for two distinct tool heads deviate from the overall trend: the auger drill bit (\(\diameter 35\) mm) with a 12.85 mm error and the chain saw blade with a 10.61 mm error. The first is the result of false detection by the ML classifier (see Section 2.2). A user without any construction skills or knowledge is falsely guided by TTool to proceed with evaluating the wrong model. Two objects that differ in diameter by only 1 cm make it difficult for an inexperienced user to identify TTool's misleading detection and correct it. The emergence of such errors highlights the necessity for enhancements in the model's predictive capabilities in the same tool's typology but of different sizes. Concerning the high error value of the chainsaw blade, a later inspection of the scanned model revealed inadequacies, specifically in its scaling, as evidenced by the approximate 2 mm error. This  
Figure 19: Graphs reporting the errors for (**a**) the base tip, (**b**) the tool tip, (**c**) the mean position, and (**d**) the mean rotation. On the \(x\)-axis, we present the error expressed in millimeters or degrees, whereas the x-axis indicates a thick for each cycle of tested operations for a total of 18 rounds for each tool head. is because models obtained from photogrammetry are, by default, scaleless. Thus, manual scaling calibration is needed. This discrepancy significantly impacts the accuracy of pose detection. The inaccurately scaled scan undermines the proposed system, emphasizing ensuring a properly calibrated dataset. In both scenarios, it is evident that TTool's rotation detection error is significantly less affected by an incorrect model than by a positional error. As a result, a drilling feedback loop is likely to be more reliably accurate than monitoring values, such as depth, which depend on the detected position of the tool head. If we exclude the aforementioned tools from the summary, the accuracy of our evaluation pipeline yields mean position and rotation errors of 3.9 \(\pm\) 1 mm and 1.19 \(\pm\) 0.6\({}^{\circ}\), respectively. The obtained rotation error value can be satisfactory within fabrication constraints. However, the positional error may be excessively high for woodworks, demanding more precision. Further, it is important to note that the positional error is significantly influenced by tolerances inherent in the physical aspects of the evaluation campaign, such as tag detection, CNC manufacturing, and wood deformations of the probing plate. Additionally, the scaling of the models, as observed, has a considerable impact on the positional error and requires thorough calibration. In summary, accounting for these additional tolerances, positional detection may exhibit better performance than indicated in the present results. Finally, the UX graphs provide insights that are distinct from the results of the rotation and positional error (Figure 20a,b).