The focus of the thesis’ work is the development of an optimal control algorithm applied to a lunar flying drone, LuNaDrone, which is an autonomous UAV with propulsion actuators designed to perform reconnaissance and, eventually, last mile delivery activities on the lunar surface. Model Predictive Control (MPC) was chosen as one of the possible candidates for controlling the system’s dynamics. Two different MPC formulations were used to study the implementation of the control algorithm: Nonlinear (NL) MPC and Linear Time Varying (LTV) MPC. The standard MPC algorithm requires the minimization of a suitable cost function that penalizes different parameters such as the deviation of the drone from a reference trajectory or an excessive consumption of propellant mass.