This paper deals with a multi-layered formation control of autonomous marine vehicles (AMVs). Each AMV is considered as an agent and modeled with a nonlinear dynamics. The nonlinear dynamics include a square law drag in the velocity of the vehicle and saturation in the acceleration input. The system is stabilized using a rigid graph-based control approach. A Lyapunov candidate is chosen and proved that it satisfies conditions for an energy function of the formulated problem. Using the proposed Lyapunov energy function and related control law, an asymptotic stability with improved rate convergence of the system is rigorously proven. The required constraints for prevention of ambiguous formations that cause failure of convergence in the system have been developed. The simulation results illustrate the effectiveness of the proposed control law.