Reachability Analysis Applied to Space Situational Awareness

摘要

Several existing and emerging applications of Space Situational Awareness (SSA) relate directly to spacecraft Rendezvous, Proximity Operations, and Docking (RPOD) and Formation / Cluster Flight (FCF). Observation correlation of nearby objects, control authority estimation, sensor-track re- acquisition, formation re-configuration feasibility 'stuck' thrusters, and worst-case passive safety analysis are some areas where analytical reachability methods have potential utility. Existing reachability theory is applied to RPOD and FCF regimes. Necessary conditions for maximum position reachability are developed, allowing for a reduction in reachable set computation dimensionality. The nonlinear relative equations of Keplerian motion are introduced and used for all reachable position set determinations. Examples for both circular and eccentric orbits are examined and compared. Weaknesses with the current implementation are discussed and future numerical improvements and analytical efforts are discussed.