A new coordination control is developed in this paper for multiple non-holonomic robots in a competitive manner for target tracking with limited communications. In this proposed control approach, only winners of the competition are allocated the task and activated to move towards the target. A distributed coordination model is proposed and its stability is proved in theory. Inspired by the besieging behaviors in social animals for predating, an effective strategy to handle the situation with higher target speed than trackers is also proposed and verified to be extraordinarily effective. (C) 2018 Published by Elsevier Ltd.