Circle formation for anonymous mobile agents with double-integrator dynamics

This paper proposes distributed control laws for a group of mobile agents with double-integrator dynamics to form any given formation on a circle of a prescribed radius. The agents are modeled by point masses with the constraint that all of them can move only on the circle. The agents 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. To make the control strategies more practical, we discuss the corresponding sampled-data control laws and finite-time control laws. Both theoretical analysis and numerical simulations are given to show the effectiveness of the proposed formation control strategies.