Rendezvous without coordinates

IEEE Transactions on Automatic Control

Volumn 57, Issue 2, 2012, Pages 421-434

  Yu, Jingjin ^a   LaValle, Steven M ^a   Liberzon, Daniel ^a  

^a University of Illinois at Urbana Champaign   (United States)

Author keywords

Consensus; distributed control; minimalism; multiagent systems; rendezvous

Indexed keywords

CONSENSUS; DISTRIBUTED CONTROL; ESTIMATION PROCEDURES; LYAPUNOV ANALYSIS; MINIMALISM; QUANTIZED CONTROL; RENDEZVOUS; SENSING MODEL; SINGLE-AGENT;

COMPUTER SIMULATION; CONTROL THEORY; DISTRIBUTED PARAMETER CONTROL SYSTEMS; MULTI AGENT SYSTEMS; WINDSHIELDS;

AUTONOMOUS AGENTS;

EID: 84863040175     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2011.2158172     Document Type: Article

References (43)

1. H. Ando, Y. Oasa, I. Suzuki, and M. Yamashita, "Distributed memoryless point convergence algorithm for mobile robots with limited visibility," IEEE Trans. Robot. Autom., vol. 15, no. 5, pp. 818-828, Oct. 1999.
2. A. Bernhart, "Polygons of pursuit," Scripta Math., vol. 24, pp. 23-50, 1959.
3. S. Bhattacharya, R. Murrieta-Cid, and S. Hutchinson, "Optimal paths for landmark-based navigation by differential-drive vehicles with field-of-view constraints," IEEE Trans. Robotics, vol. 23, no. 1, pp. 47-59, Feb. 2007.
4. R. W. Brockett and D. Liberzon, "Quantized feedback stabilization of linear systems," IEEE Trans. Autom. Control, vol. 45, no. 7, pp. 1279-1289, Jul. 2000.
5. A. M. Bruckstein, N. Cohen, and A. Efrat, Ants, crickets and frogs in cyclic pursuit Comput. Sci. Dept., Israel Inst. Technol., Haifa, Israel, Tech. Rep. CIS Rep. 9105, Jul. 1991.
6. J. Cortés, S. Martinéz, and F. Bullo, "Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions," IEEE Trans. Autom. Control, vol. 51, no. 8, pp. 1289-1298, Aug. 2006.
7. A. T. Şamiloǧlu, V. Gazi, and A. B. Koku, "Asynchronous cyclic pursuit," in Proc. SAB06, 2006, vol. 4095, Lecture Notes in Artificial Intelligence, pp. 667-678.
8. D. F. Delchamps, "Stabilizing a linear system with quantized output record," IEEE Trans. Autom. Control, vol. 35, no. 8, pp. 916-926, Aug. 1990.
9. L. E. Dubins, "On curves of minimal length with a constraint on average curvature, and with prescribed initial and terminal positions and tangents," Amer. J. Math., vol. 79, pp. 497-516, 1957.
10. N. Elia and S. K. Mitter, "Stabilization of linear systems with limited information," IEEE Trans. Autom. Control, vol. 46, no. 9, pp. 1384-1400, Sep. 2001.
11. M. A. Erdmann and M. T. Mason, "An exploration of sensorless manipulation," IEEE Trans. Rob. Autom., vol. 4, no. 4, pp. 369-379, Aug. 1988.
12. V. Gazi, "Stability of a discrete-time asynchronous swarm with timedependent communication links," IEEE Trans. Syst., Man, Cybern. B, vol. 38, no. 1, pp. 267-274, Feb. 2008.
13. K. Y. Goldberg, "Orienting polygonal parts without sensors," Algorithmica, vol. 10, pp. 201-225, 1993.
14. J. P. Hespanha, A. Ortega, and L. Vasudevan, "Towards the control of linear systems with minimum bit-rate," in Proc. 15th Int. Symp. Math. Theory Networks and Syst., 2002.
15. H. Ishii and B. A. Francis, "Stabilizing a linear system by switching control with dwell time," IEEE Trans. Autom. Control, vol. 47, no. 12, pp. 1962-1973, Dec. 2002.
16. A. Jadbabaie, J. Lin, and A. S. Morse, "Coordination of groups of mobile autonomous agents using nearest neighbor rules," IEEE Trans. Autom. Control, vol. 48, no. 6, pp. 988-1001, Jun. 2003.
17. H. Jung, "Über die kleinste kugel, die eine räumliche figur einschließ," J. Reine Angew. Math., vol. 123, pp. 241-257, 1901.
18. H. Jung, "Über den kleinsten kreis, der eine ebene figur einschließ," J. Reine Angew. Math., vol. 137, pp. 310-313, 1910.
19. I. Kamon, E. Rivlin, and E. Rimon, "Range-sensor based navigation in three dimensions," in Proc. IEEE Int. Conf. Robotics Automation, 1999.
20. S. M. LaValle, Planning Algorithms. Cambridge, U.K.: Cambridge Univ. Press, 2006.
21. D. Liberzon, Switching in Systems and Control. Cambridge, MA: Birkhäuser, 2003.
22. J. Lin, A. S. Morse, and B. D. O. Anderson, "The multi-agent rendezvous problem. Part 1: The synchronous case," SIAM J. Control Optim., vol. 46, no. 6, pp. 2096-2119, Nov. 2007.
23. J. Lin, A. S. Morse, and B. D. O. Anderson, "The multi-agent rendezvous problem. Part 2: The asynchronous case," SIAM J. Control Optim., vol. 46, no. 6, pp. 2120-2147, Nov. 2007.
24. Y. Lin, E. D. Sontag, and Y. Wang, "A smooth converse Lyapunov theorem for robust stability," SIAM J. Control Optim., vol. 34, pp. 124-160, 1996.
25. Z. Lin, M. Broucke, and B. Francis, "Local control strategies for groups of mobile autonomous agents," IEEE Trans. Autom. Control, vol. 49, no. 4, pp. 622-629, Apr. 2004.
26. D. G. Luenberger, Linear and Nonlinear Programming, 2nd ed. Reading, MA: Addison Wesley, 1984.
27. V. J. Lumelsky and A. A. Stepanov, "Path planning strategies for a point mobile automaton moving amidst unknown obstacles of arbitrary shape," Algorithmica, vol. 2, pp. 403-430, 1987.
28. J. A. Marshall, M. E. Broucke, and B. A. Francis, "Formations of vehicles in cyclic pursuit," IEEE Trans. Autom. Control, vol. 49, no. 11, pp. 1963-1974, Nov. 2004.
29. L. Moreau, "Stability of multiagent systems with time-dependent communication links," IEEE Trans. Autom. Control, vol. 50, no. 2, pp. 169-182, Feb. 2005.
30. G. N. Nair and R. J. Evans, "Stabilizability of stochastic linear systems with finite feedback data rates," SIAM J. Control Optim, vol. 43, pp. 413-436, 2004.
31. M. Pavone and E. Frazzoli, "Decentralized policies for geometric pattern formation and path coverage," J. Dynam. Syst., Meas., Control, vol. 129, no. 5, pp. 633-643, 2007.
32. I. R. Petersen and A. V. Savkin, "Multi-rate stabilization of multivariable discrete-time linear systems via a limited capacity communication channel," in Proc. 40th IEEE Conf. Decision Control, 2001, pp. 304-309.
33. W. Ren and R. W. Beard, "Consensus seeking in multi-agent systems under dynamically changing interaction topologies," IEEE Trans. Autom. Control, vol. 50, no. 5, pp. 655-661, May 2005.
34. T. Richardson, "Stable polygons of cyclic pursuit," Ann. Math. Artificial Intell., vol. 31, pp. 147-172, 2001.
35. J. Roe, Elementary Geometry. New York: Oxford Univ. Press, 1993.
36. A. V. Savkin and H. Teimoori, "Bearings-only guidance of a unicyclelike vehicle following a moving target with a smaller minimum turning radius," IEEE Trans. Autom. Control, vol. 55, no. 10, pp. 2390-2395, Oct. 2010.
37. A. Sinha and D. Ghose, "Generalization of linear cyclic pursuit with application to rendezvous of multiple autonomous agents," IEEE Trans. Autom. Control, vol. 51, no. 11, pp. 1819-1824, Nov. 2006.
38. S. L. Smith, M. E. Broucke, and B. A. Francis, "Curve shortening and the rendezvous problem for mobile autonomous robots," IEEE Trans. Autom. Control, vol. 52, no. 6, pp. 1154-1159, Jun. 2007.
39. S. Tatikonda and S. K. Mitter, "Control under communication constraints," IEEE Trans. Autom. Control, vol. 49, no. 7, pp. 1056-1068, Jul. 2004.
40. B. Tovar, R. Murrieta, and S. M. LaValle, "Distance-optimal navigation in an unknown environment without sensing distances," IEEE Trans. Robot., vol. 23, no. 3, pp. 506-518, Jun. 2007.
41. D. B.West, Introduction to Graph Theory, 2nd ed. Englewood Cliffs, NJ: Prentice-Hall, 2001.
42. W. S. Wong and R. W. Brockett, "Systems with finite communication bandwidth constraints II: Stabilization with limited information feedback," IEEE Trans. Autom. Control, vol. 44, no. 5, pp. 1049-1053, May 1999.
43. J. Yu, S. M. LaValle, and D. Liberzon, "Rendezvous without coordinates," in Proc. IEEE Conf. Decision and Control, 2008, pp. 1803-1808.