On invariance of cyclic group symmetries in multiagent formations

Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, CDC-ECC '05

Volumn 2005, Issue , 2005, Pages 746-751

  Marshall, Joshua A ^a   Broucke, Mireille E ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; GRAPH THEORY; SYSTEMS ANALYSIS; TOPOLOGY;

CIRCULANT CONNECTIVITY; CYCLIC GROUPS; INTERCONNECTION TOPOLOGY; PLANAR INTEGRATORS;

MULTI AGENT SYSTEMS;

EID: 33847191057     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2005.1582246     Document Type: Conference Paper

References (16)

1. S. H. Strogatz, Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life, New York: Hyperion, 2003.
2. L. Moreau, "Leaderless coordination via bidirectional and unidirectional time-dependent communication," in Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, December 2003, pp. 3070-3075.
3. Z. Lin, B. A. Francis, and M. Maggiore, "Necessary and sufficient graphical conditions for formation control of unicycles," IEEE Transactions on Automatica Control, vol. 50, no. 1, pp. 121-127, January 2005.
4. H. G. Tanner, A. Jadbabaie, and G. J. Pappas, "Stable flocking of mobile agents, part II: Dynamic topology," in Proceedings of the 42nd IEEE Conference on Decision and Control, Maui, Hawaii, December 2003, pp. 2016-2021.
5. S. Aranda, S. Martínez, and F. Bullo, "On optimal sensor placement and motion coordination for target tracking," in Proceedings of the IEEE Conference of Robotics and Automation, Barcelona, Spain, April 2005, to appear.
6. K. Sugihara and I. Suzuki, "Distributed motion coordination of multiple mobile robots," in Proceedings of the 5th IEEE International Symposium on Intelligent Control, 1990, pp. 138-143.
7. N. E. Leonard and E. Fiorelli, "Virtual leaders, artificial potentials and coordinated control of groups," in Proceedings of the 40th IEEE Conference on Decision and Control, Orlando, Florida, 2001, pp. 2968-2973.
8. J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations," IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1465-1476, September 2004.
9. J. A. Marshall, M. E. Broucke, and B. A. Francis, "Formations of vehicles in cyclic pursuit," IEEE Transactions on Automatic Control, vol. 49, no. 11, pp. 1963-1974, November 2004.
10. B. Recht and R. D'Andrea, "Distributed control of systems over discrete groups," IEEE Transactions on Automatic Control, vol. 49, no. 9, pp. 1446-1452, September 2004.
11. A. Pogromsky, G. Santoboni, and H. Nijmeijer, "Partial synchronization: From symmetry towards stability," Physica D, vol. 172, pp. 65-87, 2002.
12. A. M. Bruckstein, G. Sapiro, and D. Shaked, "Evolutions of planar polygons," International Journal of Pattern Recognition and Artificial Intelligence, vol. 9, no. 6, pp. 991-1014, 1995.
13. T. J. Richardson, "Stable polygons of cyclic pursuit," Annals of Mathematics and Artificial Intelligence, vol. 31, pp. 147-172, 2001.
14. H. S. M. Coxeter, Regular Polytopes. London: Methuen & Co. Ltd., 1948.
15. P. J. Davis, Circulant Matrices, 2nd ed. New York: Chelsea Publishing, 1994.
16. G. A. Jones and J. M. Jones, Elementary Number Theory, ser. Springer Undergraduate Mathematics Series. New York: Springer, 1998.