In this paper, we propose a novel methodology for achieving complex dynamic behaviors in multirobot systems. In particular, we consider a multirobot system partitioned into two subgroups: 1) dependent and 2) independent robots. Independent robots are utilized as a control input, and their motion is controlled in such a way that the dependent robots solve a tracking problem, that is following arbitrarily defined setpoint trajectories, in a coordinated manner. The control strategy proposed in this paper explicitly addresses the collision avoidance problem, utilizing a null space-based behavioral approach: this leads to combining, in a non conflicting manner, the tracking control law with a collision avoidance strategy. The combination of these control actions allows the robots to execute their task in a safe way. Avoidance of collisions is formally proven in this paper, and the proposed methodology is validated by means of simulations and experiments on real robots.