High-Continuity Path Smoothing Along Obstacle Boundaries Applied to Agricultural Headland Planning with Kinematic Constraints

High-continuity paths are a major topic of research, especially for vehicles with kinematic constraints. In this paper, we propose an approach for computing highly continuous (C
⁵
+) paths along complex polyline boundaries. The paths are restricted in their curvature, curvature derivative and minimum obstacle clearance. Unlike previous research, we minimize the gap between path and boundary. By doing so, paths for kinematic constrained vehicles that need to work near walls, fences or other obstacles can be planned. We showcase the functionality of the NURBS-based approach for the topic of agricultural headland path planning and extend the current research in this topic to organic-shaped fields. Additionally, we introduce a complexity measure for constrained smoothing of polygon outlines and rank our algorithm's performance.