Optimal periodic control of power harvesting tethered airplanes: How to fly fast without wind and without propellor?

This paper proposes reversed pumping as a strategy to keep tethered kites airborne in a wind-free condition without any on-board propulsion. In the context of kite power, it is shown to be a necessary addition to a rotational startup scheme. The enhanced scheme ultimately allows for injection into power harvesting orbits at high altitude, in case no wind is present near ground level. The need for reversed pumping is advocated with scaling laws, and is demonstrated in simulation by solving a proposed open-loop periodic optimal control problem. The obtained periodic orbits can be used as reference for feedback control.