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Research Papers

Theoretical Analysis of Flocking Algorithms in Networks of Second Order Dynamic Agents With Switching Topologies

[+] Author and Article Information
Mohammad Haeri

e-mail: haeri@sina.sharif.edu
Advanced Control Systems Lab,
Electrical Engineering Department,
Sharif University of Technology,
Tehran 11155-4363, Iran

Contributed by the Dynamic Systems Division of ASME for publication in the JOURNAL OF DYNAMIC SYSTEMS, MEASUREMENT, AND CONTROL. Manuscript received November 9, 2012; final manuscript received September 11, 2013; published online October 10, 2013. Assoc. Editor: Prashant Mehta.

J. Dyn. Sys., Meas., Control 136(1), 011013 (Oct 10, 2013) (9 pages) Paper No: DS-12-1364; doi: 10.1115/1.4025456 History: Received November 09, 2012; Revised September 11, 2013

This paper deals with a refined analysis and modification of existing results on the flocking algorithms proposed for the second order dynamic agents. In the present work, the limiting condition of ever connectivity is removed and it is proved that the flocking can be reached if only the union of the network proximity graphs during nonoverlapping time intervals becomes connected frequently enough. Also, it is proved that including a static virtual leader cannot model the group objective of achieving the desired velocity and it will stop eventually at a predefined point in the space. The convergence rate to this fixed point is determined too. The last contribution of this paper is definition of group configuration when only a fraction of agents are informed about the virtual leader.

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References

Couzin, I. D., Krause, J., James, R., Ruxton, G. D., and Franks, N. R., 2002, “Collective Memory and Spatial Sorting in Animal Groups,” Theor. Biol., 218(1), pp. 1–11. [CrossRef]
Parrish, J. K., Viscido, S. V., and Grunbaum, D., 2002, “Self-Organized Fish Schools: An Examination of Emergent Properties,” Biol. Bull., 202(3), pp. 296–305. [CrossRef] [PubMed]
O'Loan, O. J., and Evans, M. R., 1999, “Alternating Steady State in One Dimensional Flocking,” J. Phys. A: Math. General, 32(8), pp. 99–105. [CrossRef]
Mogilner, A., and Edelstein-Keshet, L., 1999, “A Non-Local Model for a Swarm,” J. Math. Biol., 38, pp. 534–570. [CrossRef]
Reynolds, C. W., 1987, “Flocks, Herds, and Schools: A Distributed Behavioral Model,” Comput. Graph., 21(4), pp. 25–34. [CrossRef]
Cortes, J., Martinez, S., and Bullo, F., 2004, “Robust Rendezvous for Mobile Autonomous Agents via Proximity Graphs in Arbitrary Dimensions,” IEEE Trans. Autom. Control, 51(8), pp. 1289–1298. [CrossRef]
Su, H., Chen, G., Wang, X., and Lin, Z., 2011, “Adaptive Second-Order Consensus of Networked Mobile Agents With Nonlinear Dynamics,” Automatica, 47(2), pp. 368–375. [CrossRef]
Tian, Y. P., and Zhang, Y., 2012, “High-Order Consensus of Heterogeneous Multi-Agent Systems With Unknown Communication Delays,” Automatica, 48(6), pp. 1205–1212. [CrossRef]
Notarstefano, G., Egerstedt, M., and Haque, M., 2011, “Containment in Leader-Follower Networks With Switching Communication Topologies,” Automatica, 47(5), pp. 1035–1040. [CrossRef]
Moreau, L., 2005, “Stability of Multi-Agent Systems With Time-Dependent Communication Links,” IEEE Trans. Autom. Control, 50(2), pp. 169–182. [CrossRef]
Tanner, H. G., Pappas, G. J., and Kumar, V., 2004, “Leader to Formation Stability,” IEEE Trans. Rob. Autom., 20(3), pp. 443–455. [CrossRef]
Lin, Z., Francis, B., and Maggiore, M., 2005, “Necessary and Sufficient Graphical Conditions for Formation Control of Unicycles,” IEEE Trans. Autom. Control, 50(1), pp. 121–127. [CrossRef]
Su, H., Wang, X., and Chen, G., 2009, “A Connectivity-Preserving Flocking Algorithm for Multi-Agent Systems Based Only on Position Measurements,” Int. J. Control, 82(7), pp. 1334–1343. [CrossRef]
Dimarogonas, D. V., and Kyriakopoulos, K. J., 2008, “Connectedness Preserving Distributed Swarm Aggregation for Multiple Kinematic Robots,” IEEE Trans. Rob., 24(5), pp. 1213–1223. [CrossRef]
Su, H., Wang, X., and Chen, G., 2010, “Rendezvous of Multiple Mobile Agents With Preserved Network Connectivity,” Syst. Control Lett., 59(5), pp. 313–322. [CrossRef]
Ogren, P., Egerstedt, M., and Hu, X., 2002, “A Control Lyapunov Function Approach to Multi-Agent Coordination,” IEEE Trans. Rob. Autom., 18(5), pp. 847–851. [CrossRef]
Leonard, N., and Friorelli, E., 2001, “Virtual Leaders, Artificial Potentials and Coordinated Control of Groups,” Proceedings of 40th IEEE Conference Decision Control, Orlando, FL, Vol. 3, pp. 2968–2973.
Fax, J. A., and Murray, R. M., 2002, “Graph Laplacians and Stabilization of Vehicle Formations,” Presented in the 15th IFAC Congress, Barcelona, Spain.
Arcak, M., 2007, “Passivity as a Design Tool for Group Coordination,” IEEE Trans. Automatic Control, 52(8), pp. 1380–1390. [CrossRef]
Qu, Z., Wang, J., and Hull, R. A., 2008, “Cooperative Control of Dynamical Systems With Application to Autonomous Vehicles,” IEEE Trans. Autom. Control, 53(4), pp. 894–911. [CrossRef]
Khatib, O., 1986, “Real-Time Obstacle Avoidance for Manipulators and Mobile Robots,” Int. J. Rob. Res., 5(1), pp. 90–98. [CrossRef]
Rimon, E., and Koditschek, D. E., 1992, “Exact Robot Navigation Using Artificial Potential Functions,” IEEE Trans. Rob. Autom., 8(5), pp. 501–518. [CrossRef]
Tanner, H. G., Jadbabaie, A., and Pappas, G. J., 2007, “Flocking in Fixed and Switching Networks,” IEEE Trans. Autom. Control, 52(5), pp. 863–868. [CrossRef]
Olfati Saber, R., 2006, “Flocking for Multi-Agent Dynamic Systems: Algorithms and Theory,” IEEE Trans. Autom. Control, 51(3), pp. 401–420. [CrossRef]
Cucker, F., and Smale, S., 2007, “Emergent Behavior in Flocks,” IEEE Trans. Autom. Control, 52(5), pp. 852–862. [CrossRef]
Su, H., Wang, X., and Chen, G., 2009, “A Connectivity-Preserving Flocking Algorithm for Multi-Agent Systems Based Only on Position Measurements,” Int. J. Control, 82(7), pp. 1334–1343. [CrossRef]
Zavlanos, M. M., Tanner, H. G., Jadbabaie, A., and Pappas, G. J., 2009, “Hybrid Control for Connectivity Preserving Flocking,” IEEE Trans. Autom. Control, 54(12), pp. 2869–2875. [CrossRef]
Su, H., Chen, G., Wang, X., and Lin, Z., 2011, “Adaptive Second-Order Consensus of Networked Mobile Agents With Nonlinear Dynamics,” Automatica, 47(2), pp. 368–375. [CrossRef]
Guo, W., Lu, J., Chen, S., and Yu, X., 2011, “Second-Order Tracking Control for Leader-Follower Multi-Agent Flocking in Directed Graphs With Switching Topology,” Syst. Control Lett., 60(12), pp. 1051–1058. [CrossRef]
Su, H., Wang, X. and Lin, Z., 2009, “Flocking of Multi-Agents With a Virtual Leader,” IEEE Trans. Autom. Control, 54(2), pp. 293–307. [CrossRef]
Luo, X., Li, S., and Guan, X., 2010, “Flocking Algorithm With Multi-Target Tracking for Multi-Agent Systems,” Pattern Recogn. Lett., 31(9), pp. 800–805. [CrossRef]
Wen, G., Duan, Z., Li, Z., and Chen, G., 2012, “Flocking of Multi-Agent Dynamical Systems With Intermittent Nonlinear Velocity Measurements,” Int. J. Rob. Nonlinear Control, 22(16), pp. 1790–1805. [CrossRef]
Godsil, C., and Royle, G., 2001, Algebraic Graph Theory, Springer-Verlag, New York.

Figures

Grahic Jump Location
Fig. 1

Flocking of 40 agents applying control protocol in Eq. (4)

Grahic Jump Location
Fig. 2

Flocking of 40 agents applying control protocol (16): (a) initial state, (b) configuration, and velocities at t = 20 s, (c) velocity convergence, and (d) position convergence of the COM

Grahic Jump Location
Fig. 3

Flocking of 40 agents applying control protocol (24): (a) initial positions, (b) velocity, and configuration at t = 70 s, and (c) trajectories of the virtual leader and the COM of three informed agents

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