This paper proposes a solution for the leader-follower consensus formation control problem of nonholonomic vehicles that exhibit input constraints. In this consensus problem, the position and the orientation of all the vehicles has to be regulated at a desired equilibrium, hence this pertains to a stabilization scenario. Therefore, in order to satisfy Brockett's theorem, the controller has to be designed to be either discontinuous or time-varying. The proposed scheme is a smooth bounded Proportional plus damping injection controller that incorporates a persistency of excitation term. A comparative simulation analysis with an unbounded control scheme is also provided.