  This paper delves into a rendezvous scenario involving a chaser and a target
spacecraft, focusing on the application of Model Predictive Control (MPC) to
design a controller capable of guiding the chaser toward the target. The
operational principle of spacecraft thrusters, requiring a minimum activation
time that leads to the existence of a control deadband, introduces
mixed-integer constraints into the optimization, posing a considerable
computational challenge due to the exponential complexity on the number of
integer constraints. We address this complexity by presenting two solver
algorithms that efficiently approximate the optimal solution in significantly
less time than standard solvers, making them well-suited for real-time
applications.
