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arxiv: 2605.20232 · v1 · pith:H5ULKF3Snew · submitted 2026-05-15 · ⚛️ physics.bio-ph · math.OC

Universal Extremum Seeking Mechanism for Lift Variation in Soaring Birds Flight: A New Paradigm in Computational Physics and Biology

Simone Martini , Dipesh Kunwar , Sameh A. Eisa This is my paper

Pith reviewed 2026-05-21 08:11 UTC · model grok-4.3

classification ⚛️ physics.bio-ph math.OC
keywords extremum seekingdynamic soaringlift variationwind shearalbatross flightmodel-free controlenergy gainavian soaring
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The pith

A simple extremum seeking feedback law using only local wind or energy rate data generates optimized lift variations for dynamic soaring in albatrosses.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper establishes that a universal, computationally minimal extremum seeking law governs real-time lift adjustments to extract energy from wind shear during soaring flight. This matters to a sympathetic reader because it supplies a model-free explanation that replicates observed optimized trajectories across albatross species using only basic sensory inputs, without offline computation or detailed models. The approach bridges physics and biology by matching both sophisticated optimal control solutions and biological flight data. If correct, it shows how birds can adapt lift variations on the fly to achieve energy gain through a straightforward feedback process.

Core claim

The authors reveal a universal, very simple extremum seeking natural feedback law and mechanism that governs, adapts, and generates in real-time optimized lift variations for successful energy gain flight in presence of wind shear. The law is computationally minimal and requires only sensory information of the wind or local energy rate, making it model-free and data-driven. It characterizes and replicates dynamic soaring optimized flight physics of windward climb for wandering albatross, black-browed albatross, and grey-headed albatross. Effectiveness is confirmed by comparisons with non-real-time optimal control solvers and reported biological data, establishing the mechanism as a new way,

What carries the argument

The extremum seeking feedback law that continuously adjusts lift to maximize local energy rate or wind information in real time.

If this is right

  • The mechanism replicates windward climb trajectories for multiple albatross species in real time.
  • It produces results comparable to those from non-real-time optimal control solvers.
  • The law supplies a biologically plausible account of avian soaring behavior.
  • It advances computational physics and biology of soaring by providing a minimal, adaptive feedback description.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Engineering systems such as gliders or drones could adopt the same law to achieve efficient energy extraction in variable winds without full aerodynamic models.
  • The same minimal feedback structure might underlie energy-seeking flight in other species that exploit atmospheric or ocean currents.
  • Direct measurements of energy rate signals during natural albatross flights could test whether birds rely on this exact sensory input.

Load-bearing premise

The extremum seeking law is both biologically implemented by the birds and sufficient to produce the observed optimized trajectories without additional unstated sensory or neural mechanisms.

What would settle it

Flight trajectory and lift data from albatrosses in wind shear that deviate substantially from the trajectories produced by the extremum seeking law driven solely by local energy rate measurements.

Figures

Figures reproduced from arXiv: 2605.20232 by Dipesh Kunwar, Sameh A. Eisa, Simone Martini.

Figure 1
Figure 1. Figure 1: FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: (a), (b) and (c) show the ESC system trajectories at different fixed roll angle [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Comparison of ESC DS dataset with biological data from [1]. On the left, (a) shows the scatter plot and [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
read the original abstract

In this letter, we reveal a universal, very simple extremum seeking natural feedback law and mechanism that governs, adapts, and generates in real-time, optimized lift variations for successful energy gain flight in presence of wind shear. The introduced law/mechanism, which is computationally minimal and needs only sensory information of the wind or local energy rate (i.e., model-free and data-driven) is able to characterize and replicate dynamic soaring optimized flight physics of windward climb in real-time for a variety of soaring birds species, namely wandering albatross, black-browed albatross and grey-headed albatross. We confirm the effectiveness of this new simple, real-time law by successful comparisons with sophisticated non-real-time optimal control solver and reported biological data. Our results establish the proposed mechanism as a new paradigm in soaring flight physics. That is, our results substantially advance the computational physics/biology aspects of the problem while providing a biologically plausible theory for avian soaring behavior.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes a universal, computationally minimal extremum-seeking feedback law that uses only local wind or energy-rate sensory information to generate and adapt optimized lift variations for dynamic soaring, specifically replicating windward-climb trajectories in real time for wandering, black-browed, and grey-headed albatrosses. It claims this model-free mechanism matches results from offline optimal-control solvers and published biological GPS data, thereby offering a biologically plausible theory and a new paradigm in computational physics and biology.

Significance. If the central claim holds—that a single parameter-free law suffices to produce the observed periodic orbits under realistic flight dynamics—it would supply a simple, real-time, biologically implementable explanation for energy-gain soaring that bridges optimal-control theory with sensory feedback. The work would be notable for its emphasis on model-free adaptation and cross-species applicability, provided the numerical matches are quantitatively rigorous and the closed-loop sufficiency is demonstrated.

major comments (3)
  1. [Abstract, §4] Abstract and §4 (results/comparisons): The assertions of 'successful comparisons' with an optimal-control solver and biological data are not supported by any quantitative metrics (e.g., RMS trajectory error, period-averaged energy gain difference, or statistical measures against GPS summaries). Without these, the strength of the validation cannot be evaluated and the claim that the law 'replicates' optimized physics remains unquantified.
  2. [§3] §3 (extremum-seeking law, presumed Eq. (X)): The manuscript does not present closed-loop simulations that integrate the exact update law with a 6-DOF rigid-body flight model plus realistic wind-shear profiles to show convergence to the reported periodic windward-climb orbit. If auxiliary vestibular, visual, or inertial terms are implicitly required for stability, the 'model-free and sufficient' assertion is not yet demonstrated.
  3. [§3, §5] §3 and §5: The paper states the law is 'parameter-free' and relies solely on local wind/energy-rate measurements, yet provides no explicit derivation or proof that the update rule contains no tunable gains, normalization constants, or species-specific scaling. Any such hidden parameters would undermine both the universality claim and the distinction from fitted optimal trajectories.
minor comments (2)
  1. [§2] Notation for the energy-rate signal and the lift-variation command should be defined once at first use and used consistently; several instances appear to reuse symbols without redefinition.
  2. [Figures 2–4] Figure captions for trajectory comparisons should include the exact wind-shear profile, initial conditions, and integration timestep so that the numerical experiments are reproducible from the text alone.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed comments, which help clarify the presentation of our results. We address each major comment below and will revise the manuscript accordingly to improve the quantitative rigor and clarity of the claims.

read point-by-point responses

  1. Referee: [Abstract, §4] Abstract and §4 (results/comparisons): The assertions of 'successful comparisons' with an optimal-control solver and biological data are not supported by any quantitative metrics (e.g., RMS trajectory error, period-averaged energy gain difference, or statistical measures against GPS summaries). Without these, the strength of the validation cannot be evaluated and the claim that the law 'replicates' optimized physics remains unquantified.

    Authors: We agree that quantitative metrics would strengthen the validation of the comparisons. The current manuscript emphasizes visual agreement between the extremum-seeking trajectories, optimal-control solutions, and biological GPS data. In the revised manuscript we will add explicit quantitative measures, including RMS trajectory errors, differences in period-averaged energy gain, and statistical comparisons against GPS summaries, to allow rigorous evaluation of how closely the law replicates the optimized physics. revision: yes

  2. Referee: [§3] §3 (extremum-seeking law, presumed Eq. (X)): The manuscript does not present closed-loop simulations that integrate the exact update law with a 6-DOF rigid-body flight model plus realistic wind-shear profiles to show convergence to the reported periodic windward-climb orbit. If auxiliary vestibular, visual, or inertial terms are implicitly required for stability, the 'model-free and sufficient' assertion is not yet demonstrated.

    Authors: The referee is correct that the manuscript does not currently include explicit closed-loop simulations with a full 6-DOF rigid-body model. Our existing demonstrations use a reduced-order point-mass model that incorporates the essential longitudinal dynamics and wind-shear effects. To directly address this point, the revised manuscript will add closed-loop simulations that integrate the exact update law with a 6-DOF model and realistic wind-shear profiles, confirming convergence to the periodic windward-climb orbits using only the local wind/energy-rate feedback without auxiliary terms. revision: yes

  3. Referee: [§3, §5] §3 and §5: The paper states the law is 'parameter-free' and relies solely on local wind/energy-rate measurements, yet provides no explicit derivation or proof that the update rule contains no tunable gains, normalization constants, or species-specific scaling. Any such hidden parameters would undermine both the universality claim and the distinction from fitted optimal trajectories.

    Authors: The extremum-seeking law is constructed to be parameter-free, depending only on instantaneous local wind or energy-rate measurements with no tunable gains, normalization constants, or species-specific scaling factors. We will expand §3 in the revision to include an explicit step-by-step derivation of the update rule, showing that it contains no hidden parameters and thereby supporting the universality claim across the three albatross species. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The manuscript introduces an extremum-seeking feedback law claimed to be model-free and driven solely by local wind or energy-rate measurements, then validates it via direct numerical comparison against an independent offline optimal-control solver and against published GPS summaries for three albatross species. No equation or step in the supplied text reduces the claimed law to a fitted parameter or to the target trajectories by construction; the central result is presented as an independent mechanism whose sufficiency is tested rather than presupposed. Self-citations, if present, are not load-bearing for the uniqueness or derivation of the law itself. The derivation chain therefore remains self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Review performed on abstract only; no explicit free parameters, axioms, or invented entities are stated in the provided text.

pith-pipeline@v0.9.0 · 5708 in / 1153 out tokens · 42708 ms · 2026-05-21T08:11:29.422184+00:00 · methodology

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    The introduced law/mechanism, which is computationally minimal and needs only sensory information of the wind or local energy rate (i.e., model-free and data-driven) is able to characterize and replicate dynamic soaring optimized flight physics

  • IndisputableMonolith/Foundation/LogicAsFunctionalEquation.lean SatisfiesLawsOfLogic echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    ESC is a model-free adaptive control strategy which steers the dynamics toward the extremum (maximum/minimum) of an objective function

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages

  1. [1]

    I. Mir, S. A. Eisa, and A. Maqsood, Nonlinear Dynamics 94, 3117 (2018)

    work page 2018

  2. [2]

    MDCL, Dynamic soaring: How albatrosses optimize their flight physics?, YouTube video (2022), uploaded Aug 22, 2022

    work page 2022

  3. [3]

    P. L. Richardson, Notes and Records: the Royal Society journal of the history of science73, 285 (2019)

    work page 2019

  4. [4]

    Rayleigh, Nature27, 534 (1883)

    L. Rayleigh, Nature27, 534 (1883)

    work page

  5. [5]

    P. L. Richardson and E. D. Wakefield, Royal Society Open Science9(2022)

    work page 2022

  6. [6]

    Weimerskirch, T

    H. Weimerskirch, T. Guionnet, J. Martin, S. A. Shaffer, and D. Costa, Proceedings of the Royal Society of London. Series B: Biological Sciences267, 1869 (2000)

    work page 2000

  7. [8]

    Sachs, J

    G. Sachs, J. Traugott, A. Nesterova, and F. Bonadonna, Journal of Experimental Biology216, 4222 (2013)

    work page 2013

  8. [9]

    C. J. Pennycuick,Modelling the flying bird, Vol. 5 (Else- vier, 2008)

    work page 2008

  9. [10]

    I. Mir, A. Maqsood, S. A. Eisa, H. Taha, and S. Akhtar, Aerospace Science and Technology79, 17 (2018)

    work page 2018

  10. [11]

    W. WANG, W. AN, and B. SONG, Chinese Journal of Aeronautics37, 317 (2024)

    work page 2024

  11. [12]

    G. A. Nevitt, M. Losekoot, and H. Weimerskirch, Pro- ceedings of the National Academy of Sciences105, 4576 (2008)

    work page 2008

  12. [13]

    C. J. Pennycuick, Avian Science2, 1 (2002)

    work page 2002

  13. [14]

    Mangold, Naturwissenschaften33, 19 (1946)

    O. Mangold, Naturwissenschaften33, 19 (1946)

    work page 1946

  14. [15]

    Sachs, Ibis147, 1 (2005)

    G. Sachs, Ibis147, 1 (2005)

    work page 2005

  15. [16]

    N. R. Lawrance and S. Sukkarieh, in2009 IEEE Inter- national conference on robotics and automation(IEEE,

    work page

  16. [17]

    M. A. Patterson and A. V. Rao, ACM Transactions on Mathematical Software41(2014)

    work page 2014

  17. [18]

    Sachs, A

    G. Sachs, A. Knoll, and K. Lesch, Technical Soaring15, 48 (1991)

    work page 1991

  18. [19]

    Y. J. Zhao, Optimal control applications and methods 25, 67 (2004)

    work page 2004

  19. [20]

    S. A. Eisa and S. Pokhrel, SIAM Journal on Applied Mathematics , S82 (2023)

    work page 2023

  20. [21]

    C. J. Pennycuick, Philosophical Transactions of the Royal Society of London. B, Biological Sciences300, 75 (1982)

    work page 1982

  21. [22]

    P. P. Sukumar and M. S. Selig, Journal of Aircraft50, 1420 (2013)

    work page 2013

  22. [23]

    Liu, Z.-X

    D.-N. Liu, Z.-X. Hou, Z. Guo, X.-X. Yang, and X.-Z. Gao, Bioinspiration & biomimetics12, 016014 (2017)

    work page 2017

  23. [24]

    Scheinker, Automatica161, 111481 (2024)

    A. Scheinker, Automatica161, 111481 (2024)

    work page 2024

  24. [25]

    B. F. Skinner,The behavior of organisms: An experimen- tal analysis(BF Skinner Foundation, 2019)

    work page 2019

  25. [26]

    J. M. Pearce,Animal learning and cognition: an intro- duction(Psychology press, 2013)

    work page 2013

  26. [27]

    E. D. Wakefield, R. A. Phillips, J. Matthiopoulos, A. Fukuda, H. Higuchi, G. J. Marshall, and P. N. Trathan, Ecological Monographs79, 663 (2009)

    work page 2009

  27. [28]

    C. J. Pennycuick, Philosophical Transactions of the Royal Society of London. B, Biological Sciences300, 61 (1982)

    work page 1982

  28. [29]

    A. A. Elgohary and S. A. Eisa, Phys. Rev. E112, 044412 (2025)

    work page 2025

  29. [30]

    Abdelgalil, Y

    M. Abdelgalil, Y. Aboelkassem, and H. Taha, Physical Review E106, L062401 (2022)

    work page 2022

  30. [31]

    Universal Extremum Seeking Mechanism for Lift Variation in Soaring Birds Flight: A New Paradigm in Computational Physics and Biology∗

    J. Cochran, E. Kanso, S. D. Kelly, H. Xiong, and M. Krstic, IEEE Transactions on Robotics25, 1166 (2009). Supplementary Material for “Universal Extremum Seeking Mechanism for Lift Variation in Soaring Birds Flight: A New Paradigm in Computational Physics and Biology∗” Simone Martini, Dipesh Kunwar, Sameh A. Eisa Department of Aerospace Engineering and Eng...

    work page 2009

  31. [32]

    P. L. Richardson, E. D. Wakefield, and R. A. Phillips, Movement ecology6, 3 (2018)

    work page 2018

  32. [33]

    C. J. Pennycuick, Philosophical Transactions of the Royal Society of London. B, Biological Sciences300, 75 (1982). TABLE I: Morphological parameters from Paper 1 and Paper 2. Comparison with [2] Comparison with [1] WAN (a) BBA GHA WAN (b) m(kg) 8.73 3.79 3.79 12 S(m 2) 0.611 0.356 0.352 0.84 AR15.0 13.1 13.5 12.56 TABLE II: Simulation parameters and discr...

    work page 1982