## 4 Experiments
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Region 1** & & & & & & \\ \hline
**Point Coding** & **x-Coordinate** & **y-Coordinate** & **z-Coordinate** & **Normal Vector \(i\)** & **Normal Vector \(j\)** & **Normal Vector \(k\)** \\ \hline L22A818 ASV & 4882.130 & \(-282.000\) & \(1602.000\) & \(-0.780\) & \(-0.030\) & \(0.632\) \\ L12A800 CSZ & 3856.000 & \(-567.000\) & \(1680.510\) & \(0.000\) & \(-0.110\) & \(0.990\) \\... &... &... &... &... &... &... \\ L22A271 AAZ & 3860.060 & \(-598.68\) & \(1703.400\) & \(0.000\) & \(-0.220\) & \(0.970\) \\ \hline
**Region 2** & & & & & & \\ \hline
**Point Coding** & **x-Coordinate** & **y-Coordinate** & **z-Coordinate** & **Normal Vector \(i\)** & **Normal Vector \(j\)** & **Normal Vector \(k\)** \\ \hline L22A771 CRP & 3392.500 & 704.345 & 1212.290 & \(0.000\) & \(-0.995\) & \(-0.100499\) \\ R22A771 ARP & 3295.200 & 705.737 & 1189.300 & \(0.000\) & \(-0.995\) & \(-0.100\) \\... &... &... &... &... &... &... \\ L22A800 ISY & 3705.500 & \(-762.500\) & 480.000 & \(0.000\) & \(-1.000\) & \(0.000\) \\ \hline
**Region 3** & & & & & & \\ \hline
**Point Coding** & **x-Coordinate** & **y-Coordinate** & **z-Coordinate** & **Normal Vector \(i\)** & **Normal Vector \(j\)** & **Normal Vector \(k\)** \\ \hline R22A781 CRE & 4234.000 & 623.549 & 1519.990 & \(0.000\) & \(-0.940\) & \(-0.340\) \\ R22A781 BCE & 4214.190 & 605.600 & 1560.620 & \(-0.037\) & \(-0.933\) & \(-0.358\) \\... &... &... &... &... &... &... \\ L12A801 FSY & 1980.000 & \(-745.000\) & 813.000 & \(0.000\) & \(-1.000\) & \(0.000\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Some inspection features with shared feasible regions. \[\mathrm{S_{k}(z)\geq z_{G}+h_{s}=-600} \tag{38}\]  
According to Equations (24)-(26), to keep the Laser Radar from colliding with the BIM, the constraints are as follows:  
\[ \begin{split} J_{1}=(\mathrm{S_{k}(y)\geq 1900\cup(S_{k}(y)\leq-1900) }\\ J_{2}=(S_{k}(x)\geq 2000\cup(S_{k}(x)\leq-2000)\end{split}  \tag{39}\]  
The robot's reachable area is decided by its location while selected. The data on the special robot are shown in Table 4, and the feasible region of stations is shown in Figure 12 when only the reachable area constraint of the wrist is considered. Finally, the optimized measurement stations were positioned with the coordinates and scanning directions corresponding to the feature orientations, which are listed in Table 5. Part of the stations are displayed in Figure 13. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**No.**} & **Distance Between** & **Angle Between Adjacent z** & **Center Distance of** & **Angle Between Adjacent** \\  & **Adjacent Axes (\(\alpha_{i}\))** & **Axes (\(\alpha_{i}\))** & **Joint (\(\mathrm{d_{i}}\))** & **X Axes (\(\beta_{i}\))** \\ \hline
1 & 312 & \(-\pi/2\) & 0 & \(\beta_{1}\) \\
2 & 1075 & 0 & 0 & \(\beta_{2}\) \\
3 & 225 & \(-\pi/2\) & 0 & \(\beta_{3}\) \\
4 & 0 & \(-\pi/2\) & 1280 & \(\beta_{4}\) \\
5 & 0 & \(-\pi/2\) & 0 & \(\beta_{5}\) \\
6 & 0 & 0 & 500 & \(\beta_{6}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters about the R-2000i robot’s arms. Figure 12: Reachable area of robot’s wrist. (**a**) Reachable area of wrist. (**b**) Section view of reachable area. (**c**) Outer border of reachable area. (**d**) Inner border of reachable area.