Fleets of autonomous vehicles offer an innovative solution to enhance logistic operations in manufacturing systems by increasing efficiency and safety. However, navigating in unstructured environments with moving obstacles presents significant challenges. This paper addresses this problem by proposing a novel control architecture that combines grid based mapping with receding horizon control techniques. Specifically, unicycle models are used to describe the dynamics of the robots, and sequences of feasible and safe way-points are computed by leveraging the real-time grid map of the entire operating scenario. A distributed set-theoretic model predictive control scheme leverages this information to ensure safe navigation. The effectiveness of the proposed approach is demonstrated through experimental results in a real-world context, where a team of three autonomous robots assists human workers along a steel production line manufacturing angle pipes, block-stages, and caps.