Identification of a quadcopter autopilot system via Box–Jenkins structure


This paper presents a method to precisely model a four rotor unmanned aerial vehicle, widely known as quadcopter autopilot system. Common system identification methods limit quadcopter models into first or second order systems, and do not count for noise characteristics. This leads to poor prediction accuracy of its longitudinal and lateral motion dynamics that ultimately affects the aircraft stabilization during flight and landing. To improve the quality of the estimated models, we utilized a statistically suitable discrete-time linear Box–Jenkins structure to model the plant and noise characteristics of the horizontal subsystems of a quadcopter autopilot system. The models were estimated using flight data acquired when the system were provided with pseudo-random binary sequence input. In this proposed method, by employing the prediction error method and least squares approach, the aircraft dynamics could be modeled up until the fifth order. The normalized root mean square fitness value showed that the predicted model output matches the experimental flight data by 94.72% in the one-step-ahead prediction test, and 84.52% in the infinite-step-ahead prediction test. These prediction results demonstrated an improvement of 52.8% when compared with a first and second order model structures proposed in previous works for the same quadcopter model. The output from this research works confirmed the effectiveness of the proposed method to adequately capture the autopilot dynamics and accurately predict the quadcopter outputs. These would greatly assist in designing robust flight controllers for the autopilot system.

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  1. 1.

    Yang H, Lee Y, Jeon SY, Lee D (2017) Multi-rotor drone tutorial: systems, mechanics, control and state estimation. Intell Serv Robot 10(2):79–93

    Article  Google Scholar 

  2. 2.

    Ebeid E, Skriver M, Terkildsen KH, Jensen K, Schultz UP (2018) A survey of open-source UAV flight controllers and flight simulators. Microprocess Microsyst 61:11–20

    Article  Google Scholar 

  3. 3.

    Benkhoud K, Bouallègue S (2018) Dynamics modeling and advanced metaheuristics based LQG controller design for a Quad Tilt Wing UAV. Int J Dyn Control 6(2):630–651

    MathSciNet  Article  Google Scholar 

  4. 4.

    Shraim H, Awada A, Youness R (2018) A survey on quadrotors: configurations, modeling and identification, control, collision avoidance, fault diagnosis and tolerant control. IEEE Aerosp Electron Syst Mag 33(7):14–33

    Article  Google Scholar 

  5. 5.

    Nadda S, Swarup A (2018) Decoupled control design for robust performance of quadrotor. Int J Dyn Control 6(3):1367–1375

    MathSciNet  Article  Google Scholar 

  6. 6.

    Nascimento TP, Saska M (2019) Position and attitude control of multi-rotor aerial vehicles: a survey. Annu Rev Control 48:129–146

    MathSciNet  Article  Google Scholar 

  7. 7.

    Cai G, Taha T, Dias J, Seneviratne L (2017) A framework of frequency-domain flight dynamics modeling for multi-rotor aerial vehicles. Proc Inst Mech Eng G J Aerosp Engi 231(1):30–46

    Article  Google Scholar 

  8. 8.

    Zhang X, Xian B, Zhao B, Zhang Y (2015) Autonomous flight control of a nano quadrotor helicopter in a GPS-denied environment using on-board vision. IEEE Trans Ind Electron 62(10):6392–6403

    Article  Google Scholar 

  9. 9.

    Wei W, Tischler MB, Cohen K (2017) System identification and controller optimization of a quadrotor unmanned aerial vehicle in hover. J Am Helicopter Soc 62(4):1–9

    Article  Google Scholar 

  10. 10.

    Guo M, Gu D, Su Y (2017) System identification of the quadrotor with inner loop stabilisation system. Int J Model Identif Control 28(3):245–255

    Article  Google Scholar 

  11. 11.

    Alabsi MI, Fields TD (2019) Real-time closed-loop system identification of a quadcopter. J Aircr 56(1):324–335

    Article  Google Scholar 

  12. 12.

    Bergamasco M, Lovera M (2014) Identification of linear models for the dynamics of a hovering quadrotor. IEEE Trans Control Syst Technol 22(5):1696–1707

    Article  Google Scholar 

  13. 13.

    Alkowatly MT, Becerra VM, Holderbaum W (2015) Body-centric modelling, identification, and acceleration tracking control of a quadrotor UAV. Int J Model Identif Control 24(1):29–41

    Article  Google Scholar 

  14. 14.

    Lei W, Li C (2017) On-line aerodynamic identification of quadrotor and its application to tracking control. IET Control Theory Appl 11(17):3097–3106

    MathSciNet  Article  Google Scholar 

  15. 15.

    Sa I, Kamel M, Khanna R, Popović M, Nieto J, Siegwart R (2018) Dynamic system identification, and control for a cost-effective and open-source multi-rotor MAV. In: Hutter M, Siegwart R (eds) Field and service robotics. Springer proceedings in advanced robotics, vol 5. Springer, Cham, pp 605–620

  16. 16.

    Sun S, de Visser CC, Chu Q (2019) Quadrotor gray-box model identification from high-speed flight data. J Aircr 56(2):645–661

    Article  Google Scholar 

  17. 17.

    Zhang X, Li X, Wang K, Lu Y (2014) A survey of modelling and identification of quadrotor robot. Abstr Appl Anal 2014:1–16

    MATH  Google Scholar 

  18. 18.

    Hoffer NV, Coopmans C, Jensen AM, Chen Y (2014) A survey and categorization of small low-cost unmanned aerial vehicle system identification. J Intell Robot Syst 74(1–2):129–145

    Article  Google Scholar 

  19. 19.

    Chovancová A, Fico T, Chovanec E, Hubinský P (2014) Mathematical modelling and parameter identification of quadrotor (a survey). Procedia Eng 96:172–181

    Article  Google Scholar 

  20. 20.

    Krajník T, Vonásek V,Fišer D, Faigl J (2011) AR-drone as a platform for robotic research and education. In: Obdržálek D, Gottscheber A(eds) Research and education in robotics—EUROBOT 2011 (EUROBOT2011). Communications in computer and information science, vol 161. Springer, Berlin, pp 172–186

  21. 21.

    Števek J, Fikar M (2016) Teaching aids for laboratory experiments with AR.Drone2 Quadrotor. IFAC-PapersOnLine 49(6):236–241

    Article  Google Scholar 

  22. 22.

    Santana LV, Brandão AS, Sarcinelli-Filho M (2016) Navigation and cooperative control using the AR.Drone Quadrotor. J Intell Robot Syst Theory Appl 84(1–4):327–350

    Article  Google Scholar 

  23. 23.

    Santiaguillo-Salinas J, Rosaldo-Serrano M, Aranda-Bricaire E (2017) Observer-based time-varying backstepping control for Parrot’s AR.Drone 2.0. IFAC-PapersOnLine 50(1):10305–10310

    Article  Google Scholar 

  24. 24.

    Mac TT, Copot C, Keyser RD, Ionescu CM (2018) The development of an autonomous navigation system with optimal control of an UAV in partly unknown indoor environment. Mechatronics 49:187–196

    Article  Google Scholar 

  25. 25.

    Rosaldo-Serrano M, Aranda-Bricaire E (2018) Trajectory tracking for a commercial quadrotor via time-varying backstepping. IFAC-PapersOnLine 51(13):532–536

    Article  Google Scholar 

  26. 26.

    Tangirala AK (2014) Principles of system identification: theory and practice, 1st edn. CRC Press, Boca Raton

    Google Scholar 

  27. 27.

    Ljung L (1999) System identification: theory for the user. Prentice Hall, Englewood Cliffs

    MATH  Google Scholar 

  28. 28.

    Isermann R, Münchhof M (2011) Identification of dynamic systems: an introduction with applications, 1st edn. Springer, Berlin

    Book  Google Scholar 

  29. 29.

    Ljung L, Singh R, Chen T (2015) Regularization features in the system identification toolbox. IFAC-PapersOnLine 48(28):745–750

    Article  Google Scholar 

  30. 30.

    Keesman KJ (2011) System identification, an introduction, advanced textbooks in control and signal processing, 1st edn. Springer, London

    Google Scholar 

  31. 31.

    Tischler MB, Remple RK (2012) Aircraft and rotorcraft system identification, 2nd edn. American Institute of Aeronautics and Astronautics Inc, Washington, DC

    Book  Google Scholar 

  32. 32.

    Panizza P, Riccardi F, Lovera M (2015) Black-box and grey-box identification of the attitude dynamics for a variable-pitch quadrotor. IFAC-PapersOnLine 48(9):61–66

    Article  Google Scholar 

  33. 33.

    Hernandez A, Murcia H, Copot C, De Keyser R (2015) Towards the development of a smart flying sensor: illustration in the field of precision agriculture. Sensors 15(7):16688–16709

    Article  Google Scholar 

  34. 34.

    Pintelon R, Schoukens J (2012) System identification: a frequency domain approach, 2nd edn. Wiley, Hoboken

    Book  Google Scholar 

  35. 35.

    Beisbart C, Saam NJ (eds) (2019) Computer simulation validation. Simulation foundations, methods and applications. Springer, Cham

    MATH  Google Scholar 

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Correspondence to Noor Hazrin Hany Mohamad Hanif.

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Bnhamdoon, O.A.A., Mohamad Hanif, N.H.H. & Akmeliawati, R. Identification of a quadcopter autopilot system via Box–Jenkins structure. Int. J. Dynam. Control 8, 835–850 (2020).

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  • Prediction error method (PEM)
  • Auto-regressive (AR) system
  • Box–Jenkins (BJ) model
  • Quadcopter
  • Autopilot system