Skip to main content
SpringerLink
Log in

Quantitative Stability Analysis of an Unmanned Tethered Quadrotor

  • Original Paper
  • Published:
International Journal of Aeronautical and Space Sciences Aims and scope Submit manuscript

Abstract

Tethered quadrotors, unmanned aerial quadrotors connected to a fixed point via tether cables, have been widely applied in numerous aerial tasks. However, their structural parameters and external disturbances give rise to dynamic stability issues, resulting in uncontrolled autonomous flight, shaking, and vibrating. Thus, this article investigates the quantitative stability of a tethered quadrotor using the Lyapunov exponent approach. First, a mathematical model of the tethered quadrotor is developed, and its dynamic stability is quantified to verify the rationality of the designed physical prototype and enhance the aerial system’s stability. Both simulation and experimental results show that the dynamic stability during the landing phase is better than that during takeoff. Finally, optimizing the structural parameters enhances the dynamic stability, which is sensitive to cable length, wind gusts, and yaw angle.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

Data availability

The parameters of the aerial robot we used have been shown in the paper. The data of the simulations and experiments can be provided if necessary.

References

  1. Imanberdiyev N, Kayacan E (2019) A fast learning control strategy for unmanned aerial manipulators[J]. J Intell Rob Syst 94(3):805–824

    Article  Google Scholar 

  2. Niedzielski T, Jurecka M, Miziński B et al (2018) A real-time field experiment on search and rescue operations assisted by unmanned aerial vehicles[J]. Journal of Field Robotics 35(6):906–920

    Article  Google Scholar 

  3. Wang G, Han Y, Li X et al (2020) Field evaluation of spray drift and environmental impact using an agricultural unmanned aerial vehicle (UAV) sprayer[J]. Sci Total Environ 737:1–15

    Article  Google Scholar 

  4. Hönig W, Preiss JA, Kumar TKS et al (2018) Trajectory planning for quadrotor swarms[J]. IEEE Trans Rob 34(4):856–869

    Article  Google Scholar 

  5. Nicotra MM, Naldi R, Garone E (2017) Nonlinear control of a tethered UAV: the taut cable case[J]. Automatica 78:174–184

    Article  MathSciNet  MATH  Google Scholar 

  6. Eskandarpour A, Sharf I (2020) A constrained error-based MPC for path following of quadrotor with stability analysis[J]. Nonlinear Dyn 99(2):899–918

    Article  MATH  Google Scholar 

  7. Liu Y, Li X, Wang T et al (2017) Quantitative stability of quadrotor unmanned aerial vehicles[J]. Nonlinear Dyn 87(3):1819–1833

    Article  Google Scholar 

  8. Chen CW (2011) Stability analysis and robustness design of nonlinear systems: an NN-based approach[J]. Appl Soft Comput 11(2):2735–2742

    Article  MathSciNet  Google Scholar 

  9. Wolf A, Swift JB, Swinney HL et al (1985) Determining Lyapunov exponents from a time series[J]. Physica D 16(3):285–317

    Article  MathSciNet  MATH  Google Scholar 

  10. Oseledec VI (1968) A multiplicative ergodic theorem, Lyapunov characteristic numbers for dynamical systems[J]. Trans Moscow Math Soc 19:197–231

    MathSciNet  Google Scholar 

  11. Amiri N, Ramirez-Serrano A, Davies RJ (2013) Integral backstepping control of an unconventional dual-fan unmanned aerial vehicle[J]. J Intell Rob Syst 69(1):147–159

    Article  Google Scholar 

  12. Pflimlin JM, Souères P, Hamel T (2007) Position control of a ducted fan VTOL UAV in crosswind[J]. Int J Control 80(5):666–683

    Article  MathSciNet  MATH  Google Scholar 

  13. Islam S, Liu PX, El Saddik A (2014) Nonlinear adaptive control for quadrotor flying vehicle[J]. Nonlinear Dyn 78(1):117–133

    Article  MathSciNet  MATH  Google Scholar 

  14. Li X, Ding R, Li J (2020) Quantitative comparison of predictabilities of warm and cold events using the backward nonlinear local Lyapunov Exponent Method[J]. Adv Atmos Sci 37(9):951–958

    Article  Google Scholar 

  15. Dai L, Xia D, Chen C (2019) An algorithm for diagnosing nonlinear characteristics of dynamic systems with the integrated periodicity ratio and lyapunov exponent methods[J]. Commun Nonlinear Sci Numer Simul 73:92–109

    Article  MathSciNet  MATH  Google Scholar 

  16. Liu Y, Li X, Wang T et al (2017) The stability analysis of quadrotor unmanned aerial vechicles[M]//wearable sensors and robots. Springer, Singapore, pp 383–394

    Google Scholar 

  17. Liu Y, Chen C, Wu H et al (2018) Structural stability analysis and optimization of the quadrotor unmanned aerial vehicles via the concept of Lyapunov exponents[J]. Int J Adv Manuf Technol 94(9):3217–3227

    Article  Google Scholar 

  18. Chen C, Dong T, Fu W et al (2019) On dynamic characteristics and stability analysis of the ducted fan unmanned aerial vehicles[J]. Int J Adv Rob Syst 16(4):1–14

    Google Scholar 

  19. Armiyoon AR, Wu CQ (2016) Lyapunov exponents-based stability analysis and integrated control of rollover mitigation and yaw stabilization of ground vehicles[J]. Int J Veh Syst Model Test 11(4):343–362

    Google Scholar 

  20. Fu JZ, Zang PF, Liu YP et al (2018) Quantitative stability of underwater robot during diving[J]. Comput Simul 35(9):343–348

    Google Scholar 

  21. Dingwell JB, Marin LC (2006) Kinematic variability and local dynamic stability of upper body motions when walking at different speeds[J]. J Biomech 39(3):444–452

    Article  Google Scholar 

  22. Li XY, Zhao B, Yao Y et al (2018) Stability and performance analysis of six-rotor unmanned aerial vehicles in wind disturbance[J]. J Comput Nonlinear Dyn 13(3):1–11

    Google Scholar 

  23. Ding L, Zhou J, Shan W (2018) A hybrid high-performance trajectory tracking controller for unmanned hexrotor with disturbance rejection[J]. Trans Can Soc Mech Eng 42(3):239–251

    Article  Google Scholar 

  24. Ding L, He Q, Wang C et al (2021) Disturbance rejection attitude control for a quadrotor: Theory and experiment[J]. Int J Aerosp Eng 2021:1–15

    Article  Google Scholar 

  25. Antonio-Toledo ME, Sanchez EN, Alanis AY et al (2018) Real-time integral backstepping with sliding mode control for a quadrotor UAV[J]. IFAC-PapersOnLine 51(13):549–554

    Article  Google Scholar 

  26. Ding YD, Wang YY, Chen B (2021) A practical time-delay control scheme for aerial manipulators[J]. Proc Inst Mech Eng Part I 235(3):371–388

    Google Scholar 

  27. Quan Q (2017) Introduction to multicopter design and control[M]. Springer, Singapore

    Book  Google Scholar 

  28. Greco L, Impollonia N, Cuomo M (2014) A procedure for the static analysis of cable structures following elastic catenary theory[J]. Int J Solids Struct 51(7–8):1521–1533

    Article  Google Scholar 

  29. Lyu P, Bao S, Lai J et al (2019) A dynamic model parameter identification method for quadrotors using flight data[J]. Proc Inst Mech Eng Part G 233(6):1990–2002

    Article  Google Scholar 

  30. Arnold L, Doyle MM, Sri NN (1997) Small noise expansion of moment Lyapunov exponents for two-dimensional systems[J]. Dyn Stab Syst 12(3):187–211

    Article  MathSciNet  MATH  Google Scholar 

  31. Yang C, Wu Q (2010) On stability analysis via Lyapunov exponents calculated from a time series using nonlinear mapping—a case study[J]. Nonlinear Dyn 59(1):239–257

    Article  MathSciNet  MATH  Google Scholar 

  32. Maus A, Sprott JC (2013) Evaluating Lyapunov exponent spectra with neural networks[J]. Chaos, Solitons Fractals 51:13–21

    Article  MathSciNet  MATH  Google Scholar 

  33. Jardin MR, Mueller ER (2009) Optimized measurements of unmanned-air-vehicle mass moment of inertia with a bifilar pendulum[J]. J Aircr 46(3):763–775

    Article  Google Scholar 

  34. Ding L, Li Y (2020) Optimal attitude tracking control for an unmanned aerial quadrotor under lumped disturbances[J]. Int J Micro Air Veh 12:1–12

    Google Scholar 

  35. Dong W, Gu GY, Zhu X et al (2014) High-performance trajectory tracking control of a quadrotor with disturbance observer[J]. Sens Actuators, A 211:67–77

    Article  Google Scholar 

Download references

Acknowledgements

We thank the anonymous reviewers for their helpful and insightful remarks. In addition, helpful discussions with Professor Xiaofeng Liu from Hohai University on his guidance in aircraft designation are gratefully acknowledged.

Funding

We thank the anonymous reviewers for helpful and insightful remarks. This work was partially supported by the National Natural Science Foundation of China (52005231, 5220505311), Social Development Science and Technology Support Project of Changzhou (CE20215050), and China-Israel Industrial Technology Research Institute Open Fund (JSIITRI202210).

Author information

Authors and Affiliations

  1. College of Mechanical Engineering, Jiangsu University of Technology, Changzhou, China

    Dong Liang, Li Ding, Mingyue Lu, Rui Ma & Jie Cao

Authors
  1. Dong Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Li Ding
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Mingyue Lu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Rui Ma
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jie Cao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Li Ding.

Ethics declarations

Conflict of Interest

The authors declare that there are no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liang, D., Ding, L., Lu, M. et al. Quantitative Stability Analysis of an Unmanned Tethered Quadrotor. Int. J. Aeronaut. Space Sci. 24, 905–918 (2023). https://doi.org/10.1007/s42405-023-00574-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s42405-023-00574-8

Keywords

Search

Navigation