Cyclic directed formations of multi-agent systems

Formations of multi-agent systems, such as satellites, aircrafts and mobile robots require that individual agents satisfy their kinematic equations while constantly maintaining inter-agent constraints. In previous work we introduced the concept of undirected formation graphs and directed formation graphs to model such formations and presented conditions to determine formation feasibility. However the directed formations were only analyzed in the absence of cycles in the formation graph. In this paper we extend our previous results to accommodate also the presence of cycles in directed formations. Differential geometric and algebraic conditions are presented to determine feasibility of directed formations with possible cycles.