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Robust Discrete-Time Markovian Control for Wheeled Mobile Robot Formation: A Fault Tolerant Approach

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Abstract

In this paper we use a recursive robust regulator for discrete time Markovian jump linear systems to control a group of wheeled mobile robots in formation. A leader-following formation is used with directed communication topology. The robustness is checked with a communication fault in blind areas and, if the fault affects the leader, the leadership is changed and the formation continues to follow the defined trajectory. When the communication is reestablished all robots that lost communication return to their position in the formation. Results based on simulation and real implementation are presented to show the effectiveness of the formation control approach used.

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References

  1. Song, Y., Lou, H., Liu, S.: IEEE/CAA Journal of Automatica Sinica 2(4), 374 (2015). https://doi.org/10.1109/JAS.2015.7296532

    Article  MathSciNet  Google Scholar 

  2. Kao, Y., Xie, J., Wang, C.: IEEE Trans. Autom. Control 59(9), 2604 (2014). https://doi.org/10.1109/TAC.2014.2313756

    Article  Google Scholar 

  3. Kwon, N.K., Park, B.Y., Park, P.: In: 2015 15th International Conference on Control, Automation and Systems (ICCAS), pp. 999–1004 (2015). https://doi.org/10.1109/ICCAS.2015.7364791

  4. Wu, Z.G., Shi, P., Su, H., Chu, J.: Automatica 50(1), 180 (2014). https://doi.org/10.1016/j.automatica.2013.09.041

    Article  MathSciNet  Google Scholar 

  5. Cerri, J.P., Terra, M.H., Ishihara, J.Y.: In: 49th IEEE Conference on Decision and Control (CDC), pp. 597–602 (2010). https://doi.org/10.1109/CDC.2010.5717301

  6. Cerri, J.P., Terra, M.H.: Recursive robust regulator for discrete-time Markovian jump linear systems. IEEE Trans. Autom. Control. PP(99), 1–1 (2017). https://doi.org/10.1109/TAC.2017.2707335, ISSN 0018-9286

    MathSciNet  MATH  Google Scholar 

  7. Dong, W., Djapic, V.: Int. J. Syst. Sci. 47(8), 1877 (2016). https://doi.org/10.1080/00207721.2014.955553

    Article  Google Scholar 

  8. Peng, Z., Wen, G., Rahmani, A., Yu, Y.: Robot. Auton. Syst. 61(9), 988 (2013). https://doi.org/10.1016/j.robot.2013.05.004

    Article  Google Scholar 

  9. Dierks, T., Brenner, B., Jagannathan, S.: IEEE Trans. Control Syst. Technol. 21(4), 1407 (2013). https://doi.org/10.1109/TCST.2012.2200484

    Article  Google Scholar 

  10. Asl, A.N., Menhaj, M.B., Sajedin, A.: Applied soft computing 14, Part C, 563 (2014). https://doi.org/10.1016/j.asoc.2013.07.030

    Google Scholar 

  11. Williams, A., Lafferriere, G., Veerman, J.: In: 44th IEEE Conference on Decision and Control, 2005 and 2005 European Control Conference. CDC-ECC ’05, pp. 72–77. Seville (2005). https://doi.org/10.1109/CDC.2005.1582133

  12. Lafferriere, G., Williams, A., Caughman, J., Veerman, J.: Syst. Control Lett. 54(9), 899 (2005). https://doi.org/10.1016/j.sysconle.2005.02.004

    Article  Google Scholar 

  13. Nakai, M.E., Inoue, R.S., Terra, M.H., Grassi, V.: In: 2016 XIII Latin American Robotics Symposium and IV Brazilian Robotics Symposium (LARS/SBR), pp. 175–180 (2016). https://doi.org/10.1109/LARS-SBR.2016.36

  14. Lafferriere, G., Caughman, J., Williams, A.: In: Proceedings of the 2004 American Control Conference, 2004, vol. 4, pp. 3729–3734 (2004)

  15. Veerman, J., Lafferriere, G., Caughman, J., Williams, A.: J. Stat. Phys. 121(5-6), 901 (2005). https://doi.org/10.1007/s10955-005-6999-9

    Article  MathSciNet  Google Scholar 

  16. Brualdi, R., Ryser, H.: Combinatorial Matrix Theory. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (1991)

    Book  Google Scholar 

  17. Fax, J.A., Murray, R.M.: IEEE Trans. Autom. Control 49(9), 1465 (2004). https://doi.org/10.1109/TAC.2004.834433

    Article  Google Scholar 

  18. Coelho, P., Nunes, U.: Robotica 21, 483 (2003). https://doi.org/10.1017/S0263574703005149

    Article  Google Scholar 

  19. Kanayama, Y., Kimura, Y., Miyazaki, F., Noguchi, T.: In: Proceedings of the 1990 IEEE International Conference on Robotics and Automation, 1990, vol. 1, pp. 384–389 (1990). https://doi.org/10.1109/ROBOT.1990.126006

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Nakai, M.E., Inoue, R.S., Terra, M.H. et al. Robust Discrete-Time Markovian Control for Wheeled Mobile Robot Formation: A Fault Tolerant Approach. J Intell Robot Syst 91, 233–247 (2018). https://doi.org/10.1007/s10846-017-0723-2

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  • DOI: https://doi.org/10.1007/s10846-017-0723-2

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