Configuration Maintenance in Multisatellite Orbits Via Co-Phase and Control Optimization

Orbital altitude deviations and perturbations (e.g., Earth’s <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$J_{2}$</tex-math></inline-formula> effect, atmospheric drag) cause phase drift among multisatellites, disrupting the overall configuration. This article presents an optimization-based relative configuration maintenance strategy to maintain the orbital configuration of multiple satellites. We propose a bi-objective optimization framework, which independently optimizes the nominal point and the control input. Unlike conventional methods, the proposed approach systematically adjusts the expected positions of all satellites to minimize relative deviations during each control cycle. The strategy ensures that all satellites reach their assigned station-keeping regions while minimizing the total energy consumption. In addition, phase errors among satellites are explicitly considered in the control input optimization, enabling a precise configuration maintenance. The strategy also accounts for a long-term orbital altitude stability. Simulation results under three distinct orbital altitude scenarios validate the effectiveness, stability, and robustness of the proposed approach in coordinating multisatellite systems under complex orbital conditions.