Skip to main content
SpringerLink
Log in

Output Tracking Dynamic Feedback Linearization of a Multirotor Suspended Load System with Disturbance Robustness

  • Regular paper
  • Published:
Journal of Intelligent & Robotic Systems Aims and scope Submit manuscript

Abstract

This paper considers motion control of a slung load system (SLS) which consists of a multirotor unmanned aerial vehicle (UAV) carrying a slung load with a cable. This paper addresses the problem of tracking smooth payload position and UAV yaw trajectories. We design an output-tracking controller which can be used on a large practical region of state space and which has locally exponentially stable (ES) error dynamics. The method uses exact dynamic state-feedback linearization, and the controller expression is derived using the dynamic extension algorithm (DEA). Flatness relations are used to determine conditions for reference trajectories which avoid singularities. The proposed design achieves error dynamics which is ES in the presence of constant force and torque disturbance acting on the UAV. Finally, the proposed control law is compared to a geometric output-tracking design through numerical simulations, and the advantages of the proposed method are highlighted including its ease of tuning and disturbance robustness.

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

Similar content being viewed by others

Code Availability

Not applicable.

References

  1. Villa, D., Brandao, A., Sarcinelli-Filho, M.: A survey on load transportation using multirotor uavs. Journal of Intelligent & Robotic Systems 98(2), 267–296 (2020). https://doi.org/10.1007/s10846-019-01088-w

    Article  Google Scholar 

  2. Lindsey, Q., Mellinger, D., Kumar, V.: Construction of cubic structures with quadrotor teams, pp. 177–184. MIT Press (2011)

  3. Pounds, P., Bersak, D., Dollar, A.: Grasping from the air: Hovering capture and load stability. In: Proc. IEEE Int. Conf. on Robotics and Automation, Toronto, ON, pp. 2491–2498 (2011). https://doi.org/10.1109/icra.2011.5980314

  4. Gawel, A., Kamel, M., Novkovic, T., Widauer, J., Schindler, D., von Altishofen, B.P., Siegwart, R., Nieto, J.: Aerial picking and delivery of magnetic objects with MAVs. In: Proc. IEEE Int. Conf. on Robotics and Automation, Singapore, pp. 5746–5752 (2017). https://doi.org/10.1109/icra.2017.7989675

  5. Shirani, B., Najafi, M., Izadi, I.: Cooperative load transportation using multiple UAVs. Aerospace Science and Technology 84, 158–169 (2019). https://doi.org/10.1016/j.ast.2018.10.027

    Article  Google Scholar 

  6. Rossomando, F., Rosales, C., Gimenez, J., Salinas, L., Soria, C., Sarcinelli-Filho, M., Carelli, R.: Aerial load transportation with multiple quadrotors based on a kinematic controller and a neural SMC dynamic compensation. Journal of Intelligent & Robotic Systems 100(2), 519–530 (2020). https://doi.org/10.1007/s10846-020-01195-z

    Article  Google Scholar 

  7. Fusato, D., Guglieri, G., Celi, R.: Flight dynamics of an articulated rotor helicopter with an external slung load. J. Am. Helicopter Soc. 46(1), 3–13 (2001). https://doi.org/10.4050/JAHS.46.3

    Article  Google Scholar 

  8. Irscheid, A., Konz, M., Rudolph, J.: A flatness-based approach to the control of distributed parameter systems applied to load transportation with heavy ropes, pp. 279–294. Springer (2019). https://doi.org/10.1007/978-3-030-21927-7_13

  9. Knüppel, T., Woittennek, F.: Control design for quasi-linear hyperbolic systems with an application to the heavy rope. IEEE Transactions on Automatic Control 60(1), 5–18 (2014). https://doi.org/10.1109/TAC.2014.2336451

    Article  MathSciNet  MATH  Google Scholar 

  10. Fliess, M., Lévine, J., Martin, P., Rouchon, P.: On differentially flat nonlinear systems. In: Nonlinear Control Systems Design. IFAC Symposia Series, pp. 159–163. Pergamon, Oxford (1993). https://doi.org/10.1016/S1474-6670(17)52275-2

  11. Murray, R.M.: Trajectory generation for a towed cable system using differential flatness. IFAC Proceedings Volumes 29(1), 2792–2797 (1996). https://doi.org/10.1016/S1474-6670(17)58099-4

    Article  Google Scholar 

  12. Goodarzi, F.A., Lee, D., Lee, T.: Geometric stabilization of a quadrotor UAV with a payload connected by flexible cable. In: Proc. American Control Conf., Portland, OR, pp. 4923–4930 (2014). https://doi.org/10.1109/ACC.2014.6859419

  13. Kotaru, P., Wu, G., Sreenath, K.: Differential-flatness and control of quadrotor(s) with a payload suspended through flexible cable(s). In:Proc. Indian Control Conf., Kanpur, India, pp. 352–357 (2018).https://doi.org/10.1109/indiancc.2018.8308004

  14. Guerrero-Sánchez, M., Lozano, R., Castillo, P., Hernández-González, O., García-Beltrán, C.D., Valencia-Palomo, G.: Nonlinear control strategies for a UAV carrying a load with swing attenuation. Applied Mathematical Modelling 91, 709–722 (2021). https://doi.org/10.1016/j.apm.2020.09.027

    Article  MathSciNet  MATH  Google Scholar 

  15. Guerrero, M., Mercado, D.A., Lozano, R., García, C.D.: Swing-attenuation for a quadrotor transporting a cable suspended payload. ISA Transactions 68, 433–449 (2017). https://doi.org/10.1016/j.isatra.2017.01.027

    Article  Google Scholar 

  16. Klausen, K., Fossen, T., Johansen, T.: Nonlinear control with swing damping of a multirotor UAV with suspended load. Journal of Intelligent & Robotic Systems 88, 379–394 (2017). https://doi.org/10.1007/s10846-017-0509-6

    Article  Google Scholar 

  17. Sreenath, K., Lee, T., Kumar, V.: Geometric control and differential flatness of a quadrotor UAV with a cable-suspended load. In: Proc. IEEE Int. Conf. on Decision and Control, Firenze, Italy, pp. 2269–2274 (2013). https://doi.org/10.1109/cdc.2013.6760219

  18. Bernard, M., Kondak, K.: Generic slung load transportation system using small size helicopters. In: Proc. IEEE Int. Conf. on Robotics and Automation, Kobe, Japan, pp. 3258–3264 (2009). https://doi.org/10.1109/ROBOT.2009.5152382

  19. Sreenath, K., Michael, N., Kumar, V.: Trajectory generation and control of a quadrotor with a cable-suspended load – a differentially-flat hybrid system. In: Proc. IEEE Int. Conf. on Robotics and Automation, Karlsruhe, Germany, pp. 4888–4895 (2013). https://doi.org/10.1109/ICRA.2013.6631275

  20. Fang, Y., Dixon, W., Dawson, D., Zergeroglu, E.: Nonlinear coupling control laws for an underactuated overhead crane system. IEEE/ASME Transactions on Mechatronics 8(3), 418–423 (2003). https://doi.org/10.1109/TMECH.2003.816822

    Article  Google Scholar 

  21. Xian, B., Yang, S.: Robust tracking control of a quadrotor unmanned aerial vehicle-suspended payload system. IEEE/ASME Transactions on Mechatronics 26(5), 2653–2663 (2021). https://doi.org/10.1109/TMECH.2020.3044183

    Article  Google Scholar 

  22. Yu, G., Cabecinhas, D., Cunha, R., Silvestre, C.: Nonlinear backstepping control of a quadrotor-slung load system. IEEE/ASME Transactions on Mechatronics 24(5), 2304–2315 (2019). https://doi.org/10.1109/TMECH.2019.2930211

    Article  Google Scholar 

  23. Reis, J., Yu, G., Cabecinhas, D., Silvestre, C.: High-performance quadrotor slung load transportation with damped oscillations. International Journal of Robust and Nonlinear Control (2022). https://doi.org/10.1002/rnc.6306

    Article  Google Scholar 

  24. Akhtar, A., Saleem, S., Shan, J.: Path invariant controllers for a quadrotor with a cable-suspended payload using a global parameterization. IEEE Transactions on Control Systems Technology (2021)

  25. Akhtar, A., Saleem, S., Shan, J.: Path following of a quadrotor with a cable-suspended payload. IEEE Transactions on Industrial Electronics (2022)

  26. Maplesoft™: Maple (2022) Accessed 13 May, 2022. https://www.maplesoft.com/products/maple/

  27. Mohammadhasani, A., Al Lawati, M., Jiang, Z., Lynch, A.F.: Dynamic feedback linearization of a UAV suspended load system. In: International Conference on Unmanned Aircraft Systems (ICUAS), pp. 865–872 (2022). https://doi.org/10.1109/ICUAS54217.2022.9836223. IEEE

  28. Nijmeijer, H., Respondek, W.: Dynamic input-output decoupling of nonlinear control systems. Transactions on Automatic Control 33(11), 1065–1070 (1988). https://doi.org/10.1109/9.14420

    Article  MathSciNet  MATH  Google Scholar 

  29. Khalil, H.: Nonlinear Systems, 3rd edn. Prentice-Hall, Englewood Cliffs, NJ (2002)

    MATH  Google Scholar 

  30. Dahleh, M.A., Díaz-Bobillo, I.J.: Control of Uncertain Systems: a Linear Programming Approach. Prentice Hall, Upper Saddle River, NJ (1995)

    MATH  Google Scholar 

  31. Green, M., Limebeer, D.: Linear Robust Control. Prentice-Hall, Englewood Cliffs, NJ (2012)

    MATH  Google Scholar 

  32. Nijmeijer, H., Schumacher, J.: The regular local noninteracting control problem for nonlinear control systems. SIAM Journal on Control and Optimization 24(6), 1232–1245 (1986). https://doi.org/10.1137/0324074

    Article  MathSciNet  MATH  Google Scholar 

  33. Roza, A., Maggiore, M.: Path following controller for a quadrotor helicopter. In: Proc. American Control Conf., Montreal, QC, pp. 4655–4660 (2012). https://doi.org/10.1109/ACC.2012.6315061

  34. Fischer, G.: NONLINCON: symbolic analysis and design package for nonlinear control systems. Master’s thesis, Eindhoven University of Technology, Eindhoven (1994)

  35. Lee, T., Leok, M., McClamroch, N.H.: Geometric tracking control of a quadrotor UAV on SE(3). In: Proc. IEEE Int. Conf. on Decision and Control, Atlanta, GA, pp. 5420–5425 (2010). https://doi.org/10.1109/CDC.2010.5717652

  36. Kai, J.-M., Allibert, G., Hua, M.-D., Hamel, T.: Nonlinear feedback control of quadrotors exploiting first-order drag effects. IFAC-PapersOnLine 50(1), 8189–8195 (2017). https://doi.org/10.1016/j.ifacol.2017.08.1267

    Article  Google Scholar 

  37. Furrer, F., Burri, M., Achtelik, M., Siegwart, R.: RotorS - a modular Gazebo MAV simulator framework. Robot Operating System (ROS) The Complete Reference (Volume 1), 595–625 (2016).https://doi.org/10.1007/978-3-319-26054-9_23

  38. PX4 Gazebo Simulation (2023). https://docs.px4.io/main/en/sim_gazebo_gz/. Accessed: 28 April 2023

  39. Jiang, Z., Al Lawati, M., Mohammadhasani, A., Lynch, A.: Quasi-static state feedback output tracking for a slung load system : PX4 SITL validation (under review). Journal of Intelligent & Robotic Systems (2023)

  40. Omari, S., Hua, M.-D., Ducard, G., Hamel, T.: Nonlinear control of VTOL UAVs incorporating flapping dynamics. In: IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 2419–2425 (2013). https://doi.org/10.1109/IROS.2013.6696696. IEEE

Download references

Acknowledgements

Not applicable.

Funding

This work was supported by Sultan Qaboos University (SQU) and the Natural Sciences and Engineering Research Council of Canada (NSERC) and Ministry of Economic Development and Trade, Government of Alberta.

Author information

Authors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Sultan Qaboos University, Al Khoud, 123, Muscat, Oman

    Mohamed Al Lawati

  2. Department of Electrical and Computer Engineering, University of Alberta, 116 St. & 85 Ave., Edmonton, T6G 2R3, Alberta, Canada

    Mohamed Al Lawati, Zifei Jiang & Alan F. Lynch

Authors
  1. Mohamed Al Lawati
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zifei Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Alan F. Lynch
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Material preparation, data collection, design and analysis were performed by Mohamed Al Lawati and Alan Lynch. The first draft of the manuscript was written by Mohamed Al Lawati, and all authors commented on previous versions of the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Alan F. Lynch.

Ethics declarations

Conflicts of interest

The authors have no relevant financial or non-financial interests to disclose.

Ethics Approval

The research does not involve human participants, their data or biological material and it does not involve animals.

Consent to participate

Not applicable.

Consent for publication

Not applicable.

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

Al Lawati, M., Jiang, Z. & Lynch, A.F. Output Tracking Dynamic Feedback Linearization of a Multirotor Suspended Load System with Disturbance Robustness. J Intell Robot Syst 108, 82 (2023). https://doi.org/10.1007/s10846-023-01904-4

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-023-01904-4

Keywords

Search

Navigation