Multi-maneuver algorithms for multi-risk collision avoidance via nonconvex quadratic optimization

Abstract

In this article, the problem of modeling and computing the optimal collision avoidance maneuvers for multiple short-term encounters is presented. Several metrics defining the overall collision risk are analyzed. These include imposing lower bounds on the miss-distance or the Mahalanobis distance at each corresponding time of closest approach (TCA) or upper-bounds on the collision probability. The avoidance maneuvers are modeled as impulsive ones in a single direction of the local frame and for a priori fixed dates for operational motivations. Station-keeping constraints are also imposed via linear inequalities on the relative states at each TCA. The specific nature of the imposed constraints is dictated by a practical framework provided by the French Space Agency (CNES). This results in formulating the maneuver design problem as an optimization problem with linear objective and non-convex quadratic constraints. Different algorithms are presented to solve this problem. Finally, the relative efficiency of the proposed approaches is evaluated and analyzed on a realistic conjunction built from data extracted from the CNES database and on academic random examples of higher complexity.