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

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Intelligent Systems: Theory, Research and Innovation in Applications

Part of the book series: Studies in Computational Intelligence ((SCI,volume 864))

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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.

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Notes

  1. 1.

    In this context, roll and pitch are Euler angles (with yaw angle) that represent the rotational movements of an object around an axis in the cartesian coordinate system.

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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.

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Authors and Affiliations

  1. Instituto Federal de Educação Ciência e Tecnologia do Maranhão, Imperatriz, Maranhão, Brazil

    Jorge Sampaio Silveira Júnior & Edson Bruno Marques Costa

Authors
  1. Jorge Sampaio Silveira Júnior
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  2. Edson Bruno Marques Costa
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Corresponding author

Correspondence to Jorge Sampaio Silveira Júnior .

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Editors and Affiliations

  1. Department of Electrical Engineering and Computers, Faculdade de Ciências e Tecnologia, UNINOVA-CTS Centre of Technology and Systems, Universidade Nova de Lisboa, Caparica, Portugal

    Ricardo Jardim-Goncalves

  2. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Sofia, Bulgaria

    Vassil Sgurev

  3. University of Library Studies and Information Technologies, Sofia, Bulgaria

    Vladimir Jotsov

  4. Systems Research Institute, Polish Academy of Sciences, Warsaw, Poland

    Janusz Kacprzyk

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Sampaio Silveira Júnior, J., Marques Costa, E.B. (2020). Fuzzy Modelling Methodologies Based on OKID/ERA Algorithm Applied to Quadrotor Aerial Robots. In: Jardim-Goncalves, R., Sgurev, V., Jotsov, V., Kacprzyk, J. (eds) Intelligent Systems: Theory, Research and Innovation in Applications. Studies in Computational Intelligence, vol 864. Springer, Cham. https://doi.org/10.1007/978-3-030-38704-4_13

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