An Obstacle Avoidence Method for Chaotic Robots Using Angular Degree Limitions

  • Youngchul Bae
  • MalRey Lee
  • Thomas M. Gatton
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3982)


This paper presents a method to avoid obstacles that have unstable limit cycles in a chaos trajectory surface using angular degree limits. It is assumed that all obstacles in the chaos trajectory surface have a Van der Pol equation with an unstable limit cycle. When a chaos robot meets an obstacle in a Lorenz, Hamilton and Hyper-chaos equation trajectory that exceed the defined angular degree limits, the obstacle repulses the robot. Computer simulation of the Lorenz equation and the Hamilton and hyper-chaos equation trajectories, with one or more Van der Pol equations as the obstacle(s) is performed and the proposed method is verified through simulation of the chaotic trajectories in any plane, which avoids the obstacle when it is found, where the target is either met or within close range.


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  1. 1.
    Ott, E., Grebogi, C., York, J.A.: Controlling Chaos. Phys. Rev.Lett. 64, 1196–1199 (1990)zbMATHCrossRefMathSciNetGoogle Scholar
  2. 2.
    Shinbrot, T., Grebogi, C., Ott, E., Yorke, J.A.: Using small perturbations to control chaos. Nature 363, 411–417 (1993)CrossRefGoogle Scholar
  3. 3.
    Itoh, M., Murakami, H., Chua, L.O.: Communication System Via Chaotic Modulations. IEICE. Trans. Fundmentals E77-A, 1000–1005 (1994)Google Scholar
  4. 4.
    Chua, L.O., Itoh, M., Kocarev, L., Eckert, K.: Chaos Synchronization in Chua’s Circuit. J. Circuit. Systems and computers 3(1), 93–108 (1993)CrossRefMathSciNetGoogle Scholar
  5. 5.
    Itoh, M., Komeyama, K., Ikeda, A., Chua, L.O.: Chaos Synchronization in Coupled Chua Circuits. IEICE. NLP. 92-51, 33–40 (1992)Google Scholar
  6. 6.
    Short, K.M.: Unmasking a modulated chaotic communications scheme. Int. J. Bifurcation and Chaos 6(2), 367–375 (1996)zbMATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    Kocarev, L.: Chaos-based cryptography: A brief overview. IEEE, 7–21 (2001)Google Scholar
  8. 8.
    Bertram, M., Mikhailov, A.S.: 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, 136–208 (2003)Google Scholar
  9. 9.
    Krantz, K., Yousse, f.H., Newcomb, R.W.: Medical usage of an expert system for recognizing chaos. In: Proceedings of the Annual International Conference of the IEEE Engineering in Medicine and Biology Society, vol. (4-7), pp. 1303–1304 (1988)Google Scholar
  10. 10.
    Nakamura, A., Sekiguchi: The chaotic mobile robot. IEEE Transactions on Robotics and Automation 17(6), 898–904 (2001)CrossRefGoogle Scholar
  11. 11.
    Okamoto, H., Fujii, H.: Nonlinear Dynamics. Iwanami Lectures of Applied Mathematics, vol. 14, Iwanami, Tokyo (1995)Google Scholar
  12. 12.
    Bae, Y., Kim, J., Kim, Y.: The obstacle collision avoidance methods in the chaotic mobile robot. 2003 ISIS, 591–594 (2003)Google Scholar
  13. 13.
    Bae, Y., Kim, J., Kim, Y.: Chaotic behavior analysis in the mobile robot: the case of Chua’s equation. In: Proceeding of KFIS Fall Conference 2003, vol. 13(2), pp. 5–8 (2003)Google Scholar
  14. 14.
    Bae, Y., Kim, J., Kim, Y.: Chaotic behavior analysis in the mobile robot: the case of Arnold equation. In: Proceeding of KFIS Fall Conference 2003, vol. 13(2), pp. 110–113 (2003)Google Scholar
  15. 15.
    Bae, Y.C., Kim, J.W., Kim, Y.I.: Chaotic Behaviour Analysis in the Mobile of Embedding some Chaotic Equation with Obstacle. J.ournal of Fuzzy Logic and Intelligent Systems 13(6), 729–736 (2003)MathSciNetGoogle Scholar
  16. 16.
    Bae, Y.C., Kim, J.W., Kim, Y.I.: Obstacle Avoidance Methods in the Chaotic Mobile Robot with Integrated some Chaotic Equation. International Journal of Fuzzy Logic and Intelligent System 3(2), 206–214 (2003)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Youngchul Bae
    • 1
  • MalRey Lee
    • 2
  • Thomas M. Gatton
    • 3
  1. 1.Division Electronic Communication and Electrical Engineering of Yosu Nat’l UniversityYosu, ChollanamdoSouth Korea
  2. 2.School of Electronics & Information EngineeringChonBuk National UniversityChonBukKorea
  3. 3.School of Engineering and TechnologyNational UniversityLa JollaUSA

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