Spacecraft Passive Safety Assessment Using Ellipse Constraints and Relative Orbital Elements

This paper presents necessary and sufficient conditions for validating spacecraft passive safety using relative orbital elements (ROE) centered around the far-field to near-field trajectory design of a hypothetical autonomous rendezvous and docking (AR&D) mission. The specific formulation of the ROEs used in this study are of quasi-nonsingular form based on elative eccentricity/inclination vectors. Current methodologies for ensuring passive safety apply keep-out volumes (KOV) to maintain appropriate separation between the Servicer and Client. Widely used techniques to assess the integrity of the KOV involve forward propagation of the relative Cartesian state to check for a potential KOV breach. In this study, an alternative approach to the propagation-based method is proposed using ROEs due to their valuable geometric insights of spacecraft relative motion. Modeling the relative trajectory
and KOV ellipsoids as ellipses into the 2-D ROE sub-space simplifies the passive safety validation to a root-finding problem within the unit disk with high computational efficiency. Other approaches to intersection detection of the KOV are also evaluated in accuracy and run-time. Furthermore, a Monte Carlo simulation was employed to compare the ROE-based and relative Cartesian approaches in terms of maneuver error.