Coverage control has been widely used for constructing mobile sensor network such as for environmental monitoring, and one of the most commonly used methods is the Lloyd algorithm based on Voronoi partitions. However, when this method is used, the result sometimes converges to a local optimum. To overcome this problem, game theoretic coverage control has been proposed and found to be capable of stochastically deriving the optimal deployment. From a practical point of view, however, it is necessary to make the result converge to the global optimum deterministically. In this paper, we propose a global optimal coverage control along with collision avoidance in continuous space that ensures multiple sensors can deterministically and smoothly move to the global optimal deployment. This approach consists of a cut-in algorithm based on neighborhood importance of measurement and a modified potential method for collision avoidance. The effectiveness of the proposed algorithm has been confirmed through numerous simulations and some experiments using multiple aerial robots.