This thesis presents two different collision avoidance and control strategies for coordinated and uncoordinated multi-agent robotic systems. In the considered setup, each agent is a differential-drive robot subject to input constraints on the wheels angular velocities. For the coordinated control problem, we propose a collision-free platooning solution utilizing a leader-follower approach. The leader robot follows a predefined reference trajectory, while the follower robots track the leader's pose with an inter-agent delay that is properly designed to avoid inter-vehicle collision. In particular, by resorting to feedback linearization tools, the kinematic models of both leader and followers are linearized, allowing a formal characterization of the platoon's error dynamics and input constraints. To address the platooning trajectory tracking control problem, we employ a set-theoretic model predictive control strategy which is complemented by an ad-hoc collision avoidance policy ensuring collision-free movement among agents. On the other hand, to address uncoordinated situations where the vehicles move in a shared environment, we propose a novel collision prevention mechanism which is inspired by traditional traffic light mechanisms.  The developed framework leverages a set-theoretic model predictive waypoint tracking strategy with feedback linearization, enabling each robot to follow a sequence of waypoints. Moreover, a centralized traffic manager identifies potential collisions using reachability arguments and models potential collisions through a connectivity graph. The collision resolution policy aims to minimize the number of agents required to stop at any given time. Furthermore,  taking advantage of a possible finite preview of future waypoints, the traffic manager can also instruct (adjust) the maximum velocity allowed for each vehicle in order to reduce the likelihood of future collisions. Finally, all the strategies presented in this thesis have been validated via hardware-in-loop experiments using three Khepera-IV differential drive robots.