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This paper studies the problem of collision/obstacle avoidance in the distributed cooperative output regulation of nonlinear multi-agent systems (MASs). First, a nonlinear distributed command governor equipped by two dynamical barrier functions is constructed to generate safe command signals. Then, a filtering-based distributed command tracking control scheme is proposed. It is shown that the MAS adaptively reconfigures its formation shape in a distributed way when entering into the barrier function's coverage to avoid collisions, and quickly recovers the desired formation shape along with the reference trajectory after being away from the barrier function's coverage. Simulation results are given to illustrate the effectiveness of the proposed scheme.