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A geometric control approach for multi-UAV cooperative payload transfer

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Abstract

This paper proposes a novel method of transporting a safety-critical rigid payload with multiple quadrotor UAVs using a geometric control approach. A simple and tractable model of the connected system has been derived directly from the configuration space of the interconnected system utilizing the framework of Lagrangian and geometric mechanics. A tractable geometric controller has been proposed directly on the configuration space of the connected system for trajectory tracking of both the payload and the quadrotors. The controller has been derived on the configuration space of the system, and the mathematical asymptotic convergence of the errors has been provided. The proposed geometric controller does not require link information and is practically less complex. Since the controller does not require linear/angular acceleration of payload, the proposed controller can be easily implemented in a practical scenario. A realistic simulation in Gazebo and ROS is carried out to validate the tracking performance.

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Data availability

The authors have no data to disclose.

Notes

  1. A Gazebo model of four quadrotors with a rigid body payload along with a basic controller written in Python and ROS was downloaded from https://github.com/intelligent-control-lab/Collaborative_Aerial_Transportation.git. The above Gazebo model written as xacro file was modified to suit our requirements. We modified the basic controller code written in Python and ROS to implement our geometric controller. Our modified code can be found at https://github.com/manmohan88/Multi-UAV-Transport.git. Please copy paste the link if it does not work.

  2. The load transportation with the proposed approach can be seen in action at https://youtu.be/jiir8mWI6QE.

References

  1. Bouabdallah, S., Noth, A., Siegwart, R.: PID vs LQ control techniques applied to an indoor micro quadrotor. In: 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS) (IEEE Cat. No.04CH37566), vol. 3, pp. 2451–2456 (2004)

  2. Bouabdallah, S., Siegwart, R.: Backstepping and sliding-mode techniques applied to an indoor micro quadrotor. In: Proceedings of the 2005 IEEE International Conference on Robotics and Automation, pp. 2247–2252 (2005)

  3. Das, A., Subbarao, K., Lewis, F.: Dynamic inversion with zero-dynamics stabilisation for quadrotor control. IET Control Theory Appl. 3(3), 303–314 (2009)

    Article  MathSciNet  Google Scholar 

  4. Antonelli, G., Cataldi, E., Arrichiello, F., Giordano, P.R., Chiaverini, S., Franchi, A.: Adaptive trajectory tracking for quadrotor MAVS in presence of parameter uncertainties and external disturbances. IEEE Trans. Control Systems Technol. 26(1), 248–254 (2018)

    Article  Google Scholar 

  5. Bouabdallah, S., Murrieri, P., Siegwart, R.: Design and control of an indoor micro quadrotor. In: Robotics and Automation, 2004. Proceedings ICRA ’04. 2004 IEEE International Conference on, vol. 5, pp. 4393–4398 (2004)

  6. Madani, T., Benallegue, A.: Control of a quadrotor mini-helicopter via full state backstepping technique. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 1515–1520 (2006)

  7. Tayebi, A., McGilvray, S.: Attitude stabilization of a four-rotor aerial robot. In 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601), vol. 2, pp. 1216–1221 (2004)

  8. Xu, R., Ozguner, U.: Sliding mode control of a quadrotor helicopter. In: Proceedings of the 45th IEEE Conference on Decision and Control, pp. 4957–4962 (2006)

  9. Xu, R., Ozguner, U.: Sliding mode control of a class of underactuated systems. Automatica 44(1), 233–241 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Koo, T. J., Sastry, S.: Output tracking control design of a helicopter model based on approximate linearization. In: Proceedings of the 37th IEEE Conference on Decision and Control (Cat. No.98CH36171), vol. 4, pp. 3635–3640 (1998)

  11. Mistler, V., Benallegue, A., M’Sirdi, N. K.: Exact linearization and noninteracting control of a 4 rotors helicopter via dynamic feedback. In: Proceedings 10th IEEE International Workshop on Robot and Human Interactive Communication. ROMAN 2001 (Cat. No.01TH8591), pp. 586–593 (2001)

  12. Li, B., Gong, W., Yang, Y., Xiao, B., Ran, D.: Appointed fixed time observer-based sliding mode control for a quadrotor UAV under external disturbances. IEEE Trans. Aerosp. Electron. Syst. 58(1), 290–303 (2022)

    Article  Google Scholar 

  13. Lee, H., Yoon, S., Han, S.: Robust attitude control scheme for constantly spinning small-sized quadrotor in the presence of imbalance characteristics. IEEE Trans. Aerosp. Electron. Syst. 58(2), 1405–1415 (2022)

    Article  Google Scholar 

  14. Yang, H., Cheng, L., Zhang, J., Xia, Y.: Leader-follower trajectory control for quadrotors via tracking differentiators and disturbance observers. IEEE Trans. Syst. Man Cybern. Syst. 51(1), 601–609 (2021)

    Article  Google Scholar 

  15. Zhao, Z., Cao, D., Yang, J., Wang, H.: High-order sliding mode observer-based trajectory tracking control for a quadrotor UAV with uncertain dynamics. Nonlinear Dyn. 102(4), 2583–2596 (2020)

    Article  Google Scholar 

  16. Zhang, Z., Chen, T., Zheng, L.: A multilayer neural dynamic controller design method of quadrotor UAV for completing time-varying tasks. Nonlinear Dyn. 104(4), 3597–3616 (2021)

    Article  Google Scholar 

  17. Wang, Z., Zhao, T.: Based on robust sliding mode and linear active disturbance rejection control for attitude of quadrotor load UAV. Nonlinear Dyn. 108(4), 3485–3503 (2022)

    Article  Google Scholar 

  18. Lee, T., Leoky, M., McClamroch, N. H.: Geometric tracking control of a quadrotor UAV on SE(3). In: 49th IEEE Conference on Decision and Control (CDC), pp. 5420–5425 (2010)

  19. Lee, T.: Robust adaptive attitude tracking on \(\rm {SO}(3)\) with an application to a quadrotor UAV. IEEE Trans. Control Syst. Technol. 21(5), 1924–1930 (2013)

    Article  Google Scholar 

  20. Invernizzi, D., Lovera, M.: Geometric tracking control of a quadcopter tiltrotor UAV, IFAC-PapersOnLine. In: 20th IFAC World Congress, pp. 11 565 – 11 570 (2017)

  21. Sharma, M., Kar, I.: Nonlinear disturbance observer based geometric control of quadrotors. Asian J. Control 23(4), 1936–1951 (2021)

    Article  MathSciNet  Google Scholar 

  22. Sharma, M., Kar, I.: Adaptive geometric control of quadrotors with dynamic offset between center of gravity and geometric center. Asian J. Control 23(4), 1923–1935 (2021)

    Article  MathSciNet  Google Scholar 

  23. Cicolani, L., Kanning, G., Synnestvedt, R.: Simulation of the dynamics of helicopter slung load systems. J. Am. Helicopter Soc. 40, 44–61 (1995)

    Article  Google Scholar 

  24. Bernard, M., Kondak, K.: Generic slung load transportation system using small size helicopters. In: IEEE International Conference on Robotics and Automation, pp. 3258–3264 (2009)

  25. Palunko, I., Cruz, P., Fierro, R.: Agile load transportation : safe and efficient load manipulation with aerial robots. IEEE Robot. Autom. Mag. 19(3), 69–79 (2012)

    Article  Google Scholar 

  26. Michael, J., Fink, N., Kumar, V.: Cooperative manipulation and transportation with aerial robots. Auton. Robots 30(3), 73–86 (2011)

    Article  MATH  Google Scholar 

  27. Maza, I., Kondak, K., Bernard, M.: Multi-UAV cooperation and control for load transportation and deployment. J. Intell. Robot. Syst. 57(3), 417–449 (2009)

    MATH  Google Scholar 

  28. Durrant-Whyte, H., Roy, N., Abbeel, P.: Construction of Cubic Structures with Quadrotor Teams, pp. 177–184. MIT Press, Cambridge (2012)

    Google Scholar 

  29. Mohammadi, K., Sirouspour, S., Grivani, A.: Control of multiple quad-copters with a cable-suspended payload subject to disturbances. IEEE/ASME Trans. Mech. 25(4), 1709–1718 (2020)

    Article  Google Scholar 

  30. Sanalitro, D., Savino, H.J., Tognon, M., Cortés, J., Franchi, A.: Full-pose manipulation control of a cable-suspended load with multiple UAVS under uncertainties. IEEE Robot. Autom. Lett. 5(2), 2185–2191 (2020)

    Article  Google Scholar 

  31. Muñoz, F., Zúñiga-Peña, N.S., Carrillo, L.R.G., Espinoza, E.S., Salazar, S., Márquez, M.A.: Adaptive fuzzy consensus control strategy for UAS-based load transportation tasks. IEEE Trans. Aerosp. Electron. Syst. 57(6), 3844–3860 (2021)

    Article  Google Scholar 

  32. Yu, B., Gamagedara, K., Kim, S., Lee, T., Suk, J.: Geometric control and experimental validation for a quadrotor UAV transporting a payload. In: 2020 59th IEEE Conference on Decision and Control (CDC), pp. 201–207 (2020)

  33. Wehbeh, J., Rahman, S., Sharf, I.: Distributed model predictive control for UAVS collaborative payload transport. In: 2020 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 11 666–11 672 (2020)

  34. Lee, S., Son, H.: Antisway control of a multirotor with cable-suspended payload. IEEE Trans. Control Syst. Technol. 29(6), 2630–2638 (2021)

    Article  Google Scholar 

  35. Sreenath, K., Lee, T., Kumar, V.: Geometric control and differential flatness of a quadrotor UAV with a cable-suspended load. In: 52nd IEEE Conference on Decision and Control, pp. 2269–2274 (2013)

  36. Lee, T., Sreenath, K., Kumar, V.: Geometric control of cooperating multiple quadrotor UAVS with a suspended payload. In: 52nd IEEE Conference on Decision and Control, pp. 5510–5515 (2013)

  37. Lee, T.: Geometric control of quadrotor UAVS transporting a cable-suspended rigid body. IEEE Trans. Control Syst. Technol. 26(1), 255–264 (2018)

    Article  Google Scholar 

  38. Lee, T.: Geometric control of multiple quadrotor uavs transporting a cable-suspended rigid body. In: 53rd IEEE Conference on Decision and Control, pp. 6155–6160 (2014)

  39. Wu, G., Sreenath, K.: Geometric control of multiple quadrotors transporting a rigid-body load. In: 53rd IEEE Conference on Decision and Control, pp. 6141–6148 (2014)

  40. Pappalardo, C.M., Guida, D.: On the dynamics and control of underactuated nonholonomic mechanical systems and applications to mobile robots. Arch. Appl. Mech. 89(4), 669–698 (2019)

    Article  Google Scholar 

  41. Bullo, F., Lewis, A.D.: Geometric control of mechanical systems. In: Texts in Applied Mathematics. Springer, New York-Heidelberg-Berlin (2004)

    Google Scholar 

  42. Bhat, S. P., Bernstein, D. S.: A topological obstruction to global asymptotic stabilization of rotational motion and the unwinding phenomenon. In Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207), vol. 5, pp. 2785–2789 (1998)

  43. Rivera, Z. B., De Simone, M. C., Guida, D.: Unmanned ground vehicle modelling in gazebo/ros-based environments, Machines (2019) [Online]. Available: https://www.mdpi.com/2075-1702/7/2/42

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Funding

The authors declare that no funds, grants, or other support were received during the preparation of this manuscript.

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Authors and Affiliations

  1. Department of Aerospace Engineering, Indian Institute of Science, Bengaluru, 560012, India

    Manmohan Sharma

  2. GITAM University, Bengaluru Campus, Bengaluru, 561203, India

    Manmohan Sharma

  3. Department of Aerospace Engineering, Indian Institute of Science, Bengaluru, 560012, India

    Suresh Sundaram

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Contributions

All authors contributed to the study conception and design. Material preparation, data collection and analysis were performed by Manmohan Sharma and Suresh Sundaram. The first draft of the manuscript was written by Manmohan Sharma, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

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Correspondence to Manmohan Sharma.

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Sharma, M., Sundaram, S. A geometric control approach for multi-UAV cooperative payload transfer. Nonlinear Dyn 111, 10077–10096 (2023). https://doi.org/10.1007/s11071-023-08346-5

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