A multi-agent system consisting of N wheeled mobile robots is considered. The robots are modeled by unicycle dynamics and the multi-agent collision avoidance problem, which lies in steering each robot from its initial position to a desired target position while avoiding collisions with obstacles and other agents is considered. The problem is solved in two steps. First, exploiting a differential game formulation, collision-free trajectories are generated for virtual agents satisfying single-integrator dynamics. Second, the previous step is used to construct dynamic feedback strategies for the wheeled mobile robots satisfying unicycle dynamics which ensure each of the robots reaches its target without collisions occurring. A numerical study of the proposed methodology is provided through a series of simulations.