Design of impulsive asteroid flybys and scheduling of time-minimal optimal control arcs for the construction of a Dyson ring (GTOC 11). (December 2022) - Ortega Absil, Carlos
Abstract: This paper describes the approach used by the team named the Eccentric Anomalies to obtain the sixth best solution to the problem of the eleventh Global Trajectory Optimization Competition, whose futuristic scenario of Dyson sphere building remained mathematically relevant for current space mission design and engineering in general. As usual for this recurring challenge, it involved large-scale combinatorics at a high level and a multitude of optimal control problems at a lower level. Furthermore it proposed additional layers of complexity by adding a strong scheduling component to the usual flyby sequencing, and by featuring both impulsive and continuous-thrust trajectories. The authors took advantage of modern theoretical techniques and open-source tools to put together a sequential process including analysis based on analytical trajectory models, tree searches using efficient data structures, global and local finite-dimensional optimization and multi-objective trade-offs. The optimal control part was both tackled with direct transcription as well as indirect shooting methods, and the mixed-integer scheduling reformulated as a bi-level optimization. From a programming point of view, the main framework was set in an interpreted language whilst using as much as possible dependencies written in compiled ones for speed. Highlights: Multiple-flyby sequences are incrementally constructed with a Beam Search using nearest-neighbor queries and multi-criteria ranking. Low-thrust transfer opportunities are computed with high fidelity as direct or indirect solution to an underlying time-minimal control problem. Mixed-integer scheduling is solved via bi-level evolutionary/heuristic optimization.