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Flocking in Fixed and Switching Networks

Herbert G. Tanner, Ali Jadbabaie, George J. Pappas

2007
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IEEE Transactions on Automatic Control
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This note analyzes the stability properties of a group of mobile agents that align their velocity vectors, and stabilize their inter-agent distances, using decentralized, nearest-neighbor interaction rules, exchanging information over networks that change arbitrarily (no dwell time between consecutive switches). These changes introduce discontinuities in the agent control laws. To accommodate for arbitrary switching in the topology of the network of agent interactions we employ nonsmooth
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... s. The main result is that regardless of switching, convergence to a common velocity vector and stabilization of inter-agent distances is still guaranteed as long as the network remains connected at all times. Abstract-This note analyzes the stability properties of a group of mobile agents that align their velocity vectors, and stabilize their inter-agent distances, using decentralized, nearest-neighbor interaction rules, exchanging information over networks that change arbitrarily (no dwell time between consecutive switches). These changes introduce discontinuities in the agent control laws. To accommodate for arbitrary switching in the topology of the network of agent interactions we employ nonsmooth analysis. The main result is that regardless of switching, convergence to a common velocity vector and stabilization of inter-agent distances is still guaranteed as long as the network remains connected at all times. Index Terms-Algebraic graph theory, cooperative control, multiagent systems, nonsmooth systems. A collision is assumed to have occurred when the coordinates of two agents coincide. The problem is to design the control input (1) so that if connectivity is maintained in the group, agent velocities are synchronized, collisions are avoided, and pair-wise distances between agents that sense each other are stabilized to steady state values within a given range. III. PRELIMINARY DEFINITIONS AND THE CASE OF FIXED COMMUNICATION TOPOLOGY For the sake of completeness, let us first consider the case where the communication network is time-invariant. We represent the communication network by means of a graph, which determines how velocity information propagates in the group.

doi:10.1109/tac.2007.895948
fatcat:ubbceyv5azgfvcxg3kc6d323cm