Constrained Formation Control Framework for Spacecraft Proximity Formation Flight

This paper presents an analytical framework for designing Artificial Potential Field (APF) gains for spacecraft formation control within the Circular Relative Orbit framework. While APF methods are effective for formation shaping, they often overlook system dynamics and constraints, risking instability. The proposed method ensures Lyapunov stability through a systematic gain design and the definition of an operational bound. Stability is verified using Structured Singular Value µ-analysis. Numerical simulations confirm the robustness and scalability of the approach, supporting safe and reliable proximity operations for future multi-satellite missions inEarth orbit.