Dynamic soaring phenomenon, exhibited by soaring birds, has long been a biological inspiration for the aerospace and control engineering communities. If this fascinating phenomenon, which allows soaring birds to perform almost un-powered flights using wind shear, can be mimicked by Unmanned-Aerial-Vehicles (UAVs), then UAVs performance have a substantial potential to enhance technologically and economically as well. Even though there have been considerable amount of research covering the modeling, optimization, control and simulation aspects of different UAVs performing dynamic soaring, there is little to non conclusive work analyzing the stability of such UAVs about the soaring orbits. In this paper, we present a comprehensive framework for determining the stability of soaring UAVs utilizing both linear (Floquet-based) and nonlinear (Contraction-theory-based) techniques. Stability analysis under Floquet remained inconclusive , which provoked nonlinear Contraction formulation in order to reach a conclusive stability assessment for the actual nonlinear fixed-wing UAV performing dynamic soaring. Furthermore, parametric variation along with numerical simulations were conducted to ascertain the response of the actual nonlinear system when perturbed from its nominal motion studied in this paper. The analysis and simulations revealed that the system posses instability as the UAV motion diverges from its nominal trajectory and follow an undesirable path. By this result, we conclude, for the first time in literature, that UAVs performing dynamic soaring in an optimal way to reduce wind shear requirements, are inherently unstable. The results of this paper suggests that mimicking dynamic soaring by UAVs, require careful investigations of tracking and regulatory controls that should be implemented.

The mystery of soaring birds, such as albatrosses and eagles, has intrigued biologists, physicists, aeronautical/control engineers, and applied mathematicians for centuries. These fascinating avian organisms are able to fly for long durations while expending little to no energy, utilizing wind to gain lift. This flight technique/maneuver is called dynamic soaring (DS). For biologists and physicists, the DS phenomenon is nothing but a wonder of the very elegant ability of these birds to interact with nature and use its physical ether in an optimal way for better survival and energy efficiency. For the engineering community, the DS phenomenon is a source of inspiration and an unequivocal opportunity for biomimicking. Mathematical characterization of the DS phenomenon in the literature has been limited to optimal control configurations that utilized developments in numerical optimization algorithms along with control methods to identify the optimal DS trajectory taken (or to be taken) by the bird/mimicking system. Unfortunately, all of these methods are highly complex and non-real-time. Hence, the mathematical characterization of the DS problem, we believe, appears to be at odds with the phenomenon/birds-behavior. In this paper, we provide a novel two-layered mathematical approach to characterize, model, mimic, and control DS in a simple real-time implementation, which we believe more effectively decodes the biological behavior of soaring birds. First, we present a differential geometric control formulation and analysis of the DS problem, which allow us to introduce a control system that is simple yet controllable. Second, we establish a link between the DS philosophy and a class of dynamical control systems known as extremum seeking systems. This linkage provides the control input that makes DS a real-time reality. We believe our framework accurately describes the biological behavior of soaring birds and opens the door for geometric control theory and extremum seeking systems to be utilized in biological systems and natural phenomena. Simulation results are provided along with comparisons to powerful optimal control solvers, illustrating the advantages of the introduced method.