Low-Thrust Under-Actuated Satellite Formation Guidance and Control Strategies

TL;DR

The paper addresses reconfiguring close-range satellite formations with $N$ under-actuated deputies and an uncontrolled chief under low-thrust propulsion. It advances centralized and distributed guidance frameworks built around a convex SOCP/SCP transcription, augmented by a dynamics-independent affine relaxation for a minimum thrust constraint and a softening mechanism to guarantee feasibility within MPC loops. Two MPC schemes, Shrinking-Horizon (SHMPC) and Fixed-Horizon (FHMPC), are developed to close the loop using onboard sensing, with SHMPC offering superior accuracy and Delta-V efficiency for longer maneuvers at the expense of higher compute, and FHMPC providing stable, predictable computation for shorter tasks. A distributed implementation is shown to scale with the number of deputies while retaining safety constraints through serialized coordination, though typically at a modest Delta-V penalty relative to the centralized approach. Overall, the work delivers a robust, onboard-capable guidance and control architecture for multi-satellite formations under realistic low-thrust and safety constraints with demonstrated gains in feasibility, performance, and scalability.

Abstract

This study presents autonomous guidance and control strategies for the purpose of reconfiguring close-range multi-satellite formations. The formation under consideration includes $N$ under-actuated deputy satellites and an uncontrolled virtual or physical chief spacecraft. The guidance problem is formulated as a trajectory optimization problem that incorporates typical dynamical and physical constraints, alongside a minimum acceleration threshold. This latter constraint arises from the physical limitations of the adopted low-thrust technology, which is commonly employed for precise, close-range relative orbital maneuvers. The guidance and control problem is addressed in two frameworks: centralized and distributed. The centralized approach provides a fuel-optimal solution, but it is practical only for formations with a small number of deputies. The distributed approach is more scalable but yields sub-optimal solutions. In the centralized framework, the chief is a physical satellite responsible for all calculations, while in the distributed framework, the chief is treated as a virtual point mass orbiting the Earth, and each deputy performs its own guidance and control calculations onboard. The study emphasizes the spaceborne implementation of the closed-loop control system, aiming for a reliable and automated solution to the optimal control problem. To this end, the risk of infeasibility is mitigated through first identifying the constraints that pose a potential threat of infeasibility, then properly softening them. Two Model Predictive Control architectures are implemented and compared, namely, a shrinking-horizon and a fixed-horizon schemes. Performances, in terms of fuel expenditure and achieved control accuracy, are analyzed on typical close-range reconfigurations requested by Earth observation missions and are compared against different implementations proposed in the literature.

Figures (18)

• Figure 1: Graphical representation of the low-thrust guidance strategy
• Figure 1: Shapes of the unforced relative orbits involved in Reconfiguration 1
• Figure 2: Graphical representation of the SCP scheme
• Figure 2: Shapes of the unforced relative orbits involved in Reconfiguration 2
• Figure 3: Feasibility region of the acceleration vector