## 1 Introduction
The traditional full-coverage path planning method is primarily applied to indoor and flat ground environments. However, for farmland environments in hilly areas, the traditional method is unable to address the increase in energy consumption caused by the undulating terrain. Over the years, researchers have proposed a series of full-coverage path planning algorithms for hilly terrain farmland environments. [PERSON] [12] designed a full-coverage path planning algorithm based on genetic algorithms for three-dimensional terrain farmland. This algorithm uses genetic algorithms to find the optimal field travel direction for three-dimensional farmland, allowing a mobile robot to complete the traversal task with less energy consumption. [PERSON] and [PERSON] [13] designed a different full-coverage path planning method for three-dimensional terrain farmland. Their method is based on the machine's coverage cost function to find the \"seed curve\" of the area. Based on the established \"seed curve\", the coverage work is carried out along both sides of the curve. However, due to the difficulties of calculating the \"seed curve\", the paths derived from this method can be too complicated for some complex terrains, potentially resulting in some areas being skipped. [PERSON] [14] and others decomposed 3D terrain into regions based on slope and used genetic algorithms to optimize the direction of coverage for the sub-regions and the order of coverage for each sub-region, which reduced the energy consumption for traversing 3D terrain farmland. However, dividing the regions based on slopes in complex terrain would result in too many subregions, leading to the increased duplication of paths when covering these subregions. [PERSON] [15] designed a full-coverage path planning algorithm for field operation environments in hilly mountainous areas. He constructed an energy consumption model and used an exhaustive algorithm to search for the optimal traveling direction for a single field. Finally, he used a genetic algorithm to plan the coverage order of multiple fields. However, this method is only applicable to agricultural fields in the form of terraces, which are sloping but flat inside. In summary, most current research focuses on finding a fixed driving direction to complete the coverage of an entire area or determining the driving direction after dividing the area. However, these methods are not effective in reducing the energy consumption of the coverage operation. For large areas of hilly terrain farmland, adopting a suitable full-coverage path planning method can significantly reduce the costs of sowing and harvesting processes, thereby improving operational efficiency and production levels. Therefore, reducing the energy consumption of full-coverage path planning is an urgent problem that needs to be addressed. In this paper, we analyze the energy consumption of mobile robots when moving across different terrains, divide the hilly terrain into regions, propose a full-coverage path planning algorithm optimized for energy consumption, and verify the feasibility and superiority of the algorithm through simulation comparison tests. The algorithms in this paper contribute to the following problems: (1) providing feasible ideas for the automation and intelligence of agricultural machinery; (2) proposing a new method for the modeling of three-dimensional terrain farmland; (3) proposing a method for dividing the area of three-dimensional farmland; and (4) designing a better algorithm for three-dimensional full-coverage path planning.