Design of an optimization algorithm for in-orbit inspection relative trajectories

The exponential increase in space activities has highlighted a growing demand for in-orbit services, which are essential to ensure the sustainability of space operations. In-Orbit Servicing (IOS) represents a true paradigm shift, introducing unprecedented scalability and system flexibility. It provides opportu-nities for in-orbit maintenance, inspection, refueling, and upgrades, and will potentially change the en-tire approach to satellite design. However, planning efficient and safe trajectories for IOS missions pos-es a complex challenge due to the non-convexity of trajectory generation problems and the multiple op-erational constraints involved. In this thesis, developed at the Mission Analysis & Operations unit of Thales Alenia Space in Turin, a di-rect numerical optimization method is presented to determine the optimal trajectories for IOS missions, with a specific focus on inspection and docking-type operations involving two spacecraft, a Servicer and a Target. Based on optimization algorithms for non-linear problems, such as Sequential Quadratic Pro-gramming (SQP) methods, a robust framework has been developed to generate trajectories that mini-mize the total ∆V and maximize fuel efficiency, while satisfying mission constraints. By including the effect of aerodynamic drag in the Hill-based relative dynamic model, the optimizer lev-erages relative drag control by adjusting the Servicer’s drag area to efficiently approach or retreat from the Target, thereby minimizing propellant consumption. The optimization framework includes various approaches, such as the use of control boxes and safety ellipses, to ensure the spacecraft remains within safe operational limits during its maneuvers. Furthermore, to test the optimizer’s robustness and adaptability to different operational scenarios, the Target has been modeled with various shapes and geometries, including a traditional cubesat, an ellipsoid-shaped object, and a 3D model of the asteroid Didymos, with the control boxes adapted accordingly. Finally, a refinement process has been carried out using genetic algorithms, which help explore a broader solution space, thus enhancing the likelihood of finding global optima in complex and multi-modal environments typical of orbital trajectory optimization problems. Altogether, the methodologies and results demonstrate the effectiveness of the proposed optimization tool in providing optimal trajectories for in-orbit inspection, addressing the increasing demand in the space industry. At the same time, this thesis lays a solid foundation for future and more in-depth stud-ies that could further enhance the safety, efficiency, and longevity of space operations, ultimately con-tributing to the progress and sustainability of both commercial and scientific in-orbit activities.