# Automated 3D Image Processing System for Inspection of Residential Wall Spalls
## 2 Materials and Methods
### Slam-Based Semi-Autonomous Data Acquisition
#### 2.2.2 Data Acquisition  
Influenced by the environmental conditions and application needs, the selection of navigation technology within mobile robotics varies significantly. The current main navigation methods include SLAM and GNSS. In comparison, GNSS faces restrictions due to satellite signal issues and is primarily designed for open outdoor settings. Meanwhile, the Cartographer algorithm [31], which is utilized for LiDAR SLAM, exhibits lower cumulative error compared to Gmapping and Hector algorithms and can perform effectively with lower-cost radar, aligning with the lightweight mobile robot inspection concept; thus, it is highly suitable for map-building autonomous navigation in complex environments. Therefore, the Cartographer SLAM algorithm is chosen in our study as the main navigation technique. For 2D map creation, the robot's position at any moment can be expressed as Equation (1):  
\[\delta=\left(\delta_{x},\delta_{y},\delta_{\theta}\right) \tag{1}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Equipment**} & **Measuring Range** & **Depth Resolution** & **RGB Max Resolution** & **Ranging Resolution** & **Frame Rate (FPS)** & **Scanning Frequency (Hz)** \\ \hline Realsense D435 & 0.11–10 & 1280 \(\times\) 720 & 1920 \(\times\) 1080 & / & 90 & / \\ \hline RPLIDAR A1 & 0.15–12 & / & / & \textless{}0.5 & / & 1–10 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Equipment parameters. Figure 4: Data acquisition UGV. where \(\delta_{x}\) denotes the offset in the x-direction, \(\delta_{y}\) denotes the offset in the y-direction, and \(\delta_{\theta}\) denotes the angle of rotation in the two-dimensional plane. The first frame data initialization corresponds to \(\text{Submap}_{1}\). As the robot moves, the information of the neighboring radar scanning frames will be inserted into the corresponding submap by the method of scan-to-map matching, and the conversion relationship is shown in Equation (2):  
\[T_{\delta}h_{k}= \begin{bmatrix}\cos\delta_{\theta}&-\sin\delta_{\theta}\\ \sin\delta_{\theta}&\cos\delta_{\theta}\end{bmatrix} h_{k}+ \begin{bmatrix} \delta_{x}\\ \delta_{x}\end{bmatrix}  \tag{2}\]  
where \(h_{k}\) is the distance information acquired by radar scanning, the reference coordinate system is the radar coordinate system, and \(T_{\delta}\) is the transformation matrix for transforming the radar scanning frame information into the subgraph Submap. Meanwhile, the Timed-Elastic-Band (TEB) algorithm [32] is employed for path planning. TEB utilizes optimal parameter control, framing local path planning as a multi-objective optimization problem. Feasible paths, obstacle constraints, as well as velocity, acceleration, and nonlinear kinematic constraints are taken into account through the formulation of a multi-objective optimization function. The corresponding formula is presented in (3):  
\[ \begin{cases}f(B)=\sum_{k}w_{k}f_{k(B)}\\ B^{*}=arg\min_{B}f(B)\end{cases}  \tag{3}\]  
where \(B^{*}\) is the optimized local path trajectory, \(f(B)\) is the comprehensive multi-objective optimization function, and \(w_{k}\) is the weight value of a certain objective. Figure 5 depicts an example of the algorithm's application in constructing a map of the test environment, along with path planning and dataset creation. The collected depth and RGB information will be utilized to perform dense reconstruction based on orbSLAM. To evaluate the effectiveness of the proposed method, we compare it with the SfM-based [33] approach. Figure 6 illustrates the texture details obtained by the  
Figure 5: Example of path planning and dataset creation. different reconstruction methods. The data comparison of different reconstruction methods is shown in Table 3.  
Reconstructing the same data revealed that the SfM-based method produced a denser point cloud with superior edge fitting in the detection region but required more time. In contrast, the SLAM-based reconstruction generated a slightly less dense point cloud with less smooth contours. However, the differences were minimal.