Combined Long-Term Collision Avoidance and Stochastic Station-Keeping in Geostationary Earth Orbit

To limit the spread of space debris, space situational awareness (SSA) delineates guidelines to preserve current space assets. Developing effective collision avoidance maneuver (CAM) strategies is emerging as a global top priority among the considered countermeasures to debris-generating events. Despite most encounters happening over very short time frames, some conjunctions occur over a longer time window, such as in geostationary Earth orbit (GEO), where the involved objects may have small relative velocities. Besides, external perturbations, particularly the geopotential, lunisolar, and solar radiation pressure ones, exert forces on the spacecraft, causing it to deviate from its designated slot and potentially endanger neighboring satellites. This issue is compounded when considering state uncertainty. The presented work, therefore, introduces convex optimization approaches for long-term CAM and tailored stochastic station-leeping (SK) policy regarding longitude and latitude in this regime. The formulation enables continuous CAM and chance-constrained SK, ensuring satellite adherence to an assigned GEO slot with a given probability. Two kinds of chance constraints are devised: the first one does not consider the correlation between longitude and latitude, but the latter does.