Geometry of cyclic pursuit

Pursuit strategies (formulated using constant-speed particle models) provide a means for achieving cohesive behavior in systems of multiple mobile agents. In the present paper, we explore an n-agent cyclic pursuit scheme (i.e. agent i pursues agent i+1, modulo n) in which each agent employs a constant bearing pursuit strategy. We demonstrate the existence of an invariant submanifold, and state necessary and sufficient conditions for the existence of rectilinear and circling relative equilibria on that submanifold. We present a full analysis of steady-state solutions and stability characteristics for two-particle ¿mutual CB pursuit¿ and then outline steps to extend the nonlinear stability analysis to the many particle case.