Encyclopedia of Systems and Control

Living Edition
| Editors: John Baillieul, Tariq Samad

Connectivity of Dynamic Graphs

Living reference work entry
DOI: https://doi.org/10.1007/978-1-4471-5102-9_213-1

Abstract

Dynamic networks have recently emerged as an efficient way to model various forms of interaction within teams of mobile agents, such as sensing and communication. This article focuses on the use of graphs as models of wireless communications. In this context, graphs have been used widely in the study of robotic and sensor networks and have provided an invaluable modeling framework to address a number of coordinated tasks ranging from exploration, surveillance, and reconnaissance to cooperative construction and manipulation. In fact, the success of these stories has almost always relied on efficient information exchange and coordination between the members of the team, as seen, e.g., in the case of distributed state agreement where multi-hop communication has been proven necessary for convergence and performance guarantees.

Keywords

Algebraic graph theory Graph connectivity Distributed and hybrid control Convex optimization 
This is a preview of subscription content, log in to check access.

Bibliography

  1. Ajorlou A, Aghdam AG (2010) A class of bounded distributed controllers for connectivity preservation of unicycles. In: Proceedings of the 49th IEEE conference on decision and control, Atlanta, pp 3072–3077Google Scholar
  2. Ajorlou A, Momeni A, Aghdam AG (2010) A class of bounded distributed control strategies for connectivity preservation in multi-agent systems. IEEE Trans Autom Control 55(12):2828–2833CrossRefMathSciNetGoogle Scholar
  3. Anderson SO, Simmons R, Goldberg D (2003) Maintaining line-of-sight communications networks between planetray rovers. In: Proceedings of the 2003 IEEE/RSJ international conference on intelligent robots and systems, Las Vegas, pp 2266–2272Google Scholar
  4. Ando H, Oasa Y, Suzuki I, Yamashita M (1999) Distributed memoryless point convergence algorithm for mobile robots with limited visibility. IEEE Trans Robot Autom 15(5):818–828CrossRefGoogle Scholar
  5. Arkin RC, Diaz J (2002) Line-of-sight constrained exploration for reactive multiagent robotic teams. In: Proceedings of the 7th international workshop on advanced motion control, Maribor, pp 455–461Google Scholar
  6. Bullo F, Cortes J, Martinez S (2009) Distributed control of robotic networks. Applied Mathematics Series. Princeton University Press, PrincetonMATHGoogle Scholar
  7. Cornejo A, Lynch N (2008) Connectivity service for mobile ad-hoc networks. In: Proceedings of the 2nd IEEE international conference on self-adaptive and self-organizing systems workshops, pp 292–297Google Scholar
  8. Cortes J, Martinez S, Bullo F (2006) Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions. IEEE Trans Autom Control 51(8):1289–1298CrossRefMathSciNetGoogle Scholar
  9. DeCouto D, Aguayo D, Bicket J, Morris R (2006) A high-throughput path metric for multihop wireless routing. In: Proceedings of the international ACM conference on mobile computing and networking, San Diego, pp 134–146Google Scholar
  10. DeGennaro MC, Jadbabaie A (2006) Decentralized control of connectivity for multi-agent systems. In: Proceedings of the 45th IEEE conference on decision and control, San Diego, pp 3628–3633Google Scholar
  11. Dimarogonas DV, Johansson KH (2008) Decentralized connectivity maintenance in mobile networks with bounded inputs. In Proceedings of the IEEE international conference on robotics and automation, Pasadena, pp 1507–1512Google Scholar
  12. Dimarogonas DV, Kyriakopoulos KJ (2008) Connectedness preserving distributed swarm aggregation for multiple kinematic robots. IEEE Trans Robot 24(5):1213–1223CrossRefGoogle Scholar
  13. Fax A, Murray RM (2004) Information flow and cooperative control of vehicle formations. IEEE Trans Autom Control 49:1465–1476CrossRefMathSciNetGoogle Scholar
  14. Fiedler M (1973) Algebraic connectivity of graphs. Czechoslovak Math J 23(98):298–305MathSciNetGoogle Scholar
  15. Flocchini P, Prencipe G, Santoro N, Widmayer P (2005) Gathering of asynchronous oblivious robots with limited visibility. Theor Comput Sci 337(1–3):147–168CrossRefMATHMathSciNetGoogle Scholar
  16. Franceschelli M, Gasparri A, Giua A, Seatzu C (2013) Decentralized estimation of laplacian eigenvalues in multi-agent systems. Automatica 49(4):1031–1036CrossRefMathSciNetGoogle Scholar
  17. Ganguli A, Cortes J, Bullo F (2009) Multirobot rendezvous with visibility sensors in nonconvex environments. IEEE Trans Robot 25(2):340–352CrossRefGoogle Scholar
  18. Ghaffarkhah A, Mostofi Y (2011) Communication-aware motion planning in mobile networks. IEEE Trans Autom Control Spec Issue Wirel Sens Actuator Netw 56(10):2478–248CrossRefMathSciNetGoogle Scholar
  19. Godsil C, Royle G (2001) Algebraic graph theory, Graduate Texts in Mathematics, vol 207. Springer, BerlinCrossRefGoogle Scholar
  20. Gustavi T, Dimarogonas DV, Egerstedt M, Hu X (2010) Sufficient conditions for connectivity maintenance and rendezvous in leader-follower networks. Automatica 46(1):133–139CrossRefMATHMathSciNetGoogle Scholar
  21. Hollinger G, Singh S (2010) Multi-robot coordination with periodic connectivity. In: Proceedings of the IEEE international conference on robotics and automation, Anchorage, Alaska, pp 4457–4462Google Scholar
  22. Hsieh MA, Cowley A, Kumar V, Taylor C (2008) Maintaining network connectivity and performance in robot teams. J Field Robot 25(1–2):111–131CrossRefGoogle Scholar
  23. Ji M, Egerstedt M (2007) Coordination control of multi-agent systems while preserving connectedness. IEEE Trans Robot 23(4):693–703CrossRefGoogle Scholar
  24. Kempe D, McSherry F (2008) A decentralized algorithm for spectral analysis. J Comput Syst Sci 74(1):70–83CrossRefMATHMathSciNetGoogle Scholar
  25. Kim Y, Mesbahi M (2006) On maximizing the second smallest eigenvalue of a state-dependent graph laplacian. IEEE Trans Autom Control 51(1):116–120CrossRefMathSciNetGoogle Scholar
  26. Knorn F, Stanojevic R, Corless M, Shorten R (2009) A framework for decentralized feedback connectivity control with application to sensor networks. Int J Control 82(11):2095–2114CrossRefMATHMathSciNetGoogle Scholar
  27. Lundgren H, Nordstrom E, Tschudin C (2002) The gray zone problem in ieee 802.11b based ad hoc networks. ACM SIGMOBILE Mobile Comput Commun Rev 6(3):104–105CrossRefGoogle Scholar
  28. Lynch N (1997) Distributed algorithms. Morgan Kaufmann, San FranciscoGoogle Scholar
  29. Merris R (1994) Laplacian matrices of a graph: a survey. Linear Algebra Appl 197:143–176CrossRefMathSciNetGoogle Scholar
  30. Michael N, Zavlanos MM, Kumar V, Pappas GJ (2009) Maintaining connectivity in mobile robot networks. In: Experimental robotics. Tracts in advanced robotics. Springer, Berlin/Heidelberg, pp 117–126Google Scholar
  31. Mohar B (1991) The laplacian spectrum of graphs. In: Alavi Y, Chartrand G, Ollermann O, Schwenk A (Eds) Graph theory, combinatorics, and applications. Wiley, New York, pp 871–898Google Scholar
  32. Montijano E, Montijano JI, Sagues C (2011) Adaptive consensus and algebraic connectivity estimation in sensor networks with chebyshev polynomials. In: Proceedings of the 50th IEEE conference on decision and control, Orlando, pp 4296–4301Google Scholar
  33. Mostofi Y (2009) Decentralized communication-aware motion planning in mobile networks: an information-gain approach. J Intell Robot Syst 56(1–2):233–256CrossRefMATHGoogle Scholar
  34. Neely MJ (2010) Universal scheduling for networks with arbitrary traffic, channels, and mobility. In: Proceedings of the 49th IEEE conference on decision and control, Altanta, pp 1822–1829Google Scholar
  35. Neskovic A, Neskovic N, Paunovic G (2000) Modern approaches in modeling of mobile radio systems propagation environment. IEEE Commun Surv 3(3):1–12CrossRefGoogle Scholar
  36. Notarstefano G, Savla K, Bullo F, Jadbabaie A (2006) Maintaining limited-range connectivity among second-order agents. In: Proceedings of the 2006 American control conference, Minneapolis, pp 2124–2129Google Scholar
  37. Olfati-Saber R, Murray RM (2004) Consensus problems in networks of agents with switching topology and time-delays. IEEE Trans Autom Control 49:1520–1533CrossRefMathSciNetGoogle Scholar
  38. Oreshkin BN, Coates MJ, Rabbat MG (2010) Optimization and analysis of distributed averaging with short node memory. IEEE Trans Signal Process 58(5):2850–2865CrossRefMathSciNetGoogle Scholar
  39. Pahlavan K, Levesque AH (1995) Wireless information networks. Willey, New YorkGoogle Scholar
  40. Parsons JD (2000) The mobile radio propagation channel. Willey, ChichesterCrossRefGoogle Scholar
  41. Pecora L, Carrollg T (1998) Master stability functions for synchronized coupled systems. Phys Rev Lett 80:2109–2112CrossRefGoogle Scholar
  42. Powers M, Balch T (2004) Value-based communication preservation for mobile robots. In: Proceedings of the 7th international symposium on distributed autonomous robotic systems, ToulouseGoogle Scholar
  43. Preciado V (2008) Spectral analysis for stochastic models of large-scale complex dynamical networks. Ph.D. dissertation, Department of Electrical Engineering and Computer Science, MITGoogle Scholar
  44. Preciado V, Verghese G (2005) Synchronization in generalized erdös-rényi networks of nonlinear oscillators. In: 44th IEEE conference on decision and control, Seville, Spain, pp 4628–463Google Scholar
  45. Ribeiro A, Luo Z-Q, Sidiropoulos ND, Giannakis GB (2007) Modelling and optimization of stochastic routing for wireless multihop networks. In: Proceedings of the 26th annual joint conference of the IEEE Computer and Communications Societies (INFOCOM), Anchorage, pp 1748–1756Google Scholar
  46. Ribeiro A, Sidiropoulos ND, Giannakis GB (2008) Optimal distributed stochastic routing algorithms for wireless multihop networks. IEEE Trans Wirel Commun 7(11):4261–4272CrossRefGoogle Scholar
  47. Sabattini L, Chopra N, Secchi C (2011) On decentralized connectivity maintenance for mobile robotic systems. In: Proceedings of the 50th IEEE conference on decision and control, Orlando, pp 988–993Google Scholar
  48. Schuresko M, Cortes J (2009a) Distributed tree rearrangements for reachability and robust connectivity. In: Hybrid systems: computetation and control. Lecture notes in computer science, vol 5469. Springer, Berlin/New York, pp 470–474Google Scholar
  49. Schuresko M, Cortes J (2009b) Distributed motion constraints for algebraic connectivity of robotic networks. J Intell Robot Syst 56(1–2):99–126CrossRefMATHGoogle Scholar
  50. Simonetto A, Kaviczky T, Babuska R (2013) Constrained distributed algebraic connectivity maximization in robotic networks. Automatica 49(5):1348–1357CrossRefMathSciNetGoogle Scholar
  51. Spanos DP, Murray RM (2004) Robust connectivity of networked vehicles. In: Proceedings of the 43rd IEEE conference on decision and control, Bahamas, pp 2893–2898Google Scholar
  52. Spanos DP, Murray RM (2005) Motion planning with wireless network constraints. In: Proceedings of the 2005 American control conference, Portland, pp 87–92Google Scholar
  53. Srivastava K, Spong MW (2008) Multi-agent coordination under connectivity constraints. In: Proceedings of the 2008 American control conference, Seattle, pp 2648–2653Google Scholar
  54. Stump E, Jadbabaie A, Kumar V (2008) Connectivity management in mobile robot teams. In: Proceedings of the IEEE international conference on robotics and automation, Pasadena, pp 1525–1530Google Scholar
  55. Tardioli D, Mosteo AR, Riazuelo L, Villarroel JL, Montano L (2010) Enforcing network connectivity in robot team missions. Int J Robot Res 29(4):460–480CrossRefGoogle Scholar
  56. Van Mieghem P, Omic J, Kooij R (2009) Virus spread in networks. IEEE/ACM Trans Networking 17(1):1–14CrossRefGoogle Scholar
  57. Wagenpfeil J, Trachte A, Hatanaka T, Fujita M, Sawodny O (2009) A distributed minimum restrictive connectivity maintenance algorithm. In: Proceedings of the 9th international symposium on robot control, GifuGoogle Scholar
  58. Wagner AR, Arkin RC (2004) Communication-sensitive multi-robot reconnaissance. In: Proceedings of the IEEE international conference on robotics and automation, New Orleans, pp 2480–2487Google Scholar
  59. Yan Y, Mostofi Y (2012) Robotic router formation in realistic communication environments. IEEE Trans Robot 28(4):810–827CrossRefGoogle Scholar
  60. Yang P, Freeman RA, Gordon GJ, Lynch KM, Srinivasa SS, Sukthankar R (2010) Decentralized estimation and control of graph connectivity for mobile sensor networks. Automatica 46(2): 390–396CrossRefMATHMathSciNetGoogle Scholar
  61. Yao Z, Gupta K (2009) Backbone-based connectivity control for mobile networks. In: Proceedings IEEE international conference on robotics and automation, Kobe, pp 1133–1139Google Scholar
  62. Zavlanos MM (2010) Synchronous rendezvous of very-low-range wireless agents. In: Proceedings of the 49th IEEE conference on decision and control, Atlanta, pp 4740–4745Google Scholar
  63. Zavlanos MM, Pappas GJ (2005) Controlling connectivity of dynamic graphs. In: Proceedings of the 44th IEEE conference on decision and control and European control conference, Seville, pp 6388–6393Google Scholar
  64. Zavlanos MM, Pappas GJ (2007) Potential fields for maintaining connectivity of mobile networks. IEEE Trans Robot 23(4):812–816CrossRefGoogle Scholar
  65. Zavlanos MM, Pappas GJ (2008) Distributed connectivity control of mobile networks. IEEE Trans Robot 24(6):1416–1428CrossRefGoogle Scholar
  66. Zavlanos MM, Jadbabaie A, Pappas GJ (2007) Flocking while preserving network connectivity. In: Proceedings of the 46th IEEE conference on decision and control, New Orleans, pp 2919–2924Google Scholar
  67. Zavlanos MM, Tanner HG, Jadbabaie A, Pappas GJ (2009) Hybrid control for connectivity preserving flocking. IEEE Trans Autom Control 54(12):2869–2875CrossRefMathSciNetGoogle Scholar
  68. Zavlanos MM, Egerstedt MB, Pappas GJ (2011) Graph theoretic connectivity control of mobile robot networks. Proc IEEE Spec Issue Swarming Nat Eng Syst 99(9):1525–154Google Scholar
  69. Zavlanos MM, Ribeiro A, Pappas GJ (2013) Network integrity in mobile robotic networks. IEEE Trans Autom Control 58(1):3–18CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag London 2014

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Materials ScienceDuke UniversityDurhamUSA
  2. 2.Department of Electrical and Systems EngineeringUniversity of PennsylvaniaPhiladelphiaUSA