Collaborative Spacecraft Servicing under Partial Feedback using Lyapunov-based Deep Neural Networks

Multi-agent systems are increasingly applied in space missions, including distributed space systems, resilient constellations, and autonomous rendezvous and docking operations. A critical emerging application is collaborative spacecraft servicing, which encompasses on-orbit maintenance, space debris removal, and swarm-based satellite repositioning. These missions involve servicing spacecraft interacting with malfunctioning or defunct spacecraft under challenging conditions, such as limited state information, measurement inaccuracies, and erratic target behaviors. Existing approaches often rely on assumptions of full state knowledge or single-integrator dynamics, which are impractical for real-world applications involving second-order spacecraft dynamics. This work addresses these challenges by developing a distributed state estimation and tracking framework that requires only relative position measurements and operates under partial state information. A novel $\rho$-filter is introduced to reconstruct unknown states using locally available information, and a Lyapunov-based deep neural network adaptive controller is developed that adaptively compensates for uncertainties stemming from unknown spacecraft dynamics. To ensure the collaborative spacecraft regulation problem is well-posed, a trackability condition is defined. A Lyapunov-based stability analysis is provided to ensure exponential convergence of errors in state estimation and spacecraft regulation to a neighborhood of the origin under the trackability condition. The developed method eliminates the need for expensive velocity sensors or extensive pre-training, offering a practical and robust solution for spacecraft servicing in complex, dynamic environments.