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Shape Control of a Multi-agent System Using Tensegrity Structures

  • Benjamin Nabet
  • Naomi Ehrich Leonard
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 366)

Abstract

We present a new coordinated control law for a group of vehicles in the plane that stabilizes an arbitrary desired group shape. The control law is derived for an arbitrary shape using models of tensegrity structures which are spatial networks of interconnected struts and cables. The symmetries in the coupled system and the energy-momentum method are used to investigate stability of relative equilibria corresponding to steady translations of the prescribed rigid shape.

Keywords

Relative Equilibrium Mobile Sensor Stress Matrix Tensegrity Structure Coadjoint Action 
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References

  1. 1.
    F. Zhang, M. Goldgeier, and P.S. Krishnaprasad. Control of small formations using shape coordinates. Proc. 2003 IEEE Int. Conf. Robotics Aut., pages 2510–2515, 2003.Google Scholar
  2. 2.
    N.E. Leonard, D. Paley, F. Lekien, R. Sepulchre, D.M. Fratantoni, and R. Davis. Collective motion, sensor networks and ocean sampling. Proceedings of the IEEE, Special Issue on Networked Control Systems, 2006. To appear.Google Scholar
  3. 3.
    E. Fiorelli, N.E. Leonard, P. Bhatta, D. Paley, R. Bachmayer, and D.M. Fratantoni. Multi-AUV control and adaptive sampling in Monterey Bay. In Proc. IEEE Workshop on Multiple AUV Operations, 2004. To appear, IEEE J. Oceanic Engineering.Google Scholar
  4. 4.
    F. Zhang and N. Leonard. Generating contour plots using multiple sensor platforms. In Proc. of 2005 IEEE Symposium on Swarm Intelligence, pages 309–314, 2005.Google Scholar
  5. 5.
    R.E. Skelton, J.W. Helton, R. Adhikari, J.P. Pinaud, and W. Chan. An introduction to the mechanics of tensegrity structures. In The Mechanical Systems Design Handbook. CRC Press, 2001.Google Scholar
  6. 6.
    K. Snelson. Continuous tension, discontinuous compression structures. U. S. Patent 3, 169, 611, 1965.Google Scholar
  7. 7.
    R. Buckminster Fuller. Tensile-integrity structures, U. S. Patent 3.063,521, 1962.Google Scholar
  8. 8.
    R. Connelly. Rigidity and energy. Invent. Math., 66:11–33, 1982.zbMATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    R. Connelly. Generic global rigidity Discrete Comput. Geom., 33:549–563, 2005.zbMATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    R. Connelly. Tensegrity structures: Why are they stable? In Rigidity Theory and Applications, pages 47–54. Plenum Press, 1999.Google Scholar
  11. 11.
    R. Connelly and W. Whiteley. Second-order rigidity and prestress stability for tensegrity frameworks. SIAM J. Discrete Math., 9(3): 453–491, 1996.zbMATHCrossRefMathSciNetGoogle Scholar
  12. 12.
    G. Zanotti and C. Guerra. Is tensegrity a unifying concept of protein folds? FEBS Letters, 534:7–10, 2003.CrossRefGoogle Scholar
  13. 13.
    D.E. Ingber. Cellular tensegrity: Defining new rules of biological design that govern the cytoskeleton. Journal of Cell Science, 104:613–627, 1993.Google Scholar
  14. 14.
    J.E. Marsden. Lectures on Mechanics. Cambridge University Press, 2004. Third ed.Google Scholar
  15. 15.
    J.E. Marsden and T.S. Ratiu. Introduction to Mechanics and Symmetry. Springer-Verlag, 1999. Second ed.Google Scholar
  16. 16.
    R.A. Horn and C.R. Johnson. Matrix Analysis. Cambridge University Press, 1985.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Benjamin Nabet
    • 1
  • Naomi Ehrich Leonard
    • 1
  1. 1.Mechanical and Aerospace EngineeringPrinceton UniversityPrincetonUSA

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