Albatrosses employ orientation and routing strategies similar to yacht racers

The way goal-oriented birds adjust their travel direction and route in response to wind significantly affects their travel costs. This is expected to be particularly pronounced in pelagic seabirds, which utilize a wind-dependent flight style called dynamic soaring. Dynamic soaring seabirds in situations without a definite goal, e.g. searching for prey, are known to preferentially fly with crosswinds or quartering-tailwinds to increase the speed and search area, and reduce travel costs. However, little is known about their reaction to wind when heading to a definite goal, such as homing. Homing tracks of wandering albatrosses (Diomedea exulans) vary from beelines to zigzags, which are similar to those of sailboats. Here, given that both albatrosses and sailboats travel slower in headwinds and tailwinds, we tested whether the time-minimizing strategies used by yacht racers can be compared to the locomotion patterns of wandering albatrosses. We predicted that when the goal is located upwind or downwind, albatrosses should deviate their travel directions from the goal on the mesoscale and increase the number of turns on the macroscale. Both hypotheses were supported by track data from albatrosses and racing yachts in the Southern Ocean confirming that albatrosses qualitatively employ the same strategy as yacht racers. Nevertheless, albatrosses did not strictly minimize their travel time, likely making their flight robust against wind fluctuations to reduce flight costs. Our study provides empirical evidence of tacking in albatrosses and demonstrates that man-made movement strategies provide a new perspective on the laws underlying wildlife movement.

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

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.

Opportunistic soaring by birds suggests new opportunities for atmospheric energy harvesting by flying robots

The use of flying robots (drones) is increasing rapidly, but their utility is limited by high power demand, low specific energy storage and poor gust tolerance. By contrast, birds demonstrate long endurance, harvesting atmospheric energy in environments ranging from cluttered cityscapes to open landscapes, coasts and oceans. Here, we identify new opportunities for flying robots, drawing upon the soaring flight of birds. We evaluate mechanical energy transfer in soaring from first principles and review soaring strategies encompassing the use of updrafts (thermal or orographic) and wind gradients (spatial or temporal). We examine the extent to which state-of-the-art flying robots currently use each strategy and identify several untapped opportunities including slope soaring over built environments, thermal soaring over oceans and opportunistic gust soaring. In principle, the energetic benefits of soaring are accessible to flying robots of all kinds, given atmospherically aware sensor systems, guidance strategies and gust tolerance. Hence, while there is clear scope for specialist robots that soar like albatrosses, or which use persistent thermals like vultures, the greatest untapped potential may lie in non-specialist vehicles that make flexible use of atmospheric energy through path planning and flight control, as demonstrated by generalist flyers such as gulls, kites and crows.

Observations and models of across-wind flight speed of the wandering albatross

Wandering albatrosses exploit wind shear by dynamic soaring (DS), enabling rapid, efficient, long-range flight. We compared the ability of a theoretical nonlinear DS model and a linear empirical model to explain the observed variation of mean across-wind airspeeds of GPS-tracked wandering albatrosses. Assuming a flight trajectory of linked, 137° turns, a DS cycle of 10 s and a cruise airspeed of 16 m s^-1, the theoretical model predicted that the minimum wind speed necessary to support DS is greater than 3 m s^-1. Despite this, tracked albatrosses were observed in flight at wind speeds as low as 2 m s^-1. We hypothesize at these very low wind speeds, wandering albatrosses fly by obtaining additional energy from updrafts over water waves. In fast winds (greater than 8 m s^-1), assuming the same 10 s cycle period and a turn angle (TA) of 90°, the DS model predicts mean across-wind airspeeds of up to around 50 m s^-1. In contrast, the maximum observed across-wind mean airspeed of our tracked albatrosses reached an asymptote at approximately 20 m s^-1. We hypothesize that this is due to birds actively limiting airspeed by making fine-scale adjustments to TAs and soaring heights in order to limit aerodynamic force on their wings.

Bioinspired dynamic soaring simulation system with distributed pressure sensors

Inspired by the albatross, this paper presents the construction of a dynamic soaring simulation system with distributed pressure sensors. The advantage of our system lies in harvesting energy from the wind shear layer and estimating the wind information using a pressure-based sensor system. Specifically, the dynamic soaring simulation system contains an offline training stage and an online estimation and control stage. In the offline training stage, computational fluid dynamics simulations are conducted and used as the data source. A surrogate model is established to correlate the local flow conditions and the surface pressure at optimal sensor positions. In the online estimation and control stage, through sensing the pressure information, the real-time wind velocity and wind gradient are estimated by the surrogate model trained in the offline stage. Moreover, wind information is adopted in the simulation of dynamic soaring control. In this study, the simulation system was applied to linear and circular path-following tasks. It was found that the dynamic soaring simulation system with distributed pressure sensors provides an acceptable estimation of wind velocity and wind gradient with a certain time delay caused by numerical differentiation.

How did extinct giant birds and pterosaurs fly? A comprehensive modeling approach to evaluate soaring performance

The largest extinct volant birds (Pelagornis sandersi and Argentavis magnificens) and pterosaurs (Pteranodon and Quetzalcoatlus) are thought to have used wind-dependent soaring flight, similar to modern large birds. There are 2 types of soaring: thermal soaring, used by condors and frigatebirds, which involves the use of updrafts to ascend and then glide horizontally; and dynamic soaring, used by albatrosses, which involves the use of wind speed differences with height above the sea surface. Previous studies have suggested that P. sandersi used dynamic soaring, while A. magnificens and Quetzalcoatlus used thermal soaring. For Pteranodon, there is debate over whether they used dynamic or thermal soaring. However, the performance and wind speed requirements of dynamic and thermal soaring for these species have not yet been quantified comprehensively. We quantified these values using aerodynamic models and compared them with that of extant birds. For dynamic soaring, we quantified maximum travel speeds and maximum upwind speeds. For thermal soaring, we quantified the animal's sinking speed circling at a given radius and how far it could glide losing a given height. Our results confirmed those from previous studies that A. magnificens and Pteranodon used thermal soaring. Conversely, the results for P. sandersi and Quetzalcoatlus were contrary to those from previous studies. P. sandersi used thermal soaring, and Quetzalcoatlus had a poor ability both in dynamic and thermal soaring. Our results demonstrate the need for comprehensive assessments of performance and required wind conditions when estimating soaring styles of extinct flying species.

A stability perspective of bioinspired unmanned aerial vehicles performing optimal dynamic soaring

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.

Soaring energetics and glide performance in a moving atmosphere

Here, we analyse the energetics, performance and optimization of flight in a moving atmosphere. We begin by deriving a succinct expression describing all of the mechanical energy flows associated with gliding, dynamic soaring and thermal soaring, which we use to explore the optimization of gliding in an arbitrary wind. We use this optimization to revisit the classical theory of the glide polar, which we expand upon in two significant ways. First, we compare the predictions of the glide polar for different species under the various published models. Second, we derive a glide optimization chart that maps every combination of headwind and updraft speed to the unique combination of airspeed and inertial sink rate at which the aerodynamic cost of transport is expected to be minimized. With these theoretical tools in hand, we test their predictions using empirical data collected from a captive steppe eagle (Aquila nipalensis) carrying an inertial measurement unit, global positioning system, barometer and pitot tube. We show that the bird adjusts airspeed in relation to headwind speed as expected if it were seeking to minimize its aerodynamic cost of transport, but find only weak evidence to suggest that it adjusts airspeed similarly in response to updrafts during straight and interthermal glides.

This article is part of the themed issue ‘Moving in a moving medium: new perspectives on flight’.

Optimal dynamic soaring consists of successive shallow arcs

Albatrosses can travel a thousand kilometres daily over the oceans. They extract their propulsive energy from horizontal wind shears with a flight strategy called dynamic soaring. While thermal soaring, exploited by birds of prey and sports gliders, consists of simply remaining in updrafts, extracting energy from horizontal winds necessitates redistributing momentum across the wind shear layer, by means of an intricate and dynamic flight manoeuvre. Dynamic soaring has been described as a sequence of half-turns connecting upwind climbs and downwind dives through the surface shear layer. Here, we investigate the optimal (minimum-wind) flight trajectory, with a combined numerical and analytic methodology. We show that contrary to current thinking, but consistent with GPS recordings of albatrosses, when the shear layer is thin the optimal trajectory is composed of small-angle, large-radius arcs. Essentially, the albatross is a flying sailboat, sequentially acting as sail and keel, and is most efficient when remaining crosswind at all times. Our analysis constitutes a general framework for dynamic soaring and more broadly energy extraction in complex winds. It is geared to improve the characterization of pelagic birds flight dynamics and habitat, and could enable the development of a robotic albatross that could travel with a virtually infinite range.

Flight paths of seabirds soaring over the ocean surface enable measurement of fine-scale wind speed and direction

Ocean surface winds are an essential factor in understanding the physical interactions between the atmosphere and the ocean. Surface winds measured by satellite scatterometers and buoys cover most of the global ocean; however, there are still spatial and temporal gaps and finer-scale variations of wind that may be overlooked, particularly in coastal areas. Here, we show that flight paths of soaring seabirds can be used to estimate fine-scale (every 5 min, ∼5 km) ocean surface winds. Fine-scale global positioning system (GPS) positional data revealed that soaring seabirds flew tortuously and ground speed fluctuated presumably due to tail winds and head winds. Taking advantage of the ground speed difference in relation to flight direction, we reliably estimated wind speed and direction experienced by the birds. These bird-based wind velocities were significantly correlated with wind velocities estimated by satellite-borne scatterometers. Furthermore, extensive travel distances and flight duration of the seabirds enabled a wide range of high-resolution wind observations, especially in coastal areas. Our study suggests that seabirds provide a platform from which to measure ocean surface winds, potentially complementing conventional wind measurements by covering spatial and temporal measurement gaps.