Smooth free-cycle dynamic soaring in unspecified shear wind via quadratic programming

Harvesting wind energy is promising for extending long-endurance flights, which can be greatly facilitated by a flight technique called dynamic soaring. The presented study is concerned with generating model-based trajectories with smooth control histories for dynamic soaring maneuvers exploiting wind gradients. The desired smoothness is achieved by introducing a trigonometric series parameterization for the controls, which are formulated with respect to the normalized time. Specifically, the periodicity of the trigonometric functions is leveraged to facilitate the connection of cycles and streamline the problem formulation. Without relying on a specified wind profile, a free-final-time quadratic programming-based control strategy is developed for the online correction of the flight trajectory, which requires only the instant wind information. Offline and online numerical studies show the trade-off to achieve the smoothness and demonstrate the effectiveness of the proposed method in a varying wind field.