Skip to main content
SpringerLink
Log in

Global tracking control of quadrotor based on adaptive dynamic surface control

  • Published:
International Journal of Dynamics and Control Aims and scope Submit manuscript

Abstract

This paper presents a global nonlinear tracking control system for a quadrotor unmanned aerial vehicle (UAV) in the presence of underactuation, external disturbances and model uncertainties. Quadrotor systems lack enough independent control inputs to control their entire configuration space directly due to underactuation. The proposed solution is to adopt a cascade feedback technique that splits the system dynamics into attitude and position dynamics. The proposed controller is developed directly on the special Euclidean group with a region of attraction covering the entire configuration space where its stability is proven using Lyapunov functions. The controller guarantees the asymptotical convergence of tracking error in the presence of model uncertainties and external disturbances. In particular, the control method combines three techniques: a second-order sliding mode control (SMC), a dynamic surface control, and a non-parametric adaptation mechanism. The SMC is used to stabilize the position dynamics (internal dynamics) by generating a proper attitude command for the attitude controller. The DMC control guarantees the attitude dynamics stability globally and tracking performance while avoiding the mathematical complexities associated with the highly nonlinear dynamics. The adaptation mechanism includes a radial basis function neural network to observe uncertainties without the need for prior training. The uncertainties considered include unmodeled dynamics, external disturbances and parameter uncertainties including the mass and inertial matrices as well as motor coefficients. The desirable features of the proposed control system are illustrated by both numerical simulation and experiments on a UAV testbed.

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

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12

Similar content being viewed by others

References

  1. Máthé K, Buşoniu L (2015) Vision and control for UAVs: a survey of general methods andof inexpensive platforms for infrastructure inspection. Sensors 15(7):14887–14916. https://doi.org/10.3390/s150714887

    Article  Google Scholar 

  2. Heredia G, Jimenez-Cano AE, Sanchez I, Llorente D, Vega V, Braga J, Acosta JA, Ollero A (2014) Control of a multirotor outdoor aerial manipulator. In: IEEE/RSJ international conference on intelligent robots and systems, pp 3417–3422. https://doi.org/10.1109/IROS.2014.6943038

  3. Emran BJ, Dias J, Seneviratne L, Cai G (2015) Robust adaptive control design for quadcopter payload add and drop applications. In: Chinese control conference (CCC), vol 34, pp 3252–3257. https://doi.org/10.1109/ChiCC.2015.7260141

  4. Emran BJ, Tannant DD, Najjaran H (2017) Low-altitude aerial methane concentration mapping. Remote Sens 9(8):823. https://doi.org/10.3390/rs9080823

    Article  Google Scholar 

  5. Roza A, Maggiore M (2014) A class of position controllers for underactuated VTOL vehicles. IEEE Trans Autom Control 59(9):2580–2585. https://doi.org/10.1109/TAC.2014.2308609

    Article  MathSciNet  MATH  Google Scholar 

  6. Emran BJ, Najjaran H (2017) Adaptive neural network control of quadrotor system under the presence of actuator constraints. In: IEEE international conference on systems, man, and cybernetics (SMC), pp 2619–2624

  7. Xiong J-J, Zhang G-B (2017) Global fast dynamic terminal sliding mode control for a quadrotor UAV. ISA Trans 66:233–240. https://doi.org/10.1016/j.isatra.2016.09.019

    Article  Google Scholar 

  8. Zheng E-H, Xiong J-J, Luo J-L (2014) Second order sliding mode control for a quadrotor UAV. ISA Trans 53(4):1350–1356. https://doi.org/10.1016/j.isatra.2014.03.010

    Article  Google Scholar 

  9. Dydek ZT, Annaswamy AM, Lavretsky E (2013) Adaptive control of quadrotor UAVs: a design trade study with flight evaluations. IEEE Trans Control Syst Technol 21(4):1400–1406. https://doi.org/10.1109/TCST.2012.2200104

    Article  Google Scholar 

  10. Liu H, Wang X, Zhong Y (2015) Quaternion-based robust attitude control for uncertain robotic quadrotors. In: IEEE transactions on industrial informatics, vol 11, pp 406–415. https://doi.org/10.1109/TII.2015.2397878

  11. Das A, Lewis F, Subbarao K (2009) Backstepping approach for controlling a quadrotor using Lagrange form dynamics. J Intell Robot Syst Theory Appl 56(1–2):127–151. https://doi.org/10.1007/s10846-009-9331-0

    Article  MATH  Google Scholar 

  12. Das A, Lewis FL, Subbarao K (2011) Sliding mode approach to control quadrotor using dynamic inversion. In: Bartoszewicz A (ed) Challenges and paradigms in applied robust control, Chap. 1. InTech, London, pp 3–24. https://doi.org/10.5772/16599

    Chapter  Google Scholar 

  13. Choi YC, Ahn HS (2015) Nonlinear control of quadrotor for point tracking: actual implementation and experimental tests. IEEE/ASME Trans Mechatron 20(3):1179–1192. https://doi.org/10.1109/TMECH.2014.2329945

    Article  Google Scholar 

  14. Ha C, Zuo Z, Choi FB, Lee D (2014) Passivity-based adaptive backstepping control of quadrotor-type UAVs. Robot Auton Syst 62(9):1305–1315. https://doi.org/10.1016/j.robot.2014.03.019

    Article  Google Scholar 

  15. Emran BJ, Najjaran H (2017) Switching control of quadrotor with adaptation mechanism. In: IEEE International conference on systems, man, and cybernetics (SMC)—conference proceedings, Budapest, pp 4872–4877. https://doi.org/10.1109/SMC.2016.7845000

  16. Goodarzi F a, Lee D, Lee T (2015) Geometric adaptive tracking control of a quadrotor unmanned aerial vehicle on SE(3) for agile maneuvers. J Dyn Syst Meas Control 137(9):091007. https://doi.org/10.1115/1.4030419. arXiv:1411.2986v1

    Article  Google Scholar 

  17. Cabecinhas D, Naldi R, Silvestre C, Cunha R, Marconi L (2016) Robust landing and sliding maneuver hybrid controller for a quadrotor vehicle. IEEE Trans Control Syst Technol 24(2):400–412. https://doi.org/10.1109/TCST.2015.2454445

    Article  Google Scholar 

  18. Branicky MS (1998) Multiple Lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Trans Autom Control 43(4):475–482. https://doi.org/10.1109/9.664150

    Article  MathSciNet  MATH  Google Scholar 

  19. Goodarzi F A, Lee D, Lee T (2014) Geometric adaptive tracking control of a quadrotor UAV on SE(3) for agile maneuvers. J Dyn Syst Meas Control 137(9):091007. https://doi.org/10.1115/1.4030419. arXiv:1411.2986

    Article  Google Scholar 

  20. Min B-C, Hong J-H, Matson ET (2011) Adaptive robust control (ARC) for an altitude control of a quadrotor type UAV carrying an unknown payloads. In: International conference on control, automation and systems, pp 1147–1151

  21. Zhao B, Xian B, Zhang Y, Zhang X (2015) Nonlinear robust adaptive tracking control of a quadrotor UAV via immersion and invariance methodology. IEEE Trans Ind Electron 62(5):2891–2902. https://doi.org/10.1109/TIE.2014.2364982

    Article  Google Scholar 

  22. Nicol C, MacNab CJB, Ramirez-Serrano A (2011) Robust adaptive control of a quadrotor helicopter. Mechatronics 21(6):927–938. https://doi.org/10.1016/j.mechatronics.2011.02.007

    Article  MATH  Google Scholar 

  23. Peng C, Bai Y, Gong X, Gao Q, Zhao C, Tian Y (2015) Modeling and robust backstepping sliding mode control with adaptive RBFNN for a novel. IEEE/CAA J Autom Sin 2(1):56–64. https://doi.org/10.1109/JAS.2015.7032906

    Article  MathSciNet  Google Scholar 

  24. Emran BJ, Najjaran H (2018) A review of quadrotor: an underactuated mechanical system. Annu Rev Control 46:165–180. https://doi.org/10.1016/J.ARCONTROL.2018.10.009

    Article  MathSciNet  Google Scholar 

  25. Song B, Hedrick JK (2011) Dynamic surface control of uncertain nonlinear systems, an LMI approach. Springer, Berlin

    Book  Google Scholar 

  26. Liu Z, Hedrick K (2016) Dynamic surface control techniques applied to horizontal position control of a quadrotor. In: International conference on system theory, control and computing (ICSTCC). IEEE, pp 138–144

  27. Hua M-D, Hamel T, Morin P, Samson C (2013) Introduction to feedback control of underactuated VTOL vehicles: a review of basic control design ideas and principles. IEEE Control Syst 33(1):61–75. https://doi.org/10.1109/MCS.2012.2225931

    Article  MathSciNet  MATH  Google Scholar 

  28. Mahony R, Kumar V, Corke P (2012) Multirotor aerial vehicles: modeling, estimation, and control of quadrotor. IEEE Robot Autom Mag 19(3):20–32. https://doi.org/10.1109/MRA.2012.2206474

    Article  Google Scholar 

  29. Liu J (2013) Radial basis function (RBF) neural network control for mechanical systems design, analysis and Matlab simulation, vol.1, SpringerLink ebooks. arXiv:1011.1669v3, https://doi.org/10.1017/CBO9781107415324.004

Download references

Author information

Authors and Affiliations

  1. University of British Columbia, Kelowna, BC, V1V 1V7, Canada

    Bara J. Emran & Homayoun Najjaran

Authors
  1. Bara J. Emran
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Homayoun Najjaran
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bara J. Emran.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Emran, B.J., Najjaran, H. Global tracking control of quadrotor based on adaptive dynamic surface control. Int. J. Dynam. Control 9, 240–256 (2021). https://doi.org/10.1007/s40435-020-00634-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40435-020-00634-x

Keywords

Search

Navigation