A multi-layer temporal network model of the space environment

With the advent of the New Space era and the increase in the population of resident objects in Earth orbit, there is a compelling need to adopt new tools to study the complexity of the space environment. In particular, there is a need to consider the different layers of functionalities and services in an integrated and consistent framework that allows a global analysis of the evolution of the space environment. In the past two decades, there has been intense research to describe and model physical, engineering, information, social and biological systems using network theory. Most recently, multilayer networks, or networks of networks, have demonstrated a higher capability of describing failures, relationships, connectivity, and patterns, with respect to their single-layer counterpart. This paper presents a representation of the space environment as a dynamic multilayer network, where space objects are nodes and their relationships are captured through dynamic links; each layer represents a different type of interaction. In this paper, in particular, we consider two layers: the physical and the information layer. The former models the collision between pairs of objects and how disruptions tend to propagate in the network, while the latter models the exchange of information among satellites via telecommunication. Links are probabilistic in that they model the probability of an interaction between two nodes. Moreover, the spreading dynamics of disruptions among nodes is mathematically described with a susceptible-infectious-susceptible epidemiological model. By using a bottom-up approach, where we stochastically simulate the spreading of a disruptive event in the network, we show how it is possible to investigate different spreading scenarios and analyze the network weak links and nodes, which can then be targeted for improving the space environment resilience

MHACO : a multi-objective hypervolume-based ant colony optimizer for apace trajectory optimization

In this paper, we combine the concepts of hypervolume, ant colony optimization and nondominated sorting to develop a novel multi-objective ant colony optimizer for global space trajectory optimization. In particular, this algorithm is first tested on three space trajectory bi-objective test problems: an Earth-Mars transfer, an Earth-Venus transfer and a bi-objective version of the Jupiter Icy Moons Explorer mission (the first large-class mission of the European Space Agency’s Cosmic Vision 2015-2025 programme). Finally, the algorithm is applied to a four-objectives low-thrust problem that describes the journey of a solar sail towards a polar orbit around the Sun. The results on both the test cases and the more complex problem are reported by comparing the novel algorithm performances with those of two popular multi-objective optimizers (i.e., a nondominated sorting genetic algorithm and a multi-objective evolutionary algorithm with decomposition) in terms of hypervolume metric. The numerical results of this study show that the multi-objective hypervolume-based ant colony optimization algorithm is not only competitive with the standard multi-objective algorithms when applied to the space trajectory test cases, but it can also provide better Pareto fronts in terms of hypervolume values when applied to the complex solar sailing mission

A network-based evolutionary model of the space environment

Recently, the first treatment of the space population as a multi-layer temporal network was introduced. This model has allowed the application of network theory techniques for a holistic treatment of the space environment. In this work, we go one step further by focusing on the physical layer of the network, investigating its structure, dynamics, and stability. The interactions among resident space objects are modeled through their collision rates: each node represents a population of satellites in a given orbital class, and each link represents their time-varying collision rates with other nodes. Satellites can flow in between these classes and populations, depending on several sink and source phenomena, including explosions, collisions, natural decay due to atmospheric drag, post-mission disposal strategies, operational lifetime duration, and new launches. The underlying dynamics on the network is modeled as a stochastic contact process, in which nodes can assume two possible states: operational and non-operational. The network, therefore, presents a time-varying structure where the number of active and inactive objects, their distribution, their time-varying collision rates, and many other key variables can be studied. The conceptual simplicity and versatility of the network allow to study various topologies and dynamics, and therefore investigate interactions among space objects under different levels. In this framework, several aspects are studied: first of all, two network topologies are introduced. Then, the concept of global stability of the network is introduced and discussed, and a stochastic evolutionary network model is built to simulate the sink and source phenomena in the space environment and evolve the overall population of objects in low Earth orbit for long periods of time. Finally, we perform experiments using a lattice network structure to show how this model can be used to probabilistically study the evolution of space objects and all the key variables involved, such as the number of collisions, the fragments generated, the collision rates evolution, and many others

Improving Thermospheric Density Predictions in Low‐Earth Orbit With Machine Learning

Thermospheric density is one of the main sources of uncertainty in the estimation of satellites' position and velocity in low-Earth orbit. This has negative consequences in several space domains, including space traffic management, collision avoidance, re-entry predictions, orbital lifetime analysis, and space object cataloging. In this paper, we investigate the prediction accuracy of empirical density models (e.g., NRLMSISE-00 and JB-08) against black-box machine learning (ML) models trained on precise orbit determination-derived thermospheric density data (from CHAMP, GOCE, GRACE, SWARM-A/B satellites). We show that by using the same inputs, the ML models we designed are capable of consistently improving the predictions with respect to state-of-the-art empirical models by reducing the mean absolute percentage error (MAPE) in the thermospheric density estimation from the range of 40%–60% to approximately 20%. As a result of this work, we introduce Karman: an open-source Python software package developed during this study. Karman provides functionalities to ingest and preprocess thermospheric density, solar irradiance, and geomagnetic input data for ML readiness. Additionally, it facilitates developing and training ML models on the aforementioned data and benchmarking their performance at different altitudes, geographic locations, times, and solar activity conditions. Through this contribution, we offer the scientific community a comprehensive tool for comparing and enhancing thermospheric density models using ML techniques

Kessler : A machine learning library for spacecraft collision avoidance

As megaconstellations are launched and the space sector grows, space debris pollution is posing an increasing threat to operational spacecraft. Low Earth orbit is a junkyard of dead satellites, rocket bodies, shrapnels, and other debris that travel at very high speed in an uncontrolled manner. Collisions at orbital speeds can generate fragments and potentially trigger a cascade of more collisions endangering the whole population, a scenario known since the late 1970s as the Kessler syndrome. In this work we present Kessler: an open-source Python package for machine learning (ML) applied to collision avoidance. Kessler provides functionalities to import and export conjunction data messages (CDMs) in their standard format and predict the evolution of conjunction events based on explainable ML models. In Kessler we provide Bayesian recurrent neural networks that can be trained with existing collections of CDM data and then deployed in order to predict the contents of future CDMs in a given conjunction event, conditioned on all CDMs received up to now, with associated uncertainty estimates about all predictions. Furthermore Kessler includes a novel generative model of conjunction events and CDM sequences implemented using probabilistic programming, simulating the CDM generation process of the Combined Space Operations Center (CSpOC). The model allows Bayesian inference and also the generation of large datasets of realistic synthetic CDMs that we believe will be pivotal to enable further ML approaches given the sensitive nature and public unavailability of real CDM data

Towards automated satellite conjunction management with Bayesian deep learning

After decades of space travel, low Earth orbit is a junkyard of discarded rocket bodies, dead satellites, and millions of pieces of debris from collisions and explosions.Objects in high enough altitudes do not re-enter and burn up in the atmosphere, but stay in orbit around Earth for a long time. With a speed of 28,000 km/h, collisions in these orbits can generate fragments and potentially trigger a cascade of more collisions known as the Kessler syndrome. This could pose a planetary challenge, because the phenomenon could escalate to the point of hindering future space operations and damaging satellite infrastructure critical for space and Earth science applications. As commercial entities place mega-constellations of satellites in orbit, the burden on operators conducting collision avoidance manoeuvres will increase.For this reason, development of automated tools that predict potential collision events (conjunctions) is critical. We introduce a Bayesian deep learning approach to this problem, and develop recurrent neural network architectures (LSTMs) that work with time series of conjunction data messages (CDMs), a standard data format used by the space community. We show that our method can be used to model all CDM features simultaneously, including the time of arrival of future CDMs, providing predictions of conjunction event evolution with associated uncertainties

Calathus: A sample-return mission to Ceres

Ceres, as revealed by NASA's Dawn spacecraft, is an ancient, crater-saturated body dominated by low-albedo clays. Yet, localised sites display a bright, carbonate mineralogy that may be as young as 2 Myr. The largest of these bright regions (faculae) are found in the 92 km Occator Crater, and would have formed by the eruption of alkaline brines from a subsurface reservoir of fluids. The internal structure and surface chemistry suggest that Ceres is an extant host for a number of the known prerequisites for terrestrial biota, and as such, represents an accessible insight into a potentially habitable “ocean world”. In this paper, the case and the means for a return mission to Ceres are outlined, presenting the Calathus mission to return to Earth a sample of the Occator Crater faculae for high-precision laboratory analyses. Calathus consists of an orbiter and a lander with an ascent module: the orbiter is equipped with a high-resolution camera, a thermal imager, and a radar; the lander contains a sampling arm, a camera, and an on-board gas chromatograph mass spectrometer; and the ascent module contains vessels for four cerean samples, collectively amounting to a maximum 40 g. Upon return to Earth, the samples would be characterised via high-precision analyses to understand the salt and organic composition of the Occator faculae, and from there to assess both the habitability and the evolution of a relict ocean world from the dawn of the Solar System.The attached document is the authors’ final accepted version of the journal article provided here with a Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) Creative Commons Licence. You are advised to consult the publisher’s version if you wish to cite from it.

Optimizing a Solar Sailing Polar Mission to the Sun: Development and Application of a New Ant Colony Optimizer

In the context of metaheuristic global optimization, we present the definition and development of two new ant colony optimizers (ACO): a single-objective mixed-integer one, called ACOmi, and a multi-objective hypervolume-based one, called MHACO. In particular, after having performed a verification and validation phase over a wide set of problems (including various space missions such as Cassini, Messenger, Rosetta, and others), we focus on their application to a solar polar sailing mission to the Sun, attempting to minimize its mission cost and duration. Therefore, building on previous studies of such a mission scenario, we first constructed a model for simulating the journey of the sail from a geocentric GTO to the Sun, not only accounting for gravitational forces, but also atmospheric forces, the non-ideal solar radiation pressure force, and other environmental aspects. Then, a guidance model for the sail was set up, so that the attitude of the sail could be controlled during its journey to the Sun. This entire framework was formulated as both a single and multi-objective problem. Finally, a trade-off was performed between the newly developed ACO and other state-of-art global optimizers. For the single-objective case, these include artificial bee colony, simple genetic algorithm, self-adaptive differential evolution, particle swarm optimization, and other methods. While for the multi-objective scenario three different optimizers have been tested against the multi-objective ant colony extension: an evolutionary algorithm with decomposition, a nondominated sorting genetic algorithm and a multi-objective variant of particle swarm optimization. The found results are very promising: for the single-objective problem, the ant colony optimizer has managed to outperform all the algorithms. Whilst for the multi-objective case, the genetic algorithm seems to provide the best Pareto fronts, although the results are very competitive with those of the ACO, especially for lower function evaluations. In the end, besides providing the scientific community with new powerful global optimizers for SO and MO problems, we managed to halve the mass of the solar sail compared to previous studies, while still keeping a similar time of flight.Aerospace Engineerin

On the solution of the Fokker-Planck equation without diffusion for uncertainty propagation in orbital dynamics

This paper presents a method to transform the Fokker-Planck partial differential equation without diffusion into a set of linear ordinary differential equations. This is achieved by first representing the probability density function (pdf) through a summation of time-varying coefficients and spatial basis functions and by then employing Galerkin projection in the Fokker-Planck equation. We show that this method, compared to other numerical techniques, can bring several advantages in the field of uncertainty propagation in orbital dynamics, by not only allowing to retain the entire shape of the pdf through time but also to very rapidly compute the pdf at any time and with any initial condition, once that the spatial support is chosen and several time-independent integrals on the chosen support are computed

MHACO: A Multi-Objective Hypervolume-Based Ant Colony Optimizer for Space Trajectory Optimization

In this paper, we combine the concepts of hyper-volume, ant colony optimization and nondominated sorting to develop a novel multi-objective ant colony optimizer for global space trajectory optimization. In particular, this algorithm is first tested on three space trajectory bi-objective test problems: an Earth-Mars transfer, an Earth-Venus transfer and a bi-objective version of the Jupiter Icy Moons Explorer mission (the first large-class mission of the European Space Agency's Cosmic Vision 2015-2025 programme). Finally, the algorithm is applied to a four-objectives low-thrust problem that describes the journey of a solar sail towards a polar orbit around the Sun. The results on both the test cases and the more complex problem are reported by comparing the novel algorithm performances with those of two popular multi-objective optimizers (i.e., a nondominated sorting genetic algorithm and a multi-objective evolutionary algorithm with decomposition) in terms of hypervolume metric. The numerical results of this study show that the multi-objective hypervolume-based ant colony optimization algorithm is not only competitive with the standard multi-objective algorithms when applied to the space trajectory test cases, but it can also provide better Pareto fronts in terms of hypervolume values when applied to the complex solar sailing mission.Astrodynamics & Space Mission