Combined Collision Avoidance and Station-Keeping Maneuver Optimization by Collision Probability Inversion

This work tackles the problem of combining collision avoidance maneuvers with station-keeping planning in the geostationary regime when dealing with low-thrust propulsion systems. Firstly, a fast and reliable algorithm inverts the Chan collision probability function for a given threshold to a square Mahalanobis distance constraint. An analytical solution to the maneuver design problem for short-term encounters is attained by adopting a three-point boundary value problem to satisfy conditions on the collision probability and final desired state. The dynamics are framed in equinoctial orbital elements encompassing the [Formula: see text] term. They are specifically tailored to the motion of objects in this region, enabling a more straightforward station-keeping terminal state targeting and reducing the overall computational burden.