In this thesis, we explore the formation control of unmanned ground vehicles (UGVs) using a Nonlinear Model Predictive Control (NMPC) approach based on the Pontryagin Minimum (maximum, in the original form) Principle. The UGV model incorporates essential information about the involved agents dynamics, guiding our pursuit of optimal trajectories while concurrently establishing a dynamic network among them. The main goal of the thesis is to bridge the theoretical constructs with practical realities by introducing disturbances into the model. These disturbances, representing real-world uncertainties, contribute to the complexity of the control problem. To address the robust NMPC problem, we formulate the optimal control problem, in presence of exogeneous disturbance, as min-max optimization, wherein the goal is to minimize the trajectories for formation while maximizing the disturbances.