Formation Coordination with Connectivity Preservation in Presence of Obstacles

This paper presents a geometric approach to multi-robots group formation with connectivity preservation (from a graph-theoretic perspective) among group members. The controller demonstrates consistency among different formations, as well as stability while performing dynamic switching between formations. Inter-robots collision avoidance is delivered through formation preservation, while permitting high degree of formation re-adjustability. It has been proven that such formation approach would result into complete, isomorphic formations (with regards to its first and second isogonic) with edge connectivity Λ(G) = 1/4n(n – 1), and a unique, shortest connectivity link among group members. The complete connectivity along with the isomorphic property of the formations would, in essence, not only guarantee that the communication among the robotic agents will be preserved, but also relax the topological requirements for message passing among group members that might be needed while switching between different formations. In addition, the existence of the inter-robot shortest connectivity link at the group level, would ease the message routing once the information sharing among all the members of the group is necessary.