Mega-Constellation Design Optimisation

Abstract

Given the rapid growth in popularity of mega-constellations for telecommunication purposes, this thesis aims to identify methods for designing orbital layouts of such constellations. Traditional optimisation methods for regularly sized constellations do not scale due to the number of satellites involved. Therefore, this thesis investigates the design of mega-constellations and how to achieve an optimal layout within a reasonable timeframe.

Initially, the figures of merit most commonly used in mega-constellation design were identified. The most important figure of merit used in all types of missions, except for Earth observation, is visibility, i.e., the number of satellites visible from a point on the ground. For Earth observation missions, the revisit time is more relevant than visibility. Thus, the thesis focused on mission objectives where visibility is the main figure of merit, such as Satcom, Satnav, IoT, etc. There is also more literature and data available on such constellations, including Starlink, OneWeb, Project Kuiper, and others. Consequently, two closely related figures of merit were selected for this study: minimum visibility and mean visibility. The former ensures an N-fold uninterrupted coverage, while the latter provides a general metric of how many satellites are visible over time. Also, the main focus was on Walker constellations as this is the most common geometry used for mega-constellations.

The visibility computation begins with constellation propagation. Due to the large number of satellites in a mega-constellation, existing tools used at ESOC, such as Godot, are insufficient. Therefore, a self-written tool was developed, named mcdo (Mega-Constellation Design Optimisation), which utilises the basic functionality of Godot and takes advantage of NumPy by applying vectorisation to notoriously slow Python. This approach resulted in a decrease in computational time by a factor of 100x with respect to godot.cosmos.BallisticPropagator.

Moreover, the visibility computation was accelerated with the utilisation of graphic processing units (GPU) and simplifications such as North-South symmetry, longitude averaging, or estimating visibility for a single time instance. Depending on the methods and simulation setups used, a reduction of 400x-120,000x in computational time was achieved for visibility computation.

Additionally, the parametric analysis of large Walker constellations yielded some valuable discoveries. For instance, the number of planes P and phasing parameter F do not influence the mean visibility but may have a significant effect on minimum visibility. This means that P and F can be omitted when designing for the mean visibility. It was also revealed that the mean visibility curve scales linearly with the number of satellites N, allowing to avoid propagation of very large constellations, and to scale up the mean visibility curve from smaller constellations instead. Parametric analysis of other parameters provided a general insight into their effect on visibility.

The improved computational efficiency of visibility computation for large Walker constellations enabled the application of multi-shell constellation design. A case study was set up with a requirement of uninterrupted coverage of 50 satellites over European latitudes (35-70 deg), assuming that all shells were at the same altitude of 700 km with a goal to minimise N. The analysis revealed that for two- and three-shell layouts, the minimum N was attained when higher-inclination shells had more satellites than lower-inclination ones. Moreover, methods for design acceleration were discussed.

The "building blocks" method was proposed for designing mega-constellations with more than three shells. This method starts from placing shells at high inclinations and then gradually lowers the inclination of the subsequent shells. It takes advantage of visibility properties of Walker constellations: the higher-inclination shells can cover both high and low latitudes, while the lower-inclination shells can only cover low latitudes. This method reduces the computational time drastically: by a factor of 150x for three-shell layouts and even more for larger numbers of shells.

The presented research offered valuable insights into initial phases of design of the orbital layout of mega-constellations. The mcdo tool and the obtained results were already applied for internal projects at ESA, demonstrating their relevance and usefulness.