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Differential Game-based Formation Flight for Quadrotors

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Abstract

This paper focuses on a novel algorithm for the control of formation flight of a set of n-quadrotors based on the differential game approach. The mathematical model of n-quadrotors is presented using the Newton-Euler formulation considering the disturbances, and the formation flight scheme based on the game approach consists of one vehicle acting as a leader following a pre-designed trajectory meanwhile the others vehicles just follow the leader even in the presence of disturbances. A reduced dimension Riccati equation is solved in order to obtain the desired coordination. A numerical example is given in order to illustrate the effectiveness of the approach for the formation flight.

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Author information

Authors and Affiliations

  1. Faculty of Physics-Mathematics Sciences, Autonomous University of Nuevo Leon, San Nicolas de los Garza, NL, 66455, Mexico

    Manuel Jimenez-Lizarraga & Ricardo Chapa-Garcia

  2. Aeronautic Engineering Research and Innovation Center, Faculty of Mechanical and Electrical Engineering, Autonomous University of Nuevo Leon, Apodaca, NL, 66616, Mexico

    Octavio Garcia & Erik G. Rojo-Rodriguez

Authors
  1. Manuel Jimenez-Lizarraga
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  2. Octavio Garcia
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  3. Ricardo Chapa-Garcia
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  4. Erik G. Rojo-Rodriguez
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Corresponding author

Correspondence to Manuel Jimenez-Lizarraga.

Additional information

Recommended by Associate Editor Hongyi Li under the direction of Editor Yoshito Ohta. Manuel Jimenez-Lizarraga was supported by project 169734 of National Council of Science and Technology of Mexico (CONACYT).

Manuel Jimenez-Lizarraga received the B.Sc. degree in electrical engineering from Culiacan Institute of Technology, Sinaloa Mexico, and the M.S. and Ph.D. degrees in Automatic Control from CINVESTAV-IPN Mexico, in 1996, 2000, and 2006 respectively. He was postdoc fellow at the ECE Department of the Ohio State University, USA from 2008–2009. He is currently with the Faculty of Physical and Mathematical Sciences of Autonomous University of Nuevo Leon, Mexico. His research interests include differential games, robust, optimal and sliding mode control and applications.

Octavio Garcia obtained a B.Sc. degree in electronic engineering and the M.Sc. in electrical engineering from the Technological Institute of La Laguna, Torreon Coahuila Mexico, in 2000 and 2003 respectively. He obtained a Ph.D. in control systems from the University of Technology of Compiegne, France, in 2009. From January 2010 to December 2011, he held a post as a CNRS postdoctoral researcher in the laboratory LAFMIA UMI 3175 CNRS-CINVESTAV Mexico DF, Mexico. From January 2012 to December 2012, he was as visiting researcher in the Biomedical Engineering and Physics Division and the Laboratory of Non-inertial Robots and Man-machine Interfaces, CINVESTAV Monterrey. Since January 2013, he has been working in the Faculty of Mechanical and Electrical Engineering of the Autonomous University of Nuevo Leon, Monterrey Nuevo Leon Mexico. His research interests are in nonlinear control theory with applications in aerospace, robotics and mechanical systems, guidance, navigation and control of UAVs, digital signal processing and instrumentation.

Ricardo Chapa-Garcia received the B.Sc. degree in Mechatronics Engineering, Area of Automatization from the Technological University of Escobedo, Nuevo Leon, Mexico, in 2012, and currently he is studying a Ph.D. in Industrial Physics Engineering at the Faculty of Physics and Mathematics Science from the Autonomous University of Nuevo Leon, Mexico. His research interests include differential games, mini-UAVs, robotics and simulations.

Erik G. Rojo-Rodriguez obtained a B.Sc. degree in Mechatronics in the Faculty of Mechanical and Electrical Engineering of the Autonomous University of Nuevo León, Mexico, and the M.Sc. in aeronautical engineering from the same faculty in 2017. He participated as a research assistant in the Advanced Manufacturing Laboratory of the Research and Innovation Center of Aeronautical Engineering of the same university, developing general skills in the different areas of the aeronautical field. He is currently studying his PhD degree in, and his main field of research is the cooperation of multi-agent systems using different techniques of coordination and Non-linear control for Unmanned Aerial Vehicles.

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Jimenez-Lizarraga, M., Garcia, O., Chapa-Garcia, R. et al. Differential Game-based Formation Flight for Quadrotors. Int. J. Control Autom. Syst. 16, 1854–1865 (2018). https://doi.org/10.1007/s12555-017-0137-8

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  • DOI: https://doi.org/10.1007/s12555-017-0137-8

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