Shape Control of a Multi-agent System Using Tensegrity Structures
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.
KeywordsRelative Equilibrium Mobile Sensor Stress Matrix Tensegrity Structure Coadjoint Action
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- 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.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.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.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.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.K. Snelson. Continuous tension, discontinuous compression structures. U. S. Patent 3, 169, 611, 1965.Google Scholar
- 7.R. Buckminster Fuller. Tensile-integrity structures, U. S. Patent 3.063,521, 1962.Google Scholar
- 10.R. Connelly. Tensegrity structures: Why are they stable? In Rigidity Theory and Applications, pages 47–54. Plenum Press, 1999.Google Scholar
- 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.J.E. Marsden. Lectures on Mechanics. Cambridge University Press, 2004. Third ed.Google Scholar
- 15.J.E. Marsden and T.S. Ratiu. Introduction to Mechanics and Symmetry. Springer-Verlag, 1999. Second ed.Google Scholar
- 16.R.A. Horn and C.R. Johnson. Matrix Analysis. Cambridge University Press, 1985.Google Scholar