## 2 Materials and Methods
### Experimental Validation
#### 2.2.1 Evaluation System Setup  
The experiment environment was set up with the Azure Kinect positioned at approximately 1.8 m from the ground and two meters from a wall, tilted 15 degrees downwards with respect to the horizon. The distance of the operator from the Kinect camera could be in a range between 0.80 m and 2 m, compatible with the range defined in the official documentation of the device.  
In order to evaluate the performance of the four frameworks under investigation, a highly accurate tracking of the power drill chunk pose was needed as reference. The HTC Vive (Figure 6) was selected as benchmark for the experiment since the precision of its tracking technologies has been tested to be around RMS 1.5 mm, and its accuracy around RMS 1.9 mm [32; 33; 34].  
The HTC Vive system is used for rendering 3D virtual reality and it is developed by HTC in partnership with Valve. The headset (Figure 6--Top-left) uses room scale tracking technology (Lighthouse, as shown in Figure 6--Middle) for virtual reality experiences that allow users to freely move around a play area, accurately tracking the position and orientation of the user's head-mounted display and controllers, reflecting all real-life movement in the VR simulation environment. The tracking is possible thanks to two infrared signals emitters called base stations (Figure 6--Top-right) and special active sensors that cover the surface of the headset, and controllers that intercept the infrared pulses can autonomously track their own position and orientation in the workspace determined by the field of view of the stations. The HTC Vive capabilities can be extended by means of small devices called Vive trackers (Figure 6--Bottom) [35] that implement Lighthouse technology too. They allow for a high degree of flexibility, making it possible to track items or body parts if correctly configured [36].  
HTC Vive base stations were placed in the space between Azure Kinect, delimiting a workspace that completely contained the field of view of the Kinect cameras to ensure the operator movements were in a monitored space. An HTC Vive tracker was placed on the power drill to track its pose. The position of the chunk with respect to the Vive tracker reference frame was found using the calibration procedure described above. The power drill Vive tracker was installed by means of a wooden support (Figure 7--Right) designed for the purpose.  
Figure 6: HTC Vive components: (**Top-Left**) the VR headset with a controller; (**Top-Right**) front and rear of a base station; (**Middle**) Lighthouse tracking system setup; (**Bottom**) a HTC Vive tracker with details scheme.  
Figure 7: (**Left**) The power drill used for the experiment. (**Right**) The wooden support mounted on the power drill with ArUco markers and HTC Vive tracker installed.  
It is worth noting that the position of the tool's point of interest estimated by the proposed system is referred to as the reference frame of the kinect camera. Since the accurate measure of the power drill pose is with respect to the reference system of the HTC Vive, it is necessary to know the relative pose between the two reference systems in order to compare the accurate measure with the estimated one. Hence, a second Vive tracker was fixed on the Azure kinect chassis by using a 3D-printed support (Figure 8). Such a support designed by the authors allowed for the positioning of the Vive tracker with a well-known pose with respect to the camera frame.