Optimal Abort and Re-approach Trajectories for Satellite Rendezvous and Docking

This thesis presents a detailed framework for optimizing trajectories for a spacecraft engaging in Rendezvous and Proximity Operations, with a particular emphasis on incorporating safety constraints within the context of low-thrust electric propulsion (EP) systems. The research explores a scenario where a servicing satellite equipped with innovative EP technology aims to dock with a satellite stationed in a Geostationary Earth Orbit. The study methodically formulates an optimization problem aimed at ensuring the execution of safe and efficient abort and re-approach maneuvers in the event of system malfunctions. A key distinction of this research, compared to existing collision-free rendezvous trajectory planning studies, is its use of an on-off thrust profile, necessitated by the operational approach to maximizing efficiency of thruster use within electric propulsion systems. Furthermore, this thesis also investigates re-approach trajectories for future rendezvous attempts. The research applies both indirect and direct optimization methods to solve minimum-time and minimum-fuel problems for abort and re-approach maneuvers. Initially, it presents a time-optimal rendezvous strategy augmented with safety constraints using direct optimization, employing a gradient-based Active-Set method for the time-optimal abort maneuver. Then, the newly-developed fuel-optimal direct optimization approach for the combined abort and re-approach maneuver, utilizing an on-off constant thrust, is introduced. This method begins with a genetic algorithm to determine an initial guess for the optimization variables, followed by refinement through a gradient-based Sequential Quadratic Programming method. The sensitivity analysis performed highlights the robustness of the optimization solutions against variations in initial conditions.