Control Algorithm for Position Stabilization of a Group of Mechanically Coupled UAVs

This paper addresses the problem of developing a control system for a group of multirotor unmanned aerial vehicles (UAVs) collaboratively transporting a payload. The importance of this problem arises from the growing interest in cooperative UAV systems for logistics, industrial automation, and rescue operations. The configuration of UAVs under consideration is characterized by the payload being attached to a rigid frame and each UAV connected to it through a spherical joint, forming a mechanically coupled system. Such a configuration is of particular interest for studying complex dynamical systems with mechanical couplings and for developing effective methods of cooperative control. To support analysis and controller design, a mathematical model is proposed that describes the dynamics of both individual UAVs and the coupled system as a whole, including the interaction between the aerial vehicles and the payload. Based on this model, a control algorithm was developed to ensure stable and coordinated motion of the UAV group along prescribed trajectories while maintaining the required payload orientation. The study demonstrates that the proposed algorithm stabilizes the UAV system under external disturbances and during motion along complex flight paths, while also demonstrating scalability to larger UAV groups and various payload configurations. Simulation results validate the effectiveness of the developed control system. The findings can be applied in the design of real-world cooperative transport prototypes and contribute to the advancement of cooperative UAV control methods. The presented results hold practical significance for logistics, delivery of goods to hard-to-reach areas, and the collaborative use of UAVs in various application fields. Moreover, the proposed approaches may serve as a foundation for further research in the field of cooperative unmanned system control.

1. Elmokadem T., Savkin A. V. Towards Fully Autonomous UAVs: A Survey, Sensors, 2021, vol. 21, no. 18, article 6223, DOI: 10.3390/s21186223.

2. Telli K., Kraa O., Himeur Y. et al. A Comprehensive Review of Recent Research Trends on Unmanned Aerial Vehicles (UAVs), Systems, 2023, vol. 11, article 400, DOI: 10.3390/systems11080400.

3. Pajares G. Overview and current status of remote sensing applications based on unmanned aerial vehicles (UAVs), Photogramm. Eng. Remote Sens., 2015, vol. 81, no. 4, pp. 281—330, DOI: 10.14358/PERS.81.4.281.

4. Li H., Savkin A. V., Vucetic B. Autonomous Area Exploration and Mapping in Underground Mine Environments by Unmanned Aerial Vehicles, Robotica, 2020, vol. 38, no. 3, pp. 442—456, DOI: 10.1017/S0263574719000754.

5. Goodrich M. A., Morse B. S., Gerhardt D. et al. Supporting wilderness search and rescue using a camera-equipped mini UAV, J. Field Robot., 2008, vol. 25, no. 1—2, pp. 89—110, DOI: 10.1002/rob.20226.

6. Li X., Tupayachi J., Sharmin A. et al. Drone-Aided Delivery Methods, Challenge, and the Future: A Methodological Review, Drones, 2023, vol. 7, no. 3, pp. 191, DOI: 10.3390/drones7030191.

7. Lemardelé C., Estrada M., Pagès L., Bachofner M. Potentialities of drones and ground autonomous delivery devices for last-mile logistics, Transportation Research. Part E: Logistics and Transportation Review, May 2021, vol. 149, 102325:1—102325:51. DOI: 10.1016/j.tre.2021.102325.

8. Moshref-Javadi M., Winkenbach M. Applications and Research avenues for drone-based models in logistics: A classification and review, Expert Syst. Appl., 2021, vol. 177, article 114854, DOI: 10.1016/j.eswa.2021.114854.

9. Elmokadem T. Savkin A. V. A Method for Autonomous Collision-Free Navigation of a Quadrotor UAV in Unknown Tunnel-Like Environments, Robotica, 2022, vol. 40, no. 4, pp. 835—861, DOI: 10.1017/S0263574721000849.

10. Pshikhopov V. Kh., Medvedev M. Yu., Gurenko B. V. Algorithms of Terminal Control of Multi-Copters, Mekhatronika, Avtomatizaciya, Upravlenie, 2019, vol. 20, no. 1, pp. 44—51 (in Russian), DOI: 10.17587/mau.20.44-51.

11. Melekhin V. B., Khachumov M. V. Fuzzy Model of Situa tional Control of the Flight Parameters of an Autonomous Unmanned Aircraft under Uncertainty Conditions, Mekhatronika, Avtomatizaciya, Upravlenie, 2021, vol. 22, no. 12, pp. 650—659 (in Russian), DOI: 10.17587/mau.22.650-659.

12. Li C. Artificial Intelligence Technology in UAV Equipment, 2021 IEEE/ACIS 20th International Fall Conference on Computer and Information Science (ICIS Fall), Xi’an, China, 2021, pp. 299—302, DOI: 10.1109/ICISFall51598.2021.9627359.

13. Hu J., Bhowmick P, Jang I. et al. A Decentralized Cluster Formation Containment Framework for Multirobot Systems, IEEE Transactions on Robotics, 2021, vol. 37, no. 6, pp. 1936—1955, DOI: 10.1109/TRO.2021.3071615.

14. Wooldridge M. An Introduction to MultiAgent Systems, John Wiley & Sons, 2002, 366 p.

15. Farinelli A., Iocchi L., Nardi D. Multirobot systems: a classification focused on coordination, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics), 2004, vol. 34, no. 5, pp. 2015—2028, DOI: 10.1109/TSMCB.2004.832155.

16. Munasypov R. A., Muslimov T. Z. UAVs Group Control Based on the Relative State Space Method, Mekhatronika, Avtomatizaciya, Upravlenie, 2018, vol. 19, no. 2, pp.120—125 (in Russian).

17. Lebedev G. N., Goncharenko V. I., Maximov N. A. et al. The Method of Operational Planning of Group Actions of Aircraft in the "Air Taxi" Mode. Mekhatronika, Avtomatizaciya, Upravlenie, 2021, vol. 22, no. 9, pp. 484—493 (in Russian), DOI: 10.17587/ mau.22.484-493.

18. Lee T. Geometric control of quadrotor UAVs transporting a cable-suspended rigid body, IEEE Transactions on Control Systems Technology, 2017, vol. 26, no. 1, pp. 255—264, DOI: 10.1109/CDC.2014.7040353.

19. Goodarzi F. A., Lee T. Stabilization of a rigid body payload with multiple cooperative quadrotors, Journal of Dynamic Systems, Measurement, and Control, 2016, vol. 138, no. 12, pp. 121001, DOI: 10.1115/1.4033945.

20. Filimonov A. B., Filimonov N. B. Application of the linear quadratic optimization apparatus in problems of coordinating control, Mekhatronika, Avtomatizaciya, Upravlenie, 2013, no. 4, pp. 2—8.

21. Filimonov A. B., Filimonov N. B. Analytical synthesis of the coordinating control system, Mekhatronika, Avtomatizaciya, Upravlenie, 2012, no. 7, pp. 2—8.

22. Bannikov A., Deryushev P., Nikitin Yu. Mathematical Model of a Group of Unmanned Aircraft Under Rigid Coupling Conditions, Mechatronics, Production Technologies, Digital Enterprise: latest success, challenges, trends: International Student Scientific Conference (on-line), Prague, 16. 05.2024, Ed. Ing. Jan Kudláček, Jaroměř, 2024, pp. 219—229.

23. Deryushev P. N., Bannikov A. A., Karavaev Yu. L. Modeling the motion of a group of quadrocopters during joint cargo transportation, Actual issues of power engineering, oil and gas industry: Collection of works of the V All-Russian scientific and technical conference dedicated to the 75th anniversary of the birth of Professor A. V. Aliyev, Izhevsk, Izhevsk, Kalashnikov Izhevsk State Technical University, 2025, pp. 149—150 (in Russian).

24. Fossen T. I. Handbook of Marine Craft Hydrodynamics and Motion Control, Chichester, John Wiley & Sons Ltd, 2011.

25. Markeev A. P. Theoretical Mechanics: Textbook for Higher Education Institutions, Moscow, Izhevsk, Institute of Computer Science, 2024, 712 p. (in Russian).

26. Hoerner S. F. Fluid-Dynamic Drag: Practical Information on Aerodynamic Drag and Hydrodynamic Resistance, USA, Published by the author, 1965, 504 p.

27. Hespanha J. P. Linear Systems Theory, Princeton, Princeton University Press, 2018, 352 p.