Pattern reconfiguration in swarms-convergence of a distributed asynchronous and bounded iterative algorithm

Swarms are physical realizations of self-organizing distributed robotic systems (DRS). This paper provides a rigorous analysis of swarm behavior and introduces a new methodology for using swarms to solve DRS pattern reconfiguration problems. The authors introduce the linear swarm model and show that it is an iterative method for asynchronously solving linear systems of equations under physically relevant constraints. The main result of the paper is a proof of a sufficient condition for the asynchronous convergence of a linear swarm to a synchronously achievable configuration. This is important since a large class of DRS self-organizing tasks can be mapped into reconfigurations of patterns in swarms.