Numerically Efficient Methods for Low-Thrust Collision Avoidance Maneuvers Design in GEO Regime

The rapid growth of the space debris population is leading to an uptick in satellite proximity events. The Geostationary Orbit (GEO) region is less populated than the Low Earth Orbit (LEO) regime, but the debris density is still significant despite the difference in the absolute number of satellites belonging to the two regions. In particular, the increasing number of spacecraft reaching their end-of-life and the existing debris, such as rocket bodies, could threaten operative satellites and require onboard Collision Avoidance Maneuver (CAM) planning down the road. Moreover, in this peculiar regime, spacecraft are subjected to gravitational perturbations that cause satellites to cross the assigned geostationary slot delimited by sharp latitude and longitude limits. To overcome this issue, ad-hoc control strategies are adopted to keep the spacecraft within specified boundaries through station-keeping maneuvers. Currently, the state-of-the-art treats CAMs and station-keeping as separate problems. This paper illustrates how to embed both with an analytical and a time-efficient policy designed for low-thrust propulsion systems. First, an extension of previous similar work in LEO has been carried out to GEO considering a pure Keplerian motion. Several firing strategies have been: the North-South and East-West energy-optimal maneuvers, typical of station-keeping. Then, with the inclusion of geopotential perturbation in the CAM design, a station-keeping maneuver has been formulated as a Multi-Point Boundary Value Problem (MPBVP) with specific constraints on Probability of Collision (PoC) at Time of Closest Approach (TCA) and final state. The idea is to leverage the motion linearization with the state transition matrix (STM) and transform the energy-optimal control problem into an Initial Value Problem. In particular, the problem-solution can distinguish between two possible scenarios. On one hand, station-keeping alone is enough to ensure a PoC lower than a safeguard limit. On the other, when not fulfilling this requirement, the algorithm autonomously identifies the best strategy for commanding CAM and station-keeping by imposing an arbitrary PoC at TCA. Results show a reduced computational time burden suitable for onboard CAM planning and a decreasing ∆v for longer maneuvering times.