Task-Driven Satellite Cluster Self-Organization Method Based on Linear Groups in Finite Fields

With the rapid development of space technology and satellite networks, large-scale satellite clusters have become crucial means for executing complex tasks. However, traditional centralized task allocation methods exhibit limitations in real-time responsiveness and robustness as the number of satellites increases and task demands become more complex. To address these challenges, this paper proposes a capability modeling and cognitive state representation method for satellite agents based on finite field linear groups and designs an autonomous task allocation algorithm accordingly. By mapping the capabilities and cognitive states of agents to matrices and vectors over finite fields and leveraging the algebraic properties of finite field linear groups, efficient information exchange and collaborative decision-making among agents are achieved. Additionally, we develop an interactive satellite capability publishing and subscription system based on capability views. Preliminary simulation and on-orbit verification results demonstrate the feasibility of the proposed method, providing theoretical and technical support for task-driven autonomy in satellite cluster systems.