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

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


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.


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



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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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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