Spacecraft Reachable Domain and Its Applications in Orbital Games: A Review and Future Perspectives

The spacecraft reachable domain has become increasingly important for orbital game analysis due to growing on-orbit activities such as servicing, debris removal, and space situational awareness. This paper provides a comprehensive review of reachable domain theory and its applications in orbital games. A unified mathematical framework is established through three complementary classification dimensions: spatial attributes that distinguish absolute from relative reachable domains, temporal attributes that differentiate free-time from fixed-time reachable domains, and informational attributes that contrast deterministic and predictive reachable domains. Solution methods are systematically reviewed according to this taxonomy, covering analytical and semi-analytical methods, numerical optimization approaches, and geometric and sampling methods for spatial-scale reachable domains, as well as linearized ellipsoidal approximation, exact envelope determination, and fast analytical approximation for time-scale reachable domains. Applications are examined through three representative scenarios: one-on-one pursuit-evasion games, multi-agent cooperative games, and threat-avoidance and defense games. Key limitations of existing approaches are identified, including modeling fidelity, computational efficiency, and scalability under uncertainty. Future research directions are outlined to address these challenges.