Skip to main content
SpringerLink
Log in

Robust Control of Quadrotor using Uncertainty and Disturbance Estimation

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

Abstract

In this paper, a robust position and attitude tracking control problem of a quadrotor subject to system nonlinearities, input coupling, aerodynamic uncertainties and external wind disturbances is investigated. An uncertainty and disturbance estimator (UDE) based robustified nonlinear dynamic inversion (NDI) control scheme is proposed for the purpose. The UDE technique robustifies the NDI based controller by providing estimate of the lumped or total disturbance thereby enabling rejection of the same. The effectiveness and benefits of the proposed scheme are confirmed through six–DOF simulations considering nonlinear quadrotor dynamics under ideal as well as perturbed flight conditions. Further, the efficacy and superiority of the proposed control scheme are validated through Monte–Carlo simulations and experimental validation on Quanser’s 3–DOF Hover setup.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  1. Hassanalian, M., Abdelkefi, A.: Classifications, applications, design challenges of drones: A review. Progress in Aerospace Sciences, pp. 99–131 (2017)

  2. Burggräf, P., Martínez, A.R.P., Roth, H., Wagner, J.: Quadrotors in factory applications: design and implementation of the quadrotor’s P–PID cascade control system. SN Applied Sciences 1, 722 (2019)

    Article  Google Scholar 

  3. Shastry, A.K., Bhargavapuri, M.T., Kothari, M., Sahoo, S.R.: Quaternion based adaptive control for package delivery using variable-pitch quadrotors. In: 2018 Indian Control Conference (ICC), pp 340–345 (2018)

  4. Mogili, U. R., Deepak, B.: Review on application of drone systems in precision agriculture. Procedia Computer Science 133, 502–509 (2018)

    Article  Google Scholar 

  5. Ahmed, A., El–Badawy, A., Rashad, R.: Disturbance observer–based feedback linearization control of an unmanned quadrotor helicopter. Proceedings of the Institution of Mechanical Engineers 230, 877–891 (2016)

    Google Scholar 

  6. Li, J., Li, Y.: Dynamic analysis and PID control for a quadrotor. In: 2011 IEEE International Conference on Mechatronics and Automation, pp 573–578 (2011)

  7. Bouabdallah, S., Noth, A., Siegwart, R.: PID vs LQ control techniques applied to an indoor micro quadrotor. Proceedings of 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems 3, 2451–2456 (2004)

    Google Scholar 

  8. Reyes–Valeria, E., Enriquez–Caldera, R., Camacho–Lara, S., Guichard, J.: LQR control for a quadrotor using unit quaternions: Modeling and simulation. CONIELECOMP 2013, 23rd International Conference on Electronics, Communications and Computing, pp. 172–178 (2013)

  9. Cowling, I. D., Yakimenko, O. A., Whidborne, J. F., Cooke, A. K.: Direct method based control system for an autonomous quadrotor. J. Intell. Robot. Syst. 60, 285–316 (2010)

    Article  MATH  Google Scholar 

  10. Mian, A. A., Daobo, W.: Modeling and backstepping–based nonlinear control strategy for a 6 DOF quadrotor helicopter. Chin. J. Aeronaut. 21, 261–268 (2008)

    Article  Google Scholar 

  11. Madani, T., Benallegue, A.: Backstepping control for a quadrotor helicopter. 2006 IEEE/RSJ International Conference on Intelligent Robots and Systems, pp. 3255–3260 (2006)

  12. Madani, T., Benallegue, A.: Adaptive control via backstepping technique and neural networks of a quadrotor helicopter. IFAC Proceedings Volumes 41, 6513–6518 (2008)

    Article  Google Scholar 

  13. Bouadi, H., Cunha, S. S., Drouin, A., Mora-Camino, F.: Adaptive sliding mode control for quadrotor attitude stabilization and altitude tracking. 2011 IEEE 12th International Symposium on Computational Intelligence and Informatics (CINTI), pp 449–455 (2011)

  14. Sun, L., Zuo, Z.: Nonlinear adaptive trajectory tracking control for a quad–rotor with parametric uncertainty. Proceedings of the institution of mechanical engineers, Part G: Journal of Aerospace Engineering 229, 1709–1721 (2015)

    Article  Google Scholar 

  15. Bouadi, H., Camino, F. M.: Modeling and adaptive flight control for quadrotor trajectory tracking. Journal of Aircraft 55, 666, 681 (2018)

    Article  Google Scholar 

  16. Bouadi, H., Bouchoucha, M., Tadjine, M.: Sliding mode control based on backstepping approach for an UAV type–quadrotor. World Acad Sci, Eng. Technol. 26, 22–27 (2007)

    Google Scholar 

  17. Bouadi, H., Mora–Camino, F.: Direct adaptive backstepping flight control for quadcopter trajectory tracking. 2018 IEEE/AIAA 37th Digital Avionics Systems Conference (DASC), pp 1–8 (2018)

  18. Santos, M. C. P., Rosales, C. D., Sarapura, J. A., Sarcinelli–Filho, M., Carelli, R.: An adaptive dynamic controller for quadrotor to perform trajectory tracking tasks. J. Intell. Robot. Sys. 93, 5–16 (2019)

    Article  Google Scholar 

  19. Tamayo, A. J. M., Ríos, C.A.V., Zannatha, J.M.I., Soto, S.M.O.: Quadrotor input–output linearization and cascade control. IFAC–PapersOnLine 51, 437–442 (2018)

    Article  Google Scholar 

  20. Lee, K., Back, J., Choy, I.: Nonlinear disturbance observer based robust attitude tracking controller for quadrotor UAVs. Int J Control Autom Syst 12, 1266–1275 (2014)

    Article  Google Scholar 

  21. Shao, X., Liu, J., Wang, H.: Robust back–stepping output feedback trajectory tracking for quadrotors via extended state observer and sigmoid tracking differentiator. Mech. Syst. Signal Process. 104, 631–647 (2018)

    Article  Google Scholar 

  22. 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, 2700–2719 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  23. Shao, X., Wang, L., Li, J., Liu, J.: High–order ESO based output feedback dynamic surface control for quadrotors under position constraints and uncertainties. Aerosp. Sci. Technol. 89, 288–298 (2019)

    Article  Google Scholar 

  24. Fethalla, N., Saad, M., Michalska, H., Ghommam, J.: Robust observer–based dynamic sliding mode controller for a quadrotor UAV. IEEE Access 6, 45,846–45,859 (2018)

    Article  Google Scholar 

  25. Wang, X., Shirinzadeh, B., Ang, M. H.: Nonlinear double–integral observer and application to quadrotor aircraft. IEEE Trans. Ind. Electron. 62, 1189–1200 (2014)

    Article  Google Scholar 

  26. Islam, S., Liu, P. X., El Saddik, A.: Robust control of four–rotor unmanned aerial vehicle with disturbance uncertainty. IEEE Trans. Ind. Electron. 62, 1563–1571 (2014)

    Article  Google Scholar 

  27. Zhao, B., Xian, B., Zhang, Y., Zhang, X.: Nonlinear robust sliding mode control of a quadrotor unmanned aerial vehicle based on immersion and invariance method. Int. J. Robust Nonlinear Control 25, 3714–3731 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  28. Gai, W., Liu, J., Qu, C., Zhang, J.: Trajectory tracking control for a quadrotor UAV via extended state observer. Systems Science & Control Engineering 6, 126–135 (2018)

    Article  Google Scholar 

  29. Besnard, L., Shtessel, Y. B., Landrum, B.: Quadrotor vehicle control via sliding mode controller driven by sliding mode disturbance observer. J. Franklin Inst. 349, 658–684 (2012)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  31. Zhang, J., Gu, D., Ren, Z., Wen, B.: Robust trajectory tracking controller for quadrotor helicopter based on a novel composite control scheme. Aerosp. Sci. Technol. 85, 199–215 (2019)

    Article  Google Scholar 

  32. Dai, J., Lu, Q., Ren, B., Zhong, Q. C.: Robust attitude tracking control for a quadrotor based on the uncertainty and disturbance estimator. ASME 2015 Dynamic Systems and Control Conference (2015)

  33. Sanz, R., Garcia, P., Zhong, Q. C., Albertos, P.: Robust control of quadrotors based on an uncertainty and disturbance estimator. J. Dyn. Sys. Measurement Control 138, 071006 (2016)

    Article  Google Scholar 

  34. Sanz, R., Garcia, P., Zhong, Q. C., Albertos, P.: Predictor–based control of a class of time–delay systems and its application to quadrotors. IEEE Trans. Ind. Electron. 64, 459–469 (2016)

    Article  Google Scholar 

  35. Lu, Q., Ren, B., Parameswaran, S., Zhong, Q. C.: Uncertainty and disturbance estimator–based robust trajectory tracking control for a quadrotor in a global positioning system–denied environment. J. Dyn. Syst. Meas. Control. 140 (2018)

  36. Castañeda, H., Gordillo, J. L.: Spatial Modeling and Robust Flight Control Based on Adaptive Sliding Mode Approach for a Quadrotor MAV. J. Intell. Robot. Sys. 93, 101–111 (2019)

    Article  Google Scholar 

  37. 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. Sys. 83, 315–333 (2016)

    Article  Google Scholar 

  38. Basri, M. A. M., Husain, A. R., Danapalasingam, K. A.: Enhanced backstepping controller design with application to autonomous quadrotor unmanned aerial vehicle. J. Intell. Robot. Sys. 79, 295–321 (2015)

    Article  Google Scholar 

  39. Ramirez–Rodriguez, H., Parra–Vega, V., Sanchez–Orta, A., Garcia–Salazar, O.: Robust backstepping control based on integral sliding modes for tracking of quadrotors. J. Intell. Robot. Sys. 73, 51–66 (2014)

    Article  Google Scholar 

  40. Das, A., Lewis, F., Subbarao, K.: Backstepping approach for controlling a quadrotor using lagrange form dynamics. J. Intell. Robot. Sys. 56, 127–151 (2009)

    Article  MATH  Google Scholar 

  41. Bouzid, Y., Zareb, M., Siguerdidjane, H., Guiatni, M.: Boosting a reference model–based controller using active disturbance rejection principle for 3D trajectory tracking of quadrotors: Experimental validation. J. Intell. Robot. Sys., pp. 1–18 (2020)

  42. López–Gutiérrez, R., Rodriguez–Mata, A. E., Salazar, S., González–Hernández, I., Lozano, R.: Robust quadrotor control: Attitude and altitude real–time results. J. Intell. Robot. Sys. 88, 299–312 (2017)

    Article  Google Scholar 

  43. Yacef, F., Bouhali, O., Hamerlain, M., Rizoug, N.: Observer–based adaptive fuzzy backstepping tracking control of quadrotor unmanned aerial vehicle powered by Li–ion battery. J. Intell. Robot. Sys. 84, 179–197 (2016)

    Article  Google Scholar 

  44. Liu, H., Bai, Y., Lu, G., Shi, Z., Zhong, Y.: Robust tracking control of a quadrotor helicopter. J. Intell. Robot. Sys. 75, 595–608 (2014)

    Article  Google Scholar 

  45. Slotine, J. J. E., Li, W., et al.: Applied Nonlinear Control. Prentice Hall, Englewood Cliffs (1991)

    MATH  Google Scholar 

  46. Zhong, Q. C., Rees, D.: Control of uncertain LTI systems based on an uncertainty and disturbance estimator. J. Dyn. Syst. Meas. Control. 126, 905–910 (2004)

    Article  Google Scholar 

  47. Talole, S. E., Phadke, S. B.: Model following sliding mode control based on uncertainty and disturbance estimator. J. Dyn. Syst. Meas. Control. 130, 034501 (2008)

    Article  Google Scholar 

  48. Phadke, S. B., Talole, S. E.: Sliding mode and inertial delay control based missile guidance. IEEE Trans. Aerosp. Electron. Syst. 48, 3331–3346 (2012)

    Article  Google Scholar 

  49. Dhadekar, D. D., Patre, B. M.: UDE–based decoupled full–order sliding mode control for a class of uncertain nonlinear MIMO systems. Nonlinear Dyn. 88, 263–276 (2017)

    Article  MATH  Google Scholar 

  50. Kodhanda, A., Kolhe, J. P., Zeru, T., Talole, S. E.: Robust aircraft control based on UDE theory. Proc. Inst. Mech. Eng., Part G: J. Aerosp. Eng. 231, 728–742 (2017)

    Article  Google Scholar 

  51. Chandar, T., Talole, S. E.: Improving the performance of UDE–based controller using a new filter design. Nonlinear Dyn. 77, 753–768 (2014)

    Article  Google Scholar 

  52. Hua, C. C., Wang, K., Chen, J. N., You, X.: Tracking differentiator and extended state observer–based nonsingular fast terminal sliding mode attitude control for a quadrotor. Nonlinear Dyn. 94, 343–354 (2018)

    Article  Google Scholar 

  53. Beard, R. W., McLain, T. W.: Small Unmanned Aircraft: Theory and Practice. Princeton University Press, Princeton (2012)

    Book  Google Scholar 

  54. Dhadekar, D. D., Talole, S. E.: Robust fault tolerant longitudinal aircraft control. IFAC–PapersOnLine 51, 604–609 (2018)

    Article  Google Scholar 

  55. Youcef–Toumi, K., Ito, O.: A Time Delay Controller for Systems with Unknown Dynamics. 1988 American Control Conference, pp. 904–913 (1988)

  56. Kolhe, J. P., Shaheed, M., Chandar, T., Talole, S. E.: Robust control of robot manipulators based on uncertainty and disturbance estimation. Int. J. Robust Nonlinear Control 23, 104–122 (2013)

    Article  MathSciNet  MATH  Google Scholar 

  57. Kodhanda, A., Ali, N., Sucheendran, M. M., Talole, S. E.: Robust control of nonlinear resonance in a clamped rectangular plate. J. Vib. Control. 24, 4176–4194 (2018)

    Article  MathSciNet  Google Scholar 

  58. Khalil, H. K., Grizzle, J.W.: Nonlinear Systems, vol. 3. Prentice Hall, Upper Saddle River (2002)

    Google Scholar 

  59. 3–DOF Hover User Manual (Quanser) (2013)

Download references

Funding

No funding was received to assist with the preparation of this manuscript.

Author information

Authors and Affiliations

  1. Department of Aerospace Engineering, Defence Institute of Advanced Technology, Pune, India

    Dinesh D. Dhadekar, Prithvi D. Sanghani & K. K. Mangrulkar

  2. Research and Development Establishment (Engineers), Pune, India

    S. E. Talole

Authors
  1. Dinesh D. Dhadekar
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Prithvi D. Sanghani
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. K. K. Mangrulkar
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. E. Talole
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Dinesh D. Dhadekar.

Ethics declarations

Competing interests

The authors declare that they have no competing interests.

Ethical approval

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

Additional information

Publisher’s Note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Dhadekar, D.D., Sanghani, P.D., Mangrulkar, K.K. et al. Robust Control of Quadrotor using Uncertainty and Disturbance Estimation. J Intell Robot Syst 101, 60 (2021). https://doi.org/10.1007/s10846-021-01325-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s10846-021-01325-1

Keywords

Search

Navigation