This paper addresses the Nonlinear Model Predictive Control of input-affine systems. Based on the Extended Modal Series Method, an explicit suboptimal control law is deduced that solves the two point boundary problem given by Pontryagin's Maximum Principle in the related Nonlinear Optimal Control Problem. The deduction of the control law is presented and proven. Then the proposed controller is tested in simulation in the attitude control of a quadrotor, a highly nonlinear and unstable system. The simulation results indicate good performance and near optimal behavior. This work is a background for future development of control techniques for input-affine systems.