  The albatross optimized flight maneuver -- known as dynamic soaring -- is
nothing but a wonder of biology, physics, and engineering. By utilizing dynamic
soaring, the bird can travel in the desired flight direction almost for free by
harvesting energy from the wind. Dynamic soaring biological inspiration has
triggered a momentous interest among many communities of science and
engineering. 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. However, the 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 propose an extremum seeking modeling and control
framework for the dynamic soaring problem. 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.
