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REVIEW 2 major objections 4 minor 35 references

Control Barrier Function-Based Quadratic Programming for SafeOperation of Tethered UAVs

T0 review · 2 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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Pith's one-line read A quadratic-program safety filter can keep a tethered drone inside its tether length while a backstepping controller handles trajectory tracking.

desk verdict CBF-QP safety proof fails because h has relative degree two; the application is new but the core theorem is invalid. read the letter →

arxiv 2502.08129 v1 pith:Z5FWCIHK submitted 2025-02-12 eess.SY cs.SY

Samuel O. Folorunsho , Maggi Ni , William R. Norris This is my paper · ORCID
classification eess.SYcs.SY
keywords tetheredUAVcontrolbarrierfunctionsquadraticprogrammingbacksteppingforwardinvariancetetherconstrainttrajectorytrackingsafetyfilter
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper proposes a control design that lets a tethered drone track desired trajectories while never flying beyond its maximum tether length. The scheme combines a backstepping controller, which handles trajectory tracking, with a control barrier function (CBF) and quadratic program (QP), which filters the control signal so that the distance from the ground anchor stays at or below a safety radius Lmax. The authors claim a formal guarantee: as long as the drone starts inside the safe region, the CBF-QP keeps the state inside it for all time, and simulations show tracking errors converging to zero with bounded control effort. If true, this is a practical way to embed tether limits directly into the drone's control loop instead of relying on an external supervisor.

What carries the argument

The machinery is the control barrier function $h(\chi) = L_{\max} - \|\xi\|$ together with the quadratic-program constraint derived from requiring $L_f h(\chi) + L_g h(\chi)u \geq -\alpha(h(\chi))$. Since $\nabla h = -\xi/\|\xi\|$ on the position components, the CBF condition becomes the linear inequality $\xi^{T} g_{\mathrm{pos}} u \leq \|\xi\| \alpha(h) + \xi^{T} f_{\mathrm{pos}}$, which the QP enforces while staying as close as possible to the backstepping input. The QP acts as the safety filter; $\alpha$ is an extended class-$\mathcal{K}_{\infty}$ gain that controls how strongly the filter pushes the state away from the boundary.

What would settle it

Run the proposed QP on the full second-order model and start the drone at a point on the boundary $\|\xi\| = L_{\max}$ with a small outward velocity and a desired trajectory pointing outward. If the trajectory leaves the ball $\|\xi\| \leq L_{\max}$ at any time, the claimed forward-invariance guarantee would be false, because the comparison proof would not apply when $u$ does not appear in $\dot{h}$.

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Extended reading notes

Core claim

The central claim is that the tether constraint $h(\chi) = L_{\max} - \|\xi\| \geq 0$ can be enforced on a tethered UAV by solving, at each time step, a quadratic program whose safety constraint is $\xi^{T} g_{\mathrm{pos}}(\chi) u \leq \|\xi\| \alpha(h(\chi)) + \xi^{T} f_{\mathrm{pos}}(\chi)$. The paper proves forward invariance of the safe set $\mathcal{C} = \{\chi : h(\chi) \geq 0\}$ by a comparison argument: if the QP selects a control satisfying $L_f h + L_g h \, u \geq -\alpha(h)$, then $h(t)$ cannot reach zero, so $\|\xi(t)\| \leq L_{\max}$ along the closed loop. Combined with the backstepping nominal controller, the filtered input is the closest admissible control to the nominal one, preserving tracking performance while enforcing safety. Simulations include set-point and circular reference tracking, including a desired setpoint outside the safe sphere, with the radial position stopping at the constraint surface.

Load-bearing premise

The argument assumes the control inputs can directly change how fast the drone approaches the tether limit; in the model, the inputs change acceleration, not speed, so the rate of change of the safety function does not contain the control input.

Editorial extensions

If this is right

  • Trajectory tracking and tether safety are handled in a single controller: the QP modifies the backstepping command only when needed to satisfy the tether constraint.
  • The constraint $\|\xi(t)\| \leq L_{\max}$ is enforced for set-point tracking, dynamic path following, and incorrect-user-input disturbances in the paper's simulations.
  • Tracking errors converge to zero asymptotically in the simulations while the control inputs remain bounded.
  • The same CBF-QP construction can be transferred to other tethered systems or safety-critical mobile robots, since the safety filter is decoupled from the nominal tracking design.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • Beyond the paper: the formal forward-invariance proof assumes $u$ appears directly in $\dot{h}$, but in the given second-order model $u$ enters acceleration, so $h = L_{\max} - \|\xi\|$ has relative degree two; a second-order CBF or an alternative description of the safe set would be needed for a rigorous guarantee.
  • Beyond the paper: the QP constraint involves only the position-related $g_{\mathrm{pos}}$, leaving the winch torque $U_{\mathrm{win}}$ unconstrained by the safety filter; including tether-length dynamics in the CBF could make the safety enforcement more direct.
  • Beyond the paper: the real-time appeal of the method depends on QP feasibility near the boundary; a reader could test the filter under large disturbances to see whether the linear safety constraint becomes infeasible before the boundary is reached.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper proposes a Control Barrier Function Quadratic Programming (CBF-QP) framework to enforce the tether-length constraint for a tethered UAV with winch dynamics. The safe set is defined by h(χ) = Lmax − ||ξ||, where ξ is the UAV position, and the nominal controller is a backstepping law taken from the authors' previous work. The QP is intended to minimally modify the nominal input so that the CBF condition holds. The authors claim forward invariance of the safe set and support this with a comparison-lemma argument plus qualitative simulations.

Significance. If the main guarantee were correct, the paper would offer a computationally inexpensive safety filter for tethered UAVs, a problem of practical interest. The paper correctly identifies a relevant safety-critical application and uses the standard CBF-QP architecture. However, the central technical claim is invalid: under the declared dynamics, the chosen barrier function has relative degree two, so the QP constraint contains no control input and cannot enforce safety. The empirical validation is purely qualitative, with no code, data, or quantitative metrics. The paper therefore does not deliver a verifiable safety result, and the contribution as it stands is not publishable without a fundamentally different control formulation.

major comments (2)
  1. [Section IV-B, Eq. (4) and the QP] Under the dynamics in Eq. (1), the control inputs enter only the second derivatives of the position coordinates (x, y, z) and the winch angular acceleration. In the control-affine form χdot = f(χ) + g(χ)u, the rows of g(χ) corresponding to (x, y, z) are therefore identically zero, so the paper's gpos(χ) is the zero matrix. Since ∇h = −ξ^T/||ξ|| ⊕ 0, the Lie derivative Lg h(χ) = −ξ^T gpos(χ)/||ξ|| is identically zero for all χ with ξ ≠ 0. The CBF condition (4) then reduces to Lf h(χ) ≥ −α(h(χ)), which contains no control input. The QP constraint in Section IV-B, ξ^T gpos u ≤ ||ξ|| α(h) + ξ^T fpos, becomes 0 ≤ ||ξ|| α(h) + ξ^T fpos, an inequality that does not involve u. Consequently the QP cannot shape h, and the forward-invariance proof in Section IV-B does not establish the claimed safety guarantee. The comparison-lemma argument would be valid if the inequality hdot ≥ −α(h) were enforced, but the controller never enforces this inequality because u does not appear in hdot. The statement in Section V-C that the CBF-QP 'halts further progression beyond the constraint' is therefore unsupported. A valid formulation would require a higher-order CBF (e.g., an exponential CBF on radial velocity) or a backstepping layer that places the safety constraint on a virtual input.
  2. [Section V, Results and Simulations] The validation is purely qualitative. Figures 3–5 show plots, but the manuscript provides no simulation code, no data files, no numerical values for h or the tracking error, and no convergence metrics. Claims such as 'tracking errors converging to zero' and 'control input remaining bounded' cannot be verified from the plots. In addition, there is no baseline comparison against the nominal backstepping controller without the CBF-QP or against an existing safety filter, so it is unclear what the added safety layer contributes. At minimum, reproducible code or quantitative error tables are needed to support the empirical claims.
minor comments (4)
  1. [Section IV-B, definition of h] The function h(χ) = Lmax − ||ξ|| is not differentiable at ξ = 0, yet the safe set includes the origin; the gradient ∇h is undefined there, so the CBF definition (3)–(4) is not globally well-posed. The paper should either exclude a neighborhood of the origin from the domain or use a smooth approximation of the norm.
  2. [Section IV-A, backstepping derivation] The backstepping derivation is presented for regulation of the z-position to zero, with virtual control φ(x5) = −k1 x5, while the simulations use time-varying desired trajectories. The extension from setpoint regulation to trajectory tracking is not explicitly derived; the error dynamics e(t) = x(t) − x_des(t) are mentioned in Section V-B but never introduced in the controller design.
  3. [References] References [9] and [34] are the same survey paper, and the 'On Nagumo's theorem' reference appears twice in the reference list. The duplicate entries should be consolidated.
  4. [Throughout] There are frequent spacing and typographical issues, e.g., 'UA V', 'TUA Vs', and 'predefined operational region', which should be corrected in any revision.

Circularity Check

1 steps flagged · score 6.0 of 10

The safety guarantee reduces to a drift assumption: under Eq. (1), gpos = 0 makes the QP constraint independent of u, so enforcing h >= 0 is the required inequality restated rather than achieved by control.

  1. other [Section IV-B (QP formulation and Proof of Forward Invariance), echoed in Section V-C]
    "The QP is: min_u 1/2 ∥u − unominal∥^2 subject to ξ^T gpos(χ)u ≤ ∥ξ∥α(h(χ)) + ξ^T fpos(χ). ... Along the trajectory: ˙h(χ) = Lf h(χ) + Lgh(χ)u ≥ −α(h(χ))."

    In the dynamics of Eq. (1), the control inputs appear only in the acceleration rows, so the position rows of g(χ) are zero and gpos(χ) = 0. The QP constraint then reads 0 ≤ ∥ξ∥α(h) + ξ^T fpos(χ), with no u dependence. The proof asserts the inequality ˙h ≥ −α(h) 'along the trajectory' and derives h ≥ 0 from it by comparison; but the QP has no authority to make that inequality true. The claimed guarantee therefore rests on the drift already satisfying Lf h ≥ −α(h) — the very safety property the controller was supposed to enforce — rather than on any control action. This makes the safety result the desired condition imposed as a premise, not a derived consequence.

full rationale

The rest of the derivation is mostly self-contained: h is defined from the externally set Lmax, and the comparison-lemma argument is the standard CBF sufficiency theorem. I do not treat the citation of the authors' own [32] for the backstepping controller as the dominant circularity, because the safety layer is the claimed novel contribution and at least the altitude backstepping derivation appears in Section IV-A. The score is set by the construction-level reduction in Section IV-B: because Eq. (1) gives gpos = 0, the QP safety constraint contains no decision variable. The formal forward-invariance result is the inequality ˙h ≥ −α(h) restated as a premise, and the comparison lemma then returns h ≥ 0. That is the desired property assumed rather than produced, so the claim in Section V-C that the CBF-QP controller 'halts further progression' is not supported by the derived chain.

Assumptions & free parameters 3 free parameters · 3 assumptions · 0 invented entities

The central claim rests on a free alpha(h), two unspecified backstepping gains, and an unsupported assumption that the barrier function has relative degree one. No new physical entities are introduced.

free parameters (3)
  • k1
    Backstepping virtual control gain introduced in Section IV-A; no value is provided in the paper.
  • k2
    Backstepping auxiliary control gain introduced in Section IV-A; no value is provided in the paper.
  • alpha(h)
    Extended class-K-infinity function used in the CBF condition and QP constraint; its form and parameters are never specified.
assumptions (3)
  • domain assumption The tethered UAV dynamics are control-affine and accurately described by Eq. (1) from refs. [32] and [33].
    Section III-A adopts equations of motion from prior work; the safety claim inherits any modeling error in the tether tension, drag, and winch model.
  • ad hoc to paper h = Lmax - ||xi|| is directly controllable through u, i.e., Lg h is nonzero.
    Section IV-B assumes nonzero gpos; from Eq. (1), h has relative degree two, so this premise is false without a higher-order CBF.
  • standard math Comparison lemma and Nagumo's theorem justify forward invariance from dh/dt >= -alpha(h).
    These are standard results, but they only apply if the CBF inequality can actually be enforced by the QP.

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Cite this review

Pith. "Pith review of Control Barrier Function-Based Quadratic Programming for SafeOperation of Tethered UAVs." pith.science (2026). https://pith.science/paper/Z5FWCIHK

@misc{pith2026250208129,
  author       = {Pith},
  title        = {Pith review of: Control Barrier Function-Based Quadratic Programming for SafeOperation of Tethered UAVs},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z5FWCIHK}},
  note         = {Machine review of arXiv:2502.08129}
}
read the original abstract

Consider an unmanned aerial vehicle (UAV) physically connected to the ground station with a tether operating in a space, tasked with performing precise maneuvers while constrained by the physical limitation of its tether, which prevents it from flying beyond a maximum allowable length. Violating this tether constraint could lead to system failure or operational hazards, making it essential to enforce safety constraints dynamically while ensuring the drone can track desired trajectories accurately. This paper presents a Control Barrier Function Quadratic Programming Framework (CBF-QP) for ensuring the safe and efficient operation of tethered unmanned aerial vehicles (TUAVs). The framework leverages nominal backstepping control to achieve trajectory tracking, augmented with control barrier functions to ensure compliance with the tether constraint. In this proposed method, the tether constraint is directly embedded in the control design and therefore guarantees the TUAV remains within a predefined operational region defined by the maximum tether length while achieving precise trajectory tracking. The effectiveness of the proposed framework is validated through simulations involving set-point tracking, dynamic trajectory following, and disturbances such as incorrect user inputs. The results demonstrate that the TUAV respects the tether constraint ||x(t)||</= Lmax, with tracking errors converging to zero and the control input remaining bounded.

Figures

Figures reproduced from arXiv: 2502.08129 by the authors.

Figure 1
Figure 1. FIGURE 1 [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. FIGURE 2 [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIGURE 3 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: FIGURE 4 [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: FIGURE 5 [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]

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Works this paper leans on

35 extracted references · 33 canonical work pages

  1. [32]

    C. G. Valerio, N. Aguillón, E. S. Espinoza, and R. Lozano, ``Reference generator for a system of multiple tethered unmanned aerial vehicles,'' Drones, vol. 6, no. 12, 2022. [Online]. Available: https://www.mdpi.com/2504-446X/6/12/390

    work page 2022

  2. [1]

    * ( 2 XH H Adobe_CM Adobed +

    11em plus .33em minus .07em 4000 4000 100 4000 4000 500 `\.=1000 = #1 9 12 #1 * [1] 0pt [0pt][0pt] #1 * \| ** #1 \@IEEEauthorblockNstyle \@IEEEcompsocnotconfonly \@IEEEcompsocconfonly \@IEEEauthorblockAstyle \@IEEEcompsocnotconfonly \@IEEEcompsocconfonly \@IEEEcompsocconfonly \@IEEEauthordefaulttextstyle \@IEEEcompsocnotconfonly \@IEEEauthorblockconfadjsp...

    work page

  3. [2]

    M. N. Marques, S. A. Magalhães, F. N. Dos Santos, and H. S. Mendonça, ``Tethered unmanned aerial vehicles—a systematic review,'' Robotics, vol. 12, no. 4, 2023. [Online]. Available: https://www.mdpi.com/2218-6581/12/4/117

    work page 2023

  4. [3]

    Lamport, ``Proving the correctness of multiprocess programs,'' IEEE Transactions on Software Engineering, vol

    L. Lamport, ``Proving the correctness of multiprocess programs,'' IEEE Transactions on Software Engineering, vol. SE-3, no. 2, pp. 125--143, 1977

    work page 1977

  5. [4]

    K.-C. Hsu, H. Hu, and J. F. Fisac, ``The safety filter: A unified view of safety-critical control in autonomous systems,'' Annual Review of Control, Robotics, and Autonomous Systems, vol. 7, no. Volume 7, 2024, pp. 47--72, 2024. [Online]. Available: https://www.annualreviews.org/content/journals/10.1146/annurev-control-071723-102940

    doi:10.1146/annurev-control-071723-102940 2024

  6. [5]

    K. P. Wabersich, A. J. Taylor, J. J. Choi, K. Sreenath, C. J. Tomlin, A. D. Ames, and M. N. Zeilinger, ``Data-driven safety filters: Hamilton-jacobi reachability, control barrier functions, and predictive methods for uncertain systems,'' IEEE Control Systems Magazine, vol. 43, no. 5, pp. 137--177, 2023

    work page 2023

  7. [6]

    Koopman, U

    P. Koopman, U. Ferrell, F. Fratrik, and M. Wagner, ``A safety standard approach for fully autonomous vehicles,'' in Computer Safety, Reliability, and Security, A. Romanovsky, E. Troubitsyna, I. Gashi, E. Schoitsch, and F. Bitsch, Eds. 1em plus 0.5em minus 0.4em Cham: Springer International Publishing, 2019, pp. 326--332

    work page 2019

  8. [7]

    K. Shi, J. Chang, S. Feng, Y. Fan, Z. Wei, and G. Hu, ``Safe human dual-robot interaction based on control barrier functions and cooperation functions,'' IEEE Robotics and Automation Letters, vol. 9, no. 11, pp. 9581--9588, 2024

    work page 2024

Show all 35 references
  1. [8]

    X. Ding, H. Wang, Y. Ren, Y. Zheng, C. Chen, and J. He, ``Online control barrier function construction for safety-critical motion control of manipulators,'' IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 54, no. 8, pp. 4761--4771, 2024

    2024

  2. [9]

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

    2019

  3. [10]

    B. Li, S. Wen, Z. Yan, G. Wen, and T. Huang, ``A survey on the control lyapunov function and control barrier function for nonlinear-affine control systems,'' IEEE/CAA Journal of Automatica Sinica, vol. 10, no. 3, pp. 584--602, 2023

    2023

  4. [11]

    A. D. Ames, J. W. Grizzle, and P. Tabuada, ``Control barrier function based quadratic programs with application to adaptive cruise control,'' in 53rd IEEE Conference on Decision and Control, 2014, pp. 6271--6278

    2014

  5. [12]

    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

    2017

  6. [13]

    Rauscher, M

    M. Rauscher, M. Kimmel, and S. Hirche, ``Constrained robot control using control barrier functions,'' in 2016 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), 2016, pp. 279--285

    2016

  7. [14]

    Li, ``Comparison between safety methods control barrier function vs

    Z. Li, ``Comparison between safety methods control barrier function vs. reachability analysis,'' 2021. [Online]. Available: https://arxiv.org/abs/2106.13176

    2021 arXiv

  8. [15]

    B. T. Lopez, J.-J. E. Slotine, and J. P. How, ``Robust adaptive control barrier functions: An adaptive and data-driven approach to safety,'' IEEE Control Systems Letters, vol. 5, no. 3, pp. 1031--1036, 2021

    2021

  9. [16]

    Lindemann, A

    L. Lindemann, A. Robey, L. Jiang, S. Das, S. Tu, and N. Matni, ``Learning robust output control barrier functions from safe expert demonstrations,'' 2024. [Online]. Available: https://arxiv.org/abs/2111.09971

    2024 arXiv

  10. [17]

    Singletary, A

    A. Singletary, A. Swann, Y. Chen, and A. D. Ames, ``Onboard safety guarantees for racing drones: High-speed geofencing with control barrier functions,'' IEEE Robotics and Automation Letters, vol. 7, no. 2, pp. 2897--2904, 2022

    2022

  11. [18]

    Panja, J

    P. Panja, J. B. Hoagg, and S. Baidya, ``Control barrier function based uav safety controller in autonomous airborne tracking and following systems,'' 2023. [Online]. Available: https://arxiv.org/abs/2312.17215

    2023 arXiv

  12. [19]

    Tayal, R

    M. Tayal, R. Singh, J. Keshavan, and S. Kolathaya, ``Control barrier functions in dynamic uavs for kinematic obstacle avoidance: A collision cone approach,'' 2024. [Online]. Available: https://arxiv.org/abs/2303.15871

    2024 arXiv

  13. [20]

    Zheng, J

    Z. Zheng, J. Li, Z. Guan, and Z. Zuo, ``Constrained moving path following control for uav with robust control barrier function,'' IEEE/CAA Journal of Automatica Sinica, vol. 10, no. 7, pp. 1557--1570, 2023

    2023

  14. [21]

    L. Wang, E. A. Theodorou, and M. Egerstedt, ``Safe learning of quadrotor dynamics using barrier certificates,'' in 2018 IEEE International Conference on Robotics and Automation (ICRA), 2018, pp. 2460--2465

    2018

  15. [22]

    Z. Wang, T. Hu, and L. Long, ``Multi-uav safe collaborative transportation based on adaptive control barrier function,'' IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 53, no. 11, pp. 6975--6983, 2023

    2023

  16. [23]

    B. Liu, Y. Wang, M. A. Sepestanaki, M. Pouzesh, S. Mobayen, S. H. Rouhani, and A. Fekih, ``Event-trigger-based adaptive barrier function higher-order global sliding mode control technique for quadrotor uavs,'' IEEE Transactions on Aerospace and Electronic Systems, vol. 60, no....

    2024

  17. [24]

    Kosarnovsky and S

    B. Kosarnovsky and S. Arogeti, ``Geometric and constrained control for a string of tethered drones,'' Robotics and Autonomous Systems, vol. 133, p. 103609, 2020. [Online]. Available: https://www.sciencedirect.com/science/article/pii/S0921889020304498

    2020

  18. [25]

    Singh and J

    L. Singh and J. Fuller, ``Trajectory generation for a uav in urban terrain, using nonlinear mpc,'' in Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), vol. 3, 2001, pp. 2301--2308 vol.3

    2001

  19. [26]

    Lindqvist, S

    B. Lindqvist, S. S. Mansouri, A.-a. Agha-mohammadi, and G. Nikolakopoulos, ``Nonlinear mpc for collision avoidance and control of uavs with dynamic obstacles,'' IEEE Robotics and Automation Letters, vol. 5, no. 4, pp. 6001--6008, 2020

    2020

  20. [27]

    Hermand, T

    E. Hermand, T. W. Nguyen, M. Hosseinzadeh, and E. Garone, ``Constrained control of uavs in geofencing applications,'' in 2018 26th Mediterranean Conference on Control and Automation (MED), 2018, pp. 217--222

    2018

  21. [28]

    Ankit, S

    K. Ankit, S. M. S, S. Kolathaya, and D. Ghose, Reachability Analysis of UAVs through Cluttered Environments. [Online]. Available: https://arc.aiaa.org/doi/abs/10.2514/6.2024-2017

    2024 doi

  22. [29]

    Zhou and J

    Y. Zhou and J. S. Baras, ``Reachable set approach to collision avoidance for uavs,'' in 2015 54th IEEE Conference on Decision and Control (CDC), 2015, pp. 5947--5952

    2015

  23. [30]

    J. Ding, J. Sprinkle, C. J. Tomlin, S. S. Sastry, and J. L. Paunicka, ``Reachability calculations for vehicle safety during manned/unmanned vehicle interaction,'' Journal of Guidance, Control, and Dynamics, vol. 35, no. 1, pp. 138--152, 2012

    2012

  24. [31]

    Bolognini, D

    M. Bolognini, D. Saccani, F. Cirillo, and L. Fagiano, ``Autonomous navigation of interconnected tethered drones in a partially known environment with obstacles,'' in 2022 IEEE 61st Conference on Decision and Control (CDC), 2022, pp. 3315--3320

    2022

  25. [33]

    Folorunsho, M

    S. Folorunsho, M. Ni, and W. Norris, ``Nonlinear control and stability analysis of a unified tethered uav-winder system,'' 2024. [Online]. Available: https://arxiv.org/abs/2412.09502

    2024 arXiv

  26. [34]

    C. Liu, L. Ding, and J. Gu, ``Dynamic modeling and motion stability analysis of tethered uav,'' in 2021 5th International Conference on Robotics and Automation Sciences (ICRAS). 1em plus 0.5em minus 0.4em IEEE, 2021, pp. 106--110

    2021

  27. [35]

    Constantin, ``On nagumo's theorem,'' 2010

    A. Constantin, ``On nagumo's theorem,'' 2010

    2010

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