This paper contributes with a multi-level, hierarchical control system for a fleet of mobile robots sharing a common 2D motion space. The system consists of three levels, with the top level being a supervisor based on a discrete representation of the Multiple Mobile Robot System (MMRS), in which robot motion processes are seen as sequences of stages. The supervisor controls centrally the changes of their stages by robots, ensuring their collision-, and deadlock-free concurrent movement. The intermediate control level supervises locally the execution of robot motion on individual stages in a manner consistent with the decisions of the top level. The lowest level, robot control, is responsible for motion execution as determined by the local supervisor. We capitalize on some earlier results concerning the supervisory control of MMRS and propose a common framework for three supervisory control models. Then we propose relevant solutions for the local supervisors, in particular, a DES-based robot-motion-mode control and application of the Artificial Potential Field model for ensuring collision-free motion of two robots sharing a space sector. Next we assume simple robot control and subject the system to simulation experiments aimed at comparing the impact of the different solutions on the performance of MMRS.