Skip to main content
SpringerLink
Log in

Mu-based trajectory tracking control for a quad-rotor UAV

  • Research Article
  • Published:
Control Theory and Technology Aims and scope Submit manuscript

Abstract

In this paper, the design and application of a robust mu-synthesis-based controller for quad-rotor trajectory tracking are presented. The proposed design approach guarantees robust performance over a weakly nonlinear range of operation of the quad-rotor, which is a practical range that suits various applications. The controller considers different structured and unstructured uncertainties, such as unmodeled dynamics and perturbation in the parameters. The controller also provides robustness against external disturbances such as wind gusts and wind turbulence. The proposed controller is fixed and linear; therefore, it has a very low computational cost. Moreover, the controller meets all design specifications without tuning. To validate this control strategy, the proposed approach is compared to a linear quadratic regulator (LQR) controller using a high-fidelity quad-rotor simulation environment. In addition, the experimental results presented show the validity of the proposed control strategy.

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
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27
Fig. 28
Fig. 29
Fig. 30
Fig. 31

Similar content being viewed by others

References

  1. Weng, K. W. (2006). Design and control of a quad-rotor flying robot for aerial surveillance. In 2006 4th student conference on research and development (pp. 173–177). IEEE.

  2. Máthé, K., Buşoniu, L., Barabás, L., Iuga, C.-I., Miclea, L., & Braband, J. (2016). Vision-based control of a quadrotor for an object inspection scenario. In 2016 International conference on unmanned aircraft systems (ICUAS) (pp. 849–857). IEEE.

  3. Silvagni, M., Tonoli, A., Zenerino, E., & Chiaberge, M. (2017). Multipurpose UAV for search and rescue operations in mountain avalanche events. Geomatics, Natural Hazards and Risk, 8(1), 18–33.

    Article  Google Scholar 

  4. Valente, J., Sanz, D., Del Cerro, J., Barrientos, A., & de Frutos, M. Á. (2013). Near-optimal coverage trajectories for image mosaicing using a mini quad-rotor over irregular-shaped fields. Precision agriculture, 14(1), 115–132.

    Article  Google Scholar 

  5. Flodell, A., & Christensson, C. (2016). Wildlife surveillance using a UAV and thermal imagery. Master’s thesis. Linköping, Sweden: Linköping University.

  6. Alshbatat, A. I. N. (2018). Fire extinguishing system for high-rise buildings and rugged mountainous terrains utilizing quadrotor unmanned aerial vehicle. International Journal of Image, Graphics & Signal Processing, 10(1), 23.

    Article  Google Scholar 

  7. Ravankar, A.A., Ravankar, A., Kobayashi, Y., & Emaru, T. (2018). Autonomous mapping and exploration with unmanned aerial vehicles using low cost sensors. In Multidisciplinary digital publishing institute proceedings (pp. 44).

  8. Zulu, A., & John, S. (2016). A review of control algorithms for autonomous quadrotors. arXiv:1602.02622.

  9. Han, B., Zhou, Y., Deveerasetty, K. K., & Hu, C. (2018). A review of control algorithms for quadrotor. In 2018 IEEE international conference on information and automation (ICIA) (pp. 951–956). IEEE.

  10. Bouabdallah, S., Noth, A., & Siegwart, R. (2004). 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) (pp. 2451–2456). IEEE.

  11. Martins, L., Cardeira, C., & Oliveira, P. (2019). Linear quadratic regulator for trajectory tracking of a quadrotor. IFAC-PapersOnLine, 52(12), 176–181. https://doi.org/10.1016/j.ifacol.2019.11.195

    Article  Google Scholar 

  12. Fossen, T., & Strand, J. (1999). Tutorial on nonlinear backstepping: Applications to ship control. Modeling, Identification and Control: A Norwegian Research Bulletin, 20(2), 83–135.

    Article  MathSciNet  Google Scholar 

  13. Aboudonia, A., El-Badawy, A., & Rashad, R. (2017). Active anti-disturbance control of a quadrotor unmanned aerial vehicle using the command-filtering backstepping approach. Nonlinear Dynamics, 90(1), 581–597.

    Article  MATH  Google Scholar 

  14. Zheng, E.-H., Xiong, J.-J., & Luo, J.-L. (2014). Second order sliding mode control for a quadrotor UAV. ISA Transactions, 53(4), 1350–1356.

    Article  Google Scholar 

  15. Lee, K., Kim, S., Kwak, S., & You, K. (2021). Quadrotor stabilization and tracking using nonlinear surface sliding mode control and observer. Applied Sciences, 11(4), 1417.

    Article  Google Scholar 

  16. Eskandarpour, A., & Sharf, I. (2020). A constrained error-based MPC for path following of quadrotor with stability analysis. Nonlinear Dynamics, 99(2), 899–918.

    Article  MATH  Google Scholar 

  17. Islam, M., Okasha, M., & Sulaeman, E. (2019). A model predictive control (MPC) approach on unit quaternion orientation based quadrotor for trajectory tracking. International Journal of Control, Automation and Systems, 17(11), 2819–2832.

    Article  Google Scholar 

  18. Skogestad, S., & Postlethwaite, I. (2007). Multivariable feedback control: Analysis and design (Vol. 2). Wiley.

    MATH  Google Scholar 

  19. Hamza, A., Mohamed, A. H., & El-Badawy, A. (2022). Robust H-infinity control for a quadrotor UAV. In AIAA SCITECH 2022 forum (pp. 2033).

  20. Pirat, C., Ankersen, F., Walker, R., & Gass, V. (2019). H infinity and mu-synthesis for nanosatellites rendezvous and docking. IEEE Transactions on Control Systems Technology, 28(3), 1050–1057.

    Article  Google Scholar 

  21. Ravikumar, N., & Saraswathi, G. (2020). Towards robust controller design using mu-synthesis approach for speed regulation of an uncertain wind turbine. Electrical Engineering, 102(2), 515–527.

    Article  Google Scholar 

  22. Liu, J., & Zhou, K. (2018). Active vibration control of a dynamic hysteresis system using mu-synthesis. IEEE Access, 6, 76831–76837.

    Article  Google Scholar 

  23. Kürkçü, B., & Kasnakoğlu, C. (2018). Robust temperature control of a thermoelectric cooler via mu-synthesis. Journal of Electronic Materials, 47(8), 4421–4429.

    Article  Google Scholar 

  24. Chen, M., & Huzmezan, M. (2003). A combined MPBC/2DOF H-infinity controller for a quadrotor UAV. In Proceedings of the conference on AIAA guidance, navigation and control (pp. 11–14). Austin, Texas, USA.

  25. Mokheari, A., Benallegue, A., & Daachi, B. (2005). Robust feedback linearization and GH-infinity controller for a quadrotor unmanned aerial vehicle. In Proceedings of the 2005 IEEE/RSJ international conference on intelligent robots and systems (pp. 1198–1203). Edmonton, AB, Canada.

  26. Rich, M., Elia, N., & Jones, P. (2013). Design and implementation of an H-infinity controller for a quadrotor helicopter. In 21st Mediterranean conference on control and automation (pp. 1189–1198). IEEE.

  27. Bouabdallah, S. (2007). Design and control of quadrotors with application to autonomous flying. Technical report.

  28. Carrillo, L. R. G., López, A. E. D., Lozano, R., & Pégard, C. (2013). Modeling the quad-rotor mini-rotorcraft. In M. J. Grimble, M.A. Johnson (Eds.), Quad rotorcraft control (pp. 23–34). Springer.

  29. Zerz, E. (1999). LFT representations of parametrized polynomial systems. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 46(3), 410–416.

    Article  MathSciNet  MATH  Google Scholar 

  30. Safonov, M. G. (1987). Imaginary-axis zeros in multivariable h-infinity-optimal control. In R. F. Curtain (Eds.), Modelling, robustness and sensitivity reduction in control systems (pp. 71–81). Springer.

  31. Packard, A., Doyle, J., & Balas, G. (1993). Linear, multivariable robust control with a mu perspective. Journal of Dynamic Systems, Measurement, and Control, 115(2B), 426–438. https://doi.org/10.1115/1.2899083

    Article  MATH  Google Scholar 

  32. Zhou, K., & Doyle, J. C. (1998). Essentials of robust control (Vol. 104). Prentice Hall.

    MATH  Google Scholar 

  33. Varga, A. (1991). Balancing free square-root algorithm for computing singular perturbation approximations. In: Proceedings of the 30th IEEE conference on decision and control (pp. 1062–10652). IEEE. https://doi.org/10.1109/CDC.1991.261486

  34. Moorhouse, D. & Woodcock, R. (1980). US military specification MIL-F-8785c. US Department of Defense.

  35. Aboudonia, A., El-Badawy, A., & Rashad, R. (2016). Disturbance observer-based feedback linearization control of an unmanned quadrotor helicopter. Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, 230(9), 877–891.

    MATH  Google Scholar 

  36. Christian, A., & Lawrence, J. (2016). Initial development of a quadcopter simulation environment for auralization. In American Helicopter Society Annual Forum. West Palm Beach, FL, USA.

  37. Ogata, K. (2010). Modern control engineering (Vol. 5). Prentice Hall.

    MATH  Google Scholar 

  38. Bryson, A. (1975). Applied optimal control: optimization, estimation, and control (1st ed.). New York: Taylor & Francis.

    Google Scholar 

  39. Motion capture systems. https://optitrack.com/

  40. Koken, M. (2017). The experimental determination of the moment of inertia of a model airplane. Williams Honors College, Honors Research Projects. https://ideaexchange.uakron.edu/honors_research_projects/585

Download references

Author information

Authors and Affiliations

  1. Mechatronics Engineering Department, German University in Cairo, 5th Settlement, New Cairo, Cairo, 11835, Egypt

    Abdallah Hossam & Ayman El-Badawy

Authors
  1. Abdallah Hossam
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ayman El-Badawy
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ayman El-Badawy.

Rights and permissions

Springer Nature or its licensor 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

Hossam, A., El-Badawy, A. Mu-based trajectory tracking control for a quad-rotor UAV. Control Theory Technol. 20, 536–554 (2022). https://doi.org/10.1007/s11768-022-00114-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11768-022-00114-x

Keywords

Search

Navigation