Optimal plan for multiple debris removal missions

Cerf, Max

RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 4, pp. 1005-1032.

In order to keep a safe access to space in the coming years, it will be necessary to clean the near Earth region from the most dangerous debris like spent satellites or launchers stages. An average removal rate of 5 debris per year is recommended to at least stabilize the current debris population. Successive missions must be planned over the years using similar vehicles in order to limit the development cost. This paper addresses the problem of the mission plan so that they can be achieved at minimal cost by a generic vehicle designed for such Space Debris Collecting missions. 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 model 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 plan. 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 plan. 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 a 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 sun-synchronous debris to be selected in a list of 21 candidates.

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