## 1 Introduction  
One of the challenges facing modern agriculture is the falling income rates of farmers due to labor shortages and rising labor costs. One of the most labor-intensive tasks in field farming is ridge formation, and considering the rising labor costs, there is interest in new technology that can replace labor. Autonomous driving technology for agricultural machinery is being actively developed for this purpose, using ICT technology and advanced sensors. Such systems are expected to help address problems in the agricultural sector, such as a declining farm population, labor shortages, and food shortages. Global agricultural machinery companies such as John Deere, CNH Industrial, and Yanmar have launched autonomous tractors that combine sensors such as GNSS, cameras, and lidar with AI [1]. Since autonomous agricultural machinery driving is performed along a pre-defined path, generating the autonomous driving path is essential for autonomous operation. In addition, the cultivation rate and efficiency also depend on path generation, so the path generation must be designed to match the driving and working methods of the agricultural machinery. For this reason, much research has been conducted on path-generating methods for autonomous agricultural machinery. Current methods for generating autonomous driving paths can be divided into those that use location data obtained by driving the route in advance [2; 3; 4] and methods that employ a geometric map [5; 6; 7; 8; 9; 10]. The location data method obtained by driving a path in advance has the advantage of being relatively simple to execute, and creates a driving path that considers the positions and rotation spaces of surrounding obstacles. For example, [PERSON] and [PERSON] [2] defined an autonomous driving path by saving the location coordinates obtained by driving the route manually as waypoints. [PERSON] et al. [3] generated an autonomous driving path by extracting essential waypoints required for autonomous driving based on the location data for the route acquired through manual driving, the intervals between waypoints, and the angles of straight lines generated by adjacent waypoints. [PERSON] et al. [4] proposed a method to obtain location data for individual passages in an orchard, merge them to create an orchard map, and then generate an autonomous driving route based on this. However, it takes a lot of time and labor to create a route over a large area, and there is a disadvantage in that it is difficult to change the driving pattern according to the work method. Therefore, the above method is best suited for fruit farming, such as orchards, where permanent obstacles exist and the same work is performed each time. The geometric map method defines a space in which the autonomous work can be performed using objects made up of points and lines, and it generates a path which considers the rotation and working methods of the agricultural machinery. For example, [PERSON] et al. [5] suggested a method that generated predetermined efficient courses using a field map to reduce overlapping and missed courses. [PERSON] et al. [6] proposed an algorithm based on the treatment of convex cells and the definition of characteristic points to generate field-work tracks in the polygonal fields. [PERSON] and [PERSON] [7] presented an algorithm to solve coverage path planning using a geometric map. This algorithm splits a complex-shaped field into simple trapezoid fields and generates straight field-work tracks. [PERSON] et al. [8] presented a method for the generation of a geometric field representation to provide a map, on which the operational planning of field operations could be carried out. [PERSON] et al. [9] developed a 3D coverage algorithm where 2D coverage paths are projected through the field terrain. [PERSON] et al. [10] introduces the automatic boom section control technology based on a map. The advantage of using geometric maps is that autonomous driving routes can be generated regardless of the shape of the field or the working method.