Design of a Combinatorial Tool for Preliminary Space Mission Analysis, applied to the GTOC2 Problem

Abstract

In recent years, space missions to asteroids have been a focus of research. This type of mission has introduced a new challenge in space mission analysis: target selection. Indeed, given the large number of small Solar System bodies and their various orbital and physical characteristics, selecting a specific target is a rather complex task. This problem of target selection was given to the participants of the second Global Trajectory Optimization Competition (GTOC2) in 2006. The GTOC2 problem relies on the design of a low-thrust mission with four consecutive asteroid rendezvous. The main challenge in finding good solutions for GTOC2 stems from the vast search space and stringent constraints set out in the problem description. At the time, a TUDelft-led team of students participated in GTOC2. Since then, there has been a concerted effort within the Astrodynamics & Space Missions (A&S) research group to further investigate feasible solutions and develop new methods to achieve better results. Building on the lessons learned from these previous efforts, we design and implement an algorithm aiming at reducing the pool of candidate targets in a computationally fast manner. This is achieved by decoupling the integer and continuous aspects of the problem. The combinatorial problem is modelled as a static, single-source Shortest Path Problem, tackled with a multi-path greedy algorithm. The continuous aspect is optimized on a leg-per-leg basis with two different optimization techniques. With computational efficiency in mind, the individual transfers are modelled as bi-impulsive, high- thrust arcs, computed with an efficient Lambert solver. The resulting combinatorial tool builds on and contributes to the existing capabilities of Tudat, an Astrodynamics toolbox developed within the A&S Department. The greedy searches in the complete asteroid pool are performed with different parameters and different directions, the sensitivity to the bounds of the continuous optimization problem is analyzed, two different costs functions are investigated. The computational times achieved with the designed greedy algorithm are very attractive. For the largest time intervals considered, where the impact of phasing is reduced, the sequence corresponding to the GTOC2 runner-up is present within a reduced set of asteroid combinations. This points to a fast and accurate pruning of the initial integer search space.