Navigation of multiple mobile robots (MMRs) has gained significant interest in recent years because of its growing applications such as in exploration, search and rescue, and scientific data collection. Many of these applications require collision-free navigation of MMRs to allow safe and efficient operation which is subjected to many challenges, such as dynamic and cluttered environments, robots' kinematic and dynamic constraints, motion-liveness, and scalability for large-scale systems. Therefore, this thesis develops navigation methodologies for two models of robots:​ (i) kinematics and (ii) dynamics;​ both in centralized and distributed schemes.

For navigation of MMRs considering kinematics in the centralized scheme, a new conflict resolution strategy is developed that coordinates the robots using only velocity to ensure motion-liveness, especially for cluttered and dynamic environments. Results showed this method is scalable while satisfies robots' non-holonomic and velocity constraints. Regarding the distributed scheme, a new predictive collision avoidance methodology is developed that navigates the robots safely through environment uncertainties relying only on onboard sensors. A robust non-linear controller is subsequently designed to achieve simultaneous tracking and collision avoidance of the robots. For navigation of MMRs considering dynamics, one key element for their safe navigation is the calculation of the time to collision (TTC). A generic method is presented for calculating the TTC among MMRs based on their dynamics to effectively quantify the collision potential and subsequently develop new distributed and centralized navigation methodologies. The results verified that the developed methods are more reliable navigation especially for MMRs with different masses and provide a safer distance among them compared to kinematics-based methods, notably in confined spaces in which some conservative cases result in failures. It was shown in simulations and experiments that the consideration of robots' mass and dynamics are imperative for safety and energy efficiency of MMRs.

This thesis enhanced the collision-free navigation methodologies for cluttered and dynamic environments with live and deadlock-free motion. The developed methodologies are scalable and tried to address the MMRs' collision-free navigation issues with realistic constraints. As a future work, more efficient algorithms can be developed to reduce the computational costs of the proposed navigation methodologies for MMRs.