The goal of the navigation process is to find the optimal path for the mobile robot and control its motion on that path without any oscillation. This work aims to find the optimal paths for multi-mobile robots working in the same static environment. To achieve this goal, the proposed quarter orbits particle swarm optimization (QOPSO) algorithm, which is an enhancement of the cell decomposition algorithm, will be used. The main advantage of using the QOPSO algorithm is to generate the shortest path and avoid collision with static obstacles. Moreover, to direct the motion of the three mobile robots on the desired predefined paths, a proposed inverse differential kinematic neural network trajectory tracking (IDKNNTT) controller based on a modified Elman recurrent neural network (MERNN) will be used. This proposed controller is used to control the nonlinear kinematics mobile robots' system to smoothly and quickly generate the left and right wheels' velocities of the multi mobile robots, which are used to control the orientation and position of each mobile robot. Furthermore, using the proposed controller minimizes the tracking error in the X-axis and the Y-axis positions, approximately zeroes the orientation error, and provides no oscillation in the responses. In particular, the controller guarantees that all the mobile robots will follow their desired paths quickly and correctly. Finally, we validate the numerical simulation results of the proposed control strategy by comparing them to those of other types of controllers in terms of the maximum error enhancement in the X-position and the Y-position. Particularly, when the proposed controller was compared to the convolutional neural network trajectory tracking (CNNTT) controller, the comparison results show that the proposed controller improves the tracking error rate on the X-axis by 75.5 % and enhances the tracking error rate on the Y-axis by 21.2 %. In addition, the proposed controller was compared to the MIMO-PID-MENN controller, and the comparison results show that the proposed controller improves the tracking error rate on the X-axis by 33.3 % and on the Y-axis by 40.6 %.