This paper proposes a novel cost-effective robust Model Predictive Control (RMPC) approach that can handle stochastic uncertainties with infinite support. The robust controller is developed by explicitly considering system and uncertainty properties and is applied to waterborne AGVs against environmental disturbances due to wind, waves, and currents. Specifically, probabilistic distributions are modeled and integrated in tube-based RMPC with optimized uncertainty bounds. Furthermore, successive linearizations of nonlinear system dynamics and non-convex constraints are implemented for ease of computational complexity and the robust design. Simulation results are presented to demonstrate the effectiveness of the proposed approach.