Space Mission Design Research Articles

Semantic-based systems engineering for digitalization of space mission design

The engineering of space systems is a collaborative, iterative process that integrates various domain-specific viewpoints to represent the final system. To ensure consistency across these viewpoints, the European Space Agency (ESA) employs Model-Based System Engineering (MBSE) and Semantic-Based System Engineering (SBSE) methodologies together to improve digital continuity and interoperability across collaborative space system developments. One significant application of semantic engineering in SE is the ESA MBSE Methodology. The ESA MBSE Methodology provides a standardized approach aligned with the European Cooperation for Space Standardization (ECSS), promotes interoperability across MBSE methodologies and tools, and overcomes integration challenges. ESA MBSE Methodology is the input for the Overall Semantic Modeling for Space System Engineering (OSMoSE) which leverages interoperability in the space community. Case studies, such as the EagleEye Earth Observation mission, demonstrate practical applications, highlighting how semantic models enhance efficiency in complex space systems. This paper discusses the importance of semantics and data management in SE and presents a practical solution derived from the ESA MBSE Methodology.

Space interferometer orbit determination with multi-GNSS

Spacecraft positioning plays a crucial role in scientific space mission design, as well as in the further scheduling of scientific observations for such a mission. We examine the application of global navigation satellite systems (GNSS) to solve the orbit determination problem in a pure space very long baseline interferometer (VLBI) project. A network of GPS, GLONASS, Galileo and BeiDou navigation satellites may be a more efficient solution to determining the position and velocity of space radio telescopes and space interferometer baselines. For such a project, it is necessary to take into account the special conditions of GNSS observations, as well as the high accuracy of determining not only position but also velocity. In this paper, we estimate visibility of navigation satellite systems for Low and Medium orbits of a pure space-VLBI system and simulate GNSS code and phase measurements. Orbit determination was performed on smoothed code measurements. Phase measurements simulated with a step of 1 s and combined in Doppler measurements yield average position and velocity errors of 1.01 m and 8.8 mm/s in Medium Earth orbit. The results showed that GNSS observations are sufficient to solve the problems of orbit determination of a space-VLBI interferometer both in Low-Earth and Medium Earth orbits.

Relative E/I vector-based optimal and suboptimal control for continuous low thrust formation reconfiguration in circular orbits

This paper addresses the fuel-optimal satellite formation reconfiguration problem with continuous low-thrust control. Based on the relative eccentricity and inclination (E/I) theory, a comprehensive approach to optimal continuous low-thrust reconfiguration in circular or near-circular orbits is proposed. By analyzing the feasible fuel cost lower bound, the reconfiguration scenarios are categorized into four types, and the corresponding optimal or suboptimal control schemes are derived. More specifically, for suboptimal continuous control schemes, the relation between user-defined variables with fuel-cost is derived, providing a clear direction for better fuel cost. Compared with previous work that gives only feasible analytical solutions or obtains optimal solutions with numerical methods, the proposed method provides an efficient approach to optimal continuous low thrust reconfiguration for feasible scenarios and adjustable sub-optimal schemes for unfeasible scenarios. The proposed framework contributes to the practical application in engineering, enabling the design and analysis of more cost-effective space missions. The analysis of fuel cost reveals that the optimal continuous low thrust reconfiguration is limited with scenarios. The overall solutions are simulated and validated in four reconfiguration scenarios.

Non-linear dynamics of a test particle near the Lagrange points L4 and L5 (Earth-Moon and Sun-Earth case)

The two-bodies problem can be fully solved, and was solved by Kepler (1609) and Newton (1687). The general three-body problem is often given as an example of a mathematical problem that ‘can’t be solved’. So, there is no general analytical solution. This problem can be significant and a special case of this problem is the Circular Restricted Three-Body Problem (CRTBP), which can be applied to the Earth-Moon system with a spacecraft, the Sun-Earth system with an asteroid, etc. In this paper, let’s focus on the motion of a test particle near the triangular Lagrange points L4 and L5 in the Earth-Moon and the Sun-Earth systems. Studying the movement of an object around these points is especially important for space mission design. To generate a trajectory around these points, the non-linear equations of motion for the circular restricted three-body problem were numerically integrated into MATLAB® 2023 software and the results are presented in the plane (x, y) and the phase plane (x, vx) and (y, vy). By numerical orbit integration, it is possible to investigate what happens when the displacement is relatively large or short from the Lagrange points. Then the small astronomical body may vibrate around these points. The results in this paper are shown in the rotating and inertia axes. Various initial positions near the Lagrange points and velocities are used to produce various paths the test particle can take. The same examples of numerical studies of trajectories associated with Lagrange points are shown in the inertial and the rotating coordinates system and are discussed. From the results of the numerical tests performed in MATLAB® 2023, it is possible to saw that there are different types of periodic, quasi-periodic, and chaotic orbits

CORTO: The Celestial Object Rendering TOol at DART Lab

The Celestial Object Rendering TOol (CORTO) offers a powerful solution for generating synthetic images of celestial bodies, catering to the needs of space mission design, algorithm development, and validation. Through rendering, noise modeling, hardware-in-the-loop testing, and post-processing functionalities, CORTO creates realistic scenarios. It offers a versatile and comprehensive solution for generating synthetic images of celestial bodies, aiding the development and validation of image processing and navigation algorithms for space missions. This work illustrates its functionalities in detail for the first time. The importance of a robust validation pipeline to test the tool’s accuracy against real mission images using metrics like normalized cross-correlation and structural similarity is also illustrated. CORTO is a valuable asset for advancing space exploration and navigation algorithm development and has already proven effective in various projects, including CubeSat design, lunar missions, and deep learning applications. While the tool currently covers a range of celestial body simulations, mainly focused on minor bodies and the Moon, future enhancements could broaden its capabilities to encompass additional planetary phenomena and environments.

NanoSMAD – A First Order System Configuration Design Tool for Nano and Micro Satellites

The emergence of nano and micro satellites, which weigh less than 100 kg, is causing a significant transformation in the space industry. The existing Space Mission Analysis and Design (SMAD) tools, which are primarily designed for larger satellites, often become irrelevant for these smaller satellites in terms of spacecraft mass, power, pointing requirement, total mission duration, fault tolerance, and design cost. To address this, we have developed a web based nanoSMAD tool specifically for designers of nano and micro satellites. This tool utilizes a comprehensive database of approximately 140 nano and micro satellites along with their internal subsystem specifications. By using the nanoSMAD tool, designers can efficiently develop nano and micro satellite systems by entering their requirements, which then generates high-level system design and requirement specifications. This process enables the tool to provide a basic satellite configuration design and generates a Master Equipment List (MEL) of subsystems. To further customize the design, users can provide more specific parameter inputs or select components from a drop-down menu, resulting in an iterative custom design approach. The satellite database used by the nanoSMAD tool is regularly updated through online surveys, including web scraping, to gather information on the latest non-space-grade off-the-shelf nano and micro satellite subsystems. This ensures that the tool stays up-to-date with the newest advancements in the field. Additionally, the nanoSMAD tool offers a unique feature of verifying the electrical interface compatibility of subsystems, which is an innovative aspect of the tool. Novice small satellite communities will greatly benefit from the nanoSMAD tool as it seamlessly generates an initial nano and micro satellite system design, providing a first-order understanding of the satellite’s configuration and requirements.

Duty-cycle-aware low-thrust trajectory optimization using embedded homotopy

In space mission design, an important operational constraint is planned periodic coast arcs during which various mission-critical tasks such as navigation or ground communications are performed. These constraints, typically implemented as thruster duty cycles, can be characterized as discrete coast arcs enforced periodically during intervals of deterministic thrusting. A typical approach to incorporate duty cycles is by enforcing maximum thrust levels that are less than a nominal value. This work presents an embedded homotopy indirect optimization method for a smooth enforcement of discrete duty-cycle constraints for low-thrust trajectory optimization. The complexity of enforcing such discrete constraints is two-fold: (1) a precise event-detection strategy is needed to determine the beginning of deterministic thrust arcs, which must be successively updated along the trajectory and (2) a smooth modeling of the discrete coast events occurring on the order of 10s or even 100s depending on the duration of deterministic thrust arcs. Duty cycle constraints are enforced at the level of the Hamiltonian using a Composite Smooth Control (CSC) method, producing high-resolution optimal control solutions conscious of planned duty cycle coast arcs. Numerical solutions are presented for the heliocentric transfer phases of three space missions. The results are then validated against the Evolutionary Mission Trajectory Generator (EMTG), one of NASA’s global trajectory optimization tools used for interplanetary mission design and capable of the explicit enforcement of periodic duty cycle coasting. The proposed indirect method is suitable for obtaining high-resolution trajectory solutions with realistically enforced thruster duty cycle, which could then be used as high-quality initial guesses in flight-fidelity mission planning tools. The proposed smooth modeling of discrete coast arcs can also be customized to enforce periodic and non-periodic thrust shutdown constraints.

Thermal surrogate model for spacecraft systems using physics-informed machine learning with POD data reduction

Thermal analysis of spacecraft systems is one of the most critical processes in the design and operation of space missions. However, it is computationally costly to predict the temperature under all conditions including attitude, orbit, or all combinations of equipment use cases. This study proposes a novel surrogate model for full-scale thermal models using data reduction via proper orthogonal decomposition and physicsinformed machine learning. The prediction accuracy of the proposed method is evaluated using two types of thermal mathematical models to investigate the dependency of the training dataset and the size of the models. In addition, the prediction accuracy and training cost were compared between data-driven machine learning and physics-informed machine learning. As a result, the proposed method successfully predicted the full model temperature for both models under various heat input conditions. Moreover, the proposed method decreased the total training cost by 26% to 81% compared to data-driven machine learning.

Proton radiation hardness of GaInAsP alloys for space solar cell applications

AbstractRecent technology development in space mission design has raised a demand for space solar cells with a higher level of radiation tolerance as compared with state‐of‐the‐art, commercially available products. Therefore, new material systems are being investigated. Recently, we highlighted the superior radiation tolerance of GaInAsP solar cells to 1 MeV electron irradiation as compared with standard GaAs solar cells. A high InP fraction within this semiconductor compound was found to foster the regeneration rate of electron‐induced defects when the solar cells were annealed at 60°C under AM0 illumination, which are typical space‐operating conditions. In light of considering this material system in future radiation‐hard designs, the degradation of GaInAsP solar cells subjected to proton irradiation also needs to be investigated. Here, we report on the degradation and regeneration of GaInAsP solar cells lattice‐matched to InP substrates after 1 MeV proton irradiation. A detailed description of the radiation damage is achieved by solar cell numerical modeling combined with deep‐level transient spectroscopy analysis. The irradiation‐induced defects are quantified, and their evolution during annealing is monitored. The results are compared with the degradation data of similar solar cells obtained after 1 MeV electron irradiation. A slower regeneration rate of the proton‐induced defects is found in comparison with the electron‐induced defects. This difference is ultimately attributed to a different topology of the radiation damage caused by proton irradiation.

The Conley–Zehnder indices of the spatial Hill three-body problem

We explore the interaction between the Conley–Zehnder index and bifurcation points of symmetric planar as well as spatial periodic orbits in the spatial Hill three-body problem. We start with the fundamental families of planar periodic orbits which are those of direct (family g) and retrograde periodic orbits (family f). Since the spatial system is invariant under a symplectic involution, whose fixed point set corresponds to the planar problem, planar orbits have planar and spatial Floquet multipliers, and planar and spatial Conley–Zehnder indices. When the Floquet multipliers move through a root of unity, new families of periodic orbits bifurcate and the index jumps. For very low energies, the families g and f arise dynamically from the rotating Kepler problem, and in a recent work (Aydin From Babylonian lunar observations to Floquet multipliers and Conley-Zehnder Indices) we determined analytically their indices. By their numerical continuations for higher energies, we determine the index of various families of planar and spatial periodic orbits bifurcating from g and f. Since these families can bifurcate again and meet each other, this procedure can get complicated. This index leads to a grading on local Floer homology. Since the local Floer homology and its Euler characteristic stay invariant under bifurcation, the index provides important information about the interconnectedness of such families, which we illustrate in form of bifurcation graphs. Since the solutions of Hill’s system may serve as orbits for space mission design or astronomical observations, our results promote the interaction between Symplectic Geometry and practical problems.

Framework Development for Efficient Mission-Oriented Satellite System-Level Design

The space mission analysis and design process defines a space system at the system level to accomplish space mission objectives. Although the traditional process is well established and comprehensive through several years of experience, we propose a novel design process framework in this paper to aid the traditional process focusing on the following areas of improvement: (1) clarification of the direct connection between mission objectives and final system-level baseline design and requirements, (2) development of a comprehensive quantitative judgment criterion to evaluate various design alternatives, (3) derivation of system drivers and critical requirements after obtaining sufficient design knowledge based on the analysis of big data obtained from exploration of entire design space using an integrated design environment, and (4) system optimization even at the system level with a holistic perspective to guarantee that the baseline design meets the mission objectives. Examples of design steps in the proposed framework are characterizing stakeholder needs and engineering characteristics, building an integrated design environment, exploring and analyzing design space, optimizing system-level design, and elaborating mission utility to ensure an efficient mission-oriented design approach. The proposed framework is implemented in an example space mission involving quantum cryptographic communication. Accordingly, we demonstrate that the proposed framework provides an efficient mission-oriented satellite system-level baseline design.

Current Status of the HERD Space Mission Design

HERD (High Energy Radiation Detector) is a future experiment for space-based detection of cosmic rays and gamma ray astronomy onboard the Chinese Space Station. Its most innovative feature will be the event collection from 5 sides, and with its large size it will result in a one-order-of-magnitude jump in acceptance with respect to current largest calorimetric experiments. This will make possible to investigate cosmic ray spectra for each species up to the so-called knee region at PeV energies. The all-electron spectrum will be also measured up to about 10 TeV (depending on the actual flux) and the gamma sky will be studied with a large effective area from a few hundreds MeV up to few TeV, also allowing for the search for possible signatures from dark matter particles in our galaxy.

Towards a pattern language for complex-mode mission concept generation

New space mission profiles arise from the convergence of reduced launch prices, miniaturization of electronics and the maturation of on-orbit servicing technologies. Additionally, a shift towards challenging Lunar objectives pushes for interconnected and complex-mode missions, and trends towards low-cost, sustainability and autonomy also encourage complex modes. The field of space logistics aims to develop conceptual and computational tools to optimize multi-node material-flow networks. However, existing tools insufficiently address the challenge of generating and comparing mission concepts methodically. Through a comprehensive literature review and a case study, we: (1) establish a need for a design support tool for early-phase complex space mission concept generation; (2) establish the potential of a novel approach using pattern languages; (3) propose and describe a concept for an innovative interdisciplinary tool using the identified methods; (4) verify the proposed support tool concept by replicating the Apollo study results as a proof of concept. We created a pattern language in which words are mission concept of operations elements, the grammar is an assembly algorithm allowing to generate options automatically, and the writing system is intuitively readable diagrams illustrating candidate mission modes. Key figures of merit are also automatically compiled. Among the concepts we generated for the Apollo proof of concept study, the four principal candidates considered in 1962 were captured and ranked in the same order as historically and in recent literature. Findings are consistent with Apollo’s choice of designing two modules to be separated in Lunar orbit, thus confirming the proposed tool’s potential. Decision-makers could be supported in the early stages of the mission design process, where most of the value is locked in, by complementing existing methods such as concurrent engineering. Efficiently designing complex-mode missions is key to enabling cost-effective and highly ambitious missions, therefore supporting cislunar economy development. • Gap for a design support tool for early-phase complex space mission design. • Potential of a novel approach using pattern languages and matheuristics. • Proposition and description of a concept for an innovative interdisciplinary tool using pattern languages and matheuristics. • Verification of the proposed support tool concept by recreating the Apollo study results as a proof-of-concept.

Life cycle engineering of space systems: Preliminary findings

The application of Life Cycle Engineering (LCE) within the concurrent engineering process presents a viable method for assessing environmental, social and economic impacts of space missions. Despite this, the novelty of the concept within space mission design has meant that the approach has not yet been widely implemented. This paper successfully demonstrates this technique for the first time and presents LCE results of three SmallSat missions designed at the University of Strathclyde using the concurrent engineering approach. The Strathclyde Space Systems Database (SSSD) was deployed to calculate the total life cycle impacts of each mission, including the identification of common design hotspots. A novel technique called Multi-Criteria Decision Analysis (MCDA) was also trialled, whereby several impact categories were converted into single scores as a test case to reduce the learning curve for engineers. Overall, the LCE results indicate that the manufacturing & production of the launcher dominate the majority of impact categories. Other common hotspots were found to relate to the use of germanium as a substrate as well as the launch event. As an additional observation, in terms of the behavioural aspects, it was clear that study participants were more open to the concept of LCE with each new concurrent engineering session, evidenced by increasing levels of interaction amongst study participants. These findings are intended to provide industrial stakeholders with a preliminary benchmark relating to the general sustainability footprint of SmallSats, whilst demonstrating the viability of integrating LCE within the concurrent engineering process of space missions.

Saddle transport and chaos in the double pendulum

Pendulums are simple mechanical systems that have been studied for centuries and exhibit many aspects of modern dynamical systems theory. In particular, the double pendulum is a prototypical chaotic system that is frequently used to illustrate a variety of phenomena in nonlinear dynamics. In this work, we explore the existence and implications of codimension-1 invariant manifolds in the double pendulum, which originate from unstable periodic orbits around saddle equilibria and act as separatrices that mediate the global phase space transport. Motivated in part by similar studies on the three-body problem, we are able to draw a direct comparison between the dynamics of the double pendulum and transport in the solar system, which exist on vastly different scales. Thus, the double pendulum may be viewed as a table-top benchmark for chaotic, saddle-mediated transport, with direct relevance to energy-efficient space mission design. The analytical results of this work provide an existence result, concerning arbitrarily long itineraries in phase space, that is applicable to a wide class of two degree of freedom Hamiltonian systems, including the three-body problem and the double pendulum. This manuscript details a variety of periodic orbits corresponding to acrobatic motions of the double pendulum that can be identified and controlled in a laboratory setting.

A Tutorial on the Tracking, Telemetry, and Command (TT&C) for Space Missions

This paper presents a tutorial on the Tracking, Telemetry, and Command (TT&C) for spacecraft and satellite missions. In particular, it provides a thorough summary of the design of the TT&C, starting from elementary system aspects and going down to the details of the on-board TT&C subsystem design, its units, and the physical layer. The paper is then complemented with a description of emerging TT&C techniques and technologies, the standardization framework, and practical examples of actual spacecraft design of European space missions. The here-presented tutorial is thought for professionals (also in other telecommunication engineering fields) willing to face the challenges and state-of-the-art of the TT&C, and know more about this fundamental function that allows us to control and monitor our spacecraft on a daily basis.

On the scientific impact of the uncertainties in the Athena mirror effective area

The design of space missions faces resource limitations that may severely restrict the extent of ground-based calibration programs. Ensuring that the knowledge requirements on key scientific performance are commensurate to the scientific goals of a mission is therefore crucial. In this paper, we describe a method to verify the adequacy of the X-ray effective area calibration requirements and apply it to the mirrors of Athena, the next large-class X-ray observatory of the European Space Agency. It is based on a Monte Carlo algorithm producing a set of energy-dependent mirror effective areas, which describe the limitations in our knowledge of the true performance as embedded in the calibration requirements. Applying this method to a number of simplified astrophysical scenarios related to the “hot and energetic” science themes of Athena, we conclude that the current calibration requirements of the mirror effective area are commensurate to the driving scientific requirements. Our results also stress the need to fulfill, or possibly to exceed the calibration requirements on the relative effective area to ensure fidelity in the reconstruction of X-ray, broad-band spectral features, e.g., those expected from the reflection by relativistic accretion disks around accreting black holes.

Event-based safety and reliability analysis integration in model-based space mission design

Model-based safety and reliability (S&R) analysis, which improves analysis accuracy and reduces cost and development time is applied in various industries. With the developments in model-based systems engineering (MBSE) and the use of systems modelling language (SysML), S&R analysis based on SysML models is gaining more attention. However, the emerging methods are inadequate for complex space missions. Thus, the main objective of this study involves integrating S&R analysis in SysML-based space mission design. First, a framework for integrating S&R analysis in model-based space mission design is presented. Based on the characteristics of the development of complex space missions and the MBSE process, a multisystem collaborative failure analysis method is proposed to comprehensively identify the failure modes (FMs) of the entire system. Subsequently, an event-based analysis method integrating the process of functional architecture definition is proposed, which fills the identified gaps in model-based S&R analysis for mission-level systems. Based on the identified FMs and proposed criterion, the event tree can be mapped from the SysML activity diagram. Finally, the proposed methodology is applied to a case study of a complex space mission in the near future: the manned mission to the Moon.

Design of impulsive asteroid flybys and scheduling of time-minimal optimal control arcs for the construction of a Dyson ring (GTOC 11)

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.

Space Life Cycle Assessment: A Risk or Opportunity for the USA?

Life Cycle Assessment (LCA) is a standardized method of analysis which is used to scientifically quantify environmental impacts associated with products, processes, or services over their entire lifetime. Within the European space sector, the application and perceived importance of LCA has exponentially increased in recent years to the point that it is beginning to become entwined with the procurement process. As such, it is highly probable the technique will become a common element of space mission design within Europe before the end of the decade. In comparison, very little work on space LCA has been conducted within the United States of America (USA), meaning the country is beginning to lag behind others in its ability to account for the life cycle environmental impacts of its space operations. This could become a serious problem for United States (U.S.) original equipment manufacturers (OEMs) and suppliers in the near-term future due to misalignment or non-compliance with European procurement policies, with the potential to cause widespread supply chain disruption. Therefore, this work examines the extent to which the USA has fallen behind Europe on LCA of space assets and the risk this poses. However, the identified benefits of space LCA highlight the method could also act as an indispensable mechanism to further business success within the U.S. space sector beyond solely policy compliance. As such, a set of recommendations are outlined to encourage an intensification of research and development (R&D) on the concept within the U.S. space sector as a foundational principle to a sustainable global space economy.