Interception Domain Approach to Orbital Multi-Player “Encirclement-Capture” Games: Theoretical Foundations and Solutions

In recent years, with the development of micro-satellite clusters and large-scale satellite constellations, the likelihood of multiple spacecraft engaging in orbital pursuit–evasion games has increased. This paper establishes a novel interception domain theory for planar orbital multi-player “encirclement-capture” differential games, and it proves the partitioned structure and classification properties of Nash equilibrium solutions. The main contributions of our study are the following: (1) Proposing the first rigorous definition of interception domains in orbital pursuit–evasion games, proving their convexity, developing computational methods for domain intersections, and establishing a complete classification of equilibrium for planar multi-pursuer interception games, which establishes a theoretical foundation for analyzing multi-spacecraft orbital pursuit–evasion games. (2) Analyzing Nash equilibrium properties for “encirclement-capture” differential games with two, three, or more pursuers, classifying degenerate/non-degenerate scenarios via spatial inclusion relationships. The equilibrium results indicate that as the number of pursuers increases, the game tends toward a degenerate scenario where the likelihood of redundant pursuers (whose actions do not affect the game outcome) rises.