Graph Diffusion-Based Satellite Swarm Deployment for Curse-of-Dimensionality Mitigation

This paper presents a reliable connectivity maintenance strategy for autonomous satellite formation control in $J_2$-perturbed swarm array deployment. Autonomous satellites have a limited controllable range of formation control due to sensing and actuator constraints, requiring high-certainty connectivity maintenance under uncertainty. Traditional missions ensure uncertainty attenuation through extensive numerical validation and real-time human management. However, in large-scale swarms, statistical guarantees for successful deployment are impractical due to the curse of dimensionality, while centralized methods impose excessive computational burdens. Decentralized nonlinear approaches offer theoretical guarantees but can be overly conservative under strict resource constraints. To address this challenge, this study proposes a fully decentralized multi-leader-based guidance and reference gain-tuning that guarantees successful deployment. We show that enforcing linear structural constraints results in predictable, operation-ready deployment while guaranteeing escape-avoidance and scalability beyond the curse of dimensionality. Each satellite predicts local influence by assigning a tuned interaction 'flight' plan, which provides a sufficient condition for decentralized gain decisions via online multi-hop intersatellite communication.