Distributed Pi formation control design for autonomous vehicles using edge dynamics

A novel fully distributed proportional-integral (PI) formation controller design approach is proposed in this paper for general linear multi-agent systems (MASs) with model uncertainties and disturbances. First, an edge dynamics is developed for uncertain and perturbed linear MASs, based on which the formation control problem for the initial MAS is shown to be equivalent to a decentralized stabilizing problem for the obtained edge dynamics. Afterward, a necessary and sufficient condition for the PI controller gains is derived. A corollary of this condition shows that for integrator agents, PI controller gains can be any positive scalars. This result is then applied to the formation control of autonomous four-wheel vehicles described by nonlinear models, of which the efficiency of the proposed method is demonstrated in presence of both uncertainties and disturbances.