On oscillations of a quadrotor-slung pendulum with a cavity partially filled with liquid

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription Access

Abstract

Dynamics of a pendulum suspended to a quadrotor and having a spherical cavity partially filled with the ideal liquid is considered. It is supposed that the system moves in the vertical plane. The drag force acting on the pendulum is taken into account. In order to simulate oscillations of the liquid inside the cavity, a phenomenological “pendulum” model is used. An algorithm for constructing the quadrotor acceleration control is proposed that ensures the transition of the system to the steady horizontal flight with the specified speed along with damping of oscillations of both the pendulum and the liquid inside it (including in the presence of a constant wind).

Full Text

Restricted Access

About the authors

A. P. Holub

Lomonosov Moscow State University

Email: seliutski@imec.msu.ru

Institute of Mechanics

Russian Federation, Moscow

B. Ya. Lokshin

Lomonosov Moscow State University

Email: seliutski@imec.msu.ru

Institute of Mechanics

Russian Federation, Moscow

Yu. D. Selyutskiy

Lomonosov Moscow State University

Author for correspondence.
Email: seliutski@imec.msu.ru

Institute of Mechanics

Russian Federation, Moscow

References

  1. Omar H.M., Akram R., Mukras S.M.S., Mahvouz A.A. Recent Advances and Challenges in Controlling Quadrotors with Suspended Loads // Alexandria Engineering J. 2022. V. 63. P. 253-270. https://doi.org/10.1016/j.aej.2022.08.001
  2. Estevez J., Garate G., Lopez-Guede J.M., Larrea M. Review of Aerial Transportation of Suspended-Cable Payloads with Quadrotors // Drones. 2024. V. 8. № 2. P. 35. https://doi.org/10.3390/drones8020035
  3. Xian B., Wang S., Yang S. An Online Trajectory Planning Approach for a Quadrotor UAV with a Slung Payload // IEEE Trans. Ind. Electron. 2019. V. 67. P. 6669–6678. https://doi.org/10.1109/TIE.2019.2938493
  4. De Angelis E.L., Giulietti F., Pipeleers G. Two-Time-Scale Control of a Multirotor Aircraft for Suspended Load Transportation // Aerosp. Sci. Technol. 2019. V. 84. P. 193–203. https://doi.org/10.1016/j.ast.2018.10.012
  5. Sun L., Wang K., Mishamandani A.H.A., Zhao G., Huang H., Zhao X., Zhang B. A Novel Tension-Based Controller Design for the Quadrotor-Load System // Control Eng. Pract. 2021. V. 112. P. 104818.
  6. Baraean A., Hamanah W.M., Bawazir A., Quama M.M., El-Ferik S., Baraean S., Abido A.M. Optimal Nonlinear Backstepping Controller Design of a Quadrotor-Slung Load System Using Particle Swarm Optimization // Alexandria Engineering J. 2023. V. 68. P. 551–560. https://doi.org/10.1016/j.aej.2023.01.050
  7. Kong L., Reis J., He W., Yu X., Silvestre C. On Dynamic Performance Control for a Quadrotor-Slung-Load System with Unknown Load Mass // Automatica. 2024. V. 162. P. 111516. https://doi.org/10.1016/j.automatica.2024.111516
  8. Goodarzi F.A., Lee D., Lee T. Geometric Control of a Quadrotor UAV Transporting a Payload Connected via Flexible Cable // Int. J. Control. Autom. Syst. 2015. V. 13. P. 1486–1498. https://doi.org/10.1007/s12555-014-0304-0
  9. Chang P., Yang S., Tong J., Zhang F. A New Adaptive Control Design for a Quadrotor System with Suspended Load by an Elastic Rope // Nonlinear Dyn. 2023. V. 111. P. 19073–19092.
  10. Kaya U.C., Subbarao K. Momentum Preserving Simulation of Cooperative Multirotors with Flexible-Cable Suspended Payload // J. Dyn. Syst. Meas. Control. 2022. V. 144. P. 041007. https://doi.org/10.1115/1.4053343
  11. Wu P.X., Yang C.C., Cheng T.H. Cooperative Transportation of UAVs Without Inter-UAV Communication // IEEE/ASME Trans. Mechatron. 2023. V. 28. P. 2340–2351. https://doi.org/10.1109/TMECH.2023.3234511
  12. Bisgaard M., Bendtsen J.D., La Cour-Harbo A. Modeling of Generic Slung Load System // J. Guid. Control. Dyn. 2009. V. 32. № 2. P. 433–449. https://doi.org/10.2514/1.36539
  13. Куликов В.Е., Чукаева А.Н. Система управления квадрокоптером при транспортировке груза на внешней подвеске // Тр. Московск. ин-та электромеханики и автоматики. 2016. Т. 14. С. 2–16.
  14. Sun L., Wang K., Mishamandani A.H.A., Zhao G., Huang H., Zhao X., Zhang B. A Novel Tension-Based Controller Design for the Quadrotor–Load System // Control Eng. Pract. 2021. V. 112. P. 104818.
  15. Голуб А.П., Зудов В.Б., Локшин Б.Я., Селюцкий Ю.Д. О робастной стабилизации движения квадрокоптера с подвешенным грузом // Мехатроника, автоматизация, управление. 2024. Т. 25. № 9. С. 490–500. https://doi.org/10.17587/mau.25.490-500
  16. Охоцимский Д.Е. К теории движения тел с полостями, частично заполненными жидкостью // ПММ. 1956. Т. 20. Вып. 1. С. 3–20.
  17. Abramson H.N., Chu W.H., Ransleben G.E. Representation of Fuel Sloshing in Cylindrical Tanks by an Equivalent Mechanical Model // ARS Journal. 1961. V. 31. № 12. P. 1697–1705.
  18. Колесников К.С. Колебания жидкости в цилиндрическом сосуде. М.: Изд-во МВТУ им. Н.Э. Баумана, 1964. 97 с.
  19. Stofan A.J., Armstead A.L. Analytical and Experimental Investigation of Forces and Frequencies Resulting from Liquid Sloshing in a Spherical Tank. Washington: NASA. 1962. Technical Note D-1281.
  20. Abramson H.N., Chu W.H., Garza L.R. Liquid Sloshing in Spherical Tanks // AIAA Journal. 1963. V. 1. № 2. P. 384–389. https://doi.org/10.2514/3.1542
  21. Chu W.H. Fuel Sloshing in a Spherical Tank Filled to an Arbitrary Depth // AIAA Journal. 1964. V. 2. № 11. P. 1972–1979. https://doi.org/10.2514/3.2713
  22. Aliabadi S., Johnson A., Abedi J. Comparison of Finite Element and Pendulum Models for Simulation of Sloshing // Computers & Fluids. 2003. V. 32. № 4. P. 535–545. https://doi.org/10.1016/S0045-7930(02)00006-3
  23. Godderidge B., Turnock S.R., Tan M. A Rapid Method for the Simulation of Sloshing Using a Mathematical Model Based on the Pendulum Equation // Computers & Fluids. 2012. V. 57. P. 163–171. https://doi.org/10.1016/j.compfluid.2011.12.018
  24. Moriello L., Biagiotti L., Melchiorri C., Paoli A. Manipulating Liquids with Robots: A Sloshing-Free Solution // Control Engineering Practice. 2018. V. 78. P. 129–141. https://doi.org/10.1016/j.conengprac.2018.06.018
  25. Sayyaadi H., Soltani A. Modeling and Control for Cooperative Transport of a Slung Fluid Container Using Quadrotors // Chinese J. of Aeronautics. 2018. V. 31. № 2. P. 262–272. https://doi.org/10.1016/j.cja.2017.12.005
  26. Колесников К.С. Динамика ракет. М.: Машиностроение. 1980. 376 с.
  27. Ibrahim R.A. Liquid Sloshing Dynamics. Theory and Applications. Cambridge, 2005. 972 p.
  28. Квакернаак Х., Сиван Р. Линейные оптимальные системы управления. М.: Мир, 1977. 650 с.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Pendulum with liquid suspended from a quadcopter.

Download (89KB)
Indexing metadata
3. Fig. 2. Dependence of the values ​​of u, v, φ, ψ on time under control (4.1).

Download (109KB)
Indexing metadata
4. Fig. 3. Examples of acceleration and braking processes during control (4.3) in the absence of wind.

Download (117KB)
Indexing metadata
5. Fig. 4. Examples of acceleration and braking processes during control (4.3) for different wind speed values.

Download (261KB)
Indexing metadata

Copyright (c) 2025 Russian Academy of Sciences