# Path Planning for Conformal Antenna Surface Detection Based on Improved Genetic Algorithm
## 1 Introduction  
The airborne electronic countermeasures (ECM) system is a key piece of electronic information equipment on military aircraft which significantly impacts combat results [1]. Compared with the traditional planar ECM antenna, the conformal antenna can fit well with the aircraft's wings, fuselage, and other areas, retain excellent aerodynamic performance, and reduce the radar-scattering cross-sectional area. Thus, it is one of the main directions of the future development of antenna technology [2; 3]. Figure 1 shows the schematic diagram of a certain type of conformal antenna, which consists of a conformal substrate and a radiating surface. The radiating surface is distributed with many feature points, mainly for the welding pads and feeding holes distributed along the curved surface, which need to be processed one by one, and finally, each point is inspected for quality. Currently, this type of conformal antenna is usually assembled manually. Due to the small size and large number of feature points and their distribution on curved surfaces, this leads to extremely low production efficiency and makes it impossible to improve the quality consistency of the product and the qualification rate [4]. To address the above problems, an intelligent assembly system as shown in Figure 2 was designed. It uses a 3D optical scanning measurement system to reconstruct the workpiece. Then, the conformal antenna is coated, mounted, and welded. The 3D optical scanning measurement system can only detect the normal direction and the approximateposition of the feature points. Therefore, after reconstruction, it is necessary to use a high-resolution industrial camera to detect the precise position of the feature points to provide positional guidance for coating, mounting, welding, and auto optical inspection (AOI). Therefore, the planning of detection paths, including position and quality detection, is one of the key factors affecting production efficiency, and it also provides guidance for the planning of paths for plaster coating and welding. The above problems can be grouped into constrained three-dimensional traveling salesman problems (TSP), and there is no essential difference between two-dimensional TSP problems and three-dimensional TSP problems. Thus, the algorithms for solving two-dimensional TSP problems can be improved to solve three-dimensional TSP problems. Therefore, to realize the efficient and high-quality production of conformal antennas, suitable TSP-solving algorithms are needed to plan the detection paths correctly. TSP-solving algorithms can be divided into two categories: deterministic algorithms and intelligent algorithms. Deterministic algorithms include the enumeration method, dynamic programming method [5], branch and bound method [6], etc. Deterministic algorithms seek the exact solution to a TSP problem at the cost of a huge amount of time. The dynamic programming method, for example, has an exponential time complexity of O(N\({}^{2}\)2N) and a space complexity of O(N2N), which makes it almost impossible to deal with problems with more than 30 cities. Intelligent algorithms include the particle swarm optimization algorithm [7], ant colony algorithm [8], simulated annealing algorithm [9], sparrow search algorithm [10], hybrid algorithm [11], etc. The intelligent algorithms reach the solution by performing multiple iterations and utilizing the most useful information  
Figure 1: A certain type of conformal antenna. Figure 2: Intelligent assembly system. from each generation. Although the exact solution cannot be guaranteed, this achieves the best balance between time and accuracy and is one of the best solutions for solving TSPs. The genetic algorithm, an intelligent algorithm proposed by [PERSON] in 1967, can also be used to solve TSPs. As one of the earliest of the intelligent algorithms, the genetic algorithm has evolved many variants, including the binary coded genetic algorithm, real number coded genetic algorithm, parallel genetic algorithm, hybrid genetic algorithm, etc.