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

Abstract

Abstract The albatross optimized flight maneuver—known as dynamic soaring—is nothing but a wonder of biology, physics, and engineering. By utilizing dynamic soaring, this fascinating bird can travel in the desired flight direction almost for free by harvesting energy from the wind. This phenomenon has been observed for centuries as evidenced by the writings of Leonardo da Vinci and Lord Rayleigh. Moreover, dynamic soaring biological inspiration has triggered a momentous interest among many communities of science and engineering, particularly aeronautical, control, and robotic engineering communities. That is, if dynamic soaring is mimicked, we will have arrived at a new class of unmanned aerial vehicles that are very energy-efficient during part (or the full) duration of their flight. Studying, modeling, and simulating dynamic soaring have been conducted in literature by mostly configuring dynamic soaring as an optimal control problem. Said configuration requires accurate dynamic system modeling of the albatross/mimicking-object, accurate wind profile models, and a defined mathematical formula of an objective function that aims at conserving energy and minimizing its dissipation; the solution then of such optimal control problem is the dynamic soaring trajectory taken—or to be taken—by the bird/mimicking-object. Furthermore, the decades-long optimal control configuration of the dynamic soaring problem resulted in non-real-time algorithms and control solutions, which may not be aligned well with the biological phenomenon itself; experimental observations of albatrosses indicate their ability to conduct dynamic soaring in real-time. Indeed, a functioning modeling and control framework for dynamic soaring that allows for a meaningful bio-mimicry of the albatross needs to be autonomous, real-time, stable, and capable of tolerating the absence of mathematical expressions of the wind profiles and the objective function—hypothetically similar to what the bird does. The qualifications of such modeling and control framework are the very same characteristics of the so-called extremum seeking systems. In this paper, we show that extremum seeking systems existing in control literature for decades are a natural characterization of the dynamic soaring problem. We propose an extremum seeking modeling and control framework for the dynamic soaring problem hypothesizing that the introduced framework captures more features of the biological phenomenon itself and allows for possible bio-mimicking of it. We provide and discuss the problem setup, design, and stability of the introduced framework. Our results, supported by simulations and comparison with optimal control methods of the literature, provide a proof of concept that the dynamic soaring phenomenon can be a natural expression of extremum seeking. Hence, dynamic soaring has the potential to be performed autonomously and in real-time with stability guarantees.