Consensus control for relative configuration maintenance of large-scale LEO constellations

Relative configurations of large-scale Low Earth Orbit constellations are susceptible to drift under initial insertion errors and long-term perturbations, rendering scalable and robust maintenance control both crucial and challenging. Conventional methods based on global optimization or reference satellites encounter prohibitive computational complexity and heavy communication loads, particularly at mega-constellation scales. Moreover, the strongly nonlinear nature of orbital dynamics poses additional difficulties for controller design and stability analysis. To overcome these limitations, this paper introduces a fully distributed consensus-based control framework that relies exclusively on local inter-satellite information. Orbital dynamics accounting for multiple perturbations, including Earth’s non-spherical gravity, atmospheric drag, and third-body effects from the Sun and Moon, are embedded within a graph-theoretic network model. A sliding-mode consensus controller is designed for both continuous- and discrete-time systems, and its global asymptotic stability is rigorously established through Lyapunov analysis. To enhance robustness against unmodeled disturbances, a radial basis function neural network is incorporated for adaptive compensation, along with a systematically derived weight update law and corresponding stability proof. Simulations of a 50,000-satellite constellation demonstrate rapid convergence of relative drifts within tight bounds, minimal steady-state control effort, and scale-independent computational complexity, validating the effectiveness and scalability of the proposed framework for maintaining relative configurations in large-scale LEO constellations.