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In designing distributed control architecture of multiple autonomous robot system, behaviors and cooperative control strategies using by insects, birds, fishes, animals and human being are usually considered as good models because they are with many very nice features such as simplicity, flexibility, robustness and fault tolerance, etc. Within them, schooling behavior of fish and flocking behavior of birds were well studied for controlling group motion of robots with local sensing ability and local interaction only. Several research groups have proposed and successfully demonstrated full distributed control architectures for various size robot swarm system via simulations or experiments. To many types of fish schools, we can observe another very interesting behavior, Group Escape Behavior which shows that all fish change their moving directions rapidly and cooperatively without global broadcasting communications while some fish sense a predator. In this study, we proposed a distributed algorithm to perform Group Escape Behavior without inter-robot communication by mimicking behaviors of fish schools. It provides an alternate method for robot teams to achieve some emergency tasks while inter-robot communication is restricted. In this paper, the proposed control mechanism for achieving group escape behavior is introduced, and the characteristics of escape motion mode transition in the swarm are discussed. Some simulation results and experimental results are provided for illustrating the validity of the proposed algorithm, and for analyzing performance of the group escape behavior implemented.