Applied Reachability for Space Situational Awareness and Safety in Spacecraft Proximity Operations

Abstract

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-conguration 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. An optimal control policy is developed to maximize the reachability set and optimal control law discontinuities (switching) are examined. 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. The linearized ClohessyWiltshire equations of motion are normalized to accentuate relative control authority for spacecraft propulsion systems at both Low Earth Orbit (LEO) and Geostationary Earth Orbit (GEO). Several examples with traditional and low thrust propulsion systems in LEO and GEO are explored to illustrate the eects of relative control authority on the timevarying reachability set surface using the nonlinear equations of motion. Both monopropellant spacecraft at LEO and Hall thruster spacecraft at GEO are shown to be strongly actuated while Hall thruster spacecraft at LEO are found to be weakly actuated. Weaknesses with the current implementation are discussed and future numerical improvements and analytical eorts are discussed.