This paper presents a novel decentralized framework for the Multi-Agent dynamical coverage problem subject to anti-collision constraints. The control objective is to authorize each agent operating strictly in its safety zone and then enhance the coverage. These zones are the result of a spatial Voronoi partition of the common working space of the Multi-Agent system based on the current positions of the agents. Each zone provides the local information to design the control policies that make each agent converging to a fixed point inside its Voronoi cell. The performance/effectiveness of the proposed techniques will be demonstrated via numerical examples.