To accomplish cooperative tasks, robotic systems are often required to communicate with each other. Thus, maintaining connectivity of the communication graph is a fundamental issue in the field of multi-robot systems. In this paper we present a completely decentralized control strategy for global connectivity maintenance of the communication graph. Considering the disk communication model, we describe a gradient-based control strategy that exploits decentralized estimation of the algebraic connectivity. Unlike previous approaches available in the literature, the proposed control algorithm solves the global connectivity problem in a decentralized manner providing theoretical guarantees, without requiring maintenance of the local connectivity between robotic systems. Moreover, results obtained with simulations and experiments on real robots are described for demonstrating the efficacy of the proposed algorithm.
AjorlouAMomeniAAghdamAG (2010) A class of bounded distributed control strategies for connectivity preservation in multi-agent systems. IEEE Transactions on Automatic Control55: 2828–2833.
2.
BhattacharyaSBasarT (2010) Graph-theoretic approach for connectivity maintenance in mobile networks in the presence of a jammer. In: Proceedings of the IEEE International Conference on Decision and Control, pp. 3560–3565.
3.
BulloFCortésJMartnezS (2009) Distributed Control of Robotic Networks ( Applied Mathematics Series). Princeton, NJ: Princeton University Press.
4.
CaoYRenW (2010) Distributed coordinated tracking via a variable structure approach – part I: consensus tracking. part II: swarm tracking. In: Proceedings of the American Control Conference, pp. 4744–4755.
5.
De GennaroMCJadbabaieA (2006) Decentralized control of connectivity for multi-agent systems. In: Proceedings of the IEEE International Conference on Decision and Control, pp. 3628–3633.
6.
DimarogonasDVJohanssonKH (2010) Bounded control of network connectivity in multi-agent systems. IET Control Theory & Applications4: 1751–8644.
7.
DoKD (2008) Formation tracking control of unicycle-type mobile robots with limited sensing ranges. IEEE Transactions on Control Systems Technology16: 527–538.
8.
FallatSKirklandS (1998) Extremizing algebraic connectivity subject to graph theoretic constraints. The Electronic Journal of Linear Algebra3: 48–74.
9.
FielderM (1973) Algebraic connectivity of graphs. Czechoslovak Mathematical Journal23(98): 298–305.
10.
FinkJRibeiroAKumarV (2012) Robust control for mobility and wireless communication in cyber-physical systems with application to robot teams. Proceedings of the IEEE100(1): 164–178.
11.
FranceschelliMGasparriAGiuaASeatzuC (2009) Decentralized laplacian eigenvalues estimation for networked multi-agent systems. In: Proceedings of the 48h IEEE Conference on Decision and Control CDC held jointly with 2009 28th Chinese Control Conference, pp. 2717–2722.
12.
FreemanRAYangPLynchKM (2006) Stability and convergence properties of dynamic consensus estimators. In: Proceedings of the IEEE International Conference on Decision and Control, pp. 338–343.
13.
GodsilCRoyleG (2001) Algebraic Graph Theory. New York: Springer.
14.
HollingerGSinghS (2010) Multi-robot coordination with periodic connectivity. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 4457–4462.
15.
HsiehMACowleyAKumarVTalyorCJ (2008) Maintaining network connectivity and performance in robot teams. Journal of Field Robotics25(1): 111–131.
16.
JiMEgerstedtM (2007) Distributed coordination control of multiagent systems while preserving connectedness. IEEE Transactions on Robotics23(4): 693–703.
17.
KimYMesbahiM (2005) On maximizing the second smallest eigenvalue of a state-dependent graph laplacian. In: Proceedings of the IEEE American Control Conference, pp. 99–103.
18.
MartinezSBulloFCortesJFrazzoliE (2005 a) On synchronous robotic networks part I: Models, tasks and complexity notions. In: 44th IEEE Conference on Decision and Control, pp. 2847–2852.
19.
MartinezSBulloFCortesJFrazzoliE (2005 b) On synchronous robotic networks part II: Time complexity of rendezvous and deployment algorithms. In: 44th IEEE Conference on Decision and Control, pp. 8313–8318.
20.
MondadaFBonaniMRaemyX. (2009) The E-Puck, a robot designed for education in engineering. In: Proceedings of the 9th Conference on Autonomous Robot Systems and Competitions, pp. 59–65.
21.
MorbidiFGiannitrapaniAPrattichizzoD (2010) Maintaining connectivity among multiple agents in cyclic pursuit: A geometric approach. In: Proceedings of the IEEE International Conference on Decision and Control, pp. 7461–7466.
22.
NotarstefanoGSavlaKBulloFJadbabaieA (2006) Maintaining limited-range connectivity among second-order agents. In: Proceedings of the American Control Conference, pp. 2134–2129.
23.
Olfati-SaberRFaxJAMurrayRM (2007) Consensus and cooperation in networked multi-agent systems. Proceedings of the IEEE95(1): 215–233.
24.
SabattiniLChopraNSecchiC (2011 a) Distributed control of multi-robot systems with global connectivity maintenance. In: 2011 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pp. 2321–2326.
25.
SabattiniLChopraNSecchiC (2011 b) On decentralized connectivity maintenance for mobile robotic systems. In: Proceeding of the IEEE Conference on Decision and Control and European Control Conference (CDC-ECC), Orlando, FL, USA, pp. 988–993.
26.
SabattiniLSecchiCChopraN (2012) Decentralized connectivity maintenance for networked Lagrangian dynamical systems. In: Proceedings of the IEEE International Conference on Robotics and Automation (ICRA), St. Paul, MN, USA, pp. 2433–2438.
27.
SabattiniLSecchiCChopraN (2013) Decentralized control for maintenance of strong connectivity for directed graphs. In: Proceedings of the IEEE Mediterranean Conference on Control and Automation (MED). Platanias-Chania, Crete - Greece, pp. 978–986.
28.
SangLAroraAZhangH (2007) On exploiting asymmetric wireless links via one-way estimation. In: Proceedings of the 8th ACM International Symposium on Mobile Ad Hoc Networking and Computing, pp. 11–21.
29.
SchureskoMCortésJ (2009 a) Distributed motion constraints for algebraic connectivity of robotic networks. Journal of Intelligent and Robotic Systems56: 99–126.
30.
SchureskoMCortésJ (2009 b) Distributed Tree Rearrangements for Reachability and Robust Connectivity (Lecture Notes in Computer Science, vol. 5469). Berlin: Springer-Verlag, pp. 470–474.
31.
StumpEJadbabaieAKumarV (2008) Connectivity management in mobile robot teams. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 1525–1530.
32.
StumpEMichaelNKumarVIslerV (2011) Visibility-based deployment of robot formations for communication maintenance. In: Proceedings of the IEEE International Conference on Robotics and Automation, pp. 4498–4505.
33.
TrefthenLNBauD (1997) Numerical Linear Algebra. Philadelphia, PA: SIAM.
34.
TseDViswanathP (2005) Fundamentals of Wireless Communication. New York, NY: Cambridge University Press.
35.
YanYMostofiT (2012) Robotic router formation in realistic communication environments – a bit error rate approach. IEEE Transactions on Robotics28: 810–827.
36.
YangPFreemanRAGordonGJLynchKMSrinivasaSSSukthankarR (2010) Decentralized estimation and control of graph connectivity for mobile sensor networks. Automatica46: 390–396.
37.
ZavlanosMMEgerstedtMBPappasGJ (2011 a) Graph-theoretic connectivity control of mobile robot networks. Proceedings of the IEEE99: 1525–1540.
38.
ZavlanosMMPappasGJ (2005) Controlling connectivity of dynamic graphs. In: Proceedings of the IEEE Conference on Decision and Control, pp. 6388–6393.
39.
ZavlanosMMPappasGJ (2007) Potential fields for maintaining connectivity of mobile networks. IEEE Transactions on Robotics23(4): 812–816.
40.
ZavlanosMMRibeiroAPappasGJ (2011 b) Distributed control of mobility & routing in networks of robots. In: Proceedings of the IEEE 12th International Workshop on Signal Processing Advances in Wireless Communications, pp. 236–240.
41.
ZavlanosMMRibeiroAPappasGJ (2013) Network integrity in mobile robotic networks. IEEE Transactions on Automatic Control58(1): 3–18.
42.
ZavlanosMMTannerHGJadbabaieAPappasGJ (2009) Hybrid control for connectivity preserving flocking. IEEE Transactions on Automatic Control54: 2869–2875.
