Skip to main content
SpringerLink
Log in

Stabilization of a quadrotor system using an optimal neural network controller

  • Technical Paper
  • Published:
Journal of the Brazilian Society of Mechanical Sciences and Engineering Aims and scope Submit manuscript

Abstract

This paper presents a new and practical neural network-based optimal control method for a quadrotor system. Due to the difficulty in obtaining the exact model of the quadrotor system and also to deal with its nonlinear characteristic in both simulation and practice, choosing an effective intelligent controller possessing less complexity can increase system stability. For this purpose, the kinematic relations and the 6–DOF dynamic model of the quadrotor are first extracted. Subsequently, a neural network control method is proposed as the main controller to overcome the system nonlinearities as well as the corresponding unstable dynamics. Accordingly, an enumerative learning method is used to optimize the neural network’s weights. At last, the performance of the proposed control method is evaluated and then compared to a PID control method using simulation and experiment. The outcomes of this paper clearly reveal that the optimal neural network controller has a good performance in achieving minimum error.

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

Similar content being viewed by others

Abbreviations

\(X\) :

Linear position along xe-axis with (m)

\(Y\) :

Linear position along ye-axis (m)

\(Z\) :

Linear position along ze-axis (m)

\(U\) :

Linear velocity along xe-axis (m/s)

\(V\) :

Linear velocity along ye-axis (m/s)

\(W\) :

Linear velocity along ze-axis (m/s)

\(P\) :

Angular velocity along xe-axis (rad/s)

\(Q\) :

Angular velocity along ye-axis (rad/s)

\(R\) :

Angular velocity along ze-axis (rad/s)

\(l\) :

Quadrotor arm length (m)

M :

Quadrotor mass (kg

c :

Torque constant (m)

\(I\) :

Inertia matrix (kg.m−2)

\(f\) :

Thrust force (N)

\(\eta\) :

Linear positions vector with respect to the earth frame

\(\xi\) :

Linear velocities vector with respect to the body frame

\(\varphi\) :

Roll angle (rad)

\(\theta\) :

Pitch angle (rad)

\(\psi\) :

Yaw angle (rad)

\(\lambda\) :

Euler angles vector

\(\Omega\) :

Angular velocities vector with respect to the body frame

References

  1. Bouadi H, Bouchoucha M, Tadjine M (2007) Sliding mode control based on backstepping approach for an UAV type-quadrotor. World Acad Sci, Eng Tech 1(2):39–44

    Google Scholar 

  2. Cabecinhas D, Cunha R, Silvestre C (2014) A nonlinear quadrotor trajectory tracking controller with disturbance rejection. Control Eng Pract 26:1–10. https://doi.org/10.1016/j.conengprac.2013.12.017

    Article  Google Scholar 

  3. Chovancová A et al (2016) Comparison of various quaternion-based control methods applied to quadrotor with disturbance observer and position estimator. Robot Auton Syst 79:87–98

    Article  Google Scholar 

  4. Davoodi E, Rezaei M (2014) Dynamic modeling, simulation and control of a quadrotor using mems sensors’ experimental data. Modares Mech Eng 14(3):175–184

    Google Scholar 

  5. Emran BJ, Al-Omari M, Abdel-Hafez MF, Jaradat MA (2014) A cascaded approach for quadrotor’s attitude estimation. Procedia Technol 15:268–277. https://doi.org/10.1016/j.protcy.2014.09.080

    Article  Google Scholar 

  6. Gonzalez A, Garcia P, Albertos P, Castillo P, Lozano R (2012) Robustness of a discrete-time predictor-based controller for time-varying measurement delay. Control Eng Pract 20(2):102–110. https://doi.org/10.1016/j.conengprac.2011.09.001

    Article  Google Scholar 

  7. Guo K et al (2020) Multiple observers based anti-disturbance control for a quadrotor UAV against payload and wind disturbances. Control Eng Pract 102:104560

    Article  Google Scholar 

  8. Hatamleh KS, Al-Shabi M, Al-Ghasem A, Asad A (2015) Unmanned aerial vehicles parameter estimation using artificial neural networks and iterative bi-section shooting method. Appl Soft Comput 36(3):457–467. https://doi.org/10.1016/j.asoc.2015.06.031

    Article  Google Scholar 

  9. Lee D, Kim HJ, Sastry SH (2009) Feedback linearization vs adaptive sliding mode control for a quadrotor helicopter. Int J Control, Automat Sys 7(3):419–428

    Article  Google Scholar 

  10. Li Sh, Wang Y, Tan J, Zheng Y (2016) Adaptive RBFNNs/Integral sliding mode control for a quadrotor aircraft. Neurocomputing 216:126–134. https://doi.org/10.1016/j.neucom.2016.07.033

    Article  Google Scholar 

  11. Liu C, Xhen W, Andrews J (2012) Tracking control of small-scale helicopter using explicit MPC augmented with disturbance observers. Control Eng Pract 20(3):258–268. https://doi.org/10.1016/j.conengprac.2011.10.015

    Article  Google Scholar 

  12. Liu H, Li D, Zuo Z, Zhong Y (2017) Robust attitude control for quadrotors with input time delays. Control Eng Pract 58:142–149. https://doi.org/10.1016/j.conengprac.2016.10.006

    Article  Google Scholar 

  13. Luque L, Castillo B, Loukianov AG (2012) Robust block second order sliding mode control for a quadrotor. J Franklin Inst 349(2):719–739. https://doi.org/10.1016/j.jfranklin.2011.10.017

    Article  MathSciNet  MATH  Google Scholar 

  14. Masaud K, Macnab C (2014) Preventing bursting in adaptive control using an introspective neural network algorithm. Neurocomputing 136:300–314. https://doi.org/10.1016/j.neucom.2014.01.002

    Article  Google Scholar 

  15. Mohebbi A, Achiche S, Baron L (2019) Integrated and concurrent detailed design of a mechatronic quadrotor system using a fuzzy-based particle swarm optimization. Eng Appl Artif Intell 82:192–206. https://doi.org/10.1016/j.engappai.2019.03.025

    Article  Google Scholar 

  16. Noormohammadi-Asl A et al (2020) System identification and H∞-based control of quadrotor attitude. Mech Sys Signal Process 135:106358

    Article  Google Scholar 

  17. Oner KT, Cetinsoy E, Sirimoglu E, Hancer C, Ayken T, Unel M, (2009) LQR and SMC stabilization of a new unmanned aerial vehicle. World Acad Sci, Eng Tech, 3(10):1190–1195. https://scholar.waset.org/1999.8/2009

  18. Pitarch JL, Sala A (2014) Multicriteria fuzzy-polynomial observer design for a 3DoF nonlinear electromechanical platform. Eng Appl Artif Intell 30:96–106. https://doi.org/10.1016/j.engappai.2013.11.006

    Article  Google Scholar 

  19. Palm W (2014) System dynamics, 3ed edn. Mc GraHill, NY

    Google Scholar 

  20. Sarabakha A, Imanberdiyev N, Kayacan E, Ahmadie M, Hagras H (2017) Novel levenberg–marquardt based learning algorithm for unmanned aerial vehicles. Inf Sci 417:361–380. https://doi.org/10.1016/j.ins.2017.07.020

    Article  MATH  Google Scholar 

  21. Shirzadeh M, Jabbari H, Amirkhani A, Jalali AA (2017) Vision-based control of a quadrotor utilizing artificial neural networks for tracking of moving targets. Eng Appl Artif Intell 58:34–48. https://doi.org/10.1016/j.engappai.2016.10.016

    Article  Google Scholar 

  22. Tran H, Chiou J (2016) PSO-based algorithm applied to quadcopter micro air vehicle controller design. Micromachines 7(9):168–175. https://doi.org/10.3390/mi7090168

    Article  Google Scholar 

  23. Wu B, Han Sh, Xiao J, Hu X, Fan J (2016) Error compensation based on BP neural network for airborne laser ranging. Int J Light Electron Optics 127(8):4083–4088. https://doi.org/10.1016/j.ijleo.2016.01.066

    Article  Google Scholar 

  24. Xiong J, Zhang G (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 

  25. Yang Y, Yan Y (2016) Attitude regulation for unmanned quadrotors using adaptive fuzzy gain-scheduling sliding mode control. Aerosp Sci Technol 54:208–217. https://doi.org/10.1016/j.ast.2016.04.005

    Article  Google Scholar 

Download references

Acknowledgements

The authors wish to express their deep gratitude to the Shiraz University of Technology for providing research facilities and supports. A special thank is dedicated to Dr. T. Binazadeh from Electrical and Electronics Engineering Department at SUTech for her constructive comments and advices.

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, Shiraz University of Technology, Shiraz, Iran

    M. M. Farzaneh & A. R. Tavakolpour-Saleh

Authors
  1. M. M. Farzaneh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. R. Tavakolpour-Saleh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. R. Tavakolpour-Saleh.

Additional information

Technical Editor: Victor Juliano De Negri.

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

Farzaneh, M.M., Tavakolpour-Saleh, A.R. Stabilization of a quadrotor system using an optimal neural network controller. J Braz. Soc. Mech. Sci. Eng. 44, 26 (2022). https://doi.org/10.1007/s40430-021-03326-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40430-021-03326-5

Keywords

Search

Navigation