Multiple Space Debris Collecting Mission -- Optimal Mission Planning
  This paper addresses the problem of planning successive Space Debris Collecting missions so that they can be achieved at minimal cost by a generic vehicle. The problem mixes combinatorial optimization to select and order the debris among a list of candidates, and continuous optimization to fix the rendezvous dates and to define the minimum fuel orbital maneuvers. The solution method proposed consists in three stages. Firstly the orbital transfer problem is simplified by considering a generic transfer strategy suited either to a high thrust or a low thrust vehicle. A response surface modelling is built by solving the reduced problem for all pairs of debris and for discretized dates, and storing the results in cost matrices. Secondly a simulated annealing algorithm is applied to find the optimal mission planning. The cost function is assessed by interpolation on the response surface based on the cost matrices. This allows the convergence of the simulated algorithm in a limited computation time, yielding an optimal mission planning. Thirdly the successive missions are re-optimized in terms of transfer maneuvers and dates without changing the debris order. These continuous control problems yield a refined solution with the performance requirement for designing the future Space Debris Collecting vehicle. The method is applicable for large list of debris and for various assumptions regarding the cleaning program (number of missions, number of debris per mission, total duration, deorbitation scenario, high or low thrust vehicle). It is exemplified on an application case with 3 missions to plan, each mission visiting 5 SSO debris to be selected in a list of 21 candidates. 
Max Cerf
math.OC astro-ph.IM