A novel hypothesis for how albatrosses optimize their flight physics in real-time: an extremum seeking model and control for dynamic soaring

Abstract

The albatross optimized flight maneuver -- known as Dynamic Soaring (DS) -- is nothing but a wonder of physics, biology, and engineering. In an ideal DS cycle, this fascinating bird can travel in the desired flight direction, for free, by harvesting energy from the wind, and hence, it achieves a neutral energy cycle. This phenomenon has triggered a momentous interest among aeronautical, control and robotic engineering communities; if DS is mimicked, we have arrived at a new class of Unmanned Aerial Vehicles (UAVs) which are very energy-efficient during part (or the full) duration of their flight. However, the DS problem is highly nonlinear, under-actuated, and dependent on the wind profiles. This has resulted in decades of DS control literature that, while making progress in addressing the control problem, seem not to be aligned well with the nature of the DS phenomenon itself. The control works associated with DS in the literature rely heavily on constrained optimal control algorithms, control designs that require a mathematical expression of the objective function, and predefined wind profile models. Clearly, a functioning controller for DS that allows meaningful bio-mimicry of the albatross, needs to be autonomous, real-time, stable, and capable of tolerating the absence of the expression of the objective function (similar to what the bird does). The qualifications of such controller are the very same characteristics of Extremum Seeking Control (ESC) systems. In this paper, we show that ESC systems existing in control literature for decades are a natural characterization of the DS problem. We provide the DS problem setup, design, stability, and simulation results of the introduced ESC systems. The results, supported by comparison with optimal control solvers, emphasize that the DS phenomenon is a natural expression of ESC systems in nature and that DS can be performed autonomously in real-time.