Formation control of multiple unmanned vehicles based on graph theory: A Comprehensive Review

In recent years, formation control for multiple unmanned vehicles becomes an active research topic that has received a lot of attention from scientists due to its superior advantages compared with other conventional systems. Algebraic graph and graph rigidity theories are the two main mathematical backgrounds of the formation control theory. The graph theory is used to describe the interconnections among vehicles in formation while rigid graph theory - an important subset of graph theory - ensured that the inter-vehicle distance constraints of the desired formation are enforced via the graph rigidity. This paper provides a comprehensive review of graph theory supporting formation control for groups of unmanned aerial vehicles (UAV) or swarm UAVs. The background of the theory and the recent developments of graph-theory-based formation control are reviewed. We provide a cohesive overview of the formation control and coordination of multiple vehicles. Finally, some challenges and future potential directions in formation control are discussed.