On the use of A* search for active debris removal mission planning

Abstract

This paper focuses on the optimal design of an active debris removal mission. A cluster of debris orbiting in sun-synchronous orbit is considered. A numerical score is associated with each debris on the basis of its level of threat. The mission goal is to maximize the cumulative score of the removed debris, while meeting operational constraints on both the total mission ΔV and time. The optimization problem, that is equivalent to a Time-Dependent Orienteering Problem, is formulated in the paper as a search problem on a graph and solved by A*, an optimal tree search algorithm. Three admissible heuristics for enhancing A* performance on the ADR mission design problem are derived in the paper as the exact solutions of relaxed versions of the original combinatorial problem. Their effectiveness is assessed on missions of increasing dimension and complexity, and compared with that of a commercial branch-and-bound solver on an original 0–1 integer linear programming formulation of the problem. A fast-computation near-optimal transfer strategy, which cleverly exploits the J2 perturbation to achieve the correct alignment between the orbital planes, is used to pre-calculate the ΔV spent by the spacecraft to move between any pair of debris on a discrete grid of departure/arrival epochs. Numerical results are presented for a 21-debris cluster, by analyzing the effect of the debris score distribution, of the total mission time, and of the maximum transfer duration on the computational time required by the different algorithms to optimally solve the problem.