A new distributed collision-free formation trajectory tracking strategy is presented for Euler-Lagrangian multi-agent systems (MASs). To constraint control performance within the expected range, a new adaptive prescribed performance function (PPF) is presented. An adaptive adjustment factor is added to relax the restrictions when the agent performs the obstacle avoidance behavior. Subsequently, the expected velocity is designed for formation trajectory tracking with collision avoidance. Finally, a distributed control algorithm is proposed to drive the agent velocity convergence to the desired velocity.