A single controller is designed for a nonholonomic wheeled robot systems to synthesize formation, connectivity and collision avoidance, yielding a distributed control battier function(CBF) based controller, which is naturally relevant to the Lyapunov-like function. A novel class of Lyapunov-like barrier functions which encode the inequality constraints of connectivity and collision avoidance, is introduced into the controller. The corresponding barrier inequality constraints are proposed, and the robot achieves connectivity maintenance and collision avoidance objectives when ensuring the positive invariance of the constraint set. This method provides continues change of control velocity reducing the mechanical fatigue of the actuator. In addition, it can be extended to more secondary control objectives considering different control barrier functions. Moreover, the proposed cooperative control algorithm has no special requirements for formation, and is suitable for different formation requirements and communication topologies. Simulation results are included to verify the effectiveness of the cooperative control algorithm under different situations.