Warehouse mobile robotics is nowadays entering the mass-production market. Increasing the number of mobile robots up to decades raises new challenges: current industrial practice relies on centralized fleet management, which might hinder efficacy in the case of large fleets. This paper proposes and discusses a partially and a fully distributed extension of a centralized loosely coupled algorithm for multi-robot coordination. In particular, we aim at investigating: 1) how coordination can be distributed among robots, and 2) which is the minimum amount of local information required to enforce safety. Simulation results show that a partial distribution may improve performance in terms of arrival times while preserving safety and liveness.