This paper focuses on the problem of target tracking using k fittest robots in a group of n mobile robots with n>k. We present centralized and distributed coordination models with all-to-all and limited communications, respectively. For the case of all-to-all communication between robots, theoretical analysis is presented to prove the exponential stability of the whole system. In real applications of robotic networks, a robot may only be allowed to exchange information with a limited number of neighbors. In such a limited (...) communication case where centralized quantity is not available, a consensus filter is used to estimate the centralized quantities in a distributed way, and a distributed competitive target tracking is thus achieved. The stability of the distributed control is also proved in theory. Finally, illustrative examples are provided and analyzed to substantiate the efficacy of the proposed models for tracking moving target in a competition manner with all-to-all communications and limited communications. (shrink)