Exact formation control with very coarse information

This paper investigates a formation control problem for agents modeled as double integrators when very coarse information is exchanged. We assume that neighboring agents only know whether their relative position is larger or smaller than the prescribed one. The use of this binary information results in very simple control inputs that direct the agents closer or away from each other and take values in finite sets. We also show that the task of keeping a formation and tracking a reference velocity which is only known to the formation's leader is still achievable under the very coarse information scenario that we consider. In contrast with the other results of practical convergence with coarse or quantized information, here the control task is achieved exactly.