A controllability perspective of dynamic soaring

Dynamic soaring is an exquisite flying technique to acquire energy from the atmospheric wind shear. In this study, a geometric nonlinear controllability analysis of an unmanned aerial vehicle (UAV) under dynamic soaring conditions is performed. To achieve such an objective, the state-of-the-art mathematical tools of nonlinear controllability are summarized and presented to an aeronautical engineering audience. The dynamic soaring optimal control problem is then formulated and solved numerically. The controllability of the UAV along the optimal soaring trajectory is analyzed. More importantly, the geometric nonlinear controllability characteristics of generic flight dynamics are analyzed in the presence and absence of wind shear to provide a controllability explanation for the role of wind shear in the physics of dynamic soaring flight. It is found that the wind shear is instrumental in ensuring controllability as it allows the UAV attitude controls (pitch and roll) to play the role of thrust in controlling the flight path angle. The presented analysis represents a controllability-based mathematical proof for the energetics of flight physics.