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Journal of Intelligent & Robotic Systems

, Volume 93, Issue 1–2, pp 213–226 | Cite as

Robust Consensus-Based Formation Flight for Multiple Quadrotors

  • E. G. Rojo-Rodriguez
  • O. GarciaEmail author
  • E. J. Ollervides
  • P. Zambrano-Robledo
  • E. S. Espinoza-Quesada
Article
  • 156 Downloads

Abstract

In this paper, the robust consensus of the multiple quadrotors for formation flight is proposed as a solution for the multi-agent system (MAS) problem. The Newton-Euler formulation is used in order to describe the mathematical model of the N quadrotors considered as agents and a Super Twisting algorithm controls the translational and rotational dynamics of each agent so that this control algorithm drives the general sliding manifold to zero in finite time. This general sliding manifold consists of a sliding surface for the navigation of each agent and an auxiliary sliding surface for the consensus of the MAS. In this sense, the Super Twisting algorithm provides robustness against parameter uncertainty and disturbances. Then, the robust consensus algorithm guarantees that the MAS executes the formation flight and pursuit in the trajectory tracking even in presence of disturbances. Finally, real-time experiments show that the MAS successfully reaches the consensus.

Keywords

Multi-agent systems Super twisting algorithm Robust consensus Distributed navigation Formation flight Quadrotors 

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Notes

Acknowledgements

This work was partially supported by the Mexican National Council for Science and Technology (CONACYT) Mexico with the project “Apoyo al Fortalecimiento y Desarrollo de la Infraestructura Científica y Tecnológica-204363”, and the TecNM with the project “Redes 5939.16-P”.

References

  1. 1.
    Abdessameud, A., Tayebi, A.: Motion coordination for VTOL unmanned aerial vehicles: Attitude synchronisation and formation control. Springer, London (2013)CrossRefzbMATHGoogle Scholar
  2. 2.
    Bircher, A., Kamel, M., Alexis, K., Burri, M., Oettershagen, P., Omari, S., Mantel, T., Siegwart, R.: Three-dimensional coverage path planning via viewpoint resampling and tour optimization for aerial robots. Auton. Robot. 40(6), 1059–1078 (2016)CrossRefGoogle Scholar
  3. 3.
    Alexis, K., Papachristos, C., Siegwart, R., Tzes, A.: Uniform coverage structural inspection path-planning for micro aerial vehicles. In: IEEE Multiconference on systems and control, Sydney NSW (2015)Google Scholar
  4. 4.
    Bircher, A., Alexis, K., Burri, M., Oettershagen, P., Omari, S., Mantel, T., Siegwart, R.: Structural inspection path planning via iterative viewpoint resampling with application to aerial robotics. In: IEEE international conference on robotics and automation (ICRA), Seattle (2015)Google Scholar
  5. 5.
    Cao, Y., Ren, W.: Distributed coordinated tracking via a variable structure approach - Part I: Consensus tracking. In: 2010 american control conference marriott waterfront, Baltimore (2010)Google Scholar
  6. 6.
    Chapa-Garcia, R., Jimenez-Lizarraga, M., Garcia, O., Espinoza-Fraire, T.: Formation flight of fixed-wing UAVs based on linear quadratic affine game. In: 2016 international conference on unmanned aircraft systems (ICUAS), Arlington (2016)Google Scholar
  7. 7.
    Derafa, L., Benallegue, A., Fridman, L.: Super twisting control algorithm for the attitude tracking of a four rotors UAV. J. Franklin Inst. 349, 685–699 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Dong, X., Yu, B., Shi, Z., Zhong, Y.: Time-varying formation control for unmanned aerial vehicles: Theories and applications. IEEE Trans. Control Syst. Technol. 23(1) (2014)Google Scholar
  9. 9.
    Dong, X., Zhou, Y., Ren, Z., Zhong, Y.: Time-varying formation control for unmanned aerial vehicles with switching interaction topologies. Control. Eng. Pract. 46, 26–36 (2016)CrossRefGoogle Scholar
  10. 10.
    Escobar, A.G., Alazki, H., Valenzuela, J.E., Garcia, O.: Embedded super twisting control for the attitude of a quadrotor. IEEE Lat. Am. Trans. 14(9), 3974–3979 (2016)CrossRefGoogle Scholar
  11. 11.
    Hernandez-Gonzalez, M., Jimenez-Lizarraga, M.A.: Real-time laser beam stabilization by sliding mode controllers, Int. J. Adv. Manuf. Technol., Springer 91(9–12) (2017)Google Scholar
  12. 12.
    Hou, Z.G., Cheng, L., Tan, M.: Decentralized robust adaptive control for the multiagent system consensus problem using neural networks. IEEE Trans. Syst. Man Cybern. B Cybern. 39(3) (2009)Google Scholar
  13. 13.
    Liu, N., Ling, R., Huang, Q., Zhu, Z.: Second-order super-twisting sliding mode control for finite-time leader-follower consensus with uncertain nonlinear multiagent systems. Hindawi Publishing Corporation, Mathematical Problems in Engineering, vol. 2015, Article ID 292437Google Scholar
  14. 14.
    Li, Z., Duan, Z., Lewis, F.L.: Distributed robust consensus control of multi-agent systems with heterogeneous matching uncertainties. Automatica 50(3), 883–889 (2014)MathSciNetCrossRefzbMATHGoogle Scholar
  15. 15.
    Lozano, R.: Unmanned aerial vehicles embedded control. John Wiley-ISTE Ltd, USA (2010)Google Scholar
  16. 16.
    Luque-Vega, L., Castillo-Toledo, B., Loukianov, A.G.: Robust block second order sliding mode control for a quadrotor. J. Franklin Inst. 349, 719–739 (2012)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Montijano, E., Cristofalo, E., Zhou, D., Schwager, M., Sagues, C.: Vision-based distributed formation control without an external positioning system. IEEE Trans. Robot. 32(2), 339–351 (2016)CrossRefGoogle Scholar
  18. 18.
    Montufar, D.I., Munoz, F., Espinoza, E.S., Garcia, O., Salazar, S.: Multi-UAV testbed for aerial manipulation applications. In: IEEE international conference on unmmaned aircraft systems (ICUAS 2014), Orlando FL (2014)Google Scholar
  19. 19.
    Moreno, J.A., Osorio, M.: A Lyapunov approach to second-order sliding mode controllers and observers. In: 47Th IEEE conference on decision and control cancun, Mexico (2008)Google Scholar
  20. 20.
    Munoz Palacios, F., Espinoza Quesada, E.S., Sanahuja, G., Salazar, S., Garcia Salazar, O., Garcia Carrillo, L.R.: Test bed for applications of heterogeneous unmanned vehicles. Int. J. Adv. Robot. Syst., 1–14 (2017)Google Scholar
  21. 21.
    Munoz, F., Espinoza Quesada, E.S., La, H.M., Salazar, S., Commuri, S., Garcia Carrillo, L.R.: Adaptive consensus algorithms for real-time operation of multi-agent systems affected by switching network events. Int. J. Robust Nonlinear Control 27(9), 1566–1588 (2017)MathSciNetzbMATHGoogle Scholar
  22. 22.
    Ogata, K.: Modern control engineering. 5th edn. Prentice Hall, Englewood Cliffs (2009)Google Scholar
  23. 23.
    Piskorsky, S., Brulez, N., Eline, P.: ARDrone SDK 1.7 Developer Guide. Parrot AR.Drone (2011)Google Scholar
  24. 24.
    Poznyak, A. S.: Advanced mathematical tools for automatic control engineers: Deterministic techniques vol. 1. Elsevier Science (2007)Google Scholar
  25. 25.
    Sanchez, A., Parra-Vega, V., Izaguirre, C., Garcia, O.: Position-yaw tracking of quadrotors. J. Dyn. Syst. Meas. Control., ASME, 137(6) (2015)Google Scholar
  26. 26.
    Shtessel, Y., Edwards, C., Fridman, L., Levant, A.: Sliding mode control and observation. Control Engineering. Birkhäuser, New York (2014)CrossRefGoogle Scholar
  27. 27.
    Ren, G., Yu, Y.: Robust consensus of fractional multi-agent systems with external disturbances. Neurocomputing 218, 339–345 (2016)CrossRefGoogle Scholar
  28. 28.
    Rojo-rodriguez, E.G., Ollervides, E.J., Rodriguez, J.G., Espinoza, E.S., Zambrano-Robledo, P., Garcia, O.: Implementation of a super twisting controller for distributed formation flight of multi-agent systems based on consensus algorithms. In: 2017 international conference on unmanned aircraft systems (ICUAS 2017), Miami (2017)Google Scholar
  29. 29.
    Stengel, R.F.: Flight dynamics. Princeton University Press, USA (2004)Google Scholar
  30. 30.
    Turpin, M., Michel, N., Kumar, V.: Trajectory design and control for aggressive formation flight with quadrotors. Auton. Robot. 33(1), 143–156 (2012)CrossRefGoogle Scholar
  31. 31.
    Tron, R., Thomas, J., Loianno, G., Daniilidis, K., Kumar, V.: A distributed optimization framework for localization and formation control: Applications to Vision-Based measurements. IEEE Control. Syst. 36(4), 22–44 (2016)MathSciNetCrossRefGoogle Scholar
  32. 32.
    Utkin, V., Guldner, J., Shi, J.: Sliding mode control in electro-mechanical systems. CRC Press, 2nd edn., Boca Raton (2009)CrossRefGoogle Scholar
  33. 33.
    Wu, Y., Meng, X., Xie, L., Lu, R., Su, H., Wu, Z.-G.: An input-based triggering approach to leader-following problems. Automatica 75, 221–228 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  34. 34.
    Wu, Y., Lu, R., Shi, P., Lu, R., Su, H., Wu, Z.-G.: Adaptive output synchronization of heterogeneous network with an uncertain leader. Automatica 76, 183–192 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Yan, M., Zhu, X., Zhang, X., Qu, Y.: Consensus-based three-dimensional multi-UAV formation control strategy with high precision. Frontiers of Information Technology and Electronic Engineering 18(7), 968–977 (2017)CrossRefGoogle Scholar
  36. 36.
    Zhu, X., Zhang, X., Yan, M., Qu, Y.: Three-dimensional formation keeping of multi-UAV based on consensus. J. Cent. South Univ. 24(6), 1387–1395 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Aerospace Engineering Research and Innovation Center, Faculty of Mechanical and Electrical EngineeringAutonomous University of Nuevo LeonApodacaMexico
  2. 2.Laboratoire Franco-Mexicain d’Informatique et AutomatiqueLAFMIA UMI 3175 CNRS-CINVESTAVMexico CityMexico

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