Distributed self-organisation of a homogeneous swarm of robots into a uniform closed-chain, with creating informational connectivity

We consider a team of anonymous and silent robots with second-order dynamics and uncertainties. The robots cannot play dissimilar roles, their speeds and control inputs are limited, any of them is partly characterised by a cyclic output variable. Every robot measures its own speed and the relative value of the output of any peer such that is within a given sensing distance and nothing ‘obscures the view’ to it. A distributed protocol is presented that creates a situation where the outputs are evenly spaced and evolve with a given time-varying speed. This protocol does not need initial informational connectivity of the team, is robust against losses and insertions of robots, and excludes collisions among them. The main findings are applied to two problems of sweeping coverage of a 1D barrier snaking in 3D. The convergence of the algorithm is rigorously justified and is confirmed by computer simulations.