Abstract: In this paper, we discuss the formation consensus problem of a class of wheeled robots with a nonholonomic constraint and directed communication topology. We design a formation consistency protocol with a coupling weight based on a Zipf distribution to reduce the information exchange between robots and reduce the dependence on state information of all robots in complex communication environments. Thus, we transform the formation consensus problem of the multi-robot system into a stability analysis of the error system. We identify the consistency condition for the formation of the multi-robot system, and use the graph and Lyapunov theories to prove that the formation can converge to the desired geometry and the desired motion rules of the virtual leader under this condition. We perform nontrivial simulations to validate the effectiveness of the distributed cooperative algorithm with coupling weights.