A client-server network is one of the most important topics in a computer network. In this work, a real-time computer control system is designed based on the Client-Server Model for a Multi-Agent Mobile Robot System (CSM-MAMRS) and is applied to a building that consists of (N) floors and uses one mobile robot on each floor that has specific actions in different types of environments. The new proposed CSM-MAMRS consists of four layers. The first stage manages the network communication for each agent. The second stage solves the major problems of path planning by using a proposed hybrid algorithm that combines the Rapidly Exploring Random Tree Star (RRT*) and the Particle Swarm Optimization (PSO) algorithms in order to provide the shortest and smoothest path with collision avoidance between the starting and the target points in a static and dynamic robot environments are used.. In the third stage, a velocity planner controller is based on an inverse kinematic mobile robot model. In the fourth stage, the Hypertext Transfer Protocol HTTP is used to send velocity values to real mobile robots via the Wireless Network Control Administration. The simulation results and experimental works successfully achieved to significant improvement in real-time when using three missions of three mobile robots on different static map floors in the building. The maximum tracking pose errors for three robots in the static enviormnets are 0.39 cm, 0.02 cm, 0.32 cm respectively, but the maximum tracking pose error in the dynamic environments are 2.94 cm and 2.8 cm only for two mobile robots along the maximum distance of 250 cm. Index Terms— Real-time computer control, Mobile robot, Multi-agent system, Path planning algorithms.