## 4 Discussion and Conclusions  
In this paper, an autonomous driving path-generation algorithm was developed to generate waypoints for an autonomous driving crawler-type ridge-forming robot, using the geodetic coordinates of the field boundary points. The proposed algorithm defines outer- and inner-field boundaries, generates working line segments in the inner-field boundary and the headland area, and then uses the working line segments to generate waypoints according to the autonomous driving scenario. Three types of waypoints were generated based on the autonomous driving scenario: waypoints for autonomous ridge-forming in the inner field, waypoints for returning to the starting point in the headland area, and waypoints for autonomous ridge-forming in the headland area. To verify the proposed algorithm, waypoint generation tests were conducted based on four types of fields with different shapes (a rectangle, trapezoid, pentagon, and hexagon). The results for the three steps in the autonomous driving algorithm, a field boundary definition, working lines' generation, and waypoint generation, are summarized as follows. Using the field boundary definition, the inner boundary of the field was generated appropriately by considering the shape of the field and the rotation radius of the robot. The working line segments in the inner-field boundary were generated by considering the width of the ridge, and the working line segments in the headland area were generated along the field boundaries. Lastly, the waypoints, which are the autonomous driving path, were appropriately generated sequentially, based on the shortest distance using the working line segments, so that the robot could drive and work continuously from the starting point. The test results confirm that the proposed algorithm can be used to generate an autonomous driving path for a crawler-type ridge-forming robot. Based on the test results, the key elements discussed in this study are as follows. First, the proposed algorithm can efficiently generate a path using only the coordinates of field boundary points. The proposed algorithm has the advantage of reducing the time for acquiring data compared to methods [2, 3, 4] that generate routes using location data through manual driving and reducing the computation time compared to methods [5, 6, 7, 8, 9, 10] that use complex geometric maps. The proposed algorithm has the advantage of increasing the working area because it generates a path considering the minimum turning section for a crawler-type ridge-forming robot. Therefore, the path can be generated more simply than  
Figure 15: Waypoints for the hexagon-shaped field: external boundaries (black lines), internal boundaries (magenta line), autonomous driving path (blue lines), start waypoint (triangle), straight or turning waypoint (plus), work-starting waypoint (circle), work-ending waypoint (diamond), ending waypoint (star); (**a**) waypoints for ridge-forming work in the inner-field boundary; (**b**) waypoints for returning to the starting point; (**c**) waypoints for ridge-forming work in the headland area. the path generation methods [12; 13] for wheeled agricultural machinery without considering the turning, and the area of the headland area for the turning can also be minimized. Future research will focus on the efficiency and practical applicability of the proposed algorithm. The details of future research are as follows. First, to verify the practical applicability of the proposed algorithm, we will conduct various field tests of autonomous ridge-forming using a crawler-type ridge-forming robot. Second, by implementing the existing path-generation algorithms, we will investigate the strengths and weaknesses of the proposed algorithm by deeper analysis and improve the algorithm. Third, we will conduct research to analyze the working method of the ridge-forming robot according to the shape of various fields and supplement the algorithm so that it can create a reliable path in fields of various shapes.