Coordination and control of multi-agent dynamic systems: models and approaches
SAB'06 Proceedings of the 2nd international conference on Swarm robotics
Optimal consensus seeking in a network of multiagent systems: an LMI approach
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Journal of Global Optimization
Safe flocking in spite of actuator faults
SSS'10 Proceedings of the 12th international conference on Stabilization, safety, and security of distributed systems
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In this correspondence, we consider a discrete time one-dimensional asynchronous swarm. First, we describe the mathematical model for motions of the swarm members. Then, we analyze the stability properties of that model. The stability concept that we consider, which matches exactly with stability of equilibria in control theory, characterizes stability of a particular position (relative arrangement) of the swarm members. We call that position the comfortable position (with comfortable intermember distances). Our swarm model and stability analysis are different from other asynchronous swarm models considered in the literature. In particular, in our analysis we employ results on contractive mappings from the parallel and distributed computation literature. The application of these results to the swarm coordination problem is important by itself since they might prove useful also in n-dimensional swarms.