Stable flocking of mobile formation in 3-dimensional space

The paper investigates the flocking behaviors of multi-agent formation in 3-dimensional space which are based on leader following. 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 and dynamically time-variant, respectively. 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. According to the algebraic graph theory, differential inclusions and non-smooth analysis, we model the interconnection relationship of multi-agent formation, and achieve the stability analysis of the system by Lyapunov theory.