Keywords: Formation Flying missions, Mission Analysis tool for Mission Control, Perturbations Analysis
Abstract: Spacecraft formation flying is an anticipated critical technology, needed to enhance astrophysical and science missions in near-Earth and interplanetary environments. Enabling a set of distributed spacecraft to cooperate, collectively fulfilling a mission objective, has proven to have several benefits over the conventional large single entity spacecraft. Mission cost and risk are reduced, while the retrieval of scientific data is significantly increased. Augmented adaptability and flexibility will play a crucial role in future space missions which require radar apertures that are excessively large and not practical to build. The key strategic goal of our work is to develop active and passive radar remote sensing applications based on distributed array architectures. Distributed formations of low-cost SmallSats, either deployable or free-flying, can deliver a comparable or greater mission capability than large mono- lithic spacecraft, but with significantly enhanced flexibility (adaptability, scalability, evolvability, and maintainability) and robustness (reliability, survivability, and fault-tolerance). The macro topic treated in this paper is the analysis of the feasibility and problems related to the operation of autonomous satellite formations serving as a Synthetic Aperture Radar (SAR) in low Earth orbit (LEO).

Keywords: Modelling and Parametrization of Relative Dynamics, Formation Flying missions, Perturbations Analysis
Abstract: The NUMES (New Mission End-to-End Simulator) is the TAS simulation framework used for the development of ad-hoc End-to-End simulators, which is used as a fundamental design analysis and verification tool, providing an high fidelity performance prediction of the overall spacecraft control system. The wide applicability of the NUMES relies both on the trajectory and dynamics simulation during the whole mission phases and on the utilization as GNC algorithm validation tool across the overall project phases (e.g. from the feasibility study to the post-flight analysis). These transversal capacities made NUMES a powerful tool for the simulation of the spacecraft control of different missions. NUMES is particularly suited to simulate complex constellation and formation flying missions such as the Laser Interferometry Space Antenna (LISA) and the Next Generation Gravity Mission (NGGM) as relying on C++ code it allows multiple instantiation of the same code reducing the code complexity, and facilitating its test and verification, when multiple SC twins in terms of SW and HW shall be simulated.

The following paper briefly describes the LISA scientific mission challenges and the TAS LISA simulator environments. Some preliminary results are shown to illustrate the NUMES features for constellation and formation flying missions.

Keywords: Innovative technologies for distributed systems, Earth-bounded Missions
Abstract: This paper covers the design of a constellation of CubeSat formation flights for Synthetic Aperture Radar surveillance of maritime traffic.

Fig. 1. Geometry of a N=3 sensors SIMO / MIMO SAR formation.

Compact SAR formations can operate either in SIMO or MIMO mode: in the first case there are N sensors of which one is active, in the second, all the N sensors are active, simultaneously receiving the scene backscatter. Both formations are getting more and more interest in literature, while some flying demonstrations are appearing since the combination of all the received signals provides a single image that at one time: - has a Signal-to-Noise-Ratio higher by a factor N (for the SIMO) and N² (for the MIMO), respect to the single sensor, - has a potential swath coverage N time wider than the single SAR, thanks to a processing that nulls the first N-1 ambiguities. Otherwise, multiple images can be generated of the same scene in slightly different times, enabling the identification and measures of moving targets (be them vehicles or sea currents), by Along-Track-Interferometric approaches. These advantages are to be considered on the top of the flexibility, robustness, and scalability common to distributed sensors formation. Both SNR gain and ambiguity suppression enables the design of a new generation of CubeSat-based SAR sensors, otherwise impossible. The all-weather-day-and-night capabilities of SAR imaging, make these formations valuable for several application in the field of hazards, emergency, and security. The system proposed here is mainly targeted for maritime traffic monitoring. A frequent revisit systema can be implemented by constellations of N-SAR formations, leveraging developments in MIMO distributed SAR systems to achieve system performance. The entails some challenge, like the precise keeping of the inter-sensor distance of the formation along and across-track, and the design of the orbits for the constellations of formations to meet the observational requirements. The design is conducted using a set performance baseline for individual satellites and a hypothetical set of requirements for minimum system performance, including an operational area of interest set as the Mediterranean Sea. T

Keywords: Innovative technologies for distributed systems, Formation Flying missions, Sensor fusion
Abstract: The CloudCT mission measures Sun light backscattered from a cloud through a sensor network of multi-spectral cameras from different perspectives. In CloudCT a formation of 10 nano-satellites in LEO will be implemented to cooperate in joint observations, based on a challenging coordination of attitude and orbit control. These data are then further processed on ground by computed tomography methods to characterize the interior of clouds, slice by slice. Essential prerequisite for this approach is the self-organizing satellite formation system. It is based on an interdisciplinary approach combining nano-satellite system engineering, tomographic imaging, and cloud modelling for improving climate predictions.

A mayor technology challenge is the coordination of the CloudCT satellite formation for appropriate data acquisition. Thus, orbit analyses in combination with precision attitude determination and control provide the basis for realizing an appropriate formation configuration in the computed tomography scenario. These self-organization properties for multi-satellite system were already objective in the formation technology demonstration mission NetSat (launched 2020), composed of 4 nano-satellites.

Progress in miniaturization technologies enables realization of necessary high accuracy attitude control as well as formation flying capabilities at nano-satellite level. Crucial for the CloudCT mission are specific miniature, low power reaction wheels, providing a 3-axis attitude control. Orbit control uses an electric propulsion system, which orients the thrust vector in combination with the attitude control system. Distributed networked control methods using inter-satellite links are the basis for self-organization of the satellites to achieve an appropriate observation geometry. Advanced in-orbit autonomy, distributed computing, as well as precision attitude and orbit determination are additional key features for realization of this formation mission.

Crucial performance parameters were tested with engineering models with two high precision turntables in hardware-in-the-loop simulations regarding inter-satellite links, networked control, relative navigation, and camera data fusion algorithms.

Keywords: Vision-based Navigation
Abstract: Angles-only navigation methods are compelling for distributed space systems (DSS) such as swarms and constellations. However, complex dependencies between state observability and system parameters present a challenging design problem. This paper proposes a unified angles-only observability analysis and design framework enabling designers of a DSS to 1) analytically determine whether its orbit state is observable, 2) numerically estimate its expected navigation performance, and 3) intelligently optimize the system to meet navigation requirements. First, a new system measurement topology representation is proposed for which analytic orbit observability can be assessed via a set of graphical conditions. Second, methods for numeric estimation of the achievable state covariance are augmented with auxiliary state variables, dynamics uncertainty, and measurement availability constraints. Third, a system cost function is developed and the topological and numeric methods are placed within a quasi-Newton optimization framework to enable automatic system design. The optimization is applied to a distributed science swarm and a space situational awareness constellation in lunar orbit. Both scenarios converge to a global cost minimum and output designs that achieve user requirements under realistic measurement conditions and constraints. Combined analytic and numeric methods therefore presents a powerful tool for design of angles-only DSS.

Keywords: Innovative solutions for Intelligent Scheduling and Operations
Abstract: This paper aims to describe Leaf Space’s approach to providing Ground Segment connectivity as an automated service, why it can be upgraded to support Multiple Spacecraft Per Aperture (MSPA), and the benefits provided by this upgrade. The inner workings of this service and the changes needed for full MSPA support will be detailed, and some previous results in the use of a more limited MSPA solution on the network will be presented. The interfaces provided by Leaf Space’s service and how a Mission control Software (MCS) can be designed to automate a satellite cluster’s operation will also be discussed.

Keywords: Constellation missions, Sensor fusion, Inertial Navigation
Abstract: The renewed interest of several space agencies towards the Moon led to an increasing number of missions planned to visit the Earth natural satellite. Indeed, being the Moon a relevant target for scientific, techno- logical and possibly commercial purposes, the next decades will experience a continuous increase of launches to send to the lunar environment different spacecraft with specific navigation and dynamics control needs. The Earth orbiting assets taught how effective is in terms of spacecraft performance to transfer complex on board functionalities on dedicated specialised infrastructures: the most evident success in that approach stays in the service offered by the Global Navigation Satellite System (GNSS) which simplifies on board components for the users preserving their state reconstruction needed level of accuracy. In planetary arenas, supposed to be largely and regularly visited in the future, such the Moon is, the deployment of a GNSS-like constellation can result in a strategic investment that may provide revenues for the service vendors and enabled performance for the future users. Exploiting a third-party navigation constellation on the Moon may be extremely beneficial for a potential orbital user which would embark a relatively reduced sensor suite consisting in a GNSS receiver coupled with an Inertial Measurement Unit (IMU) only. The paper presents a strategy to settle a lunar GNSS system well balanced with respect to cost/effectiveness, which includes simulation of the navigation capabilities needed on board the user, depending on the con- stellation adopted architecture. Attention is here focused on polar orbiters operational in Low Lunar Orbit (LLO) environment.

Keywords: Formation Flying missions, Innovative technologies for distributed systems, Ground Operations for Distributed Systems
Abstract: The “Telematics earth Observation Mission (TOM)” employs three small cooperating satellites to image from different perspectives the same surface area. Coordination of the satellites in a formation is required to enable subsequent data processing on ground in order to generate 3D images of the Earth surface by photogrammetric methods. Specific emphasis of TOM is on characterization of ash clouds from volcano eruptions. TOM will be launched into a polar low Earth orbit (LEO) and will experiment with different configurations, in order to analyze effects on image quality in camera data fusion. Nominally, the three TOM satellites form a triple pendulum formation with a baseline distance of about 100 km. The quality of final image product in simulations indicate that such a triangle formation provides favorable stability for imaging operations.

This contribution addresses technical details of the mission analyses, the self-organization of the formation by networked control approaches, the satellite hardware with emphasis on the attitude and orbit control system. Technology challenges include integration of a propulsion system for orbit control and a 3-axes attitude control system into a 3U-CubeSat of just 4 kg of mass. The attitude control system is based on redundant miniature reaction wheels and magnetorquers as actuators, while gyros, magnetometers, sun sensors provide the inputs to the control algorithms. Orbit position will be determined from GNSS receivers mounted on all side panels. Orbit control is based on a bi-propellant propulsion system, orienting the thrust vector in the appropriate direction supported by the attitude control system. The thruster performance is sufficient for formation initialization and formation maintenance. The satellites are currently in the final implementation stage for a launch in late 2022.

Keywords: Constellation missions
Abstract: This research is focused on the problem of agile attitude maneuvering, aimed at precise pointing of a satellite that forms a typical constellation in low Earth orbit. Two different operational scenarios are considered: (a) pointing toward a specific ground station, located on the Earth surface (for downlink data routing), and (b) pointing toward a companion satellite (for establishing an intersatellite connection). The two preceding operational requirements can be both formulated as attitude tracking problems. This study uses an inertia-free nonlinear attitude control algorithm based on rotation matrices and enjoying remarkable stability properties, in conjunction with a pyramidal array of single-gimbal control momentum gyroscopes. Numerical simulations demonstrate that the attitude control architecture proposed in this work is effective for the purpose of performing agile attitude maneuvering, aimed at precise pointing during downlink and intersat data routing.

Keywords: Ground Operations for Distributed Systems, Machine Learning for distributed system, Innovative technologies for distributed systems
Abstract: Space Situational Awareness (SSA) includes the capacities to acquire knowledge, collect and process data on all Resident Space Objects (RSO) orbiting a specific region, by means of different ground-based facilities and space-based sensors, and monitor Space Weather (SWE) events, in order to avoid in-orbit collisions and damages to active missions. Traditionally, this monitoring and operational activity has been accomplished in the near-Earth space regions, primarily due to the increasing number of debris caused by different phenomena such as fragmentations or in-orbit collision, non-cooperative spacecrafts, and, more recently, due to the launch of mega-constellations of small-to medium-sized satellites. However, thanks to the renewed interest in the human/robotic Moon exploration and soil resources exploitation, along with the expected and challenging objectives to establish a first and stable human outpost both on the Moon surface and lunar orbit, the SSA is rapidly evolving into a more general concept of Space Domain Awareness, which shall consider the lunar surface and cislunar regions as part of the entire scenario. The primary objective is to avoid the situation generated around the Earth in the last sixty years, in which thousands of inactive objects are threatening current active missions, but the future increase of artificial objects around the Moon is a possibility that must be taken into account in the next Lunar commercialization age. In the last period, Space Agencies are making their very best effort to support ambitious programs that require reliable and efficient navigation and communication capabilities to prepare the future Lunar Exploration and Lunar Commercialization ages. In this respect, in-orbit scientific space platforms, multi-purpose outposts such as the Lunar Gateway, lunar relays, lunar ground stations, and assets are only some of the elements that will require an adequate level of safety and security from space weather and SSA points of view. On the other hand, due to the temporary lack of artificial RSO orbiting the Moon, the Cislunar Space Domain Awareness (CSDA) should be primarily devoted to the monitoring of natural RSO, such as micro-meteorites, and asteroids in order to guaran

Keywords: Innovative solutions for Intelligent Scheduling and Operations, Constellation traffic management, Fault detection, isolation and recovery
Abstract: The amount of space debris is increasing day by day, and the number of human-launched satellites is also growing explosively. Large-scale constellation plans such as starlink and oneweb are attracting more and more attention. The growing number of space objects has posed a serious threat to the safety of important space assets including the International Space Station and the Chinese Space Station. In view of the frequent occurrence of space dangerous collision events, we hope to observe the space dangerous collision events through a small number of observation satellites to form a constellation, in order to improve the observation accuracy of key events. According to the observation data, the collision event is studied and judged, and when it is really necessary, the satellite operator is notified to take evasive actions to maintain the safety of space assets. By establishing an optical nanosatellite constellation model for observing the dangerous collision events of low-orbit space debris, we establish the evaluation criteria for the monitoring efficiency of space-based optical satellite constellations. Considering the number of observable objects, the number of arcs, the revisit period, the redundancy, the observable window and other factors, the performance parameters of the spaceborne optical telescope are designed, and the constellation configuration evaluation function is constructed. The optimal orbit parameters and constellation configuration are obtained by efficient optimization through genetic algorithm. Finally, a constellation of more than 6 optical nano-satellites is obtained, which can track and observe more than 90% of potentially dangerous collision objects in time 24 hours before the dangerous collision. Obtaining high-precision orbital data greatly reduces the false alarm rate, so that evasive actions are only taken when the space object is really in danger. It greatly reduces frequent evasion caused by false early warnings, maintains the safety of space assets, and reduces the operating costs of space assets.

Keywords: Earth-bounded Missions, Constellation missions
Abstract: In the field of Cryptography, Quantum Key Distribution (QKD) is an application of Quantum Information theory that obtained a great deal of attention in recent years. It allows to establish secret keys between two or more parties, in a much safer way than that implemented by classic cryptography (based on discrete logarithms and factorization of prime numbers). The most promising way of realizing a QKD network in the near future is in a constellation of satellites. This paper considers the problem of optimizing the orbits of the satellites in order to maximize the minimum key length shared in a network of ground stations. Different networks of stations are considered and the influence of their disposition on the design choices is highlighted, including a global constellation, a regional European constellation, and two in which there are groups of stations in two different bands of latitude. Finally, the effect of Inter-satellite links is taken into account and how, in some cases, they can improve the performances.

Keywords: Formation Flying missions, Constellation missions, Earth-bounded Missions
Abstract: A major motivation for the development of this study is the ITASAT-2 mission of the Aeronautics Institute of Technology, whose one of the main objectives is to be able to geolocate an electromagnetic emitting source on the Earth's surface. For this, the mission will have a formation flying of three CubeSats. The topology and configuration must be chosen such that the geolocation system presents the necessary precision, while the other objectives of the mission are fulfilled. Thus, this study intends to simulate various topologies by using the dynamics of orbital motion and a geolocation algorithm based on combined measurements of TDOA and FDOA. It is expected to obtain a base of results that will assist the development team of the ITASAT-2 mission and related missions in choosing the best topology and configurations for the formation flying. Therefore, this study proves to be important as it demonstrates great potential of contributions to the scientific and technical community of the aerospace area. This scenario, therefore, serves as a motivation for the development of the study presented here, which is also based on the current development of the ITASAT-2 mission, by the Technological Institute of Aeronautics (ITA) in collaboration, in terms of research, with the National Institute of Space Research (INPE) and researchers from Brazilian public universities. The ITASAT-2 mission is designed to be composed of a formation flying of three identical CubeSats 8U or even 12U. The main objectives of the mission are: to conduct scientific and technological investigations around the appearance and growth of irregularities in the plasma structure of the ionosphere; and propose a specific formation flying for the CubeSats so that they are able to locate an electromagnetic emitting source on the Earth's surface. To achieve the necessary requirements of the ITASAT-2 mission, it is necessary to evaluate the possible topologies and configurations for the formation that enable, at the same time, the study of the space climate and the geolocation process.

Keywords: Formation Flying missions
Abstract: This paper outlines the main mission aspects and functional design of ESA’s Proba-3 mission. Proba-3 will be the first attempt to achieve a closed-loop extended and tight formation flying between two spacecraft in orbit. This level of controlled formation flight allows for the in-orbit construction of ‘virtual structures’ by means of only 2 small spacecraft, but well beyond the capabilities of other larger, more complex and much more costly space missions. The current status of the mission is at phase D. Platforms are in the process of completing integration, soon to begin integrated testing. Software and GNC design are now complete and beginning a long phase of system integrated tests. Launch is foreseen in a little under 2 years’ time. SENER Aeroespacial acts as mission prime contractor, defining the overall mission and formation flight concept. Proba-3 will achieve two main goals simultaneously: technology demonstration for in-flight formation flying; and unprecedented Solar coronal scientific observations. The SC will fly in a 20h highly elliptical orbit around Earth. The apogee, where relative gravitational disturbances are weakest, is used for the tight formation control, while perigee is passed on a relative trajectory that is autonomously computed to be safe from collision.

Keywords: Low-thrust orbit acquisition, Mission Analysis tool for Mission Control, Optimal Control
Abstract: The purpose of the following paper is to structure an optimal control law that supports transfer maneuvers of LEO satellites exploiting electric propulsion while minimizing maneuver time and satisfying mission and operational constraints. Typically, this problem is mathematically formulated as an optimal control problem; however, this is limited to cases where the satellite operates in continuous dynamics. Therefore, an alternative solution is proposed that sees the combination of direct and indirect optimization methods and aims to reduce the computation time of the solution. Optimal control theory coupled with Edelbaum assumptions is exploited to provide a sub-optimal first attempt solution to direct optimization. The results presented, validated through STK, refer to the station keeping, orbit correction and collision avoidance maneuvers of M3 - Optical Micro-Satellite, an OHB-I microsatellite. It is clear from the results that the constrained optimization of the propulsive phases leads to a substantial reduction of the maneuver times of the various cases and, moreover, that the combined use of direct and indirect methods leads to significant computational savings. The analyses are not restricted to M3 alone but can be reformulated for various mission scenarios and needs, such as maintaining the relative distance between multiple satellites in a constellation or reducing the mass of propellant used in a transfer.

Keywords: Mission Analysis tool for Mission Control, Perturbations Analysis, Optimal Control
Abstract: Multiple platform missions devoted to Earth Observation, either as spacecraft constellations or formations, are often targeted to provide a combined coverage from sensors accommodated onboard different satellites. Therefore, the evaluation of the effective overlap at specific locations becomes an important ingredient of the orbital design phase. This step can be tackled starting from the coverage area offered by each satellite (a parameter also known as instantaneous access area, or IAA), and then using spherical trigonometry to obtain the Instantaneous Overlap Area (IOA). Overall, the coverage can be expressed in mathematical terms, depending on the orbital parameters of the constellation or formation. This paper presents the extension of the evaluation to the case of eccentric orbits, which is deemed of interest especially when the overlap will be targeted to specific areas, and not to be maintained all along the orbits. The solutions are provided referring to the combination of coverage granted by two or by three spacecraft, either in close proximity (indeed implemented as formations, ruled by relative dynamics) or maintained at a significant distance (therefore individually ruled by absolute dynamics, as in the case of constellations). Moreover, the paper investigates the case of non Keplerian environment by considering the perturbation due to the Earth oblateness (J2 effect), by far the more relevant one in the range of altitude of most of the case of practical interest for Earth observation. Additionally, drag can be included, mainly evaluated as a reduction on the altitude applied at each orbital period plus an additional effect considered as an uncertainty affecting the position of the spacecraft. Then, the work looks at the orbital control issues, evaluating the effort to maintain the requested coverage overlap in time. To this aim a cost function combining the thrust needed to counter-act orbital perturbations and a term representing the granted overlap is minimised. A number of examples, within a range of parameters interesting for realistic design, is presented and the trade-off between the overlap reduction in time and the control effort is discussed.

Keywords: Formation Flying missions, Constellation missions, Earth-bounded Missions
Abstract: The exploitation of natural environmental forces as an alternative means of satellite control is an enabling technology that increases the feasibility range of small satellite operations when the performance of continuous station-keeping or reconfiguration maneuvers is required. On a Low Earth Orbit, for instance, differential atmospheric drag accelerations that arise due to small differences in attitude, mass or exposed surface area between satellites in otherwise nearly identical trajectories can be used as a phasing mechanism [1] or for implementing rendezvous maneuvers in satellite formations [2]. On higher orbits, forces such as those created by solar radiation pressure can be used to generate differential accelerations between the members of a satellite formation [3]. This work aims to analyze the simultaneous use of aerodynamic forces, including both differential lift and differential drag, and solar radiation pressure as a means of satellite formation control, including full attitude dynamics and a Lyapunov-based control system for reference tracking. Historically, the idea of using differential aerodynamic forces in satellite formations can be traced back to the work of Carolina L. Leonard [4], who proposed the use of differential drag for satellite formation control, using the linearized relative motion model of the Hill-Clohessy-Wiltshire equations. In this case, the acting drag force was controlled by drag plates that could be rotated in order to adjust the magnitude of the acceleration. This idea would be further explored by various authors, such as Kumar and Ng [5], Bevilacqua and Romano [6], and Lambert et al. [7]. The use of differential lift, on the other hand, was often neglected due to the lift forces being orders of magnitude smaller than the atmospheric drag, in most circumstances. Horsley [8], however, proposed the use of lift in order to control the out-of-plane motion of each satellite, developing an algorithm for satellite rendezvous. Horsley’s algorithm would be further improved by Shao et al. [9] and Smith et al. [10], removing certain collision risks present in the original algorithm. Other studies further contemplated the simultaneous use of differential lift and drag.

Keywords: Formation Flying missions, Non-Earth Missions, Adaptive control
Abstract: Formation flying represents a promising opportunity for next space missions, due to its benefits in cost saving, redundancy and fault tolerance given by multiple small and cheap space segments exploitation, with comparable performance of a single, large monolithic spacecraft. That's even more relevant in asteroid exploration, as the harsh environment poses great risks to the probes survival. The low, irregular gravity field, the poor knowledge of shape and composition, and the possible presence of floating particles in the surroundings suggest adopting a low-risk strategy for the exploration of these bodies, delegating proximity operations to multiple nanosatellites, while keeping the main spacecraft at safe distance. As a downside, multiple cooperating spacecraft imply advanced capabilities in accurately reconstructing the relative positions and displacements and in fixing reconfiguration maneuvers. Moreover, whenever relative distance is very close, agents' guidance and control shall be autonomously computed by the spacecraft, as promptness of commands is not ensured relying on ground segment only. This is further exacerbated when dealing with the irregular gravity field of the asteroids and with multiple attractors. By leveraging the Circular Restricted Three Body Problem, this paper explores natural motion structures, which can be easily parametrised and implemented on-board to control a leader-follower formation through reference-tracking. In particular, the paper explores the effectiveness of a Model Predictive Control scheme for reconfigurations of the leader-follower relative states. Furthermore, navigation error requirements are explored and defined, to ensure the deasibility of the guidance and control scheme.

Keywords: Vision-based Navigation, Modelling and Parametrization of Relative Dynamics, Nonlinear filtering
Abstract: A fast and efficient method for initial relative orbit determination from bearing angle measurements is introduced. The range ambiguity problem for angles-only relative navigation is addressed by modeling nonlinear effects with a novel second-order mapping from relative orbit elements (ROE) to relative position coordinates. This model is used to form a system of polynomial constraint equations linking the line-of-sight measurements to the ROE. An efficient method for solving this system is developed around the insight that the ROE scale with the ratio of the inter-spacecraft separation to the orbit radius and are therefore small for most applications of interest. The method uses a truncated expansion of the quadratic formula to recursively eliminate unknowns, reduce the dimension of the system, and ultimately acquire an approximate solution. Strategies for improving robustness, efficiency, and accuracy are developed and the method is applied to general second-order systems as well as to a broad range of IROD scenarios. Modifications to the constraint equations and solution algorithm are introduced to address the challenge of bias in the bearing angle measurements.

Keywords: Formation Flying missions, Perturbations Analysis, Optimal Control
Abstract: Nowadays, satellite constellations are a crucial topic in the space field. Remote sensing missions can particularly benefit from formations of satellites bringing a distributed payload. One of the last development consists of multi-satellite passive microwave interferometric radiometry. The so-called Synthetic Aperture Radiometry allows to obtain excellent spatial resolution. This paper presents a remote sensing mission of satellites flying in formation in a geosynchronous equatorial orbit. Precise modelling of the relative motion control is developed by exploiting mean Relative Orbital Elements (ROE) as state variables. First, a new State Transition Matrix is introduced to include the effect due to the non-spherically symmetry of Earth's mass distribution up to J_{22} in an analytical model. The accounted perturbation acts on the satellites making their orbit and the formation change. On one hand, the relative position has to be kept as rigid as possible for granting the spatial resolution of the imaging system, at the same time the satellites must remain in their longitudinal slot. The system dynamics is linearized. This allows the design and verification of autonomous relative guidance and control based on Linear Quadratic Regulators. The implemented control algorithm, using continuous feedback, effectively achieves the performances required by satellite constellation maintenance. Cold gas and electric thrusters are eligible to perform the control action needed. The objective of this research is to analyse a remote sensing mission in a geostationary orbit exploiting a distributed payload. The dynamic model aims at improving the computational efficiency, thanks to the use of a state transition matrix, which includes the main perturbation effects in GEO: J_2 and J_{22}. The closed-loop control provides the accuracy of the centimetres expected for this scenario. The simulation carried out shows how optimal low-thrust control minimises the formation-keeping Delta v. Finally, the present work opens up to future studies aiming at implementing this technology on a real mission.

Keywords: Nonlinear filtering, Vision-based Navigation, Modelling and Parametrization of Relative Dynamics
Abstract: This work addresses the design of an extended Kalman filter for pose estimation to support close-range navigation with respect to a noncooperative target satellite. The filter estimates the relative pose, relative angular rate and linear velocity, inertia ratios, and pose of the target principal axes frame, where the noisy pose to a point of reference of the target is assumed to be provided by an electro-optical sensing device. The design takes into account the coupling between rotational and translational motion. To render the equations of the relative dynamics into a compact form, the pose is parametrized by a unit dual-quaternion and the formal expression of the dual relative velocity vector-quaternion is defined to comply with the relative kinematic law. Accordingly, the 6 degree-of-freedom relative equations in dual-quaternion are formally equivalent to the quaternion-based rotation-only relative dynamics. This aspect paves the way to a straightforward extension of available methods for attitude-only filtering to relative pose estimation. In this framework, the filter handles the components of the state corresponding to the relative pose and the orientation of target's principal axes in a multiplicative fashion. Provided the mathematical background and a critical comparison between the derivation of the coupled dynamic equations in classical and dual-quaternion forms, the paper describes design, implementation, and performance of the filter.

Keywords: Vision-based Navigation, Optimal Control, Artificial intelligence for autonomous guidance and control
Abstract: Cislunar space is an exciting frontier for space system development, particularly with respect to formation flying because of modular and sustainable architectures like the Lunar Gateway. This motivates the development of autonomous cislunar formation flight capabilities to alleviate logistical challenges and facilitated understanding of proximity operations in the region. Previous work on cislunar navigation has shown that relative optical measurements between two spacecraft provide full observability for inertial state of both vehicles. Still, challenges remain associated with large uncertainties and thus guidance techniques to obtain additional state information become crucial to system performance. Thus, this paper seeks to expand guidance schemes for information gathering in cislunar space given optical sensors. Three guidance policies are introduced: a heuristic, an analytic control to maximize measurement deviations, and an optimal control to minimize range uncertainty. All three policies are assessed with a covariance analysis and improve the range uncertainty by more than an order of magnitude. The effectiveness and computational complexity of the policies increase from the heuristic, to analytic, to optimal control. Finally, the analytic guidance method is executed within the loop of an Unscented Kalman Filter to simulate the full autonomous GNC system, which performs marginally better than the covariance analysis. In conclusion, this paper develops online guidance methods which improve state estimation for formation flight using optical sensors.