Optimal Control of a Ballistically-Linked Group of Small Spacecraft for Broadband Communication

This article addresses the critical challenge of developing optimal control algorithms for ballistically linked groups (BLGs) of small satellites within broadband communication constellations. The research is driven by the global shift towards large-scale low Earth orbit (LEO) megaconstellations, where precise, long-term, and fuel-efficient maintenance of the orbital structure is paramount. The core difficulty stems from the severe mass, size, and power constraints of CubeSats, which render traditional high-propellant control strategies impractical. The primary objective is to design, compare, and validate algorithms for accurate formation flying while minimizing propellant consumption, thereby extending mission lifetime and reducing operational costs. The study uses model relative motion in a near-circular orbit. Transfer of a deputy spacecraft to a 100 km along-track separation serves as the test case. The first method applies Pontryagin’s maximum principle, solving the two-point boundary value problem via a Newton metod. The second employs a predictive control framework. The third strategy is based on parametric optimization of a predefined control input structure, with subsequent gradient-based correction. Numerical simulations for different transfer durations confirm the efficacy of all methods. The Newton method provides exceptional accuracy in meeting terminal state constraints at a fixed final time. The predictive controller demonstrates superior fuel economy by incorporating extended passive coasting arcs. The parametric optimization approach offers implementation flexibility, albeit with sensitivity to initial parameter guesses. This comparative analysis confirms the practical viability of these algorithms for the autonomous, fuel-conscious station-keeping and reconfiguration of future small-satellite communication swarms, a vital capability for next-generation global connectivity networks.

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