Journal of the Korean Institute of Intelligent Systems (한국지능시스템학회논문지)

Korean Institute of Intelligent Systems (한국지능시스템학회)
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Chaotic behavior analysis in the mobile robot of embedding some chaotic equation with obstacle

  • Bae, Youngchul (Division of electronic communication and electrical engineering of Yosu National University) ;
  • Kim, Juwan (Division of electronic communication and electrical engineering of Yosu National University) ;
  • Kim, Yigon (Division of electronic communication and electrical engineering of Yosu National University)
  • Published : 2003.12.01
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Abstract

In this paper, we propose that the chaotic behavior analysis in the mobile robot of embedding some chaotic such as Chua`s equation, Arnold equation with obstacle. In order to analysis of chaotic behavior in the mobile robot, we apply not only qualitative analysis such as time-series, embedding phase plane, but also quantitative analysis such as Lyapunov exponent In the mobile robot with obstacle. We consider that there are two type of obstacle, one is fixed obstacle and the other is VDP obstacle which have an unstable limit cycle. In the VDP obstacles case, we only assume that all obstacles in the chaos trajectory surface in which robot workspace has an unstable limit cycle with Van der Pol equation.

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References

  1. E. Ott, C.Grebogi, and J.A York," Controlling Chaos", Phys. Rev.Lett., vol. 64, no.1196-1199, 1990.
  2. T. Shinbrot, C.Grebogi, E.Ott, and J.A.Yorke, " Using small perturbations to control chaos", Nature, vol. 363, pp. 411-417, 1993. https://doi.org/10.1038/363411a0
  3. M. Itoh, H. Murakami and L. O. Chua, "Communication System Via Chaotic Modulations" IEICE. Trans. Fundmentals. vol.E77 - A, no. , pp.1000-1005, 1994.
  4. L. O. Chua, M. Itoh, L. Kocarev, and K. Eckert, "Chaos Synchronization in Chua's Circuit" J. Circuit. Systems and computers, vol. 3, no. 1, pp. 93-108, 1993. https://doi.org/10.1142/S0218126693000071
  5. M. Itoh, K. Komeyama, A. Ikeda and L. O. Chua, " Chaos Synchronization in Coupled Chua Circuits", IEICE. NLP. 92-51. pp. 33-40. 1992.
  6. K. M. Short, " Unmasking a modulated chaotic communications scheme", Int. J. Bifurcation and Chaos, vol. 6, no. 2, pp. 367-375, 1996. https://doi.org/10.1142/S0218127496000114
  7. L. Kocarev, " Chaos-based cryptography: A brief overview," IEEE, Vol. pp. 7-21. 2001.
  8. M. Bertram and A. S. Mikhailov, "Pattern formation on the edge of chaos: Mathematical modeling of CO oxidation on a Pt(110) surface under global delayed feedback", Phys. Rev. E 67, pp. 036208, 2003. https://doi.org/10.1103/PhysRevE.67.036208
  9. K. Krantz, f. H. Yousse, R.W, Newcomb, "Medical usage of an expert system for recognizing chaos", Engineering in Medicine and Biology Society, 1988. Proceedings of the Annual International Conference of the IEEE, 4-7, pp. 1303 -1304,1988 .
  10. Nakamura, A. , Sekiguchi. "The chaotic mobile robot", IEEE Transactions on Robotics and Automation , Volume: 17 Issue: 6, pp. 898-904, 2001. https://doi.org/10.1109/70.976022
  11. F. Takens, " Detecting strange attractors in turbulence in Dynamical systems and turbulence", Lecture Notes in Mathematics, 898, pp. 363-381. Springer, 1998.
  12. J.P. Eckmann, S.O.Kamphorst, D.Ruelle, S.Ciliberto,"Liapunov exponents from time series", Phys. Rev. A34 (6), pp. 4971-4979, 1986.
  13. Okamoto and H. Fujii, Nonlinear Dynamics, Iwanami Lectures of Applied Mathematics, Iwanami, Tokyo, 1995, vol. 14.
  14. Y. Bae, J. Kim, Y.Kim, " The obstacle collision avoidance methods in the chaotic mobile robot", 2003 ISIS, pp.591-594, 2003.
  15. Y. Bae, J. Kim, Y.Kim, " Chaotic behavior analysis in the mobile robot: the case of Chua's equation" , Proceeding of KFIS Fall Conference 2003, vol. 13, no. 2, pp.5-8, 2003.
  16. Y. Bae, J. Kim, Y.Kim, " Chaotic behavior analysis in the mobile robot: the case of Arnold equation" , Proceeding of KFIS Fall Conference 2003, vol. 13, no. 2, pp110-113, 2003.