Stability of potential function formation control with communication and processing delay

We derive conditions for which a circular formation of nonholonomic robots under potential function control is stable, where robots assume a radially-directed pose at equilibrium. In addition to the delay-free case, we investigate the stability of the equilibrium when communication and local processing introduce delay. It is shown that while sufficiently large processing delay always leads to instability, with the right choice of control parameters, the system can tolerate unbounded communication delay. The analytical results are compared with simulations of a fleet of nonholomonic robots as well as with experimental data.