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Fuzzy Modelling Methodologies Based on OKID/ERA Algorithm Applied to Quadrotor Aerial Robots

  • Jorge  Sampaio Silveira JúniorEmail author
  • Edson Bruno Marques Costa
Chapter
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Part of the Studies in Computational Intelligence book series (SCI, volume 864)

Abstract

In this paper, we propose to use a state-space Takagi-Sugeno (TS) fuzzy model to tackle quadrotor aerial robots complexities, such as highly nonlinear dynamics, multivariable coupled input and output variables, parametric uncertainty, are naturally unstable and underactuated systems. To estimate the fuzzy model parameters automatically through input and output multivariable dataset, two fuzzy modelling methodologies based on Observer/Kalman Filter Identification (OKID) and Eigensystem Realization Algorithm (ERA) are proposed. In both methods, the fuzzy nonlinear sets of the antecedent space are obtained by a fuzzy clustering algorithm; in this paper we approach the Fuzzy C-Means algorithm. These two methods differ in the way to obtain the fuzzy Markov parameters: a method based on pulse-response histories and another through an Observer/Kalman filter. From the fuzzy Markov parameters, the Fuzzy ERA algorithm is used to estimate the discrete functions in state-space of each submodel. Results for identification of a quadrotor aerial robot, the Parrot AR.Drone 2.0, are presented, demonstrating the efficiency and applicability of these methodologies.

Keywords

Fuzzy Modelling Pulse response histories Observer/Kalman Filter Nonlinear systems Quadrotor aerial robots 

Notes

Acknowledgements

This work was financed by Fundação de Amparo à Pesquisa e ao Desenvolvimento Científico e Tecnológico do Maranhão (FAPEMA) under UNIVERSAL-01298/17 and TIAC-06615/16 projects and was supported by Instituto Federal de Educação, Ciência e Tecnologia do Maranhão (IFMA). Also, the authors would like to thank Prof. Luís Miguel Magalhães Torres and Prof. Selmo Eduardo Rodrigues Júnior for the important contributions in this work.

References

  1. 1.
    S. Gupte, P.I.T. Mohandas, J.M. Conrad, A survey of quadrotor unmanned aerial vehicles, in 2012 Proceedings of IEEE Southeastcon (IEEE, 2012), pp. 1–6Google Scholar
  2. 2.
    S.-J. Chung, A.A. Paranjape, P. Dames, S. Shen, V. Kumar, A survey on aerial swarm robotics. IEEE Trans. Robot. 34(4), 837–855 (2018)CrossRefGoogle Scholar
  3. 3.
    J.S. Silveira Júnior, E.B.M. Costa, L.M.M. Torres, Multivariable fuzzy identification of unmanned aerial vehicles, in XXII Congresso Brasileiro de Automática (CBA 2018) (João Pessoa, Brasil, 2018), pp. 1–8Google Scholar
  4. 4.
    J.S. Silveira Júnior, E.B.M. Costa, Data-driven fuzzy modelling methodologies for multivariable nonlinear systems, in IEEE International Conference on Intelligent Systems (IS’18) (Funchal, Portugal, 2018), pp. 1–7Google Scholar
  5. 5.
    Y.B. Dou, M. Xu, Nonlinear aerodynamics reduced-order model based on multi-input Volterra series, in Material and Manufacturing Technology IV, volume 748 of Advanced Materials Research (Trans Tech Publications, 2013), pp. 421–426Google Scholar
  6. 6.
    S. Solodusha, K. Suslov, D. Gerasimov, A new algorithm for construction of quadratic Volterra Model for a non-stationary dynamic system. IFAC-PapersOnLine 48(11), 982–987 (2015)CrossRefGoogle Scholar
  7. 7.
    Z. Wang, Z. Zhang, K. Zhou, Precision tracking control of piezoelectric actuator using a Hammerstein-based dynamic hysteresis model, in 2016 35th Chinese Control Conference (CCC) (2016), pp. 796–801Google Scholar
  8. 8.
    J. Kou, W. Zhang, M. Yin, Novel Wiener models with a time-delayed nonlinear block and their identification. Nonlinear Dyn. 85(4), 2389–2404 (2016)CrossRefGoogle Scholar
  9. 9.
    H.K. Sahoo, P.K. Dash, N.P. Rath, Narx model based nonlinear dynamic system identification using low complexity neural networks and robust H\(\infty \) filter. Appl. Soft Comput. 13(7), 3324–3334 (2013)CrossRefGoogle Scholar
  10. 10.
    H. Liu, X. Song, Nonlinear system identification based on NARX network, in 2015 10th Asian Control Conference (ASCC) (2015), pp. 1–6Google Scholar
  11. 11.
    T. Xiang, F. Jiang, Q. Hao, W. Cong, Adaptive flight control for quadrotor UAVs with dynamic inversion and neural networks, in 2016 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems (MFI) (2016), pp. 174–179Google Scholar
  12. 12.
    Q. Ma, S. Qin, T. Jin, Complex Zhang neural networks for complex-variable dynamic quadratic programming. Neurocomputing 330, 56–69 (2019)CrossRefGoogle Scholar
  13. 13.
    S. Zaidi, A. Kroll, NOE TS fuzzy modelling of nonlinear dynamic systems with uncertainties using symbolic interval-valued data. Appl. Soft Comput. 57, 353–362 (2017)CrossRefGoogle Scholar
  14. 14.
    M. Sun, J. Liu, H. Wang, X. Nian, H. Xiong, Robust fuzzy tracking control of a quad-rotor unmanned aerial vehicle based on sector linearization and interval matrix approaches. ISA Trans. 80, 336–349 (2018)CrossRefGoogle Scholar
  15. 15.
    E.B.M. Costa, G.L.O. Serra, Optimal recursive fuzzy model identification approach based on particle swarm optimization, in 2015 IEEE 24th International Symposium on Industrial Electronics (ISIE) (IEEE, 2015), pp. 100–105Google Scholar
  16. 16.
    G. Feng, A survey on analysis and design of model-based fuzzy control systems. IEEE Trans. Fuzzy syst. 14(5), 676–697 (2006)CrossRefGoogle Scholar
  17. 17.
    T. Takagi, M. Sugeno, Fuzzy identification of systems and its applications to modeling and control, in Readings in Fuzzy Sets for Intelligent Systems (Elsevier, 1993), pp. 387–403Google Scholar
  18. 18.
    E.B.M. Costa, G.L.O. Serra, Robust Takagi-Sugeno fuzzy control for systems with static nonlinearity and time-varying delay, in 2015 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (2015), pp. 1–8Google Scholar
  19. 19.
    F. Sun, N. Zhao, Universal approximation for takagi-sugeno fuzzy systems using dynamically constructive method-siso cases, in 2007 IEEE 22nd International Symposium on Intelligent Control (2007), pp. 150–155Google Scholar
  20. 20.
    K. Zeng, N.-Y. Zhang, W.-L. Xu, A comparative study on sufficient conditions for Takagi-Sugeno fuzzy systems as universal approximators. IEEE Trans. Fuzzy Syst. 8(6), 773–780 (2000)CrossRefGoogle Scholar
  21. 21.
    L.M.M. Torres, G.L.O. Serra, State-space recursive fuzzy modeling approach based on evolving data clustering. J. Control Autom. Electr. Syst. 29(4), 426–440 (2018)CrossRefGoogle Scholar
  22. 22.
    D.S. Pires, G.L.O. Serra, Fuzzy Kalman filter modeling based on evolving clustering of experimental data, in 2018 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE) (2018), pp. 1–6Google Scholar
  23. 23.
    P. Garcia-Aunon, M.S. Peñas, J.M.C. García, Parameter selection based on fuzzy logic to improve UAV path-following algorithms. J. Appl. Logic 24, 62–75 (2017)MathSciNetCrossRefGoogle Scholar
  24. 24.
    G. Serra, C. Bottura, An IV-QR algorithm for neuro-fuzzy multivariable online identification. IEEE Trans. Fuzzy Syst. 15(2), 200–210 (2007)CrossRefGoogle Scholar
  25. 25.
    R. Babuška, Fuzzy Modeling for Control. International Series in Intelligent Technologies (Kluwer Academic Publishers, 1998)Google Scholar
  26. 26.
    J. Bezdek, R. Erlich, W. Full, FCM: the fuzzy c-means clustering algorithm. Comput. Geosci. 10(2–3), 191–203 (1984)CrossRefGoogle Scholar
  27. 27.
    L.-X. Wang. A Course in Fuzzy Systems and Control (Prentice-Hall Press, 1999)Google Scholar
  28. 28.
    J.N. Juang, Applied System Identification (Prentice-Hall Inc., Upper Saddle River, 1994)zbMATHGoogle Scholar
  29. 29.
    J.N. Juang, M. Phan, L.G. Horta, R.W. Longman, Identification of observer/Kalman filter Markov parameters—theory and experiments. J. Guidance Control Dyn 16, 320–329 (1993)CrossRefGoogle Scholar
  30. 30.
    D. Sanabria, AR Drone Simulink Development-Kit V1.1 - File Exchange—MATLAB Central. Available at: http://bit.ly/AD2Toolbox (2014). Last accessed on 09 Jan. 2019
  31. 31.
    J.S. Silveira Júnior, ARDrone2Data. Available at: http://bit.ly/ARDrone2Data (2019). Last acessed on 23 Jan. 2019

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  • Jorge  Sampaio Silveira Júnior
    • 1
    Email author
  • Edson Bruno Marques Costa
    • 1
  1. 1.Instituto Federal de Educação Ciência e Tecnologia do MaranhãoImperatrizBrazil

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