## 1 Introduction  
In recent years, with the wave of \"Industry 4.0\" and smart manufacturing, the structure of the global manufacturing industry has been greatly impacted. With rising labor costs, traditional manufacturing factories are in need of transformation and development towards digitization and intelligence. Most factories have introduced a lot of automation equipment since traditional production is no longer suitable. The logistics and warehousing industry is also a focus in Industry 4.0. Whether it is manufacturing, logistics, e-commerce, etc., the manpower consumption can be greatly reduced by the introduction of warehousing automation. In order to expand the e-commerce market, Uniado has cooperated with the logistics company, Daifuku, to transform the traditional warehouse into fully automated logistics. All the processes of procurement, logistics, and distribution to the hands of consumers can be solved by artificial intelligence and robots [1]. At present, logistics labor costs account for 65% of the average operating budget of most warehouses. With such a high proportion, low gross profit, and huge competitive pressure, the logistics industry needs to try to find better ways to automate the warehouse process as much as possible. As a result, the market for warehouse automation equipment is constantly growing. According to MarketsandMarkets Research, the warehouse robotics market is expected to grow from USD 4.7 billion in 2021 to USD 9.1 billion in 2026, at a CAGR of 14.0% [2]. It is also becoming more and more popular for factories to introduce robotic arms into automation stacks. To use effective resources correctly is more important in the fierce competition of enterprises. Warehousing logistics is one of the factors that affect the profit of the entire supply chain. Good cargo stacking planning helps to place more cargo and save on the costs of transportation and storage. The Pallet Loading Problem (PLP) focuses on finding space optimization to pack the maximum quantity of goods onto the pallet [3]. With regard to solving the Pallet Loading Problem, there are mainly two options. The first one is using an exact depth-first algorithm [4]. A search tree, which is a tree data structure, is used to simulate all the possible arrangements of objects on the pallet; therefore, using this method can arrange the maximum number of objects on the pallet. Because the simulation is based on the search tree, the results of the arrangement are usually unpredictable. Meanwhile, the algorithm did not propose the methods of stacking and object coordinate marking and only discussed the arrangement of the two-dimensional planes, which makes it difficult to apply this algorithm. As for [PERSON]'s heuristic algorithm [5] and re-cursive partitioning algorithm [6], the pallet is regarded as a two-dimensional plane and then partitioned and arranged. This kind of algorithm can deduce the arrangement of the object according to the logic. However, the number of objects arranged according to the logical rules is relatively lower than that of the heuristic algorithm. Additionally, the heuristic packing algorithm [7], which is similar to exact depth-first algorithm, also got the arrangement result by using a search tree. Nevertheless, not all objects can be reversely arranged in the practical operation process, which does not conform to the actual container packing principle. As a result, this method is not adopted in this study. Therefore, this article will improve the shortcomings of the above four algorithms and propose an improved symmetric algorithm. The relevant comparison is shown in Table 1. All object coordinates will be established by this algorithm following the system's actual requirements to optimize the development of automated robotic arms. The improved symmetric algorithm reduces the waste of a large area caused by [PERSON]'s algorithm's one-time arrangement planning. The remaining area after each arrangement will be planned again until the remaining area cannot be arranged.