Collective motions and formations under pursuit strategies on directed acyclic graphs

A novel pursuit-based approach is presented to investigate collective motions and formations of a large number of agents with both single-integrator kinematics and double-integrator dynamics on directed acyclic graphs (DAGs). Each agent pursues its neighbors according to a directed acyclic graph, in which the agents without neighbors are leaders. Based on signal flow graph analysis and Mason’s rule, necessary and sufficient conditions are derived for BIBO stability of resulting pursuit systems. Moreover, achievable collective motions and formations are analyzed by adjusting a set of control parameters when leaders keep stationary, perform uniform rectilinear motions, and perform uniform circular motions. Finally, simulations are provided for achieving a static formation and mimicking several complex collective behaviors observed in nature, such as V-formation, vortex motions, and tornado motions.