No abstract

The space close to our planet is getting more and more polluted. Orbiting debris are posing an increasing threat to operational orbits and the cascading effect, known as Kessler syndrome, may result in a future where the risk of orbiting our planet at some altitudes will be unacceptable. Many argue that the debris density at the Low Earth Orbit (LEO) has already reached a level sufficient to trigger such a cascading effect. An obvious consequence is that we may soon have to actively clean space from debris. Such a space mission will involve a complex combinatorial decision as to choose which debris to remove and in what order. In this paper, we find that this part of the design of an active debris removal mission (ADR) can be mapped into increasingly complex variants to the classic Travelling Salesman Problem (TSP) and that they can be solved by the Inver-over algorithm improving the current state-of-the-art in ADR mission design. We define static and dynamic cases, according to whether we consider the debris orbits as fixed in time or subject to orbital perturbations. We are able, for the first time, to select optimally objects from debris clouds of considerable size: hundreds debris pieces considered while previous works stopped at tens.

The design of interplanetary trajectories often involves a preliminary search for options later refined/assembled into one final trajectory. It is this broad search that, often being intractable, inspires the international event called Global Trajectory Optimization Competition. In the first part of this chapter, we introduce some fundamental problems of space flight mechanics, building blocks of any attempt to participate successfully in these competitions, and we describe the use of the open source software PyKEP to solve them. In the second part, we formulate an instance of a multiple asteroid rendezvous problem, related to the 7th edition of the competition, and we show step by step how to build a possible solution strategy. In doing so, we introduce two new techniques useful in the design of this particular mission type: the use of an asteroid phasing value and its surrogates and the efficient computation of asteroid clusters. We show how the basic building blocks, sided to these innovative ideas, allow designing an effective global search for possible trajectories.

No abstract

Abstract. The design of spacecraft trajectories for missions visiting multiple celestial bodies is here framed as a multi-objective bilevel optimization problem. A comparative study is performed to assess the performance of different Beam Search algorithms at tackling the combinatorial problem of finding the ideal sequence of bodies. Special focus is placed on the development of a new hybridization between Beam Search and the Population-based Ant Colony Optimization algorithm. An experimental evaluation shows all algorithms achieving exceptional performance on a hard benchmark problem. It is found that a properly tuned deterministic Beam Search always outperforms the remaining variants. Beam P-ACO, however, demonstrates lower parameter sensitivity, while offering superior worst-case performance. Being an anytime algorithm, it is then found to be the preferable choice for certain practical applications.