Controlling anonymous mobile agents with unidirectional locomotion to form formations on a circle

We study the circle forming problem in which a group of anonymous mobile agents are required to form a formation when moving on a given circle. The agents are constrained to move in the one-dimensional space of the circle only in the counterclockwise direction, but not the opposite way. Distributed, cooperative, sampled-data control strategies are designed that only take nonnegative values. We prove that the multi-agent system under such constrained control input can be guided to reach the prescribed circle formation asymptotically with the additional guarantee that no collision between agents ever takes place. The theoretical analysis is further validated through simulations.