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A machine-learning enabled digital-twin framework for the rapid design of satellite constellations for “Planet-X”

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Abstract

Worldwide communication bandwidth growth has largely been driven by (1) multimedia demands, (2) multicommunication-point demands and (3) multicommunication-rate demands, and has increased dramatically over the last two decades due to e-commerce, internet communication and the explosion of cell-phone use, in particular for in-flight services, all of which necessitate broadband use and low latency. In order to accommodate this huge surge in demand, next generation “mega-constellations” of satellites are being proposed combining a mix of heterogeneous unit types in LEO, MEO and GEO orbital shells, in order to provide continuous lower-latency and high-bandwidth service which exploits a wide-range of frequencies for fast internet connections (broadband, which is not possible with single satellite-type orbital shell systems). Accordingly, in this work, we develop a computationally-efficient digital-twin framework for a constellation of satellites around an arbitrary planet (“Planet-X”). The rapid speed of these simulations enables the ability to explore satellite infrastructure parameter combinations, represented by a multicomponent satellite constellation design vector \(\varvec{\Lambda }{\mathop {=}\limits ^\textrm{def}}\) (number of satellites, satellite orbital radii, satellite orbital speeds, satellite types), that can deliver desired communication signal or camera coverage on “Planet-X", while simultaneously incorporating satellite infrastructural resource constraints. In order to cast the objective mathematically, we set up the system design as an inverse problem to minimize a cost function via a Genetic Machine Learning Algorithm (G-MLA), which is well-suited for nonconvex optimization. Numerical examples are provided to illustrate the framework.

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Notes

  1. From this, one can ascertain the “escape” velocity for a non-propelled object to escape gravitational pull by setting the second-state velocity to be zero and the radius to be infinity:

    $$\begin{aligned} \underbrace{\left( \frac{1}{2}m\varvec{v}^e \cdot \varvec{v}^e-\frac{GM_{px}m}{r_{px}}\right) }_{launch}=\underbrace{0+0}_{{\textit{second state}}}\Rightarrow v^e=\left( \frac{2GM_{px}}{r_{px}}\right) ^{1/2}.\nonumber \\ \end{aligned}$$
    (7.30)

    With Earth’s parameters, \(M_{px}=M_e\) and \(r_{px}=r_e\), this corresponds to \(v^e \approx 11{,}200\) m/s.

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Acknowledgements

This work has been supported by the UC Berkeley College of Engineering.

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  1. Department of Mechanical Engineering, University of California, 6117 Etcheverry Hall, Berkeley, CA, 94720-1740, USA

    T. I. Zohdi

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Zohdi, T.I. A machine-learning enabled digital-twin framework for the rapid design of satellite constellations for “Planet-X”. Comput Mech (2024). https://doi.org/10.1007/s00466-024-02467-3

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