Distributed nonlinear algorithms for building chain formations by fully homogeneous multi-agent teams, with establishing informational connectivity

A fully homogeneous team of an unknown size consists of agents that carry no communication facilities and cannot distinguish among the peers or play distinct roles and so should be subjected to a common control rule. Every agent has access to the relative state of any peer that is within a finite “visibility range” if nothing obscures the view to the peer. Distributed continuous-time computationally cheap nonlinear protocols are offered for (a) self-deployment of the team into nodes of a uniform lattice with a given spacing and (b) for even self-distribution over an unknown interval. These findings are illustrated by design of navigation strategies for cruise control of a platoon of vehicles on a road, for navigation of robotic swarms for dense sweep coverage of corridor environments, and for building a virtual antenna array in 3D by aerial drones. The proposed algorithms are justified by rigorous global convergence results; their performance is confirmed by computer simulation tests.