Decentralized formation control via the edge Laplacian

Formation keeping strategies for groups of interconnected agents have recently been of great research interest in the systems community. In this work, we explore the utility of the edge variant of the graph Laplacian in the synthesis of formation keeping control laws. Along the way, we show a general duality relation between networked dynamic systems with measurement restrictions and those with control constraints. In both cases, it is shown that the closed loop error dynamics for the formation reduces to the edge agreement problem- which in turn-can be fully characterized via the spanning trees of the underlying interconnection topology.