One of the pivotal challenges in a multi-robot system is how to give attention to accuracy and efficiency while ensuring safety. Prior arts cannot strictly guarantee collision-free for an arbitrarily large number of robots or the results are considerably conservative. Smoothness of the avoidance trajectory also needs to be further optimized. This paper proposes an accelerationactuated simultaneous obstacle avoidance and trajectory tracking method for arbitrarily large teams of robots, that provides a nonconservative collision avoidance strategy and gives approaches for deadlock avoidance. We propose two ways of deadlock resolution, one involves incorporating an auxiliary velocity vector into the error function of the trajectory tracking module, which is proven to have no influence on global convergence of the tracking error. Furthermore, unlike the traditional methods that they address conflicts after a deadlock occurs, our decision-making mechanism avoids the near-zero velocity, which is much more safer and efficient in crowed environments. Extensive comparison show that the proposed method is superior to the existing studies when deployed in a large-scale robot system, with minimal invasiveness.