Recent activities in the research on swarm robotics have emerged from the application of concepts from swarm intelligence into multi-robot systems (MRSs) that model the realistic interaction between robots in the system and the environment. Fundamentally, the literature on swarm robotics is biologically inspired by systems as insect colonies, flocks of birds, schools of fish and bacteria colonies. Recently, the flocking formation control behaviour in multi-agent systems (MASs) has encouraged astounding attention among the researchers. Researchers from various disciplines including physics, biophysics, computer science and control engineering have been fascinated by the emergence of flocking, swarming and schooling in MASs under local interactions. In this research, we focus on flocking algorithms for MRSs. The flocking phenomenon is characterized as a form of collective behaviour of a swarm of robots with a distributed architecture that involves locality of the computation, sensing, communication and effector capabilities. Flocking algorithms have the potential to introduce selfhealing, self-organizing and self-configuring capabilities in the functioning of distributed MRSs. However, despite an exhaustive list concerning flocking formation control algorithms is given in the literature, most of the existing results deal with simple mathematical modelled robots. In practice, mobile robots embrace more complex nonlinear dynamic mathematical models and involve non-holonomic constraints. Therefore, it is of scientific and practical interest to study the effectiveness of the flocking algorithms for such complex nonlinear systems involving non-holonomic constraints. This thesis study, expanding novel features on the existing literature, presents a connectivity-preserving artificial potential function (APF)-based flocking algorithm for formation control of mobile networked non-holonomic Euler-Lagrange (EL) dynamical agents under a proximity graph interaction architecture involving a limited sensing radius. In specific, we consider three algorithms: (i) flocking; (ii) (virtual) leader-following flocking; (iii) flocking with obstacle avoidance. Proximity graphs are viewed as a useful and decent mathematical tool to incorporate the practical time-varying communication topology of MRSs in flocking algorithms. The preservation of the network connectivity is of significant importance for the flock stability and synchronization (i.e. consensus) since they firmly depend on it. The use of APF, to encode the local interaction rules for achieving global performance, is inspired by the observations and models of the biologists. APF-based flocking control algorithms are mainly interesting as they are not limited to higher-level models and can be exploited for more advanced nonlinear dynamic models and control strategies for flocking and collision avoidance purposes. The aforementioned algorithm setting improves the practical relevance of the problems to be addressed in this study and meanwhile, it poses technical challenges to the design of the flocking control algorithm and theoretical stability proof, respectively. In all proposed algorithms in this study, being the first author in the literature to study flocking algorithms for non-holonomic EL systems in specific, novel theoretical results for this class of systems, exploiting nonlinear control theory concepts where a nonnegative lower bounded ”energy-like” Lyapunov function candidate is defined, are obtained. Advanced numerical simulation studies and some performance metrics are presented as a complement to the analytical framework in order to verify the effectiveness of the theoretical results.