# Path Optimization of Two-Posture Manipulator of Apple Packing Robots
## 2 Literature Background  
As the core part of a robot, manipulators are consistently investigated in agricultural robots. Since the 1980s, researchers have conducted several studies on the structural design of manipulators for grasping and picking fruits and vegetables in Japan, the Netherlands, the UK, France, and other countries [4; 5; 6; 7]. [PERSON] et al. [8] developed a manipulator with multi-end effectors for grasping various spherical fruits. [PERSON] et al. [9] and [PERSON] et al. [10] studied the manipulator of a picking robot safely separating kiwifruit from fruit stalks under natural growth conditions. [PERSON] et al. [11] conducted research on a manipulator positioning and grasping apples based on visual detection. [PERSON] et al. [12] designed a new robot for picking strawberries, and the picking tongs of this robot come with a fruit container that can effectively reduce the traveling time for the manipulator between each berry and a separate punnet. Packaging efficiency is one of the main indexes used to evaluate the performance of apple automatic packaging, and the path optimization of the mechanical arm for packaging is the basis for ensuring the efficiency of apple automatic packaging. Path optimization of manipulators has been widely investigated in recent years to smoothly grasp and place objects and improve the work efficiency [13; 14; 15; 16; 17; 18]. Methods for path optimization include algorithms for optimal path planning in discrete spaces [19; 20], optimal path planning in continuous spaces [21], and trajectory generation in continuous spaces with constraints [22]. [PERSON] et al. [23] studied piecewise polynomial interpolation in trajectory planning by setting constraint conditions for the trajectory equation to realize smooth operation for the connecting rod of excavators. However, the computational amount is relatively large because of many trajectory equations, and the solution efficiency is low. [PERSON] et al. [24] investigated the friction problem in trajectory planning and proposed a discretization solution that plays a good role in vibration reduction and stability. However, the calculation amount is extremely large. The method based on the trajectory equation has a large amount of calculation. Genetic algorithms have the advantage of wide applicability, strong global search ability, strong parallelism, and no need for derivative information. In the path optimization of the manipulator of apple packing robots, the combined optimization of multiple factors must be considered, such as the grasping position, placing position, and posture of the manipulator, and the advantage of the strong global search ability of genetic algorithms is very suitable. The solution process of the genetic algorithm is simpler than that of the trajectory equation. [PERSON] et al. [25] used the particle swarm optimization and genetic algorithm to plan the set path. The test results showed that the optimized performance of the genetic algorithm is better than that of the particle swarm optimization. However, the genetic algorithm is prone to premature convergence when the number of path points and data are large [26; 27]. [PERSON] et al. [28] used an improved genetic algorithm to realize the path optimization for automatic transplanting of tray seedlings, thereby reducing the operating time and improving the transplanting efficiency. Although the operation of reinserting offspring individuals in every iteration increases the possibility of chromosome optimization, it reduces the rapid convergence of the algorithm. [PERSON] et al. [29] improved the premature phenomenon of the genetic algorithm by enhancing the crossover operator and fitness function, but the application environment of the operator was relatively limited. The main problems of the current genetic algorithms are that they easily fall into a premature state and the optimization process is not stable [30].