Building Regular Formations with Establishing/Preserving Information Connectivity by Multi-Agent Robotic Teams

We consider a team of identical agents that are unaware of the team size, cannot discern between the peers or play distinct roles, and should be driven a common control rule, which is to be individually run at any of them. Every agent has access to the relative state of any peer that lies within a finite “visibility range” if nobody “obscures the view” to the peer. Computationally inexpensive distributed algorithms are presented for solution of the following problems: distribution of the agents into nodes of a uniform grid with a given step without gaps and multiple occupancy of nodes; reaching consensus on a quantity of interest (QoI); even self-distribution between two given values of QoI. These algorithms are illustrated by using them as building blocks for control laws that ensure first, dense sweep coverage of corridor environments by planar robotic swarms and second, autonomously building a virtual antenna array in 3D by mobile devices. The proposed algorithms are justified by mathematically rigorous global convergence results; their performance is confirmed by computer simulation tests.