Circle formation for anonymous mobile robots with order preservation

This paper proposes a distributed control law for a group of mobile robots to form any given formation on a circle of a prescribed radius. The robots are modeled by point masses with the constraint that all of them can move only on the circle. In particular, robots are oblivious, anonymous, and unable to communicate directly; they share the common knowledge of the orientation of the circle, and can only measure the relative angular positions of their neighbors. A sampled-data control law is proposed as well. For both cases, theoretical analysis and numerical simulations are given to show the effectiveness of the proposed formation control strategies with the desired property of order preservation.