# Research on Three-Dimensional Scanning Path Planning of Casing Parts Based on Industrial Robot
## 2 Automated Tracking Type 3D Scanning Measurement System
### System Scanning Principle and Technical Parameters  
The automatic tracking 3D scanning measurement system takes the optical tracker and the three-dimensional scanner as the core components, and its scanning principle is shown in Figure 4. The coordinate system of the three-dimensional scanning probe is \(O_{B}\), the laser generator emits a laser line projected onto the scanned object, and the laser changes with the shape of the measured object. The coordinate system of the binocular camera of the 3D scanner is \(O_{B}\), and the camera can obtain the three-dimensional coordinates of the laser projected onto the scanned object. The point P is a point on the measured surface, and the distance to the surface of the object to be measured is L, which is represented by a blue laser line. A and B are the scan area sizes. During the scanning operation, the shape of the area composed of laser lines changes, as shown in the red laser line in Figure 4. The coordinate system of the optical tracker is \(O_{A}\). Through the reflective marker point-tracking technology, the coordinate position of the reflective target on the laser three-dimensional scanning probe was obtained at a speed of 60 Hz per second. The phase measurement method was used to calculate the three-dimensional coordinate value \({}^{B_{i}}P_{i}\) of each reflective target in the working space of the optical tracker, and the pose matrix \(\left[{}^{B_{i}}P_{i}\right]\) of the three-dimensional scanner was obtained. If \({}^{C}P_{i}\) is a point on a workpiece in the  
Figure 3: System communication structure.  
\(O_{B}\) coordinate system, the three-dimensional coordinates of the laser line projection point in the binocular camera coordinate system \(O_{C}\) are \({}^{B}P_{i}\), the three-dimensional coordinates in the optical tracker coordinate system \(O_{A}\) are \({}^{A}P_{i}\):  
\[{}^{A}P_{i}={}^{B}_{A}T_{i}{}^{C}T_{i}{}^{C}P_{i} \tag{1}\]  
where \(\mathbb{C}_{B}T_{i}\) is the conversion matrix between the coordinate system \(O_{B}\) and the binocular camera coordinate system \(O_{C}\) of the 3D scanning probe; \({}^{B}_{A}T_{i}\) is the conversion matrix between the coordinate system \(O_{A}\) of the optical tracker and the coordinate system \(O_{B}\) of the 3D dimensional scanning probe. It is obtained from the attitude matrix \(\left[{}^{B}_{j}P_{i}\right]\) of tracking target coordinates.  
Using the linear three-dimensional information obtained by the three-dimensional scanner and the relative position of the optical tracker in space, when the scanner moves, the three-dimensional information of the position where the laser passes is continuously obtained, thereby forming continuous three-dimensional point cloud data. The free surface data or geometric data of the measured object will be obtained from each image and calculated by the software. The 3D laser scanner model in this paper is Metra SCAN 3D, and its specific parameters are shown in Table 1. The working distance between the scanner and the workpiece surface is 20-40 cm. When the optimal reference distance is 30 cm, the scanning field of the 3D scanner is 27.5 cm \(\times\) 25 cm, as shown in Figure 5. Due to the use of active shutter technology, it has good adaptability to the surface of workpieces with different degrees of grayness, and can collect enough pictures to achieve efficient scanning.  
\begin{table}
\begin{tabular}{c c c c c} \hline
**Accuracy (mm)** & **Resolution Ratio (mm)** & **Base Distance L (mm)** & **Scan Area A \(\times\) B (mm)** & **Measuring Rate (r/s)** \\ \hline
0.03 & 0.05 & 300 & \(275\times 250\) & 480,000 \\ \hline \end{tabular}
\end{table}
Table 1: Metra SCAN 3D scanner parameters.  
Figure 4: Scanner point cloud scanning principle.