Guidance Strategy for Proximity Operations for non-cooperative Targets

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. This technique uses an initial general guess for the maneuver solution in the form of position, velocity, and deltaV at predefined grid points. It transforms complex relative motion dynamical equations into simpler polynomial equations, with the polynomial degree depending on the accuracy required for the solution. This approach reduces computational time and is capable of providing accurate solutions. The thesis analyzes two different methods for determining the solution at the collocation points as required in the Direct Collocation technique: (i) the trapezoid method, which applies a second-degree polynomial, and (ii) the Hermite-Simpson method, with a three-degree polynomial. Both methods use Hill’s equations of motion, with drag disturbance included. All simulations are executed in a MATLAB/SIMULINK environment. To ensure the achievement of a global minimum solution, a multi-start function is implemented. The effectiveness of this method is shown analyzing three different case studies for inspection maneuvers: the first is a radial boost, the second performs three repeated loops in the same plane around the target, and the third one is a walking safety ellipse. Each maneuver is executed using both the trapezoid and Hermite-Simpson methods, with a comparison made in terms of deltaV budget and computational time. To assess the effectiveness of this method, the same maneuvers are performed using the classical method of multiple shooting, and a comparison between the resulting deltaVs is conducted. The results from both methods are then supplied, after thickening the grid, to a high-fidelity Rendezvous (RdV) GNC simulator developed by Thales Alenia Space to verify if the obtained guidance trajectory is followed by the RdV GNC navigation and control components of the simulator while maintaining a good level of stability and confirming the reduction in fuel consumption. Finally, with a focus on the safety ellipse maneuver, a further analysis is conducted where the Walking Safety Ellipse equations are imposed instead of Hill’s equations, and a comparison is made with the solution obtained using Hill’s equations. Overall, the used methods and the results obtained demonstrate the efficacy of the Direct Collocation technique, primarily by providing optimized deltaVs in less computational time compared to the classical approach.