Graphical and Analytical Approaches for Analyzing Collective Behavior of Dynamic Multi-Agent Systems Governed by Generalized Cyclic Pursuit Mechanism

In this study, we use graphical and analytical methods to study the collective behavior of a swarm of dynamic agents controlled by the generalized cyclic pursuit (GCP) scheme. The proposed graphical approach reveals the occurrence mechanisms of various formation patterns in terms of agents' dynamics and tuning parameters of the GCP scheme, including the rendezvous, diverging spirals, circular pattern, and spirograph-like patterns. Then, we develop an analytical tool to obtain the crucial information needed to formulate expressions of the circular and spirograph-like steady-state trajectories generated by the GCP-controlled dynamic multi-agent system. In addition, the steady-state formation trajectories of a swarm of dynamic agents are formulated by explicitly considering the agents' general continuous-time linear time-invariant model and the scenario in which more than two pairs of closed-loop poles exist on the imaginary axis of the complex plane. Numerical simulation cases of the GCP-controlled dynamic multi-agent system are presented to demonstrate the effectiveness of the proposed analysis methodology.