A Finite-Field Algebraic Mapping Method for Capability Cognition Modeling of Micro/Nano Satellite Clusters

Micro/nano satellite clusters performing cooperative missions lack a unified, computable capability cognition base, because heterogeneous resource configurations impede consensus on task competence. This paper proposes a capability cognition modeling method based on finite-field algebraic mapping. A physical quantizer maps five configurable physical resources (mass, fuel, peak power, thermal dissipation, storage) onto discrete levels of the finite field GF(2003); three further dimensions (attitude pointing, orbit maneuver, payload imaging) are derived. Physics-driven dual-mode coupling matrices, derived from the Tsiolkovsky equation and a power-budget model and then discretized, encode each propulsion type’s differentiated couplings. Stacking the capability vectors forms the cognition matrix used for comparison, ranking, and clustering. On a five-satellite heterogeneous-propulsion synthetic aperture radar (SAR) cluster, the SAR capability upper bounds are 164 (chemical) and 146 (electric), differing by 18; unlike single-matrix and weighted-sum baselines, the method preserves this propulsion-dependent gap. Under ±40% perturbation of all non-diagonal coupling coefficients, the median |ΔSAR| is 0 and the mean relative deviation is 2.37%, and the chemical-above-electric ordering is preserved in 97.4% of cross-validation pairs. The results characterize the framework’s numerical behavior and internal consistency rather than independent physical validation; an optical-imaging scenario reproduces the payload-dependent penalty by re-calibrating one row.