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. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This journal article is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/279 IEEE TRANSACTIONS ON AUTOMATIC CONTROL, VOL. 52, NO. 5, MAY 2007 863 Technical Notes and Correspondence Flocking in Fixed and Switching NetworksHerbert G. Tanner, Ali Jadbabaie, and George J. PappasAbstract-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.

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Abstract-In this paper we derive necessary and sufficient conditions for a group of systems interconnected via nearest neighbor rules, to be controllable by one of them acting as a leader. It is indicated that connectivity seems to have an adverse effect on controllability, and it is formally shown why a path is controllable while a complete graph is not. The dependence of the graph controllability property on the size of the graph and its connectivity is investigated in simulation. Results suggest analytical means of selecting the right leader and/or the appropriate topology to be able to control an interconnected system with nearest neighbor interaction rules.

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The paper investigates the stability properties of mobile agent formations which are based on leader following. We derive nonlinear gain estimates that capture how leader behavior affects the interconnection errors observed in the formation. Leader-to-formation stability (LFS) gains quantify error amplification, relate interconnection topology to stability and performance, and offer safety bounds for different formation topologies. Analysis based on the LFS gains provides insight to error propagation and suggests ways to improve the safety, robustness, and performance characteristics of a formation. This material is posted here with permission of the IEEE. Such permission of the IEEE does not in any way imply IEEE endorsement of any of the University of Pennsylvania's products or services. Internal or personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution must be obtained from the IEEE by writing to pubs-permissions@ieee.org. By choosing to view this document, you agree to all provisions of the copyright laws protecting it.This journal article is available at ScholarlyCommons: http://repository.upenn.edu/ese_papers/44 IEEE TRANSACTIONS ON ROBOTICS AND AUTOMATION, VOL. 20, NO. 3, JUNE 2004 443 Leader-to-Formation Stability Herbert G. Tanner, Associate Member, IEEE, George J. Pappas, Member, IEEE, and Vijay Kumar, Senior Member, IEEE Abstract-The paper investigates the stability properties of mobile agent formations which are based on leader following. We derive nonlinear gain estimates that capture how leader behavior affects the interconnection errors observed in the formation. Leader-to-formation stability (LFS) gains quantify error amplification, relate interconnection topology to stability and performance, and offer safety bounds for different formation topologies. Analysis based on the LFS gains provides insight to error propagation and suggests ways to improve the safety, robustness, and performance characteristics of a formation.

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Abstract-We present a navigation function through which a group of mobile agents can be coordinated to achieve a particular formation, both in terms of shape and orientation, while avoiding collisions between themselves and with obstacles in the environment. Convergence is global and complete, subject to the constraints of the navigation function methodology. Algebraic graph theoretic properties associated with the interconnection graph are shown to affect the shape of the navigation function. The approach is centralized but the potential function is constructed in a way that facilitates complete decentralization. The strategy presented will also serve as a point of reference and comparison in quantifying the cost of decentralization in terms of performance.