RESUMO
The phenomenon of dynamic soaring, as exhibited by soaring birds, has long been a biological inspiration for aerospace and control engineers. If this fascinating phenomenon, which allows soaring birds to perform almost unpowered flight using wind shear, can be mimicked by unmanned aerial vehicles (UAVs), then there is substantial potential for technological and economic enhancement of UAV performance. Although there has been a considerable amount of research covering the modeling, optimization, control and simulation aspects of different UAVs performing dynamic soaring, there is little to no conclusive work analyzing the stability of such UAVs in 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. Floquet stability analysis was inconclusive, which led to the use of a nonlinear contraction formulation to reach a conclusive stability assessment for an 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 the nominal motion studied in this paper. The analysis and simulations revealed that the system possesses instability as the UAV motion diverges from its nominal trajectory and follows an undesirable path. From this result we conclude, for the first time in the literature as far as we are aware, that UAVs performing dynamic soaring in an optimal way to reduce wind shear requirements are inherently unstable. The results of this work suggest that mimicking of dynamic soaring by UAVs will require careful investigation of tracking and regulatory controls that need to be implemented.