Stabilisation of infinitesimally rigid formations of multi-robot networks

International Journal of Control

Volumn 82, Issue 3, 2009, Pages 423-439

  Krick, Laura ^a   Broucke, Mireille E ^a   Francis, Bruce A ^a  

^a UNIVERSITY OF TORONTO   (Canada)

Author keywords

Cooperative control; Graph rigidity; Multiagent formations

Indexed keywords

GRAPH THEORY; RIGIDITY;

ASYMPTOTICAL STABILITIES; COOPERATIVE CONTROL; DIRECTED GRAPHS; FORMATION CONTROLS; GRAPH RIGIDITY; LOCAL INFORMATIONS; MULTI ROBOTS; MULTI-VEHICLE SYSTEMS; MULTIAGENT FORMATIONS; POTENTIAL FUNCTIONS; REGULAR POLYGONS; RIGID FORMATIONS; STABILISATION; SUFFICIENT CONDITIONS;

SYSTEM STABILITY;

EID: 61349149430     PISSN: 00207179     EISSN: 13665820     Source Type: Journal    
DOI: 10.1080/00207170802108441     Document Type: Article

References (24)

1. Asimow, L., and Roth, B. (1979), 'The Rigidity of Graphs II', Journal of Mathematical Analysis and Applications, 68, 171-190.
2. Asimow, L., and Roth, B. (1978), 'The Rigidity of Graphs', Transactions of the American Mathematical Society, 245, 279-289.
3. Bereg, S. (2005), 'Certifying and Constructing Minimally Rigid Graphs in the Plane', Proceedings of the Twenty-First Annual Symposium on Computational Geometry, Pisa, Italy: Annual Symposium on Computational Geometry, pp. 73-80.
4. Biggs, N. (1974), Algebraic Graph Theory, London: Cambridge University Press.
5. Boothby, W. (1986), An Introduction to Differentiable Manifolds and Reimannian Geometry, Orlando, Florida: Academic Press Inc.
6. Carr, J. (1981), Applications of Centre Manifold Theory, New York: Springer-Verlag.
7. Cortes, J., Martinez, S., and Bullo, F. (2004a), 'Robust Rendezvous for Mobile Autonomous Agents via Proximity Graphs in d Dimensions', Transactions on Automatic Control, 51, 1289-1298.
8. Cortes, J., Martínez, S., Karatas, T., and Bullo, F. (2004b), 'Coverage Control for Mobile Sensing Networks', IEEE Transactions on Robotics and Automation, 2, 243-255.
9. Goldenberg, D., Lin, J., Morse, A., Rosen, B., and Yang, Y. (2004), 'Towards Mobility as a Network Control Primitive', Proceedings of the 5th ACM International Symposium on Mobile ad hoc Networking and Computing, Japan: Tokyo, pp. 163-174.
10. Hendrickx, J., Fidan, B., Changbin, Y., Anderson, B., and Blondel, V. (2006b), 'Elementary Operations for the Reorganization of Minimally Persistent formations', Proceeds of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), June, Japan: Kyoto, pp. 859-873.
11. Hendrickx, J., Anderson, B., Delvenne, J.C., and Blondel, V. (2006a), 'Directed Graphs for the Analysis of Rigidity'and'Persistence in Autonomous Agent Systems', International Journal of Robust and Nonlinear Control, 17, 960-981.
12. Khalil, H. (2002), Nonlinear Systems, Upper Saddle River, NJ: Prentice Hall.
13. Krick, L. (2007), 'Application of Graph Rigidity in Formation Control of Multi-robot Networks', MASc Thesis, Toronto: University of Toronto, Electrical and Computer Engineering Dept.
14. Lin, J., Morse, A., and Anderson, B. (2004), 'The Multi-Agent Rendezvous Problem - The Asynchronous Case', Proceedings of the 43rd IEEE Conference on Decision and Control, December, Vol. 2 Bahamas: Atlantis, pp. 1926-1931.
15. Łojawiewicz, S. (1959), 'Sur Le ProbléMe De La Division', Studia Mathmatica, 18, 87-136.
16. Malkin, 1. (1958), Theory of Stability of Motion, United States Atomic Energy Commission Technical Information Service.
17. Marshall, J., Broucke, M., and Francis, B. (2004), 'Formations of Vehicles in Cyclic Pursuit', IEEE Transactions on Automatic Control, 9, 1963-1974.
18. Marshal], J., Broucke, M., and Francis, B. (2006), 'Pursuit Formations of Unicycles', Automatica, 42, 3-12.
19. Olfati-Saber, R. (2006), 'Flocking for Multi-agent Dynamic Systems: Algorithms and Theory', IEEE Transactions on Automatic Control, 51, 401-420.
20. Olfati-Saber, R., and Murray, R. (2002), 'Distributed Cooperative Control of Multiple Vehicle Formations using Structural Potential Functions', Proceedings of the 15th IFAC World Congress, Spain: Barcelona.
21. Smith, S., Broucke, M., and Francis, B. (2006), 'Stabilizing a Multi-Agent System to an Equilateral Polygon "formation', Proceeds of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS2006), Japan: Kyoto, pp. 2415-2424.
22. Sundarapandian, V. (2003), 'A Geometric Proof of Malkin's Stability theorem', Indian Journal of Pure and Applied Mathematics, 34, 1085-1088.
23. Whitney, H. (1957), 'Elementary Structure of Real Algebraic Varieties', The Annals of Mathematics, 66, 545-556.
24. Wiggins, S. (1990), Introduction to Applied Nonlinear Dynamical Systems and Chaos, New York: Springer-Verlag.