Multi-target spacecraft mission design using convex optimization and binary integer programming

The optimal design of multi-target rendezvous and flyby missions is challenging due to the combination of traditional spacecraft trajectory optimization and high-dimensional combinatorial problems. The typical approach to these problems generally requires large-scale global search techniques or simplified approximations relying on large amounts of manual labour to be performant. However, global search techniques are generally difficult to use in time- or cost-constrained scenarios due to their computational expense. This work proposes a novel combination of computationally efficient stages which work together to form a nested global optimization approach for multi-target mission design. The multi-target problem is split into seperate combinatorial and optimal control subproblems, which are recursively solved: the combinatorial problem using a novel Binary Integer Programming (BIP) formulation with fixed rendezvous timings obtaining optimal rendezvous ordering, and the optimal control problem with an adaptive-mesh Sequential Convex Programming (SCP) formulation obtaining optimal rendezvous timings for a fixed rendezvous ordering. These stages work recursively in tandem to improve the inputs to each subsequent stage until convergence is obtained. This methodology is demonstrated to offer state-of-the-art performance when applied to the Global Trajectory Optimization Competition 12 (GTOC 12) problem, to which several new best-known solutions are found.