This thesis was aimed for the Master of Science degree in Mechanical Engineering at The Delft University of Technology. The goal of this research was to formulate an assignment algorithm for autonomous guidance, control, and navigation system for spacecraft formation flying using a Model Predictive Control approach for estimation of fuel expenditure. This report is split into three parts. First, the earth's gravitation field and its variation are discussed. The relative motion in the orbit around the earth is briefly explained. The derivation of linearized relative dynamics by Clohessy-Wiltshire is presented. In the second part, the assignment problem is explained. The majority of the literature has been using the distance between the deployed state to the target state. A new approach is discussed using fuel as the assignment parameter including the framework for the assignment parameters is established. For the third part, fuel expenditure estimation using two types of control schemes is explained. The Artificial Potential Function approach is concisely explained. The choice of Model Predictive Control over Artificial Potential Function is discussed. The aim for the third part was the formulation of the control problem using the Model Predictive Control with a linearization dynamics model of the satellites. The system model used in the MPC formulation was constructed based on the Clohessy–Wiltshire relative equations of motion. The demonstrations were established using randomized positions. The simulations were performed and estimation of the fuel expenditure was explained based on the simulation results. The proposed assignment algorithm was tested using the fuel cost estimations from the MPC-based simulations. The results showed that the algorithm performed as designed. Lastly, the possible future research options are listed out.