Time-Dependent Reachable Domain and Its Application to Impulsive Orbital Pursuit–Evasion Analysis

Orbital pursuit–evasion (OPE) has garnered significant attention due to its potential applications in space rendezvous and proximity operations. Conventional methods using differential games do not fully address the impulsive OPE problem, which involves a discontinuous differential system. This paper presents the concept of a time-dependent reachable domain (TDRD) for analyzing the impulsive OPE problem. The range and time constraints for determining the TDRD are first given. These constraints can be solved to identify two different TDRDs: the RD at a given time and the RD over a duration. The numerical results obtained from the proposed method exhibit good agreement with those from Monte Carlo simulations, validating the practicality of using TDRDs for OPE analysis. Four different qualitatively OPE outcomes are defined based on the geometrical relationship between the spacecraft’s TDRDs. A series of application cases are comprehensively examined to prove that TDRDs directly predict the sufficient conditions leading to a specific OPE outcome. These findings demonstrate that the TDRD concept is a potent and efficacious instrument for studying the impulsive OPE problem.