Implementation of a Sequential Quadratic Programming Algorithm for GEO Satellites Relocation

Space-based technologies play an increasingly pivotal role in our interconnected world, as the need for global surveillance and continuous observation of extensive areas of the Earth becomes more and more imperative. In this context, geostationary (GEO) satellites are confirming their role as a crucial element for space-based services. Longitude relocation is a frequent operational activity required for GEO satellites, to decrease or increase its altitude and start drifting towards a new longitude in order to offer new services in a different Earth location. Even though this process is well-known to satellite operators, its optimization is not always straightforward due to the multiple constraints that must be satisfied, particularly when considering the low-thrust performances of the electric thrusters widely used in recent missions. The optimization of the maneuvers required to carry out the relocation of GEO satellites holds paramount importance in order to limit the operational and management costs of the mission. This thesis investigates a novel approach for GEO relocation optimization by implementing a sequential quadratic programming (SQP) algorithm for constrained nonlinear optimization problems. The primary focus will be directed towards the study of continuous maneuvers, thus considering the use of electric thrusters. This enhanced approach incorporates a quasi-Newton method to solve a set of variables, aiming to achieve the desired orbit targets and obtain the best feasible maneuver plans. From the operational standpoint, configurable and user-defined constraints are introduced. The solver's flexibility enables the customization of constraints for the different phases of insertion and extraction, executed both through electric or chemical propulsion. Specifically, this versatility of the method has been corroborated in the work conducted, with its broadening to impulsive maneuvers, resulting in excellent results. Firstly, a brief overview of geostationary satellites and their main characteristics will be provided. Secondly, key concepts related to orbital mechanics and space propulsion will be reviewed to better understand the analyzed problem. Then, a general mathematical description of the SQP optimization algorithm will be given. Finally, the methodology applied for the study of the problem will be presented, followed by the exposition of the principal results obtained.