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Control of Nonholonomic Systems with Bad Controllability Structure

  • Mitsuji Sampei
  • Hisashi Date
  • Shigeki Nakaura
Chapter
  • 306 Downloads
Part of the Trends in Mathematics book series (TM)

Abstract

There are many nonholonomic systems whose controllability structures are much worse than the chained form. Since it is quite hard to design feedback (type) controllers for those systems, many researchers worked on path planning rather than feedback stabilization. In this note, we will consider two of these systems, orientation control of a ball sandwiched and manipulated by two parallel plates, and propulsive control of a snake-like robot. We will analyze their controllability and design feedback type controllers.

Keywords

Nonholonomic system Time-state control form Ball-plate manipulation Manipulability Snake-like locomotion 

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References

  1. 1.
    R. W. Brockett,Asymptotic stability and feedback stabilization,in Differential Geometric Control Theory. Progress in Mathematics, vol. 27, Springer-Verlag, 1983, pp. 181–191.MathSciNetGoogle Scholar
  2. 2.
    H. Date, Y. Hoshi, and M. Sampei,Locomotion control of a snakelike robot based on dynamic manipulability,in Proceedings of the IEEE/RSJ Int. Conference on Intelligent Robots and Systems, 2000, pp. 2236–2241.Google Scholar
  3. 3.
    H. Date, Y. Hoshi, M. Sampei, and S. Nakaura, Locomotion control of a snake robot with constraint force attenuation,in Proceeding of the American Control Conference, 2001, pp. 113–118.Google Scholar
  4. 4.
    O. Khatib and J. Burdics,Dynamic optimization in manipulator design: The operational space formulation,in Proceedings of the ASME Winter Annual Meeting, 1985.Google Scholar
  5. 5.
    H. Kiyota and M. Sampei,An attitude control of planar nonholonomic space robots,in Proceedings of the 25th SICE Symposium on Control Theory, 1996, pp. 51–56.Google Scholar
  6. 6.
    H. Kiyota and M. Sampei,On the stability of a class of nonholonomic systems using time-state control form,in Proceedings of the 26th SICE Symposium on Control Theory, 1997, pp. 409–412.Google Scholar
  7. 7.
    H. Kiyota and M. Sampei,Stabilization of a class of nonholonomic systems without drift using time-state control form(in Japanese), Trans. of the Inst. of Systems, Control and Information Engineers, vol. 12, no. 11, pp. 647–654, 1999.MathSciNetCrossRefGoogle Scholar
  8. 8.
    K. Kosuge and K. Furuta,Kinematic and dynamic analysis of robot arm,in Proceedings of the IEEE International Conference on Robotics and Automation, 1985, pp. 1039–1044.Google Scholar
  9. 9.
    G. Lafferriere and H. Sussmann,Motion planning for controllable systems without drift,in Proceedings of the IEEE International Conference on Robotics and Automation, 1991,pp. 1148–1153.Google Scholar
  10. 10.
    R. T. M)Closkey and R. M. Murray,Exponential stabilization of drift-less nonlinear control systems using homogeneous feedback,IEEE Trans. on Automatic Control, vol. 42, no. 5, pp. 614–628, 1997.MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    D. J. Montana,The kinematics of contact and grasp,The International Journal of Robotics Research, vol. 7, no. 3, pp. 17–32, 1988.CrossRefGoogle Scholar
  12. 12.
    R. M. Murray, Z. Li, and S. S. Sastry, A Mathematical Introduction to Robotic Manipulation. CRC Press, 1994.Google Scholar
  13. 13.
    R. M. Murray and S. S. Sastry.Nonholonomic motion planning: Steering using sinusoids,IEEE Trans. on Automatic Control, vol. 38, no. 5, pp. 700–716, 1993.MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    P. Prautsch and T. Mita,Control and analysis of the gait of snake robots,in Proceedings of the IEEE International Conference on Control Applications, 1999, pp. 502–507.Google Scholar
  15. 15.
    M. Sampei, H. Kiyota, M. Koga, and M. Suzuki, Necessary and sufficient conditions for transformation of nonholonomic system into time-state control form,in Proceedings of the IEEE International Conference on Decision and Control, 1996, pp. 4745–4746.Google Scholar
  16. 16.
    O. J. Sordalen and O. Egeland,Exponential stabilization of nonholonomic chained systems,IEEE Trans. on Automatic Control, vol. 40, no. 1, pp. 35–49, 1995.MathSciNetCrossRefGoogle Scholar
  17. 17.
    T. Yoshikawa,Analysis and control of manipulators with redundancy,in Preprints of the 1st International Symposium of Robotics Research, 1983.Google Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Mitsuji Sampei
    • 1
  • Hisashi Date
    • 1
  • Shigeki Nakaura
    • 1
  1. 1.Department of Mechanical and Control Engineering Graduate School of Science and EngineeringTokyo Institute of TechnologyMeguro-ku, TokyoJapan

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