# Path Planning for Conformal Antenna Surface Detection Based on Improved Genetic Algorithm
## 4 Experiments
### Path Planning for Conformal Antenna Surface Detection  
The model of a conformal antenna is distributed with feature points (mounted resistors and feeders), which are uniformly distributed on the curved surface of the antenna. There is a total of 253 feature points distributed on the model that need to be accurately located and inspected after soldering, and the size of the model is not fixed, so the number of feature points and their distribution will change. Therefore, the efficiency of detection of the feature points distributed on this model is crucial. The algorithm proposed in this paper solved the path planning problem for conformal antenna surface detection well, but some changes were needed, i.e., removing the 2-opt operation and changing the fitness function. A large number of randomized spatial 3D point path planning experiments have shown that in the vast majority of cases of the three-dimensional TSP, it is not possible to intersect a straight line with another line, which eliminates the need to use the 2-opt operation and thus saves a portion of the computational time. In addition, both accurate positioning and AOI require the feature points to be leveled and then processed, i.e., the normal direction of the feature point is adjusted to be vertically upward. A schematic diagram before leveling is shown in Figure 14a. There is a total of 13 rows of feature points on the model; the feature points in the same row are separated by 9.5 mm and indicated by the same color, and the X coordinate of the first feature point is deviated between different rows. To make it easier to see, the XYZ coordinate axes are scaled down to a certain extent. Figure 14b shows a schematic diagram after leveling. The figure represents the position of each row after leveling, i.e., the actual position of each row during either detection or processing. It can be seen that additional adjustment time was required when adjusting the rotation angle to accommodate different point positions, as shown in Figure 15. Therefore, the TSP was transformed into a three-dimensional constrained TSP similar to the one described in the literature [27]. When using Formula (5) to calculate the length of each feasible path, the additional rotation angle generated when crossing different rows needed to be considered. Since the length and angle could not be  
Figure 13: (**a–e**) the optimal solutions for the datasets bayg29, eil51, berlin52, lin105, and pr144, respectively; (**f**) is the iteration curve when solving the above five datasets. measured uniformly, the time \(t\) was used uniformly as a measure, as shown in Formula (7). \[t=\sum_{i=1}^{n}\sum_{j=1,i\
eq j}^{n}k_{i,j}\bigg{(}\frac{d_{i,j}}{v}+\frac{ \alpha_{i,j}}{\omega}\bigg{)} \tag{7}\]  
where \(v\) denotes the moving speed of the end-effector; \(\alpha_{i,j}\) denotes the angle of rotation required to rotate from feature point \(i\) facing upward to feature point \(j\) facing upward; \(\omega\) denotes the angular speed of rotation of the A-axis of the 2-DOF rotary platform. The feature points in the conformal antenna were extracted and the path planning was performed using CHOP-IGA, and the obtained results are shown in Figure 16. In fact, due to the limitation of the working distance of the detection camera, the scanning path also needed to increase the height of the camera's focal length \(f\) in the Z-axis direction, i.e., the Z coordinate was shifted upwards by 100 mm. It can be seen from the figure that, to avoid crossing constantly between different rows, which led to a surge in the time spent, the optimal result was to have only one path between two different rows, which reduced the time spent on leveling. To verify the further validation of the scanning efficiency improvement, a test platform was built, as shown in Figure 17.  
A Basler industrial camera was used for detection simulation, which was mounted on the Z axis of a high-precision three-axis linear module. The conformal antenna was fixed on the 2-DOF rotary platform.