# Trajectory Planning of Shape-Following Laser Cleaning Robot for the Aircraft Radar Radome Coating
## 3 Results  
The remote-control system hardware used in the experiment consists of an ABB (Asea Brown Boveri) IRB (Industrial Robot) series 6700 robot, a control cabinet, and a computer. The computer communicates with the control cabinet using the RAPID language in RobotStudio software, which controls the robot's motion. The host computer, running laser cleaning software on the Windows operating system, acts as the main control system. It establishes communication and connection with the ABB robot through the Internet options or TCP/IP protocol of the robot's PC. Additionally, it connects and communicates with the Siemens 1200 series PLC via Ethernet or other communication methods to control the robot system and laser system and monitor device status. Offline trajectory planning is performed on the 3D point cloud, which offers more freedom and accurate trajectory planning compared to online programming in RobotStudio software. In this study, a radar dome of an aircraft was chosen as the experimental object. A 3D scanner was used to scan the radar dome and obtain point cloud data. The point cloud data were then preprocessed and aligned to generate a 3D model of the radar dome's  
Figure 11: Comparative illustration of connecting points of two different-level curves. (**a**) Connecting points of two curves without the constraint of first-order derivative consistency. (**b**) Connecting points of two curves with the constraint of first-order derivative consistency. surface. This model was imported into the offline programming software, and based on the surface curvature of the radar dome, limitations of the laser cleaning area, and focal depth requirements (in this experiment, the angle \(\theta\) is 36.87 degrees), the surface of the radar dome was divided into regions, as shown in Figure 12.  
By employing a point cloud segmentation algorithm, a series of slices were generated, as shown in Figure 12c. For each slice, a centroid calculation was performed to extract the cleansing positions of the radar radome, as shown in Figure 13a. In Figure 14a, an estimation of the normal vectors at the extracted cleaning points is presented, and numerical annotations within the figure denote the sequence of the motion trajectory during the laser cleaning process. Leveraging the B-spline curve fitting method and hierarchical stitching processing, the spatial trajectory of the laser cleaning robot was obtained, as shown in Figure 13b. Figure 12: Radome point cloud model segmentation: (**a**) vertical segmentation effect of point cloud, (**b**) top view after point cloud segmentation, (**c**) horizontal segmentation effect of point cloud, and (**d**) local segmentation effect of point cloud segmentation. Figure 13: Execution point fitting generates cleaning robot trajectory: (**a**) extracted cleaning point positions, (**b**) trajectory planning for robot laser cleaning, (**c**) local enlarged layered connections, and (**d**) cleaning the movement trajectory of the robot. Before trajectory planning for laser cleaning by the robot, it was necessary to perform point cloud-to-robot calibration, which involves transforming the coordinate system of the radar radome point cloud to that of the robot. To achieve this problem, point selection calibration between the point cloud and the robot was carried out. In order to improve accuracy, a total of 10 data sets was collected and the homogeneous transformation matrix for the point cloud-to-robot calibration was computed. The computed transformation matrix is shown below. \[M_{4\times 4}= \begin{bmatrix}-0.999999&0.00101104&0.000331104&2499.81\\ -0.00101122&-1&0.000034034&-0.0950298\\ 0.000331193&0.000033379&1&25.4204\\ 0&0&0&1\end{bmatrix} \]  
To illustrate the practicality of the proposed method in real-world scenarios, a surface coating laser cleaning was conducted on an actual radar radome.