<p>This paper develops a model predictive control based formation flying algorithm for small spacecraft with a fixed thrust magnitude constraint. This constraint models the limitations of thrusters with no ability to scale the thrust magnitude. The control calculates the optimal thrust duration which results in a mixed integer linear program (MILP). A guidance trajectory and control deadband are implemented to mitigate the increased computation time and possibility of control chattering that arise from the MILP formulation. A range of spacecraft formations are tested in a series of simulations with varying deadband widths. The performance in terms of control usage and error correction are measured. The control is found to be successful in maintaining a spacecraft formation. The performance is found to be highly dependent on the relationship between the minimum possible thrust time and the deadband width.</p>