The In-Orbit Servicing (IOS) is an emerging field aimed at extending the operational life of satellites by providing various services, both in direct contact with the client or remotely, and whether the target is cooperative or non-cooperative. These services include inspection, remote or direct enhancement, assembly, repair, refueling, trajectory modification, and space debris mitigation. This thesis focuses on inspection services, with the purpose of developing and validating an optimization method that aims to perform a maneuver with an optimized velocity (i.e. deltaV), improving fuel consumption. Based on this objective, the analyzed method is the Direct Collocation, which is an optimization technique.