Formations of Vehicles in Cyclic Pursuit.

Inspired by the so-called `tugs" problem front 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 extends 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 as- suine 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 multiivehicle 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. [ABSTRACT FROM AUTHOR]