Qualitative Heterogeneous Control of Higher Order Systems

  • Subramanian Ramamoorthy
  • Benjamin Kuipers
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2623)


This paper presents the qualitative heterogeneous control framework, a methodology for the design of a controlled hybrid system based on attractors and transitions between them. This framework designs a robust controller that can accommodate bounded amounts of parametric and structural uncertainty. This framework provides a number of advantages over other similar techniques. The local models used in the design process are qualitative, allowing the use of partial knowledge about system structure, and nonlinear, allowing regions and transitions to be defined in terms of dynamical attractors. In addition, we define boundaries between local models in a natural manner, appealing to intrinsic properties of the system. We demonstrate the use of this framework by designing a novel control algorithm for the cart-pole system. In addition, we illustrate how traditional algorithms, such as linear quadratic regulators, can be incorporated within this framework. The design is validated by experiments with a physical system.


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  1. 1.
    Kuipers, B.J., Astrom, K.: The composition and validation of heterogeneous control laws. Automatica 30 (1994) 223–249CrossRefGoogle Scholar
  2. 2.
    Kuipers, B., Ramamoorthy, S.: Qualitative modeling and heterogeneous control of global system behavior. In C. J. Tomlin and M. R. Greenstreet (Eds.), Hybrid Systems: Computation and Control, Lecture Notes in Computer Science, Volume 2289, Springer Verlag, 2002CrossRefGoogle Scholar
  3. 3.
    Slotine, J.J.E., Li, W.: Applied Nonlinear Control. Prentice Hall, Englewood Cliffs NJ (1991)MATHGoogle Scholar
  4. 4.
    Lohmiller, W., Slotine, J.J.E.: On contraction analysis for nonlinear systems. Automatica 34 (1998) 683–696MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Burridge, R.R., Rizzi, A.A., Koditschek, D.E.: Sequential composition of dynamically dexterous robot behaviors. International Journal of Robotics Research 18 (1999) 534–555CrossRefGoogle Scholar
  6. 6.
    Klavins, E., Koditschek, D.E.: Phase regulation of decentralized cyclic robotic systems. International Journal of Robotics Research 21 (2002) 257–275CrossRefGoogle Scholar
  7. 7.
    Ott, E., Grebogi, C., Yorke, J.A.: Controlling chaos. Physical Review Letters. 64 (1990) 1196–1199MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Boccaletti, S., Grebogi, C., Lai, Y.C., Mancini, H., Maza, D.: The control of chaos: Theory and Applications. Physics Reports 329 (2000) 103–197CrossRefMathSciNetGoogle Scholar
  9. 9.
    Bradley, E.: Autonomous exploration and control of chaotic systems. Cybernetics and Systems 26 (1995) 299–319CrossRefGoogle Scholar
  10. 10.
    Astrom, K.J., Furuta, K.: Swinging up a pendulum by energy control. Automatica 36 (2000) 287–295CrossRefMathSciNetGoogle Scholar
  11. 11.
    Zhao, J., Spong, M.W.: Hybrid control for global stabilization of the cart-pendulum system. Automatica 37 (2001) 1941–1951MATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    Chung, C.C., Hauser, J.: Nonlinear control of a swinging pendulum. Automatica 31 (1995) 851–862MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Full, R., U. Saranli, M. Buehler, Brown. B., N. Moore, D. Koditschek, and H. Komsuoglu. Evidence for Spring Loaded Inverted Pendulum Running in a Hexapod Robot. Proc. International Symposium on Experimental Robotics, Honolulu, Hawaii, 2000.Google Scholar
  14. 14.
    Saranli, U., Schwind, W.J., Koditschek, D.E.: Toward the control of a multi-jointed monoped runner. Proceedings of the IEEE International Conference on Robotics and Automation, pp 2676–2682, 1998Google Scholar
  15. 15.
    Pratt, J. and Pratt, G.: Intuitive control of a planar bipedal walking robot. Proceedings of the IEEE International Conference on Robotics and Automation, 1998 Google Scholar
  16. 16.
    Jordan, D.W., Smith, P.: Nonlinear Ordinary Differential Equations: An Introduction to Dynamical Systems. 3rd ed. Oxford University Press, Oxford (1999)MATHGoogle Scholar
  17. 17.
    Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, Berlin (1983)MATHGoogle Scholar
  18. 18.
    Levine, W.E., ed., The Control Handbook. CRC Press (1996)Google Scholar
  19. 19.
    Friedland, B.: Advanced Control System Design. Prentice-Hall (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Subramanian Ramamoorthy
    • 1
  • Benjamin Kuipers
    • 2
  1. 1.Electrical and Computer Engineering DepartmentUniversity of Texas at AustinAustin
  2. 2.Computer Science DepartmentUniversity of Texas at AustinAustinUSA

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