Distributed coordination inmulti-agent systems: a graph Laplacian perspective
Zhi-min HAN, Zhi-yun LIN, Min-yue FU, Zhi-yong CHEN
Distributed coordination inmulti-agent systems: a graph Laplacian perspective
This paper reviews some main results and progress in distributed multi-agent coordination from a graph Laplacian perspective. Distributed multi-agent coordination has been a very active subject studied extensively by the systems and control community in last decades, including distributed consensus, formation control, sensor localization, distributed optimization, etc. The aim of this paper is to provide both a comprehensive survey of existing literature in distributed multi-agent coordination and a new perspective in terms of graph Laplacian to categorize the fundamental mechanisms for distributed coordination. For different types of graph Laplacians, we summarize their inherent coordination features and specific research issues. This paper also highlights several promising research directions along with some open problems that are deemed important for future study.
Multi-agent systems / Distributed coordination / Graph Laplacian
[1] |
Altafini, C., 2013. Consensus problems on networks with antagonistic interactions. IEEE Trans. Automat. Contr., 58(4): 935-946. [
CrossRef
Google scholar
|
[2] |
Anderson, B.D.O., Yu, C., Fidan, B.,
CrossRef
Google scholar
|
[3] |
Bliman, P., Ferrari-Trecate, G., 2008. Average consensus problems in networks of agents with delayed communications. Automatica, 44(8): 1985-1995. [
CrossRef
Google scholar
|
[4] |
Blondel, V.D., Hendrickx, J.M., Olshevsky, A.,
CrossRef
Google scholar
|
[5] |
Boyd, S., 2006. Convex optimization of graph Laplacian eigenvalues. Proc. Int. Congress of Mathematicians, p.1311-1320.
|
[6] |
Boyd, S., Diaconis, P., Parrilo, P.,
CrossRef
Google scholar
|
[7] |
Bullo, F., Cortes, J., Martinez, S., 2009. Distributed Control of Robotic Networks. Princeton University Press, USA.
|
[8] |
Cai, K., Ishii, H., 2012. Average consensus on general strongly connected digraphs. Automatica, 48(11): 2750-2761. [
CrossRef
Google scholar
|
[9] |
Cai, K., Ishii, H., 2014. Average consensus on arbitrary strongly connected digraphs with time-varying topologies. IEEE Trans. Automat. Contr., 59(4): 1066-1071. [
CrossRef
Google scholar
|
[10] |
Cao, L., Zheng, Y., Zhou, Q., 2011. A necessary and sufficient condition for consensus of continuous-time agents over undirected time-varying networks. IEEE Trans. Automat. Contr., 56(8): 1915-1920. [
CrossRef
Google scholar
|
[11] |
Casbeer, D.W., Beard, R., Swindlehurst, A.L., 2008. Discrete double integrator consensus. Proc. 47th IEEE Conf. on Decision and Control, p.2264-2269. [
CrossRef
Google scholar
|
[12] |
Chen, J., Wang, C., Sun, Y.,
CrossRef
Google scholar
|
[13] |
Cortes, J., 2008. Distributed algorithms for reaching consensus on general functions. Automatica, 44(3): 726-737. [
CrossRef
Google scholar
|
[14] |
Cortes, J., 2009. Global and robust formation-shape stabilization of relative sensing networks. Automatica, 45(12): 2754-2762. [
CrossRef
Google scholar
|
[15] |
de Abreu, N.M.M., 2007. Old and new results on algebraic connectivity of graphs. Linear Algebra Appl., 423(1): 53-73. [
CrossRef
Google scholar
|
[16] |
Degroot, M.H., 1974. Reaching a consensus. J. Am. Statist. Assoc., 69(345): 118-121.
|
[17] |
Diao, Y., Lin, Z., Fu, M.,
CrossRef
Google scholar
|
[18] |
Diao, Y., Lin, Z., Fu, M., 2014. A barycentric coordinate based distributed localization algorithm for sensor networks. IEEE Trans. Signal Process., 62(18): 4760-4771. [
CrossRef
Google scholar
|
[19] |
Ding, W., Yan, G., Lin, Z., 2010. Collective motion and formations under pursuit strategies on directed acyclic graphs. Automatica, 46(1): 174-181. [
CrossRef
Google scholar
|
[20] |
Ding, W., Yan, G., Lin, Z., 2012. Pursuit formations with dynamic control gains. Int. J. Robust Nonlinear Contr., 22(3): 300-317. [
CrossRef
Google scholar
|
[21] |
Dominguez-Garcia, A.D., Cady, S.T., Hadjicostis, C.N., 2012. Decentralized optimal dispatch of distributed energy resources. Proc. IEEE 51st Annual Conf. on Decision and Control, p.3688-3693. [
CrossRef
Google scholar
|
[22] |
Dorfler, F., Bullo, F., 2014. Synchronization in complex networks of phase oscillators: a survey. Automatica, 50(6): 1539-1564. [
CrossRef
Google scholar
|
[23] |
Easley, D., Kleinberg, J., 2010. Networks, Crowds, and Markets: Reasoning about a Highly Connected World. Cambridge University Press, UK.
|
[24] |
Fanti, M.P., Mangini, A.M., Mazzia, F.,
CrossRef
Google scholar
|
[25] |
Ghosh, A., Boyd, S., Saberi, A., 2008. Minimizing effective resistance of a graph. SIAM Rev., 50(1): 37-66. [
CrossRef
Google scholar
|
[26] |
Godsil, C., Royle, G., 2001. Algebraic Graph Theory. Springer, New York, USA.
|
[27] |
Goldenberg, D.K., Bihler, P., Cao, M.,
CrossRef
Google scholar
|
[28] |
Gortler, S.J., Healy, A.D., Thurston, D.P., 2010. Characterizing generic global rigidity. Am. J. Math., 132(4): 897-939. [
CrossRef
Google scholar
|
[29] |
Han, T., Lin, Z., Fu, M., 2014a. Formation merging control in 3D under directed and switching topologies. Proc. 19th IFAC World Congress, p.10036-10041. [
CrossRef
Google scholar
|
[30] |
Han, T., Lin, Z., Xu, W.,
CrossRef
Google scholar
|
[31] |
Han, Y., Lu, W., Chen, T., 2013. Cluster consensus in discrete-time networks of multiagents with inter-cluster nonidentical inputs. IEEE Trans. Neur. Netw. Learn. Syst., 24(4): 566-578. [
CrossRef
Google scholar
|
[32] |
Han, Z., Wang, L., Lin, Z.,
CrossRef
Google scholar
|
[33] |
Han, Z., Wang, L., Lin, Z., 2013. Local formation control strategies with undetermined and determined formation scales for co-leader vehicle networks. Proc. IEEE 52nd Annual Conf. on Decision and Control, p.7339-7344. [
CrossRef
Google scholar
|
[34] |
Han, Z., Lin, Z., Fu, M., 2014. A fully distributed approach to formation maneuvering control of multi-agent systems. Proc. IEEE 53rd Annual Conf. on Decision and Control, p.6185-6190. [
CrossRef
Google scholar
|
[35] |
He, C., Feng, Z., Ren, Z., 2012. Flocking of multiagents based on consensus protocol and pinning control. Proc. 10th World Congress on Intelligent Control and Automation, p.1311-1316. [
CrossRef
Google scholar
|
[36] |
Hendrickx, J.M., Tsitsiklis, J.N., 2013. Convergence of type-symmetric and cut-balanced consensus seeking systems. IEEE Trans. Automat. Contr., 58(1): 214-218. [
CrossRef
Google scholar
|
[37] |
Hong, Y., Hu, J., Gao, L., 2006. Tracking control for multi-agent consensus with an active leader and variable topology. Automatica, 42(7): 1177-1182. [
CrossRef
Google scholar
|
[38] |
Huang, H., Wu, Q., 2010. H∞ control of distributed multiagent formation systems with Toeplitz-based consensus algorithms. Proc. American Control Conf., p.6840-6845. [
CrossRef
Google scholar
|
[39] |
Hwang, K., Tan, S., Chen, C., 2004. Cooperative strategy based on adaptive Q-learning for robot soccer systems. IEEE Trans. Fuzzy Syst., 12(4): 569-576. [
CrossRef
Google scholar
|
[40] |
Jadbabaie, A., Lin, J., Morse, A.S., 2003. Coordination of groups of mobile autonomous agents using nearest neighbor rules. IEEE Trans. Automat. Contr., 48(6): 988-1001. [
CrossRef
Google scholar
|
[41] |
Jiang, H., Zhang, L., Guo, S., 2014. Cluster anticonsensus in directed networks of multi-agents based on the Q-theory. J. Franklin Inst., 351(10): 4802-4816. [
CrossRef
Google scholar
|
[42] |
Kar, S., Hug, G., 2012. Distributed robust economic dispatch in power systems: a consensus+ innovations approach. Proc. IEEE Power and Energy Society General Meeting, p.1-8. [
CrossRef
Google scholar
|
[43] |
Khan, U.A., Kar, S., Moura, J.M.F., 2009. Distributed sensor localization in random environments using minimal number of anchor nodes. IEEE Trans. Signal Process., 57(5): 2000-2016. [
CrossRef
Google scholar
|
[44] |
Kingston, D.B., Beard, R.W., 2006. Discrete-time averageconsensus under switching network topologies. Proc. American Control Conf., p.3551-3556. [
CrossRef
Google scholar
|
[45] |
Kunegis, J., Schmidt, S., Lommatzsch, A., 2010. Spectral analysis of signed graphs for clustering, prediction and visualization. SIAM, 10: 559-570.
|
[46] |
Kuriki, Y., Namerikawa, T., 2014. Consensus-based cooperative formation control with collision avoidance for a multi-UAV system. Proc. American Control Conf., p.2077-2082. [
CrossRef
Google scholar
|
[47] |
Lakshmanan, H., de Farias, D.P., 2008. Decentralized resource allocation in dynamic networks of agents. SIAM J. Optim., 19(2): 911-940. [
CrossRef
Google scholar
|
[48] |
Leonard, N.E., Paley, D.A., Lekien, F.,
CrossRef
Google scholar
|
[49] |
Li, S., Du, H., Lin, X., 2011. Finite-time consensus algorithm for multi-agent systems with double-integrator dynamics. Automatica, 47(8): 1706-1712. [
CrossRef
Google scholar
|
[50] |
Li, Z., Jia, Y., Du, J.,
CrossRef
Google scholar
|
[51] |
Lin, Z., 2008. Distributed Control and Analysis of Coupled Cell Systems. VDM-Verlag, Germany.
|
[52] |
Lin, Z., Broucke, M., Francis, B., 2004. Local control strategies for groups of mobile autonomous agents. IEEE Trans. Automat. Contr., 49(4): 622-629. [
CrossRef
Google scholar
|
[53] |
Lin, Z., Francis, B., Maggiore, M., 2005. Necessary and sufficient graphical conditions for formation control of unicycles. IEEE Trans. Automat. Contr., 50(1): 121-127. [
CrossRef
Google scholar
|
[54] |
Lin, Z., Francis, B., Maggiore, M., 2007. State agreement for continuous-time coupled nonlinear systems. SIAM J. Contr. Optim., 46(1): 288-307. [
CrossRef
Google scholar
|
[55] |
Lin, Z., Chen, Z., Fu, M., 2013a. A linear control approach to distributed multi-agent formations in d-dimensional space. Proc. IEEE 52nd Annual Conf. on Decision and Control, p.6049-6054. [
CrossRef
Google scholar
|
[56] |
Lin, Z., Ding, W., Yan, G.,
CrossRef
Google scholar
|
[57] |
Lin, Z., Wang, L., Han, Z.,
CrossRef
Google scholar
|
[58] |
Lin, Z., Fu, M., Diao, Y., 2015. Distributed self localization for relative position sensing networks in 2D space. IEEE Trans. Signal Process., in press. [
CrossRef
Google scholar
|
[59] |
Liu, X., Chen, T., 2011. Cluster synchronization in directed networks via intermittent pinning control. IEEE Trans. Neur. Netw., 22(7): 1009-1020. [
CrossRef
Google scholar
|
[60] |
Lu, W., Liu, B., Chen, T., 2010. Cluster synchronization in networks of coupled nonidentical dynamical systems. Chaos, 20(1), Article 013120. [
CrossRef
Google scholar
|
[61] |
Lu, X., Austin, F., Chen, S., 2010a. Cluster consensus of nonlinearly coupled multi-agent systems in directed graphs. Chin. Phys. Lett., 27(5), Article 050503. [
CrossRef
Google scholar
|
[62] |
Lu, X., Austin, F., Chen, S., 2010b. Cluster consensus of second-order multi-agent systems via pinning control. Chin. Phys. B, 19(12), Article 120506. [
CrossRef
Google scholar
|
[63] |
Martin, S., 2014. Multi-agent flocking under topological interactions. Syst. Contr. Lett., 69: 53-61. [
CrossRef
Google scholar
|
[64] |
Mesbahi, M., Egerstedt, M., 2010. Graph Theoretic Methods for Multagent Networks. Princeton University Press, USA.
|
[65] |
Morbidi, F., 2013. The deformed consensus protocol. Automatica, 49(10): 3049-3055. [
CrossRef
Google scholar
|
[66] |
Moreau, L., 2005. Stability of multiagent systems with timedependent communication links. IEEE Trans. Automat. Contr., 50(2): 169-182. [
CrossRef
Google scholar
|
[67] |
Moshtagh, N., Jadbabaie, A., 2007. Distributed geodesic control laws for flocking of nonholonomic agents. IEEE Trans. Automat. Contr., 52(4): 681-686. [
CrossRef
Google scholar
|
[68] |
Moshtagh, N., Jadbabaie, A., Daniilidis, K., 2006. Visionbased control laws for distributed flocking of nonholonomic agents. Proc. IEEE Int. Conf. on Robotics and Automation, p.2769-2774. [
CrossRef
Google scholar
|
[69] |
Murray, R.M., 2007. Recent research in cooperative control of multivehicle systems. J. Dynam. Syst. Meas. Contr., 129(5): 571-583. [
CrossRef
Google scholar
|
[70] |
Nedic, A., Ozdaglar, A., Parrilo, P.A., 2010. Constrained consensus and optimization in multi-agent networks. IEEE Trans. Automat. Contr., 55(4): 922-938. [
CrossRef
Google scholar
|
[71] |
Oh, K., Ahn, H.S., 2014. Formation control and network localization via orientation alignment. IEEE Trans. Automat. Contr., 59(2): 540-545. [
CrossRef
Google scholar
|
[72] |
Oh, K., Lashhab, F., Moore, K.L.,
CrossRef
Google scholar
|
[73] |
Oh, K., Park, M.C., Ahn, H.S., 2015b. A survey of multi-agent formation control. Automatica, 53: 424-440. [
CrossRef
Google scholar
|
[74] |
Okubo, A., 1986. Dynamical aspects of animal grouping: swarms, schools, flocks, and herds. Adv. Biophys., 22: 1-94. [
CrossRef
Google scholar
|
[75] |
Olfati-Saber, R., Murray, R.M., 2004. Consensus problems in networks of agents with switching topology and timedelays. IEEE Trans. Automat. Contr., 49(9): 1520-1533. [
CrossRef
Google scholar
|
[76] |
Olfati-Saber, R., Fax, J.A., Murray, R.M., 2007. Consensus and cooperation in networked multi-agent systems. Proc. IEEE, 95(1): 215-233. [
CrossRef
Google scholar
|
[77] |
Passino, K.M., 2002. Biomimicry of bacterial foraging for distributed optimization and control. IEEE Contr. Syst., 22(3): 52-67. [
CrossRef
Google scholar
|
[78] |
Proskurnikov, A., 2013. Consensus in switching symmetric networks of first-order agents with delayed relative measurements. Proc. IEEE 52nd Annual Conf. on Decision and Control, p.917-921. [
CrossRef
Google scholar
|
[79] |
Qin, J., Yu, C., 2013. Cluster consensus control of generic linear multi-agent systems under directed topology with acyclic partition. Automatica, 49(9): 2898-2905. [
CrossRef
Google scholar
|
[80] |
Qin, J., Zheng, W.X., Gao, H., 2011. Consensus of multiple second-order vehicles with a time-varying reference signal under directed topology. Automatica, 47(9): 1983-1991. [
CrossRef
Google scholar
|
[81] |
Qu, Z., 2009. Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles. Springer-Verlag, London, UK.
|
[82] |
Ren, W., 2007. Consensus strategies for cooperative control of vehicle formations. IET Contr. Theory Appl., 1(2): 505-512. [
CrossRef
Google scholar
|
[83] |
Ren, W., 2008. On consensus algorithms for doubleintegrator dynamics. IEEE Trans. Automat. Contr., 53(6): 1503-1509. [
CrossRef
Google scholar
|
[84] |
Ren, W., Beard, R., 2004. Consensus of information under dynamically changing interaction topologies. Proc. American Control Conf., p.4939-4944.
|
[85] |
Ren, W., Beard, R., 2005. Consensus seeking in multiagent systems under dynamically changing interaction topologies. IEEE Trans. Automat. Contr., 50(5): 655-661. [
CrossRef
Google scholar
|
[86] |
Ren, W., Beard, R., 2008. Distributed Consensus in Multivehicle Cooperative Control: Theory and Applications. Springer, London, UK.
|
[87] |
Ren, W., Cao, Y., 2008. Convergence of sampled-data consensus algorithms for double-integrator dynamics. Proc. 47th IEEE Conf. on Decision and Control, p.3965-3970. [
CrossRef
Google scholar
|
[88] |
Ren, W., Cao, Y., 2011. Distributed Coordination of Multiagent Networks: Emergent Problems, Models, and Issues. Springer-Verlag, London, UK.
|
[89] |
Ren, W., Beard, R., Atkins, E.M., 2007. Information consensus in multivehicle cooperative control. IEEE Contr. Syst., 27(2): 71-82. [
CrossRef
Google scholar
|
[90] |
Reynolds, C.W., 1987. Flocks, herds and schools: a distributed behavioral model. ACM SIGGRAPH Comput. Graph., 21(4): 25-34. [
CrossRef
Google scholar
|
[91] |
Semnani, S.H., Basir, O.A., 2015. Semi-flocking algorithm for motion control of mobile sensors in large-scale surveillance systems. IEEE Trans. Cybern., 45(1): 129-137. [
CrossRef
Google scholar
|
[92] |
Stanković, S.S., Stankovia, M.S., Stipanović, D.M., 2009. Consensus based overlapping decentralized estimation with missing observations and communication faults. Automatica, 45(6): 1397-1406. [
CrossRef
Google scholar
|
[93] |
Sugihara, K., Suzuki, I., 1990. Distributed motion coordination of multiple mobile robots. Proc. 5th IEEE Int. Symp. on Intelligent Control, p.138-143. [
CrossRef
Google scholar
|
[94] |
Sun, J., Boyd, S., Xiao, L.,
CrossRef
Google scholar
|
[95] |
Tahbaz-Salehi, A., Jadbabaie, A., 2008. A necessary and sufficient condition for consensus over random networks. IEEE Trans. Automat. Contr., 53(3): 791-795. [
CrossRef
Google scholar
|
[96] |
Tian, Y., Liu, C., 2009. Robust consensus of multi-agent systems with diverse input delays and asymmetric interconnection perturbations. Automatica, 45(5): 1347-1353. [
CrossRef
Google scholar
|
[97] |
Tsitsiklis, J.N., 1984. Problems in Decentralized Decision Making and Computation. PhD Thesis, Massachusetts Institute of Technology, USA.
|
[98] |
Tsitsiklis, J.N., Bertsekas, D.P., Athans, M., 1986. Distributed asynchronous deterministic and stochastic gradient optimization algorithms. IEEE Trans. Automat. Contr., 31(9): 803-812. [
CrossRef
Google scholar
|
[99] |
Wang, C., Chen, J., Sun, Y.,
CrossRef
Google scholar
|
[100] |
Wang, J., Elia, N., 2010. Consensus over networks with dynamic channels. Int. J. Syst. Contr. Commun., 2(1): 275-297. [
CrossRef
Google scholar
|
[101] |
Wang, L., Han, Z., Lin, Z., 2012a. Formation control of directed multi-agent networks based on complex Laplacian. Proc. IEEE 51st Annual Conf. on Decision and Control, p.5292-5297. [
CrossRef
Google scholar
|
[102] |
Wang, L., Han, Z., Lin, Z.,
CrossRef
Google scholar
|
[103] |
Wang, L., Han, Z., Lin, Z., 2013. Realizability of similar formation and local control of directed multi-agent networks in discrete-time. Proc. IEEE 52nd Annual Conf. on Decision and Control, p.6037-6042. [
CrossRef
Google scholar
|
[104] |
Wang, L., Han, Z., Lin, Z.,
CrossRef
Google scholar
|
[105] |
Wang, L., Lin, Z., Fu, M., 2014b. Affine formation of multiagent systems over directed graphs. Proc. IEEE 53rd Annual Conf. on Decision and Control, p.3017-3022. [
CrossRef
Google scholar
|
[106] |
Wang, W., Peng, H., 2012. Flocking control with communication noise based on second-order distributed consensus algorithm. Proc. IEEE Power Engineering and Automation Conf., p.1-4. [
CrossRef
Google scholar
|
[107] |
Wasserman, S., Faust, K., 1994. Social Network Analysis Methods and Applications. Cambridge University Press, UK.
|
[108] |
Wei, J., Fang, H., 2014. Multi-agent consensus with timevarying delays and switching topologies. J. Syst. Eng. Electron., 25(3): 489-495. [
CrossRef
Google scholar
|
[109] |
Weiss, G., 1999. Multiagent Systems, a Modern Approach to Distributed Artificial Intelligence. MIT Press, USA.
|
[110] |
Wu, W., Chen, T., 2009. Partial synchronization in linearly and symmetrically coupled ordinary differential systems. Phys. D, 238(4): 355-364. [
CrossRef
Google scholar
|
[111] |
Wu, W., Zhou, W., Chen, T., 2009. Cluster synchronization of linearly coupled complex networks under pinning control. IEEE Trans. Circ. Syst. I, 56(4): 829-839. [
CrossRef
Google scholar
|
[112] |
Xia, W., Cao, M., 2011. Clustering in diffusively coupled networks. Automatica, 47(11): 2395-2405. [
CrossRef
Google scholar
|
[113] |
Xiao, L., Boyd, S., 2004. Fast linear iterations for distributed averaging. Syst. Contr. Lett., 53(1): 65-78. [
CrossRef
Google scholar
|
[114] |
Xiao, L., Boyd, S., 2006. Optimal scaling of a gradient method for distributed resource allocation. J. Optim. Theory Appl., 129(3): 469-488. [
CrossRef
Google scholar
|
[115] |
Xiao, L., Boyd, S., Kim, S., 2007. Distributed average consensus with least-mean-square deviation. J. Parall. Distr. Comput., 67(1): 33-46. [
CrossRef
Google scholar
|
[116] |
Xing, H., Mou, Y., Fu, M.,
CrossRef
Google scholar
|
[117] |
Xu, Y., Han, T., Cai, K.,
|
[118] |
Yang, S., Tan, S., Xu, J., 2013. Consensus based approach for economic dispatch problem in a smart grid. IEEE Trans. Power Syst., 28(4): 4416-4426. [
CrossRef
Google scholar
|
[119] |
Yu, J., Wang, L., 2010. Group consensus in multi-agent systems with switching topologies and communication delays. Syst. Contr. Lett., 59(6): 340-348. [
CrossRef
Google scholar
|
[120] |
Zhang, H., Chen, J., 2014. Bipartite consensus of linear muliagent systems over signed digraphs: an output feedback control approach. Proc. 19th IFAC World Congress, p.4681-4686. [
CrossRef
Google scholar
|
[121] |
Zhang, H., Chen, Z., 2014. Consensus acceleration in a class of predictive networks. IEEE Trans. Neur. Netw. Learn. Syst., 25(10): 1921-1927. [
CrossRef
Google scholar
|
[122] |
Zhang, H., Zhai, C., Chen, Z., 2011. A general alignment repulsion algorithm for flocking of multi-agent systems. IEEE Trans. Automat. Contr., 56(2): 430-435. [
CrossRef
Google scholar
|
[123] |
Zhong, J., Lin, Z., Chen, Z.,
CrossRef
Google scholar
|
[124] |
Zhu, G., Hu, J., 2014. A distributed continuous-time algorithm for network localization using angle-of-arrival information. Automatica, 50(1): 53-63. [
CrossRef
Google scholar
|
[125] |
Zhu, W., Cheng, D., 2010. Leader-following consensus of second-order agents with multiple time-varying delays. Automatica, 46(12): 1994-1999. [
CrossRef
Google scholar
|
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