Post-Capture Stabilization of Net-Based Systems in Active Debris Removal Missions Development and Analysis of Control Algorithms for Relative Positioning

The rapid increase in satellite launches has raised concerns regarding the sustainability of orbital operations, as defunct satellites and orbital debris pose significant risks to the safety and longevity of current and future space missions. Among proposed solutions, Net-Based Space Systems have emerged as a viable approach for Active Debris Removal. However, the stabilization of such systems after target capture remains a critical challenge, primarily due to the unknown and variable properties of the captured debris. Addressing these challenges necessitates the development of advanced control strategies and robust estimation techniques. This Thesis, conducted at the Space System Dynamics and Control Lab of The State University of New York at Buffalo, examines the dynamics and control of single-tethered and sub-tethered configurations for Net-Based Space Systems. To facilitate this investigation, a simplified mathematical model is initially developed in MATLAB/SIMULINK, enabling comparisons of control strategies under uniform simplifying assumptions. Afterwards, a high-fidelity Python-based simulator is implemented utilizing Google JAX's jax.numpy.array structure and the Diffrax library, allowing for more accurate numerical simulations of the net dynamics. The first part of this Thesis focuses on the analysis of single-tethered and sub-tethered configurations, introducing simplifying assumptions to enable the implementation and evaluation of various control methodologies. These include Open Loop, Proportional-Integral-Derivative, Proportional-Derivative, Linear Quadratic Regulator with Exogenous Inputs, and Wave-Based control strategies. A novel formulation of the Wave-Based control is here proposed, designed to achieve zero steady-state error conditions. A hierarchical evaluation process is later applied to assess the performance of these strategies. Among the examined approaches, the Wave-Based controller exhibits notable robustness and effectiveness, particularly in mitigating tether entanglement. The second part of the Thesis presents a sensitivity analysis of the Wave-Based controller for both configurations, examining variations in target mass, inertia, and angular rates. The results demonstrate that the controller maintains robust stability under variations in mass and inertia without necessitating parameter tuning. However, significant angular rate variations can induce destabilizing motions. The third part extends the investigation through the implementation of the Python-based simulator, which incorporates the dynamics of the net itself. This allows for a more comprehensive analysis of the system's behavior under varying debris angular rates. The results of this study underscore the advantages of the Wave-Based control strategy in Active Debris Removal operations, particularly in scenarios where debris properties are uncertain. The controller’s independence from debris parameters estimation is a significant advantage, relying solely on the chaser onboard measurements for stabilization.