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Formation Control Algorithm for Coupled Unicycle-Type Mobile Robots Through Switching Interconnection Topology

스위칭 연결 구조를 갖는 외발형 이동 로봇들에 대한 대형 제어 알고리듬

  • 김홍근 (서울대학교 전기컴퓨터공학부) ;
  • 심형보 (서울대학교 전기컴퓨터공학부) ;
  • 백주훈 (광운대학교 로봇학부)
  • Received : 2012.02.26
  • Accepted : 2012.03.27
  • Published : 2012.05.01

Abstract

In this study, we address the formation control problem of coupled unicycle-type mobile robots, each of which can interact with its neighboring robots by communicating their position outputs. Each communication link between two mobile robots is assumed to be established according to the given time-varying interconnection topology that switches within a finite set of connected fixed undirected networks and has a non-vanishing dwell time. Under this setup, we propose a distributed formation control algorithm by using the dynamics extension and feedback linearization methods, and by employing a consensus algorithm for linear multi-agent systems which provides arbitrary fast convergence rate to the agreement of the multi-agent system. Finally, the proposed result is demonstrated through a computer simulation.

Keywords

References

  1. T. D. Barfoot and C. M. Clark, "Motion planning for formations of mobile robots," Robotics and Autonomous Systems, vol. 46, no. 2, pp. 65-78, 2004. https://doi.org/10.1016/j.robot.2003.11.004
  2. C.-T. Chen, Linear System Theory and Design, 3rd Ed., Oxford University Press, New York, 1999.
  3. Q. Chen and J. Y. S. Luh, "Coordination and control of a group of small mobile robots," Proc. of IEEE International Conference on Robotics and Automation, pp. 2315-2320, 1994.
  4. J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations," IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1465-1476, 2004. https://doi.org/10.1109/TAC.2004.834433
  5. J. Ghommam, H. Mehrjerdi, M. Saad, and F. Mnif, "Adaptive coordinated path following control of non-holonomic mobile robots with quantised communication," IET Control Theory and Applications, vol. 5, no. 17, pp. 1990-2004, 2011. https://doi.org/10.1049/iet-cta.2010.0478
  6. J. Ghommam, M. Saad, and F. Mnif, "Formation path following control of unicycle-type mobile robots," Proc. of IEEE International Conference on Robotics and Automation, pp. 1966-1972, 2008.
  7. C. D. Godsil and G. Royle, Algebraic Graph Theory, Springer, Graduate Texts in Mathematics, vol. 207, 2001.
  8. A. Isidori, Nonlinear Control Systems, 3rd Ed., Springer-Verlag, Berlin, 1995.
  9. A. Jadbabaie, J. Lin, and A. S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Transactions on Automatic Control, vol. 48, no. 6, pp. 988-1001, 2003. https://doi.org/10.1109/TAC.2003.812781
  10. H. K. Khalil, Nonlinear Systems, 3rd Ed., Prentice Hall, New Jersey, 2002.
  11. H. Kim, Consensus and Synchronization Among Output-Coupled Identical and Non-Identical Linear Systems Through Fast Switching Network, Ph.D. thesis, Seoul National University, Department of Electrical Engineering and Computer Science, South Korea, 2012.
  12. H. Kim, S. Kim, H. Shim, and J. Back, "Order reduction paradigm for consensus of neutrally stable multi-agent systems," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 16, no. 3, pp. 222-226, 2010. https://doi.org/10.5302/J.ICROS.2010.16.3.222
  13. H. Kim, H. Shim, and J. Back, "Formation stabilization of unicycle-type mobile robots via consensus algorithm," Proc. of the 41st KIEE Summer Conference (in Korean), pp. 1615-1616, 2010.
  14. H. Kim, H. Shim, J. Back, and J. H. Seo, "Consensus of multi-agent systems under periodic time-varying network," Proc. of the 8th IFAC Symposium on Nonlinear Control Systems, pp. 155-160, 2010.
  15. J. Kim, H. Kim, H. Shim, and J. Back, "Output consensus of non-identical and stabilizable linear systems having the same transfer matrix," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 17, no. 9, pp. 857-862, 2011. https://doi.org/10.5302/J.ICROS.2011.17.9.857
  16. G. Lafferriere, A. Williams, J. Caughman, and J. Veerman, "Decentralized control of vehicle formations," Systems & Control Letters, vol. 54, no. 9, pp. 899-910, 2005. https://doi.org/10.1016/j.sysconle.2005.02.004
  17. B. S. Park, Adaptive Formation Control for Nonholonomic Mobile Robots Including Actuator Dynamics, Ph.D. thesis, Yonsei University, Department of Electric and Electronics, South Korea, 2011.
  18. B. S. Park, S. J. Yoo, J. B. Park, and Y. H. Choi, "A simple adaptive control approach for trajectory tracking of electrically driven nonholonomic mobile robots," IEEE Transactions on Control Systems Technology, vol. 18, no. 5, pp. 1199-1206, 2010. https://doi.org/10.1109/TCST.2009.2034639
  19. W. Ren, R. W. Beard, and E. M. Atkins, "Information consensus in multivehicle cooperative control: Collective group behavior through local interaction," IEEE Control Systems Magazine, vol. 27, no. 2, pp. 71-82, 2007. https://doi.org/10.1109/MCS.2007.338264
  20. A. Saberi, "Simultaneous stabilization with almost disturbance decoupling-uniform rank system," Automatica, vol. 23, no. 5, pp. 653-656, 1987. https://doi.org/10.1016/0005-1098(87)90062-8
  21. A. Saberi and P. Sannuti, "Time-scale structure assignment in linear multivariable systems using high-gain feedback," International Journal of Control, vol. 49, no. 6, pp. 2191-2213, 1989. https://doi.org/10.1080/00207178908559768
  22. J. H. Seo, J. Back, H. Kim, and H. Shim, "Output feedback consensus for high order linear systems having uniform ranks under switching topology," To appear in IET Control Theory and Applications, 2012.
  23. J. H. Seo, H. Shim, and J. Back, "Consensus of high-order linear systems using dynamic output feedback compensator: Low gain approach," Automatica, vol. 45, no. 11, pp. 2659-2664, 2009. https://doi.org/10.1016/j.automatica.2009.07.022
  24. S. E. Tuna, "LQR-based coupling gain for synchronization of linear systems," arXiv:0801.3390v1 [math.OC], available from http://arxiv.org/abs/ 0801.3390, 2008.
  25. P. Wieland, "From static to dynamic couplings in consensus and synchronization among identical and non-identical systems," Ph.D. thesis, University of Stuttgart, Institute for Systems Theory and Automatic Control, Germany, 2011.

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