Skip to main content
Log in

Exponentially Stable Motion Control for Multirotor UAVs with Rotor Drag and Disturbance Compensation

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

Abstract

In this paper we propose a centralized disturbance observer-based integral-augmented backstepping nonlinear motion control for a multirotor unmanned aerial vehicle (UAV). The approach explicitly compensates for rotor drag forces. The control is termed centralized as it based on the full rigid body vehicle model (i.e., rotational and translational dynamics). The dynamic state feedback includes two disturbance observers which estimate external force and torque disturbances. The effect of rotor drag is compensated in the proposed force disturbance observer and the backstepping motion controller. The closed-loop dynamics is proven to be exponentially stable in the presence of constant disturbances. The proposed control is implemented on the open-source PX4 autopilot software and validated using a Software-in-the-loop (SITL) simulation. The simulation results demonstrate the method’s robustness and steady-state error performance. Rotor drag compensation is shown to improve the tracking error performance.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

Code Availability

The code is available at https://github.com/ANCL/UAV_DOBIBS_V2

References

  1. Hua, M. -D., Hamel, T., Morin, P., Samson, C.: Introduction to feedback control of underactuated VTOL vehicle: a review of basic control design ideas and principles. IEEE Contr. Sys. Mag. 33(1), 61–75 (2013)

    Article  MathSciNet  Google Scholar 

  2. Kim, S., Choi, S., Kim, H., Shin, J., Shim, H., Kim, H.J.: Robust control of an equipment-added multirotor using disturbance observer. IEEE Trans. Control Syst. Technol. 26(4), 1524–1531 (2018)

    Google Scholar 

  3. Wang, C., Song, B., Huang, P., Tang, C.: Trajectory tracking control for quadrotor robot subject to payload variation and wind gust disturbance. J. Intell. Robot. Syst. 83(2), 315–333 (2016)

    Article  Google Scholar 

  4. Faessler, M., Franchi, A., Scaramuzza, D.: Differential flatness of quadrotor dynamics subject to rotor drag for accurate tracking of high-speed trajectories. IEEE Robot. Autom. Lett. 3(2), 620–626 (2018)

    Article  Google Scholar 

  5. 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)

    Article  Google Scholar 

  6. Aboudonia, A., El-Badawy, A., Rashad, R.: Disturbance observer-based feedback linearization control of an unmanned quadrotor helicopter. Proc. Inst. Mech. Eng., Part I: J. Syst. Control Eng. 230(9), 877–891 (2016)

    MATH  Google Scholar 

  7. Chen, F., Lei, W., Zhang, K., Tao, G., Jiang, B.: A novel nonlinear resilient control for a quadrotor UAV via backstepping control and nonlinear disturbance observer. Nonlinear Dyn. 85(2), 1281–1295 (2016)

    Article  Google Scholar 

  8. Poultney, A., Kennedy, C., Clayton, G., Ashrafiuon, H.: Robust Tracking Control of Quadrotors Based on Differential Flatness: Simulations and Experiments. IEEE/ASME Trans. Mechatron. 23(3), 1126–1137 (2018)

    Article  Google Scholar 

  9. Wang, T., Parwana, H., Umemoto, K., Endo, T., Matsuno, F.: Non-cascade adaptive sliding mode control for quadrotor UAVs under parametric uncertainties and external disturbance with indoor experiments. J. Intell. Rob. Syst. 102(1), 8 (2021)

    Article  Google Scholar 

  10. Perozzi, G., Efimov, D., Biannic, J.-M., Planckaert, L.: Trajectory tracking for a quadrotor under wind perturbation: sliding mode control with state-dependent gains. J. Franklin Inst. 355(12), 4809–4838 (2018)

    Article  MathSciNet  Google Scholar 

  11. Nicol, C., Macnab, C. J. B., Ramirez-Serrano, A.: Robust neural network control of a quadrotor helicopter. In: Canadian Conf. Electrical and Computer Engineering, pp 1233–1238 (2018)

  12. Labbadi, M., Cherkaoui, M.: Robust adaptive backstepping fast terminal sliding mode controller for uncertain quadrotor UAV. Aerosp. Sci. Technol. 93, 105306 (2019)

    Article  Google Scholar 

  13. Shao, X., Liu, J., Cao, H., Shen, C., Wang, H.: Robust dynamic surface trajectory tracking control for a quadrotor UAV via extended state observer. Int. J. Robust Nonlinear Control 28(7), 2700–2719 (2018)

    Article  MathSciNet  Google Scholar 

  14. Meier, L.: PX4 autopilot, Institute for Visual Computing, Swiss Federal Institute of Technology Zurich. [Online]. Available: https://px4.io/ (2018)

  15. Xie, W., Cabecinhas, D., Cunha, R., Silvestre, C.: Adaptive backstepping control of a quadcopter with uncertain vehicle mass, moment of inertia, and disturbances. IEEE Trans. Ind. Electron. 1–1. [Online]. Available: https://doi.org/10.1109/TIE.2021.3055181 (2021)

  16. Zou, Y.: Nonlinear robust adaptive hierarchical sliding mode control approach for quadrotors. Int. J. Robust Nonlinear Control 27(6), 925–941 (2017)

    Article  MathSciNet  Google Scholar 

  17. He, Y., Pei, H., Sun, T.: Robust tracking control of helicopters using backstepping with disturbance observers. Asian J. Control 16(5), 1387–1402 (2014)

    Article  Google Scholar 

  18. Lee, S.J., Kim, S., Johansson, K.H., Kim, H.J.: Robust acceleration control of a hexarotor UAV with a disturbance observer. In: IEEE Decis. Contr. P., pp 4166–4171 (2016)

  19. Guo, K., Jia, J., Yu, X., Guo, L., Xie, L.: Multiple observers based anti-disturbance control for a quadrotor UAV against payload and wind disturbances. Control Eng. Pract. 102, 104560 (2020)

    Article  Google Scholar 

  20. Sasaki, K., Yang, Z.-J.: Disturbance observer-based control of UAVs with prescribed performance. Int. J. Syst. Sci. 51(5), 939–957 (2020)

    Article  MathSciNet  Google Scholar 

  21. Colmenares-Vazquez, J., Marchand, N., Castillo, P., Gomez-Balderas, J.E., Alvarez-Munoz, J.U., Tellez-Guzman, J.J.: Integral backstepping control for trajectory tracking of a hybrid vehicle. In: Int. Conf. Unman. Aircr., pp 209–217 (2015)

  22. Poultney, A., Gong, P., Ashrafiuon, H.: Integral backstepping control for trajectory and yaw motion tracking of quadrotors. Robotica 37(2), 300–320 (2019)

    Article  Google Scholar 

  23. Jasim, W., Gu, D.: Integral backstepping controller for quadrotor path tracking. In: Int. Conf. Adv. Robot., pp 593–598 (2015)

  24. Jia, Z., Yu, J., Mei, Y., Chen, Y., Shen, Y., Ai, X.: Integral backstepping sliding mode control for quadrotor helicopter under external uncertain disturbances. Aerosp. Sci. Technol. 68, 299–307 (2017)

    Article  Google Scholar 

  25. Bangura, M.: Aerodynamics and control of quadrotors, Ph.D. dissertation, College of Engineering and Computer Science The Australian National University (2017)

  26. Moeini, A., Rafique, M.A., Xue, Z., Lynch, A.F., Zhao, Q.: Disturbance observer-based integral backstepping control for UAVs. In: Int. Conf. Unman. Aircr., pp 382–388 (2020)

  27. Moeini, A., Lynch, A., Zhao, Q.: Disturbance observer-based nonlinear control of a quadrotor UAV, Adv. Control Appl. 2(1), 1–20 (2019)

    Google Scholar 

  28. Moeini, A., Lynch, A.: Modified px4 autopilot firmware. [Online]. Available: https://github.com/ANCL/UAV_DOBIBS_V2 (2020)

  29. Castillo, P., Lozano, R., Dzul, A.: Modelling and control of mini flying machines. New York City USA: Springer-Verlag (2005)

  30. Cabecinhas, D., Cunha, R., Silverstre, C.: A nonlinear quadrotor trajectory tracking controller with disturbance rejection. Control Eng. Pract. 26, 1–10 (2014)

    Article  Google Scholar 

  31. Loría, A., Panteley, E.: Cascaded Nonlinear Time-Varying Systems: Analysis and Design, Advanced Topics in Control Systems Theory, pp 23–64. Springer, London (2005)

    MATH  Google Scholar 

  32. Fink, G.: Computer Vision-Based Motion Control and State Estimation for Unmanned Aerial Vehicles (UAVs), Ph.D. Dissertation, Dept. Electrical and Computer Engineering, University of Alberta, Edmonton, AB (2018)

  33. Xie, H.: Dynamic Visual Servoing of Rotary Wing Unmanned Aerial Vehicles, Ph.D. Dissertation, Dept. Electrical and Computer Engineering, University of Alberta, Edmonton, AB (2016)

  34. Cao, N.: Control of Quadrotor Unmanned Aerial Vehicles with Saturation and Time Delay, Ph.D. Dissertation, Dept. Electrical and Computer Engineering, University of Alberta, Edmonton, Alberta (2018)

Download references

Funding

The support provided by the Ministry of Economic Development and Trade, Government of Alberta, Major Innovation Fund project RCP-19-001-MIF, Autonomous Systems Initiative, is gratefully acknowledged to assist with the preparation of this manuscript.

Author information

Authors and Affiliations

Authors

Contributions

All authors contributed to the study, conception, and design. Coding, controller simulation, and data collection were performed by Amir Moeini. The first draft of the manuscript was written by Amir Moeini and all authors have assisted in editing the manuscript. All authors read and approved the final manuscript.

Corresponding author

Correspondence to Alan F. Lynch.

Ethics declarations

Ethics approval

The submitted work is original and not have been published elsewhere in any form or language.

Conflict of Interests

The authors declare that they have no conflict of interest.

Additional information

Publisher’s Note

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

A preliminary version of the submitted paper appeared in the Proceedings of the 2020 International Conference on Unmanned Aircraft Systems (ICUAS’20), Athens, Greece.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moeini, A., Lynch, A.F. & Zhao, Q. Exponentially Stable Motion Control for Multirotor UAVs with Rotor Drag and Disturbance Compensation. J Intell Robot Syst 103, 15 (2021). https://doi.org/10.1007/s10846-021-01452-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-021-01452-9

Keywords

Navigation