Modification of Typical Headland Manoeuvres Using Transition Curves

During headland manoeuvres of agricultural tractors, self-propelled machines, and autonomous agricultural vehicles, it is crucial not only to achieve the required working width but also to minimise the number of turns, path length, and time to reach the next field pass. The shortest trajectories can be obtained using Dubins curves or Reeds–Shepp paths. However, traversing such paths at constant velocity is only theoretically feasible. At the junctions between path segments, either the vehicle must stop or the steering angle must change at an infinite rate. These points exhibit abrupt changes in acceleration components, resulting in infinite jerk. This study presents the use of transition curves for executing U-turns and Ω-turns during headland manoeuvres. Implementing curves with gradually varying curvature ensures smooth transitions between trajectory segments, reducing sudden direction changes and improving motion dynamics. The curvature and tangent angle are defined using trigonometric functions. For the designed trajectory, kinematic parameters, including wheel steering angles, were determined for two models of agricultural tractors. The results provide a solid foundation for future research on refining transition curve models and integrating the proposed solutions with agricultural vehicle control systems.