Multi-agent robotics involves the coordination of large numbers of robots, which leads to significant challenges in terms of collision avoidance. This paper generates provably collision free swarm behaviours by constructing swarm safety control barrier certificates. The safety barrier, implemented via an optimization-based controller, serves as a low level safety controller formally ensuring the forward invariance of the safe operating set. In addition, the proposed method naturally combines the goals of collision avoidance and interference with the coordination laws in a uni ed and computationally efficient manner. The centralized version of safety barrier certificate is designed on double integrator dynamic model, and then a decentralized formulation is proposed as a less computationally intensive and more scalable solution. The safety barrier certificate is validated in simulation and implemented experimentally on multiple mobile robots; the proposed optimization-based controller successfully generates collision free control commands with minimal overall impact on the coordination control laws.