Graph-theoretic connectivity control of mobile robot networks

Proceedings of the IEEE

Volumn 99, Issue 9, 2011, Pages 1525-1540

  Zavlanos, Michael M ^a   Egerstedt, Magnus B ^b   Pappas, George J ^c  

^a Stevens Institute of Technology   (United States)

^b GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Algebraic graph theory; convex and subgradient optimization; graph connectivity; hybrid systems

Indexed keywords

ALGEBRA; CONVEX OPTIMIZATION; FADING (RADIO); HYBRID SYSTEMS; MOBILE ROBOTS;

ALGEBRAIC CONNECTIVITY; ALGEBRAIC GRAPH THEORY; COMMUNICATION MODELS; GRAPH CONNECTIVITY; MOBILE ROBOT NETWORKS; NETWORK CONNECTIVITY; SUB-GRADIENT OPTIMIZATION; THEORETICAL FRAMEWORK;

GRAPH THEORY;

EID: 80052022498     PISSN: 00189219     EISSN: None     Source Type: Journal    
DOI: 10.1109/JPROC.2011.2157884     Document Type: Conference Paper

References (87)

1. J. Cortes, "Achieving coordination tasks in finite time via nonsmooth gradient flows," in Proc. 44th IEEE Conf. Decision Control/Eur. Control Conf., Seville, Spain, Dec. 2005, pp. 6376-6381.
2. J. Cortes, "Distributed algorithms for reaching consensus on general functions," Automatica, vol. 44, no. 3, pp. 726-737, 2008.
3. R. Olfati-Saber and R. M. Murray, "Decentralized control of connectivity for multi-agent systems," in Proc. Amer. Control Conf., 2003, pp. 951-956.
4. R. Olfati-Saber and R. M. Murray, "Consensus problems in networks of agents with switching topology and time-delays," IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1520-1533, Sep. 2004.
5. J. A. Fax and R. M. Murray, "Information flow and cooperative control of vehicle formations," IEEE Trans. Autom. Control, vol. 49, no. 9, pp. 1465-1476, Sep. 2004.
6. 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.
7. L. Moreau, "Stability of multi-agent systems with time-dependent communication links," IEEE Trans. Autom. Control, vol. 50, no. 2, pp. 169-182, Feb. 2005. (Pubitemid 40319348)
8. 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. (Pubitemid 40784437)
9. Z. Lin, M. Brouke, 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.
10. V. Blondel, J. M. Hendrickx, A. Olshevsky, and J. N. Tsitsiklis, "Convergence in multi-agent coordination, consensus, and flocking," in Proc. 44th IEEE Conf. Decision Control/Eur. Control Conf., Seville, Spain, Dec. 2005, pp. 2996-3000. (Pubitemid 46297429)
11. D. Bauso, L. Giarre, and R. Pesenti, "Nonlinear protocols for optimal distributed consensus in networks of dynamic agents," Syst. Control Lett., vol. 55, no. 11, pp. 918-928, 2006. (Pubitemid 44344836)
12. M. Mehyar, D. Spanos, J. Pongsjapan, S. H. Low, and R. M. Murray, "Achieving coordination tasks in finite time via nonsmooth gradient flows," in Proc. 44th IEEE Conf. Decision Control/Eur. Control Conf., Seville, Spain, Dec. 2005, pp. 7446-7451.
13. P.-A. Bliman and G. Ferrari-Trecate, "Average consensus problems in networks of agents with delayed communications," in Proc. 44th IEEE Conf. Decision Control/Eur. Control Conf., Seville, Spain, Dec. 2005, pp. 7066-7071.
14. R. Olfati-Saber, J. A. Fax, and R. M. Murray, "Consensus and cooperation in networked multi-agent systems," Proc. IEEE, vol. 95, no. 1, pp. 215-233, Jan. 2007.
15. A. Neskovic, N. Neskovic, and G. Paunovic, "Modern approaches in modeling of mobile radio systems propagation environment," IEEE Commun. Surv., vol. 3, no. 3, pp. 1-12, 2000.
16. J. D. Parsons, The Mobile Radio Propagation Channel. New York: Wiley, 2000.
17. K. Pahlavan and A. H. Levesque, Wireless Information Networks. New York: Wiley, 1995.
18. A. J. Goldsmith and S. B. Wicker, "Design challenges for energy-constrained ad hoc wireless networks," IEEE Wireless Commun. Mag., vol. 9, no. 4, pp. 8-27, Aug. 2002. (Pubitemid 35426991)
19. P. Gupta and P. R. Kumar, "Critical power for asymptotic connectivity," in Proc. 37th IEEE Conf. Decision Control, Tampa, FL, Dec. 1998, pp. 1106-1110.
20. B. Chen, K. Jamieson, H. Balakrishnan, and R. Morris, "Span: An energy-efficient coordination algorithm for topology maintenance in ad hoc wireless networks," Wireless Netw., vol. 8, no. 5, pp. 481-494, Sep. 2002.
21. R. Ramanathan and R. Rosales-Hain, "Topology control of multihop wireless networks using transmit poweradjustment," in Proc. 19th Annu. Joint Conf. IEEE Comput. Commun. Soc. (INFOCOM), Tel Aviv, Israel, 2000, pp. 404-413. (Pubitemid 30584488)
22. E. L. Lloyd, R. Liu, M. V. Marathe, R. Ramanathan, and S. S. Ravi, "Algorithmic aspects of topology control problems for ad hoc networks," Mobile Netw. Appl., vol. 10, no. 1-2, pp. 19-34, Feb. 2005. (Pubitemid 40537003)
23. L. Ning, J. C. Hou, and L. Sha, "Design and analysis of an mst-based topology control algorithm," IEEE Trans. Wireless Commun., vol. 4, no. 3, pp. 1195-1206, May 2005. (Pubitemid 40683187)
24. R. D'Souza, D. Galvin, C. Moore, and D. Randall, "Global connectivity from local geometric constraints for sensor networks with various wireless footprints," in Proc. 5th Int. Conf. Inf. Process. Sensor Netw., Nashville, TN, Apr. 2006, pp. 19-26.
25. L. Li, J. Y. Halpern, P. Bahl, Y. M. Wang, and R. Wattenhofer, "A cone-based distributed topology-control algorithm for wireless multi-hop networks," IEEE/ACM Trans. Netw., vol. 13, no. 1, pp. 147-159, Feb. 2005. (Pubitemid 40400354)
26. S. Poduri, S. Pattem, B. Krishnamachari, and G. S. Sukhatme, "Using local geometry for tunable topology control in sensor networks," IEEE Trans. Mobile Comput., vol. 8, no. 2, pp. 218-230, Feb. 2009.
27. R. Wattenhofer and A. Zollinger, "Xtc: A practical topology control algorithm for ad-hoc networks," in Proc. 18th IEEE Int. Parallel Distrib. Process. Symp., Santa Fe, NM, Apr. 2004, pp. 216-223.
28. M. M. Zavlanos, A. Tahbaz-Salehi, A. Jadbabaie, and G. J. Pappas, "Distributed topology control of dynamic networks," in Proc. Amer. Control Conf., Seattle, WA, Jun. 2008, pp. 2660-2665.
29. F. Xue and P. R. Kumar, "The number of neighbors needed for connectivity of wireless networks," Wireless Netw., vol. 10, no. 2, pp. 169-181, Mar. 2004.
30. O. Dousse, F. Baccelli, and P. Thiran, "Impact of interferences on connectivity in ad hoc networks," IEEE/ACM Trans. Netw., vol. 13, no. 2, pp. 425-436, 2005. (Pubitemid 40690836)
31. M. Fiedler, "Absolute algebraic connectivity of trees," Linear Multilinear Algebra, vol. 26, pp. 85-106, 1990.
32. Y. Wan, S. Roy, X. Wang, A. Saberi, T. Yang, M. Xue, and B. Malek, "On the structure of graph edge designs that optimize the algebraic connectivity," in Proc. 47th IEEE Conf. Decision Control, Cancun, Mexico, Dec. 2008, pp. 805-810.
33. A. Ghosh and S. Boyd, "Growing well-connected graphs," in Proc. 45th IEEE Conf. Decision Control, San Diego, CA, Dec. 2006, pp. 6605-6611.
34. S. Boyd, "Convex optimization of graph Laplacian eigenvalues," in Proc. Int. Congr. Math., Madrid, Spain, Aug. 2006, pp. 1311-1319.
35. M. Mesbahi, "On state-dependent dynamic graphs and their controllability properties," IEEE Trans. Autom. Control, vol. 50, no. 3, pp. 387-392, Mar. 2005. (Pubitemid 40448590)
36. 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. (Pubitemid 30514350)
37. M. Fiedler, "Algebraic connectivity of graphs," Czechoslovak Math. J., vol. 23, no. 98, pp. 298-305, 1973.
38. B. Mohar, "The Laplacian spectrum of graphs," in Graph Theory, Combinatorics, and Applications, Y. Alavi, G. Chartrand, O. Ollermann, and A. Schwenk, Eds. New York: Wiley, 1991, pp. 871-898.
39. R. Merris, "Laplacian matrices of a graph: A survey," Linear Algebra Its Appl., vol. 197, pp. 143-176, 1994.
40. C. Godsil and G. Royle, Algebraic Graph Theory, vol. 207. Berlin, Germany: Springer-Verlag, 2001, ser. Graduate Texts in Mathematics.
41. Y. Kim and M. Mesbahi, "On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian," IEEE Trans. Autom. Control, vol. 51, no. 1, pp. 116-120, Jan. 2006. (Pubitemid 43137938)
42. M. C. DeGennaro and A. Jadbabaie, "Decentralized control of connectivity for multi-agent systems," in Proc. 45th IEEE Conf. Decision Control, San Diego, CA, Dec. 2006, pp. 3628-3633. (Pubitemid 351283394)
43. M. M. Zavlanos and G. J. Pappas, "Potential fields for maintaining connectivity of mobile networks," IEEE Trans. Robot., vol. 23, no. 4, pp. 812-816, Aug. 2007. (Pubitemid 47308118)
44. P. Yang, R. Freeman, G. Gordon, K. Lynch, S. Srinivasa, and R. Sukthankar, "Decentralized estimation and control of graph connectivity in mobile sensor networks," in Proc. Amer. Control Conf., Seattle, WA, Jun. 2008, pp. 2678-2683.
45. F. Knorn, R. Stanojevic, M. Corless, and R. Shorten, "A framework for decentralized feedback connectivity control with application to sensor networks," Int. J. Control, vol. 82, no. 11, pp. 2095-2114, 2009.
46. M. M. Zavlanos and G. J. Pappas, "Distributed connectivity control of mobile networks," IEEE Trans. Robot., vol. 24, no. 6, pp. 1416-1428, Dec. 2008.
47. M.M. Zavlanos and G. J. Pappas, "Controlling connectivity of dynamic graphs," in Proc. 44th IEEE Conf. Decision Control/Eur. Control Conf., Seville, Spain, Dec. 2005, pp. 6388-6393.
48. K. Srivastava and M. W. Spong, "Multi-agent coordination under connectivity constraints," in Proc. Amer. Control Conf., Seattle, WA, Jun. 2008, pp. 2648-2653.
49. G. Notarstefano, K. Savla, F. Bullo, and A. Jadbabaie, "Maintaining limited-range connectivity among second-order agents," in Proc. Amer. Control Conf., Minneapolis, MN, Jun. 2006, pp. 2124-2129. (Pubitemid 46531130)
50. F. Bullo, J. Cortes, and S. Martinez, Distributed Control of Robotic Networks. Princeton, NJ: Princeton Univ. Press, 2009, ser. Distributed Control of Robotic Networks.
51. D. P. Spanos and R. M. Murray, "Robust connectivity of networked vehicles," in Proc. 43rd IEEE Conf. Decision Control, "ahamas, Dec. 2004, pp. 2893-2898.
52. D. V. Dimarogonas and K. J. Kyriakopoulos, "Connectedness preserving distributed swarm aggregation for multiple kinematic robots," IEEE Trans. Robot., vol. 24, no. 5, pp. 1213-1223, Oct. 2008.
53. A. Cornejo and N. Lynch, "Connectivity service for mobile ad-hoc networks," in Proc. 2nd IEEE Int. Conf. Self-Adaptive Self-Organizing Syst. Workshops, Oct. 2008, pp. 292-297.
54. Z. Yao and K. Gupta, "Backbone-based connectivity control for mobile networks," in Proc. IEEE Int. Conf. Robot. Autom., Kobe, Japan, May 2009, pp. 1133-1139.
55. M. M. Zavlanos, A. Jadbabaie, and G. J. Pappas, "Flocking while preserving network connectivity," in Proc. 46th IEEE Conf. Decision Control, New Orleans, LA, Dec. 2007, pp. 2919-2924.
56. M. Ji and M. Egerstedt, "Coordination control of multi-agent systems while preserving connectedness," IEEE Trans. Robot., vol. 23, no. 4, pp. 693-703, Aug. 2007. (Pubitemid 47308109)
57. J. Wagenpfeil, A. Trachte, T. Hatanaka, M. Fujita, and O. Sawodny, "A distributed minimum restrictive connectivity maintenance algorithm," in Proc. 9th Int. Symp. Robot Control, Gifu, Japan, pp. 499-504, Sep. 2009.
58. M. Schuresko and J. Cortes, "Distributed motion constraints for algebraic connectivity of robotic networks," J. Intell. Robot. Syst., vol. 56, no. 1-2, pp. 99-126, Sep. 2009.
59. M. Schuresko and J. Cortes, "Distributed tree rearrangements for reachability and robust connectivity," in Hybrid Systems: Computetation and Control, vol. 5469, "erlin, Germany: Springer-Verlag, 2009, pp. 470-474.
60. D. P. Spanos and R. M. Murray, "Motion planning with wireless network constraints," in Proc. Amer. Control Conf., Portland, OR, Jun. 2005, pp. 87-92. (Pubitemid 41189353)
61. E. Stump, A. Jadbabaie, and V. Kumar, "Connectivity management in mobile robot teams," in Proc. IEEE Int. Conf. Robot. Autom., Pasadena, CA, May 2008, pp. 1525-1530.
62. A. Ganguli, J. Cortes, and F. Bullo, "Multirobot rendezvous with visibility sensors in nonconvex environments," IEEE Trans. Robot., vol. 25, no. 2, pp. 340-352, Apr. 2009.
63. J. Cortes, S. Martinez, 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. (Pubitemid 44283231)
64. M. M. Zavlanos, H. G. Tanner, A. Jadbabaie, and G. J. Pappas, "Hybrid control for connectivity preserving flocking," IEEE Trans. Autom. Control, vol. 54, no. 12, pp. 2869-2875, Dec. 2009.
65. D. V. Dimarogonas and K. H. Johansson, "Decentralized connectivity maintenance in mobile networks with bounded inputs," in Proc. IEEE Int. Conf. Robot. Autom., Pasadena, CA, May 2008, pp. 1507-1512.
66. A. Ajorlou and A. G. Aghdam, "A class of bounded distributed controllers for connectivity preservation of unicycles," in Proc. 49th IEEE Conf. Decision Control, Atlanta, GA, Dec. 2010, pp. 3072-3077.
67. A. Ajorlou, A. Momeni, and A. G. Aghdam, "A class of bounded distributed control strategies for connectivity preservation in multi-agent systems," IEEE Trans. Autom. Control, vol. 55, no. 12, pp. 2828-2833, Dec. 2010.
68. M. A. Hsieh, A. Cowley, V. Kumar, and C. Taylor, "Maintaining network connectivity and performance in robot teams," J. Field Robot., vol. 25, no. 1-2, pp. 111-131, 2008.
69. A. R. Wagner and R. C. Arkin, "Communication-sensitive multi-robot reconnaissance," in Proc. IEEE Int. Conf. Robot. Autom., New Orleans, LA, 2004, pp. 2480-2487.
70. M. Powers and T. Balch, "Value-based communication preservation for mobile robots," in Distrib. Autonom. Robot. Syst. 6, R. Alami, R. Chatila, and H. Asama, Eds. Japan: Springer, 2007, pp. 327-336.
71. Y. Mostofi, "Decentralized communication-aware motion planning in mobile networks: An information-gain approach," J. Intell. Robot. Syst., vol. 56, no. 1-2, pp. 233-256, 2009.
72. P. Flocchini, G. Prencipe, N. Santoro, and P. Widmayer, "Gathering of asynchronous oblivious robots with limited visibility," Theor. Comput. Sci., vol. 337, no. 1-3, pp. 147-168, 2005. (Pubitemid 40644671)
73. R. C. Arkin and J. Diaz, "Line-of-sight constrained exploration for reactive multiagent robotic teams," in Proc. 7th Int. Workshop Adv. Motion Control, Maribor, Slovenia, 2002, pp. 455-461. (Pubitemid 40761207)
74. S. O. Anderson, R. Simmons, and D. Goldberg, "Maintaining line-of-sight communications networks between planetray rovers," in Proc. IEEE/RSJ Int. Conf. Intell. Robots Syst., Las Vegas, NV, 2003, pp. 2266-2272.
75. G. Hollinger and S. Singh, "Multi-robot coordination with periodic connectivity," in Proc. IEEE Int. Conf. Robot. Autom., 2010.
76. T. Gustavi, D. V. Dimarogonas, M. Egerstedt, and X. Hu, "Sufficient conditions for connectivity maintenance and rendezvous in leader-follower networks," Automatica, vol. 46, no. 1, pp. 133-139, Jan. 2010.
77. D. Tardioli, A. R. Mosteo, L. Riazuelo, J. L. Villarroel, and L. Montano, "Enforcing network connectivity in robot team missions," Int. J. Robot. Res., to be published.
78. N. Michael, M. M. Zavlanos, V. Kumar, and G. J. Pappas, "Maintaining connectivity in mobile robot networks," in Experimental Robotics, New York: Springer-Verlag, 2009, pp. 117-126.
79. S. Boyd and L. Vandenberghe, Convex Optimization. Cambridge, U.K.: Cambridge Univ. Press, 2004.
80. D. Kempe and M. McSherry, "A decentralized algorithm for spectral analysis," J. Comput. Syst. Sci., vol. 74, no. 1, pp. 70-83, 2008. (Pubitemid 47625406)
81. M.Mesbahi andM. Egerstedt, Graph Theoretic Methods for Multiagent Networks. Princeton, NJ: Princeton Univ. Press, 2010.
82. A. Barbosa, "The effects of predation risk on scanning and flocking behavior in dunlin," J. Field Ornithology, vol. 68, no. 4, pp. 607-612, 1997.
83. N. Leonard and E. Fiorelli, "Virtual leaders, artificial potentials and coordinated control of groups," in Proc. 40th IEEE Conf. Decision Control, Orlando, FL, Dec. 2001, pp. 2968-2973. (Pubitemid 34139418)
84. R. O. Saber and R. M. Murray, "Flocking with obstacle avoidance: Cooperation with limited communication in mobile networks," in Proc. 42nd IEEE Conf. Decision Control, Maui, HI, Dec. 2003, pp. 2022-2028.
85. J. Toner and Y. Tu, "Flocks, herds and schools: A quantitative theory of flocking," Phys. Rev. E, vol. 58, no. 4, pp. 4828-4858, Oct. 1998. (Pubitemid 128596420)
86. C. Reynolds, "Flocks, "irds and schools: A distributed behavioral model," ACM SIGGRAPH Comput. Graph., vol. 21, no. 4, pp. 25-34, 1987. (Pubitemid 18521938)
87. H. G. Tanner, A. Jadbabaie, and G. J. Pappas, "Flocking in fixed and switching networks," IEEE Trans. Autom. Control, vol. 52, no. 5, pp. 863-868, May 2007. (Pubitemid 46796071)