Control of A Formation with One Cyclic Relation in 3-dimensional Space

The paper investigates the flocking behaviors of multi-agent formation in 3-dimensional space which are based on leader following, where the underlying model of a formation is graphical. When the graph is undirected, a class of decentralized control laws for a group of mobile agents are proposed under the conditions that the topology of the control interconnections is fixed. These control laws are a combination of attractive/repulsive and alignments forces which can guarantee the collision avoidance and cohesion of the formation and an aggregate motion along the same heading direction of the leader. And when the graph is directed, a formation of four point agents moving in 3-dimensional space is considered, where one agent is a leader, and the other agents have a cyclic ordering with each one required to maintain a given distance from its neighbor. A control law is obtained, which can be guaranteed the distance preserved for the formation.