pith. sign in

arxiv: 2604.22860 · v1 · submitted 2026-04-22 · 💻 cs.RO · cs.SY· eess.SY

Airspeed Forward-Invariance for Unpowered Fixed-Wing Aircraft

Huseyin Emre Tekaslan , Ella M. Atkins This is my paper

Pith reviewed 2026-05-09 23:34 UTC · model grok-4.3

classification 💻 cs.RO cs.SYeess.SY
keywords airspeed invarianceunpowered fixed-winggliding flightguidance commandssteady windmaneuver primitivesquadratic programming
0
0 comments X

The pith

A closed-form wind-dependent rule on guidance commands keeps unpowered fixed-wing aircraft inside a safe airspeed range.

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 mathematical tangency condition applied to airspeed dynamics yields explicit limits on commanded flight path angle that prevent the speed from leaving a chosen safe interval during gliding flight. This matters because unpowered aircraft have no thrust to correct speed and must exchange altitude for airspeed, a process easily disrupted by wind. The derived conditions are packaged into an offline quadratic program that certifies entire maneuver primitives as safe before they are used. When these certified pieces are strung together, the resulting trajectories stay strictly inside the airspeed bounds in high-fidelity simulation. The approach therefore supplies a certifiable building block for guidance-level safety in autonomous unpowered operations.

Core claim

Leveraging Nagumo's tangency condition, the authors derive a closed-form, wind-dependent characterization of admissible guidance commands that guarantees forward invariance of a safe airspeed envelope for non-ascending unpowered fixed-wing flight. These conditions are then embedded in an offline quadratic programming framework to certify maneuver primitives, which are shown through concatenation to produce gliding trajectories that maintain strict airspeed boundedness under a high-fidelity aircraft model in steady wind.

What carries the argument

Nagumo's tangency condition applied to the airspeed envelope, which supplies the exact boundary constraints on guidance commands (especially flight path angle) needed to keep the envelope forward-invariant under steady wind.

Load-bearing premise

The wind is steady and perfectly known while the aircraft obeys an exact known dynamic model and never climbs.

What would settle it

A simulation or flight test in which a sequence of certified guidance commands is executed under the assumed steady wind yet airspeed still exits the declared safe envelope.

Figures

Figures reproduced from arXiv: 2604.22860 by Ella M. Atkins, Huseyin Emre Tekaslan.

Figure 1
Figure 1. Figure 1: Fundamental forces and velocity vectors of an unpowered fixed [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Application flowchart of the viability-constrained guidance, path planning, and dynamic simulation. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: State expansion under steady horizontal wind. [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A subset of viability-constrained optimal ground-referenced maneuvers. [PITH_FULL_IMAGE:figures/full_fig_p007_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Empirical distribution of Nagumo tangency conditions evaluated [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: UAS response time history for the representative case. [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Airspeed distribution across all simulations and time steps, totaling [PITH_FULL_IMAGE:figures/full_fig_p008_8.png] view at source ↗
read the original abstract

Autonomous fixed-wing flight is becoming a key capability in aerial robotics, enabling sensing, mobility, and contingency operations across both small-scale Uncrewed Aircraft Systems and large-scale Advanced Air Mobility. During unpowered operation in fixed-wing platforms, airspeed is regulated solely through potential-kinetic energy exchange, making airspeed dynamics highly sensitive to guidance commands, particularly under wind. This paper presents a viability-based airspeed protection for ground-referenced guidance in steady wind, where airspeed evolution depends explicitly on the commanded flight path angle. Leveraging Nagumo's tangency condition, we derive a closed-form, wind-dependent characterization of admissible guidance commands that guarantees forward invariance of a safe airspeed envelope. These conditions are embedded within an offline quadratic programming framework to certify airspeed-safe maneuver primitives for non-ascending flight at the guidance level. The approach is validated using a high-fidelity unpowered fixed-wing aircraft model on gliding trajectories formed by concatenating certified maneuver primitives, demonstrating strict airspeed boundedness. Future work will address unsteady wind fields and flight experiments.

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

0 major / 4 minor

Summary. The manuscript claims that, by applying Nagumo's tangency condition to the airspeed dynamics of an unpowered fixed-wing aircraft (which depend explicitly on the commanded flight-path angle), a closed-form, wind-dependent set of admissible guidance commands can be derived that renders a prescribed safe airspeed interval forward-invariant under steady wind. These invariance conditions are then embedded as constraints in an offline quadratic program used to certify maneuver primitives for non-ascending flight; high-fidelity simulation of concatenated primitives is reported to confirm strict airspeed boundedness.

Significance. If the central derivation holds, the work supplies a rigorous, pre-computable certificate for airspeed safety at the guidance level, which is valuable for contingency and unpowered operations in aerial robotics. The explicit use of Nagumo's condition yields a closed-form characterization rather than a fitted or numerical approximation, and the offline QP formulation allows primitive-level certification without online optimization. Simulation validation on a high-fidelity model under the stated assumptions (steady wind, known dynamics, non-ascending flight) provides concrete supporting evidence, though the authors correctly flag extensions to unsteady wind and flight tests as future work.

minor comments (4)
  1. [Abstract] Abstract: the statement that the conditions 'guarantee forward invariance' should be qualified by the modeling assumptions (steady wind, non-ascending flight, known high-fidelity model) already listed later in the abstract.
  2. [Section 3] Section 3 (derivation): the transition from the Nagumo tangency condition to the explicit admissible set for the flight-path angle is central; a short remark on the regularity conditions required for the airspeed dynamics (e.g., Lipschitz continuity or differentiability) would strengthen the argument.
  3. [Section 5] Section 5 (validation): while strict boundedness is reported, quantitative metrics such as the minimum distance to the airspeed bounds across all primitives or the effect of wind-speed variation within the steady-wind assumption would make the empirical support more precise.
  4. [Throughout] Notation: the symbols for the safe airspeed interval (e.g., V_min, V_max) and the wind vector components should be defined at first use and kept consistent between the dynamics equations and the QP formulation.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript, the accurate summary of its contributions, and the recommendation for minor revision. The significance statement correctly identifies the value of the Nagumo-based closed-form invariance conditions and the offline QP certification approach.

Circularity Check

0 steps flagged

No significant circularity identified

full rationale

The paper derives a closed-form characterization of admissible guidance commands by directly applying Nagumo's tangency condition to the airspeed dynamics, where the rate depends explicitly on the commanded flight-path angle under steady wind. This is a standard application of an external viability theorem to the given aircraft model equations, producing conditions that are then embedded in an offline QP for certifying maneuver primitives. No self-definitional steps, fitted parameters renamed as predictions, or load-bearing self-citations appear in the derivation chain; the modeling assumptions (steady wind, non-ascending flight, known model) are explicitly scoped, and validation uses simulation on a high-fidelity model without reducing the central claim to its inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The claim rests on standard viability theory (Nagumo condition) applied to aircraft energy dynamics under steady wind; no free parameters, new entities, or ad-hoc axioms are described in the abstract.

axioms (1)
  • standard math Nagumo's tangency condition for forward invariance of a set
    Directly invoked to obtain the closed-form admissible guidance commands from the airspeed evolution equation.

pith-pipeline@v0.9.0 · 5488 in / 1189 out tokens · 157481 ms · 2026-05-09T23:34:46.975387+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

28 extracted references · 28 canonical work pages

  1. [1]

    Networked unmanned aerial vehicles for surveillance and monitoring: A survey,

    X. Li and A. V . Savkin, “Networked unmanned aerial vehicles for surveillance and monitoring: A survey,”Future Internet, vol. 13, no. 7,

    work page

  2. [2]

    Available: https://www.mdpi.com/1999-5903/13/7/174

    [Online]. Available: https://www.mdpi.com/1999-5903/13/7/174

    work page 1999

  3. [3]

    A robust uav system for operations in a constrained environment,

    M. Petrl ´ık, T. B´aˇca, D. He ˇrt, M. Vrba, T. Krajn ´ık, and M. Saska, “A robust uav system for operations in a constrained environment,”IEEE Robotics and Automation Letters, vol. 5, no. 2, pp. 2169–2176, 2020

    work page 2020

  4. [4]

    Autonomous navigation and mapping for inspection of penstocks and tunnels with mavs,

    T. ¨Ozaslan, G. Loianno, J. Keller, C. J. Taylor, V . Kumar, J. M. Wozencraft, and T. Hood, “Autonomous navigation and mapping for inspection of penstocks and tunnels with mavs,”IEEE Robotics and Automation Letters, vol. 2, no. 3, pp. 1740–1747, 2017

    work page 2017

  5. [5]

    Markov Decision Process Contin- gency Landing Management Autonomy for Advanced Air Mobility,

    A. A. Akinola and E. M. Atkins, “Markov Decision Process Contin- gency Landing Management Autonomy for Advanced Air Mobility,” inAIAA Aviation Forum and Ascend, 2025, p. 3399

    work page 2025

  6. [6]

    Raymer,Aircraft Design: A Conceptual Approach, Fifth Edition

    D. Raymer,Aircraft Design: A Conceptual Approach, Fifth Edition. American Institute of Aeronautics and Astronautics, Inc., Aug. 2012

    work page 2012

  7. [7]

    Gradient-Guided Search for Autonomous Contingency Landing Planning,

    H. E. Tekaslan and E. M. Atkins, “Gradient-Guided Search for Autonomous Contingency Landing Planning,”Drones, vol. 9, no. 9, 2025

    work page 2025

  8. [8]

    Navigation, guidance, and control of a micro unmanned aerial glider,

    A. D. Kahn and D. J. Edwards, “Navigation, guidance, and control of a micro unmanned aerial glider,”Journal of Guidance, Control, and Dynamics, vol. 42, no. 11, p. 2474–2484, Nov. 2019. [Online]. Available: http://dx.doi.org/10.2514/1.G004247

    work page doi:10.2514/1.g004247 2019

  9. [9]

    A vision-based flight guidance and navigation system for autonomous cross-country soaring uavs,

    M. Stolle, J. Bolting, C. D ¨oll, and Y . Watanabe, “A vision-based flight guidance and navigation system for autonomous cross-country soaring uavs,” in2015 International Conference on Unmanned Aircraft Systems (ICUAS), 2015, pp. 109–117

    work page 2015

  10. [10]

    Aubin,Viability Theory, ser

    J.-P. Aubin,Viability Theory, ser. Modern Birkh ¨auser Classics. Se- caucus, NJ: Birkhauser Boston, Jan. 1991

    work page 1991

  11. [11]

    Flexibility optimized control for robot efficient moving in corridors based on viability theory,

    L. Liu, S. Liu, Y . Wu, Y . Yang, Y . Gao, and F.-C. Wang, “Flexibility optimized control for robot efficient moving in corridors based on viability theory,”IEEE Access, vol. 7, pp. 103 583–103 594, 2019

    work page 2019

  12. [12]

    Viability-based guaranteed safe robot navigation,

    M. A. Bouguerra, T. Fraichard, and M. Fezari, “Viability-based guaranteed safe robot navigation,”Journal of Intelligent&Robotic Systems, vol. 95, no. 2, p. 459–471, Nov. 2018. [Online]. Available: http://dx.doi.org/10.1007/s10846-018-0955-9

    work page doi:10.1007/s10846-018-0955-9 2018

  13. [13]

    Safe Motion using Viability Kernels,

    B. Muhammad, T. Fraichard, and M. Fezari, “Safe Motion using Viability Kernels,” inICRA 2015 - IEEE Int. Conf. on Robotics and Automation, Seattle, United States, May 2015. [Online]. Available: https://inria.hal.science/hal-01143861

    work page 2015

  14. [14]

    Control barrier function based quadratic programs for safety critical systems,

    A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,”IEEE Transactions on Automatic Control, vol. 62, no. 8, pp. 3861–3876, 2017

    work page 2017

  15. [15]

    Control barrier functions: Theory and applications,

    A. D. Ames, S. Coogan, M. Egerstedt, G. Notomista, K. Sreenath, and P. Tabuada, “Control barrier functions: Theory and applications,” in2019 18th European Control Conference (ECC), 2019, pp. 3420– 3431

    work page 2019

  16. [16]

    Guaranteed obstacle avoidance for multi-robot operations with limited actuation: A control barrier function approach,

    Y . Chen, A. Singletary, and A. D. Ames, “Guaranteed obstacle avoidance for multi-robot operations with limited actuation: A control barrier function approach,”IEEE Control Systems Letters, vol. 5, no. 1, pp. 127–132, 2021

    work page 2021

  17. [17]

    Positive invariant sets for safe integrated vehicle motion planning and control,

    K. Berntorp, R. Bai, K. F. Erliksson, C. Danielson, A. Weiss, and S. D. Cairano, “Positive invariant sets for safe integrated vehicle motion planning and control,”IEEE Transactions on Intelligent Vehicles, vol. 5, no. 1, pp. 112–126, 2020

    work page 2020

  18. [18]

    Adaptive sampling-based motion planning with control barrier functions,

    A. Ahmad, C. Belta, and R. Tron, “Adaptive sampling-based motion planning with control barrier functions,” in2022 IEEE 61st Conference on Decision and Control (CDC), 2022, pp. 4513–4518

    work page 2022

  19. [19]

    Safe and robust motion planning for dynamic robotics via control barrier functions,

    A. Manjunath and Q. Nguyen, “Safe and robust motion planning for dynamic robotics via control barrier functions,” in2021 60th IEEE Conference on Decision and Control (CDC), 2021, pp. 2122–2128

    work page 2021

  20. [20]

    Safe and dynamically fea- sible motion planning using control lyapunov and barrier functions,

    P. Mestres, C. Nieto-Granda, and J. Cort ´es, “Safe and dynamically fea- sible motion planning using control lyapunov and barrier functions,” IEEE Transactions on Robotics, vol. 41, pp. 6440–6459, 2025

    work page 2025

  21. [21]

    Safety-critical control and planning for obstacle avoidance between polytopes with control barrier functions,

    A. Thirugnanam, J. Zeng, and K. Sreenath, “Safety-critical control and planning for obstacle avoidance between polytopes with control barrier functions,” in2022 International Conference on Robotics and Automation (ICRA), 2022, pp. 286–292

    work page 2022

  22. [22]

    Quadratic programming approach to flight envelope protection using control barrier functions,

    J. Autenrieb, “Quadratic programming approach to flight envelope protection using control barrier functions,”Journal of Guidance, Control, and Dynamics, vol. 48, no. 11, p. 2622–2633, Nov. 2025. [Online]. Available: http://dx.doi.org/10.2514/1.G009203

    work page doi:10.2514/1.g009203 2025

  23. [23]

    Prediction-based control barrier functions for input-constrained safety critical systems,

    A. Mesbah, S. H. Pourtakdoust, A. Sharifi, and A. Banazadeh, “Prediction-based control barrier functions for input-constrained safety critical systems,” 2024. [Online]. Available: https://arxiv.org/ abs/2412.12926

    work page arXiv 2024

  24. [24]

    Vision-based autonomous landing for unmanned aerial and ground vehicles cooperative systems,

    G. Niu, Q. Yang, Y . Gao, and M.-O. Pun, “Vision-based autonomous landing for unmanned aerial and ground vehicles cooperative systems,” IEEE Robotics and Automation Letters, vol. 7, no. 3, pp. 6234–6241, 2022

    work page 2022

  25. [25]

    Feasibility assurance for search-based emergency landings,

    H. E. Tekaslan and E. Atkins, “Feasibility assurance for search-based emergency landings,” inAIAA SciTech 2026 Forum, 2026

    work page 2026

  26. [26]

    R. W. Beard and T. W. McLain,Small Unmanned Aircraft: Theory and Practice. Princeton University Press, 2012

    work page 2012

  27. [27]

    J. S. Arora,Introduction to Design Optimization, 3rd ed. Elsevier, 2012

    work page 2012

  28. [28]

    M. R. Napolitano,Aircraft Dynamics: From Modeling to Simulation. John Wiley, 2011

    work page 2011