Formations of vehicles in cyclic pursuit

Inspired by the so-called "bugs" problem from mathematics, we study the geometric formations of multivehicle systems under cyclic pursuit. First, we introduce the notion of cyclic pursuit by examining a system of identical linear agents in the plane. This idea is then extended to a system of wheeled vehicles, each subject to a single nonholonomic constraint (i.e., unicycles), which is the principal focus of this paper. The pursuit framework is particularly simple in that the n identical vehicles are ordered such that vehicle i pursues vehicle i+1 modulo n. In this paper, we assume each vehicle has the same constant forward speed. We show that the system\´s equilibrium formations are generalized regular polygons and it is exposed how the multivehicle system\´s global behavior can be shaped through appropriate controller gain assignments. We then study the local stability of these equilibrium polygons, revealing which formations are stable and which are not.