Minimum-Waypoint Figure-Eight Trajectory Shaping for Airborne Wind Energy Systems

This paper presents a practical guidance algorithm for an unmanned aerial vehicle ($\mathbf{U A V}$) used in ground generation airborne wind energy systems (GG-AWESs). The flight endurance of the UAV is a crucial factor in determining the overall efficiency of GG-AWESs. Existing guidance methods utilize numerous waypoints and generate control commands to make the UAV follow a figure-eight trajectory. This approach may result in excessive energy consumption when the UAV passes through the waypoints; hence the UAV is difficult to last the pumping cycle due to its limited battery capacity. To address this issue, the minimum waypoint figure-eight guidance scheme is proposed for the traction and retraction phases. For the traction phase, a guidance law is designed to produce a semi-circular flight path. A multiple-point boundary value problem is subsequently formulated to relocate the UAV to the opposite semicircle of the trajectory during the retraction phase. Analytical solutions to these problems can be obtained by applying the Lyapunov and linear optimal control theories, respectively. The suggested algorithm has advantages in terms of increasing flight duration and ease of implementation, as it requires only five waypoints for shaping the trajectory. The effectiveness and sustainability of our solution are validated by the computer simulations.