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.
 A positive feedback on high-latitude winter marine climate change involving convective clouds has recently been proposed using simple models. This feedback could help explain data from equable climates, e.g., the Eocene, and might be relevant for future climate. Here this convective cloud feedback is shown to be active in an atmospheric GCM in modern configuration (CAM) at CO 2 = 2240 ppm and in a coupled GCM in Eocene configuration (CCSM) at CO 2 = 560 ppm. Changes in boundary conditions that increase surface temperature have a similar effect as increases in CO 2 concentration. It is also found that the high-latitude winter cloud radiative forcing over land increases with increases in surface temperature due to either increased CO 2 or changes in boundary conditions, which could represent an important part of the explanation for warm continental interior winter surface temperatures during equable climates. This is due to increased low-level layered clouds caused by increased relative humidity. Citation: Abbot, D. S., M. Huber, G. Bousquet, and C. C. Walker (2009), High-CO 2 cloud radiative forcing feedback over both land and ocean in a global climate model, Geophys. Res. Lett., 36, L05702,
In recent years, hydrofoils have become ubiquitous and critical components of high-performance surface vehicles. Twenty-meter-long hydrofoil sailing craft are capable of reaching speeds in excess of 45 knots. Hydrofoil dinghies routinely travel faster than the wind and reach speeds up to 30 knots. Besides, in the quest for super-maneuverability, actuated hydrofoils could enable the efficient generation of large forces on demand. However, the control of hydrofoil systems remains challenging, especially in rough seas. With the intent to ultimately enable the design of versatile, small-scale, highspeed, and super-maneuverable surface vehicles, we investigate the problem of controlling the lift force generated by a flexible, surface-piercing hydrofoil traveling at high speed through a random wave field. We present a test platform composed of a rudder-like vertical hydrofoil actuated in pitch. The system is instrumented with velocity, force, and immersion depth sensors. We carry out high-speed field experiments in the presence of naturally occurring waves. The 2 cm chord hydrofoil is successfully controlled with a LTV/feedback linearization controller at speeds ranging from 4 to 10+ m/s.
We revisit the classical concept of near-decomposability in complex systems, introduced by Herbert Simon in his foundational article The Architecture of Complexity, by developing an explicit quantitative analysis based on singular perturbations and nonlinear contraction theory. Complex systems are often modular and hierarchic, and a central question is whether the whole system behaves approximately as the "sum of its parts", or whether feedbacks between modules modify qualitatively the modules behavior, and perhaps also generate instabilities. We show that, when the individual nonlinear modules are contracting (i.e., forget their initial conditions exponentially), a critical separation of timescales exists between the dynamics of the modules and that of the macro system, below which it behaves approximately as the stable sum of its parts. Our analysis is fully nonlinear and provides explicit conditions and error bounds, thus both quantifying and qualifying existing results on near-decomposability.
Building upon our recent description of dynamic soaring as a succession of small amplitude arcs nearly crosswind, rather than a sequence of half-turns, we formulate an asymptotic expansion for the minimum-wind dynamic soaring cycle when the shear layer between the slow and fast regions has a thin but finite thickness. Our key assumption is that the trajectory remains approximately planar even in finite thickness shears. We obtain an analytical approximation for key flight parameters as a function of the shear layer thickness ∆. In particular we predict that the turn amplitude, maximum climb angle, and cycle altitude scale as ∆ 1/5 , ∆ 2/5 , and ∆ 3/5 , respectively. Our asymptotic expansion is validated against numerical trajectory optimizations and compared with recordings of albatross flights. While the model validity increases with wing loading, it appears to constitute an accurate description down to wing loadings as low as 4kg/m 2 for oceanic boundary layer soaring, a third that of the wandering albatross.
Convergence of Extremum Seeking (ES) algorithms has been established in the limit of small gains. Using averaging theory and contraction analysis, we propose a framework for computing explicit bounds on the departure of ES schemes from their ideal dominant-order average dynamics. The bounds remain valid for possibly large gains. This framework allows us to establish stability and to estimate convergence rates and it opens the way to selecting "optimal" finite gains for ES schemes. Moreover, it constitutes a powerful aid in the design of efficient Perturbation Based ES. We extend this study by providing a simple technique inspired by adaptive control for estimating the cost function derivatives in Numerical Optimization based ES.
Wind power is the source of propulsive energy for sailboats and albatrosses. We present the UNAv, an Unmanned Nautical Air-water vehicle, that borrows features from both. It is composed of a glider-type airframe fitted with a vertical wing-sail extending above the center of mass of the system and a vertical surface-piercing hydrofoil keel extending below. The sail and keel are both actuated in pitch about their span-wise axes. Like an albatross, the UNAv is fully streamlined, high lift-to-drag ratio and generates the gravity-cancelling force by means of its airborne wings. Like a sailboat, the UNAv interacts with water and may access the full magnitude of the wind. A trim analysis predicts that a 3.4-meter span, 3 kg system could stay airborne in winds as low as 2.8 m/s (5.5 knots), and travel several times faster than the wind speed. Trim flight requires the ability to fly at extreme low height with the keel immersed in water. For that purpose, a multi-input longitudinal flight controller that leverages fast flap actuation is presented. The flight maneuver is demonstrated experimentally.
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