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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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Figures

Grahic Jump Location
Fig. 1

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

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

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

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