Unicycles in cyclic pursuit

In this paper, we study the geometric formations of multi-vehicle systems under a control law based on cyclic pursuit. The pursuit framework is particularly simple in that, for n ordered and identical wheeled vehicles, vehicle i simply pursues vehicle i+1 modulo n. We show that, for unicycles with constant speed, the multi-vehicle system´s equilibrium formations are generalized regular polygons. We then study the local stability of these equilibrium polygons, revealing which formations are stable and which are not.