## 2 Materials and Methods
### Framework of Digital Twin System for Solid-Wood-Panel Processing
#### 2.2.3 Transport Layer
The UWB positioning system can operate across zero-, one-, two-, and three-dimensional spaces, with the ability to precisely identify and determine objects' X-Y coordinates in a two-dimensional space. The system effectively pinpoints the exact location of AGVs and other horizontal movement devices. Figure 9a demonstrates the two-dimensional positioning within the solid-wood-panel-processing system context. Positioning anchors are located at the four corners of the physical layer, designated as points A0, A1, A2, and A3. AGVs, equipped with positioning tags, communicate with the positioning base station through UWB pulse signals, which collect these data and forward them to a positioning server. An algorithm then processes these data to calculate the accurate coordinates of the positioning tags, facilitating the tracking of device movement via continuous data transmission. The base station of the UWB positioning system was interfaced with the positioning server of the solid-wood-panel-processing system through an Ethernet connection. This server was integrated with specialized software that utilized a trilateration technique to ascertain the locations. Figure 9b depicts a schematic that illustrates this trilateration method, visually explaining the location determination process using three reference points. \begin{table}
\begin{tabular}{c c c c c} \hline
**Positioning Technology** & **Precision** & **Security** & **Anti-Interference** & **Cost** \\ \hline Bluetooth & 2–10 m & High & Low & Low \\ RFID & Regional & Low & Lower & Lower \\ Wi-Fi & 5–10 m & Lower & High & Low \\ UWB & 6–15 m & Higher & Higher & High \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of each type of positioning technology. The coordinates of the three reference nodes A, B, and C are \((x_{a},y_{a})\), \((x_{b},y_{b})\), and \((x_{c},y_{c})\), respectively, and the distances to the positioned nodes \(O\) are \(d_{a}\), \(d_{b}\), and \(d_{c}\), respectively. Three circles were determined: A, B, and C, with radii of \(d_{a}\), \(d_{b}\), and \(d_{c}\), respectively. The intersection point \(O(x,y)\) of the three circles is the position of the established points [22]. Thus, we obtain Equation (6). \[ \begin{cases}\sqrt{(x-x_{a})^{2}+(y-y_{a})^{2}}=d_{a}\\ \sqrt{(x-x_{b})^{2}+(y-y_{b})^{2}}=d_{b}\\ \sqrt{(x-x_{c})^{2}+(y-y_{c})^{2}}=d_{c}\end{cases}  \tag{6}\]  
By resolving the mentioned equation, one can accurately derive the coordinates of the position point \(O\) as follows [22]:  
\[ \begin{bmatrix}x\\ y\end{bmatrix} = \begin{bmatrix}2(x_{a}-x_{c})&2(y_{a}-y_{c})\\ 2(x_{b}-x_{c})&2(y_{b}-y_{c})\end{bmatrix} ^{-1} \begin{bmatrix}{x_{a}}^{2}-{x_{c }}^{2}+{y_{a}}^{2}-{y_{c}}^{2}+{d_{c}}^{2}-{d_{a}}^{2}\\ {x_{b}}^{2}-{x_{c}}^{2}+{y_{b}}^{2}-{y_{c}}^{2}+{d_{c}}^{2}-{d_{b}}^{2}\end{bmatrix}  \tag{7}\]  
In solid-wood-panel processing production, the production elements that require the placement of UWB positioning tags include AGVs, stacker robots, and the bases of industrial robots. Their specific deployment is illustrated in Figure 10. Figure 10 illustrates the installation of UWB tags on AGVs, and Figure 10b shows the placement of UWB tags on the bases of industrial robots [22]. A calibration algorithm based on established methods was implemented to mitigate sensor bias in the UWB positioning and ranging sensors [23], which proactively calibrates the sensors by correcting for known biases before initiating the data collection cycle. Figure 10: (**a**) UWB tags installed on AGV. (**b**) UWB tags installed on the bases of industrial robots. Figure 9: (**a**) Schematic of two-dimensional spatial positioning. (**b**) Schematic of three-sided measurement method. This study leveraged WT901C-485 nine-axis angle sensors to precisely determine the orientation of industrial robots, capturing essential variables for position definition. These sensors monitor rotational operations, feeding the data into a system where it was refined into angular metrics showcased on a virtual interface, facilitating accurate robot pose acquisition.