Cyclic interconnection in 1-D vehicle formation control

In this paper, we study a formation control scheme for a 1D string of vehicles. Each member tracks the movement of its immediate predecessor but also the first vehicle tracks the position of the last member of the string. We discuss conditions for the stability of the full interconnected system and show that if a constant inter-vehicle spacing policy is used, the interconnection becomes unstable after the string size surpasses a critical value. Moreover, we show that if constant time headway is used in the spacing policy, stability can be recovered for any string size. String stability is also achieved as a consequence.