Counting critical formations on a line

SIAM Journal on Control and Optimization

Volumn 52, Issue 1, 2014, Pages 219-242

  Anderson, Brian D O ^a,b   Helmke, Uwe ^c  

^a AUSTRALIAN NATIONAL UNIVERSITY   (Australia)

^b CSIRO   (Australia)

^c UNIVERSITY OF WÜRZBURG   (Germany)

Author keywords

B zout's theorem; Bernstein theorem; Cubics; Formation control; Morse inequalities

Indexed keywords

ALGEBRAIC GEOMETRY; BERNSTEIN THEOREM; CUBICS; DECENTRALIZED CONTROL LAW; EQUILIBRIUM POINT; FORMATION CONTROL; MORSE INEQUALITIES; POTENTIAL FUNCTION;

MATHEMATICAL TECHNIQUES; OPTIMIZATION;

DECENTRALIZED CONTROL;

EID: 84897862015     PISSN: 03630129     EISSN: None     Source Type: Journal    
DOI: 10.1137/120890533     Document Type: Article

References (14)

1. B. D. O. ANDERSON, Morse theory and formation control, in Proceedings of the 19th Mediterranean Conference on Control and Automation, Corfu, Greece, 2011, pp. 656-661.
2. B. D. O. ANDERSON, C. YU, S. DASGUPTA, AND A. S. MORSE, Control of a three-coleader formation in the plane, Systems Control Lett., 56(2007), pp. 573-578.
3. B. D. O. ANDERSON, C. YU, S. DASGUPTA, AND T. H. SUMMERS, Controlling four agent formations, in Proceedings of the 2nd IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys '10), Annecy, France, 2010, pp. 139-144.
4. M. CAO, A. S. MORSE, C. YU, B. D. O. ANDERSON, AND S. DASGUPTA, Maintaining a directed, triangular formation of mobile autonomous agents, Commun. Inform. Sci., 11(2011), pp. 1-16.
5. M. CAO, C. YU, A. S. MORSE, B. D. O. ANDERSON, AND S. DASGUPTA, Generalized controller for directed triangle formations, in Proceedings of the 17th World IFAC Congress, Seoul, Korea, 2008, pp. 6590-6595.
6. D. COX, J. LITTLE, AND D. O'SHEA, Using Algebraic Geometry, Grad. Texts in Math. 185, Springer, New York, 1998.
7. M. J. GREENBERG AND J. R. HARPER, Algebraic Topology: A First Course, Math. Lecture Ser., Benjamin/Cummings, Reading, MA, 1981.
8. M. W. HIRSCH, Differential Topology, Grad. Texts in Math. 33, Springer, New York, 1976.
9. B. HUBER AND B. STURMFELS, Bernstein's theorem in affine space, Discrete Comput. Geom., 17(1997), pp. 137-141.
10. n, Math. Comp., 65(1996), pp. 1477-1484.
11. L. KRICK, M. E. BROUCKE, AND B. FRANCIS, Stabilization of infinitesimally rigid formation of multi-robot networks, Int. J. Control, 82(2009), pp. 423-439.
12. Y. MATSUMOTO, An Introduction to Morse Theory, American Mathematical Society, Providence, RI, 1997.
13. R. OLFATI-SABER AND R. MURRAY, Distributed cooperative control of multiple vehicle formations using structural potential functions, in Proceedings of the 15th IFAC World Congress, Barcelona, Spain, 2002, pp. 346-352.
14. S. L. SMITH, M. E. BROUCKE, AND B. FRANCIS, Stabilizing a multi-agent system to an equilateral polygon formation, in Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), Kyoto, Japan, 2006, pp. 2415-2424.