Mixed integer nonlinear programming applications for trajectory optimization of large-scale active debris removal missions in low Earth orbi

Abstract

Upcoming active space debris removal missions will most likely attempt to remove several objects per mission. The design of such missions involves the selection of the objects to be removed, as well as the optimization of the visit sequence and the orbital transfers interconnecting them. This thesis focuses on the efficient resolution of optimization problems that involve the aforementioned kind of missions. In particular, the considered candidate pools of objects have to be large enough to be representative of the distribution of the most hazardous objects in the region of interest. Thus providing a more realistic view of the actual deorbiting capabilities of multi-target missions. The efficient resolution of such large-scale instances poses three particular challenges, namely, the combinatorial complexity resulting from the size of the candidate object pool, the optimization of the orbital maneuvers and the interaction between the object selection and the maneuver optimization. The combinatorial complexity of the problems has been addressed with a Mixed Integer Linear Programming formulation that prevents the appearance of solutions with disjoint subtours. Regarding the maneuver optimization, both impulsive and lowthrust transfers have been considered. For impulsive maneuvers, a general Nonlinear Programming model has been proposed. Moreover, a dual-based method that is able to efficiently solve specific instances of multi-impulse maneuvers, while guaranteeing the convergence and the global optimality of the solutions, has been devised. For low-thrust maneuvers, this work presents a methodology to compute J2-perturbed low-thrust transfers between circular orbits that achieves an advantageous trade-off between the fidelity of the orbital dynamics, the optimality of the transfers and the computational efficiency. The interaction between the combinatorial decisions and the orbital dynamics has been handled with a two-stage approach that encapsulates each component of the problem in a stage. Conversely, an integrated Mixed Integer Linear Programming model that seamlessly coordinates the maneuver optimization and object selection has also been proposed. Furthermore, a Constraint Programming framework has been devised to deal with general mission analysis problems.