Satellite Formation Flight Research Articles

Numerical Simulation of Ionic Electrospray Contamination for Small Satellite Formation Flight

Numerical Simulation of Ionic Electrospray Contamination for Small Satellite Formation Flight

Target Detection for Synthetic Aperture Radiometer Based on Satellite Formation Flight.

Synthetic aperture interferometers formed by satellite formations have been adopted to improve spatial resolution. Due to the limited number of satellites and limited integrated time, the use of sparse baselines can result in distorted reconstructed images, which will generate false targets or miss true targets. When detecting a target on the Earth from a geostationary orbit, the target usually occupies only one pixel, and it is almost submerged by noise. Considering the slow-varying characteristics of the observation area, combined with historical observation data and the motion characteristics of the target itself, a target detection method based on multi-frame snapshot images is proposed. Firstly, the observation background is estimated using multi-frame historical data, and background elimination is used to suppress the background noise. Then, potential targets are selected using the local brightness temperature characteristics of the targets. Lastly, the target motion tracks are applied to erase false targets and correct the positions of missed targets. Simulation experiments have been conducted, and the false alarm rate and the missing alarm rate are counted for randomly distributed targets.

Multiple Global Navigation Satellite Systems Doppler Positioning for Low-Earth-Orbit Satellites

Multiple global navigation satellite systems (multi-GNSS) Doppler solutions are analyzed for low-Earth-orbit (LEO) satellites. Precise satellite displacement and change-in-clock offset can be calculated using four satellites if an approximate position solution is available. The position can be calculated using seven or more satellites if time is provided. The precise displacement or average velocity at the millimeter-per-second level is based on accumulated carrier-phase measurements. A novel linearized Doppler position and velocity solution smoothed at the millimeter level is presented. The Doppler position solution is combined with a high-accuracy displacement solution in a complementary filter that provides two new benefits: after initialization with a full seven-satellite position solution, the complementary filter can continue with only four satellites; and the short (1 to 5 s) Doppler tracks can be checked for faults before the complementary filter, using displacement techniques requiring five satellites versus the usual eight. The Doppler solutions are evaluated using data from a LEO satellite and contrasted against a multi-GNSS pseudorange solution. Applications of the Doppler solution include satellite maneuver control, formation flight, thruster monitoring, docking, and scientific applications that require satellite motion compensation, such as synthetic aperture radar.

Controllability Analysis of Propellant-Free Satellite Formation Flight

This paper presents a comprehensive analysis of the controllability for the relative dynamics of satellites using space environment forces. First, the constraints of the space environment forces are illustrated for circular orbits, and the integration of space environment forces for achieving full controllability is considered. Two approaches are used to estimate the controllability of various configurations of space environment forces. The first approach relies on controllability theory for linear continuous and discrete systems, including a derivation of a new linear formulation for solar radiation pressure with lower constraints. The second approach exploits extensive numerical simulations for controllability analyses of nonlinear dynamics models. The linear quadratic regulator is designed for different dynamics models of the space environment forces and implemented numerically for nonlinear dynamics using an anti-windup scheme with bounded control inputs. The numerical simulations demonstrate that the Lorentz forces and the differential atmospheric drag are more effective control forces in the low Earth orbits than the solar radiation pressure.

On Autonomous Reconfiguration of SAR Satellite Formation Flight With Continuous Control

Satellites clusters for Earth observation purposes entail precise orbit monitoring and control to satisfy application needs efficiently. Fast technological progress in GNSS receivers, intersatellite communications/vision links, and propulsion technologies have inspired and fostered autonomous orbit determination and control techniques, allowing more efficient ground segment operations. Moreover, new distributed satellite missions have been enabled by autonomous formation flying, with unprecedented Earth observation potential. These missions may adopt varying observational modes associated with different relative orbital configurations and also transit among these modes as required by mission control. In this article, we consider a hypothetic distributed synthetic aperture radar (SAR) mission with a main SAR illuminator, as CONAE's SAOCOM 1 satellites, and one or more companions able to adopt different bistatic SAR geometries, enabling interferometry, tomography, or specular acquisition. To approach this problem, we formulate a basic task for any actively controlled companion satellite (deputy satellite) consisting of following a reference maneuver relative to the chief satellite orbit. This task is performed by means of a feedback control law based on newly introduced relative orbital elements (ROEs) and suitable to continuous actuators (e.g., electric propulsion) with bounded thrust. As a main result, we prove the asymptotic stability of the maneuver orbit tracking task for low Earth, nonequatorial, and near-circular chief orbits. This required a reformulation of the relative orbit tracking problem and the associated ROEs. A control allocation along the orbit is also proposed to reduce the propellant consumption and the transient time between SAR modes. The theoretical results are validated with simulated controlled transitions between different acquisition modes.

Enhanced algorithms to ensure the success of rendezvous maneuvers using aerodynamic forces

A common practice in the field of differential lift and drag controlled satellite formation flight is to analytically design maneuver trajectories using linearized relative motion models and the constant density assumption. However, the state-of-the-art algorithms inevitably fail if the initial condition of the final control phase exceeds an orbit and spacecraft-dependent range, the so-called feasibility range. This article presents enhanced maneuver algorithms for the third (and final) control phase which ensure the overall maneuver success independent of the initial conditions. Thereby, all maneuvers which have previously been categorized as infeasible due to algorithm limitations are rendered feasible. An individual algorithm is presented for both possible control options of the final phase, namely differential lift or drag. In addition, a methodology to precisely determine the feasibility range without the need of computational expensive Monte Carlo simulations is presented. This allows fast and precise assessments of possible influences of boundary conditions, such as the orbital inclination or the maneuver altitude, on the feasibility range.

Navigator Notes

Navigator Notes

Vibration suppression and attitude control for the formation flight of flexible satellites by optimally tuned on-off state-dependent Riccati equation approach

In this paper, vibration suppression and attitude control for the formation flight of flexible satellites using optimally tuned on-off SDRE (state-dependent Riccati equation) approach is discussed. A formation consisting of flexible satellites has highly nonlinear dynamics and the corresponding satellites are subject to vibrations as well as uncertainties due to the practical conditions. Vibrations that are mainly caused by flexible modes of the satellites disorganize the coordination and hinder the formation stability as well as decreasing its performance and lifetime. Hence, flexibility should be considered in formation model and the coordination control needs to address such challenges. Owing to capabilities of SDRE approach for nonlinear systems, it is used as the coordination control. Satellites are assumed to be equipped with thrusters as their actuators which requires the control to be applied as on-off pulses. To this end, an algorithm is suggested to efficiently convert SDRE control into on-off pulses. For optimal tuning of the controller, the particle swarm optimization (PSO) algorithm is employed. Stability of the system has also been analyzed via a Lyapunov-based approach utilizing the region of attraction concept. The proposed on-off SDRE approach has shown to effectively suppress the vibrations in the presence of uncertainties leading to the accurate coordination of the whole formation while consuming less energy. Simulation results show the capability, efficiency, robustness and stability of the suggested approach.

Autonomous Precision Control of Satellite Formation Flight under Unknown Time-Varying Model and Environmental Uncertainties

This paper presents a new methodology for autonomous precision control of satellite formations in the presence of uncertainties and external disturbances. The methodology is developed in two steps. First, using a nominal system model that provides the best assessment of real-life uncertainties, a nonlinear controller that satisfies the formation configuration requirements is developed without making any linearizations/approximations. This closed-form control strategy is inspired by results from analytical dynamics and uses the fundamental equation of constrained motion. In the second step, an adaptive continuous robust controller is developed to compensate for model uncertainties and field disturbances to which the satellite formation may be subjected. This controller is based on a generalization of the concept of sliding mode control, and produces no chattering. The control gain is automatically updated in real time and the norm of the trajectory error is guaranteed to lie within user-provided desired bounds without a priori knowledge of the uncertainty/disturbance bounds. Since the control force is explicitly obtained, the approach is not computationally intensive, thereby making the approach ideal for on-orbit autonomous real-time satellite formation control. Numerical simulations demonstrate the effectiveness of the proposed control methodology, in which a desired formation configuration is required to be precisely and autonomously maintained despite large initial trajectory errors in the presence of uncertain satellite mass and environmental disturbances.

GPS‐based satellite formation flight simulation and applications to ionospheric remote sensing

The Virginia Tech Formation Flying Testbed (VTFFTB), a GNSS-based hardware-in-the-loop (HIL) simulation testbed for spacecraft formation flight, is developed and applied to ionospheric remote sensing. The current VTFFTB consists of GNSS RF hardware signal simulators, multi-constellation multifrequency GNSS receivers, a navigation and control system, an STK visualization system, and an ionospheric remote sensing system. GPS signals are emulated using GNSS simulator scenarios that include ionospheric phenomena. A formation of two spacecraft (“chief” and “deputy”) is considered. GNSS receiver data are used to produce space-based Total Electron Content (TEC) and scintillation measurements. A reference low Earth orbit (LEO) scenario is benchmarked with past simulation results to validate functionality. A LEO formation flying mission is designed to probe two Equatorial Spread F (ESF) scenarios with plasma bubbles. The results investigate the structure of ionospheric irregularities and demonstrate that the GPS-based satellite formation is able to measure vertical electron density by differencing 1D GPS vertical TEC.

The methods of relative navigation of satellites formation flight

The methods of relative navigation of satellites formation flight

The methods of relative navigation of satellites formation flight

This paper is devoted that relative navigation of satellites which fly within a formation. The concept and the methods of swarm satellites technology and architecture are explained. The difference between the constellation and the formation architecture of satellites are focused. Analyses of relative motion between satellites are simulated by mathematical model which used Hill-Clohessy-Wiltshire (HCW) equations and Keplerian orbital equations. The results of the analysis show that all axes shift by formation. The control algorithms requirements of follower satellite are decided according to the drift of the all axes. Extended Kalman filters are used for optimisation, estimation and control stability of nonlinear orbital relative motion of satellites. At last, comparison of relative navigation models are focused.

Satellite Formation Flight Simulation Using Multi-Constellation GNSS and Applications to Ionospheric Remote Sensing

The Virginia Tech Formation Flying Testbed (VTFFTB) is a global navigation satellite system (GNSS)-based hardware-in-the-loop (HIL) simulation testbed for spacecraft formation flying with ionospheric remote sensing applications. Past applications considered only the Global Positioning System (GPS) constellation. The rapid GNSS modernization offers more signals from other constellations, including the growing European system—Galileo. This study presents an upgrade of VTFFTB with the incorporation of Galileo and the associated enhanced capabilities. By simulating an ionospheric plasma bubble scenario with a pair of LEO satellites flying in formation, the GPS-based simulations are compared to multi-constellation GNSS simulations including the Galileo constellation. A comparison between multi-constellation (GPS and Galileo) and single-constellation (GPS) shows the absolute mean and standard deviation of vertical electron density measurement errors for a specific Equatorial Spread F (ESF) scenario are decreased by 32.83% and 46.12% with the additional Galileo constellation using the 13 July 2018 almanac. Another comparison based on a simulation using the 8 March 2019 almanac shows the mean and standard deviation of vertical electron density measurement errors were decreased further to 43.34% and 49.92% by combining both GPS and Galileo data. A sensitivity study shows that the Galileo electron density measurements are correlated with the vertical separation of the formation configuration. Lower C/N 0 level increases the measurement errors and scattering level of vertical electron density retrieval. Relative state estimation errors are decreased, as well by utilizing GPS L1 plus Galileo E1 carrier phase instead of GPS L1 only. Overall, superior performance on both remote sensing and relative navigation applications is observed by adding Galileo to the VTFFTB.

A nonlinear observer-based approach to fault detection, isolation and estimation for satellite formation flight application

In this paper, the problem of fault diagnosis for a satellite formation flight is considered. A scheme is investigated for fault detection, isolation, and estimation of a class of nonlinear systems. In this scheme, we consider the model uncertainty, input and environmental disturbances. For fault detection, a nonlinear observer is designed to minimize the uncertainty within ℋ∞ framework. The Linear Matrix Inequality (LMI) formulation is used to obtain the observer gain matrices. In the next step, a bank of nonlinear robust unknown input observers is designed to isolate the faulty actuator. Fault isolation is achieved based on the generalized observer strategy. The proposed observer can simultaneously estimate faults and states; it can also decouple the unknown input disturbances and attenuate the effect of model uncertainty and external disturbances. In order to fulfill these goals, a Lipschitz formulation and Linear Parameter Varying (LPV) method are used in all of the proposed observers, which lead to less conservative LMI condition. Then, the mentioned approach is applied to fault diagnosis of a formation of satellites. Moreover, a distributed fault detection, isolation, and estimation scheme based on above observers is proposed. In this scheme, each satellite not only can diagnose its own faults but also it is able to diagnose its neighbors faults.

Influence of energy accommodation on a robust spacecraft rendezvous maneuver using differential aerodynamic forces

Differential aerodynamic forces are a promising propellant-less option to control satellite formation flight. To this day, satellite lift is the most frequently neglected and, as a consequence, the methodology of differential lift only poorly studied. This is because the adsorption of atomic oxygen on the satellite’s surfaces in Very Low Earth Orbit induces diffuse reflection and high levels of energy accommodation, both of which results in the low lift coefficients experienced in-orbit so far. Analysis has shown that surface materials which promote specular or quasi-specular reflections are able to strongly increase the magnitude of the available differential lift forces. An influence of advanced surface materials on respective maneuver sequences, however, has not yet been analyzed at all. In addition, the robustness of the differential lift-based controller proposed up to now is questionable and not able to cope with the occurring uncertainties and dynamic variations. This paper aims to address these two research gaps. To do so, a robust control approach based on Lyapunov principles developed by Perez and Bevilacqua for the differential drag-based control of the in-plane relative motion is used in a subsequent second control phase to control the out-of-plane relative motion via differential lift. In a successive second step, the influence of different levels of energy accommodation on the full rendezvous maneuver sequence is analyzed. The results show that even a modest reduction in energy accommodation strongly reduces the maneuver times as well as the resulting orbital decay. In all analyzed cases, the proposed control approach led to a successful rendezvous.

On the exploitation of differential aerodynamic lift and drag as a means to control satellite formation flight

For a satellite formation to maintain its intended design despite present perturbations (formation keeping), to change the formation design (reconfiguration) or to perform a rendezvous maneuver, control forces need to be generated. To do so, chemical and/or electric thrusters are currently the methods of choice. However, their utilization has detrimental effects on small satellites’ limited mass, volume and power budgets. Since the mid-80s, the potential of using differential drag as a means of propellant-less source of control for satellite formation flight is actively researched. This method consists of varying the aerodynamic drag experienced by different spacecraft, thus generating differential accelerations between them. Its main disadvantage, that its controllability is mainly limited to the in-plain relative motion, can be overcome using differential lift as a means to control the out-of-plane motion. Due to its promising benefits, a variety of studies from researchers around the world have enhanced the state-of-the-art over the past decades which results in a multitude of available literature. In this paper, an extensive literature review of the efforts which led to the current state-of-the-art of different lift and drag-based satellite formation control is presented. Based on the insights gained during the review process, key knowledge gaps that need to be addressed in the field of differential lift to enhance the current state-of-the-art are revealed and discussed. In closer detail, the interdependence between the feasibility domain/the maneuver time and increased differential lift forces achieved using advanced satellite surface materials promoting quasi-specular or specular reflection, as currently being developed in the course of the DISCOVERER project, is discussed.

Cooperative State and Fault Estimation of Formation Flight of Satellites in Deep Space Subject to Unreliable Information

Abstract In this paper, a novel distributed cooperative estimation framework for a formation flight of satellites is proposed. This framework is developed based on the notion of sub-observers. Within a group of sub-observers each one is estimating certain states that are conditioned on a given input, output, and state information. In order to guarantee the ultimate boundedness of the estimation errors, a sub-observer dependency (SOD) digraph is introduced that is assumed to be acyclic. The overall estimation process is modeled by a weighted sub-observer dependency estimation (WSODE) digraph. By selecting an optimal path in the WSODE digraph, a high-level supervisor can then select and configure a set of sub-observers to successfully estimate all the system states. In presence of unreliable information due to large disturbances, noise, and actuator faults certain sub-observers may become invalid. In this case, the supervisor reconfigures the set of sub-observers by selecting a new path in the WSODE digraph such that the impacts of these uncertainties are managed and confined to only the local estimates of states and faults. This will consequently prevent the propagation of uncertainties to the entire estimation process and the performance degradations to the entire formation flight of satellites. Simulations are conducted for a five satellite formation flight system in deep space and the comparative results with a centralized Kalman filter (CKF) technique are shown to confirm the validity and advantages of our developed analytical work.

A Novel Interferometric Microwave Radiometer Concept Using Satellite Formation Flight for Geostationary Atmospheric Sounding

For most Earth observation applications, passive microwave radiometry from the geostationary orbit requires prohibitively large apertures for conventional single-satellite platforms. This paper proposes a novel interferometric technique capable of synthesizing these apertures using satellite formation flight. The significance of such concept is in its capacity to synthesize microwave apertures of conceptually unconstrained size in space for the first time. The technique is implemented in two formation flight configurations: a formation of a single full-sized satellite with microsatellites and a formation of several full-sized satellites. Practical advantages and challenges of these configurations are explored by applying them to geostationary atmospheric sounding at 53 GHz, the lowest sounding frequency considered for future sounder concepts Geostationary Atmospheric Sounder, GeoSTAR, and Geostationary Interferometric Microwave Sounder. The two configurations produce apertures of 14.4 and 28.8 m, respectively, and a spatial resolution of 16.7 and 8.3 km, respectively, from the geostationary orbit. The performance of these interferometers is simulated, and the challenges identified are threefold. First, intersatellite ranging in micrometer-level precision is required. Second, the extremely sparse design suggests that further innovation is necessary to improve radiometric resolution. Third, the presence of long baselines suggests extreme decorrelation effects are expected. While the first requirement has already been demonstrated on ground, the other two remain for future research. This technique can be implemented at arbitrary microwave frequencies and arbitrary circular orbits, meaning it can also be applied to other geostationary applications, or to achieve unprecedented spatial resolution from lower orbits, or to extend the accessible frequencies into lower frequency radio waves.

Analysis of the relative dynamics of a charged spacecraft moving under the influence of a magnetic field

We analyse a dynamical scenario where a constantly charged spacecraft (follower) moves in the vicinity of another one (leader) that follows a circular Keplerian orbit around the Earth and generates a rotating magnetic dipole. The mass of the follower is assumed to be negligible when compared with the one of the leader and they are supposed to be in a high-Earth orbit, so the Lorentz force on the follower due to the geomagnetic field is ignored. With these assumptions, the motion of the leader is not perturbed by the follower and it is only subjected to the Earth’s gravitational force field, while the charged follower is under to both the gravitational force of the Earth and the Lorentz force due to the magnetic dipole of the leader.We focus on the dynamical characteristics of the system as a function of its parameters, with special attention to the ratio of the leader’s mean motion around the Earth to the rotating rate of the dipole. We study the critical points of the model and their stability, the admissible and forbidden regions of motion of the deputy using the zero velocity surfaces and the families of periodic orbits emanating from equilibria. In the normal case we pay special attention to the periodic orbits of elliptic type and to the families of 2D tori surrounding them that are computed by means of a parameterisation method. The result is a fine catalog of orbits together with an accurate dynamical description suitable to researchers interested in potential applications of satellite formation flight using this kind of technology.

Treatment of temporal aliasing effects in the context of next generation satellite gravimetry missions

AbstractTemporal aliasing effects have a large impact on the gravity field accuracy of current gravimetry missions and are also expected to dominate the error budget of Next Generation Gravimetry Missions (NGGMs). This paper focuses on aspects concerning their treatment in the context of Low‐Low Satellite‐to‐Satellite Tracking NGGMs. Closed‐loop full‐scale simulations are performed for a two‐pair Bender‐type Satellite Formation Flight (SFF), by taking into account error models of new generation instrument technology. The enhanced spatial sampling and error isotropy enable a further reduction of temporal aliasing errors from the processing perspective. A parameterization technique is adopted where the functional model is augmented by low‐resolution gravity field solutions coestimated at short time intervals, while the remaining higher‐resolution gravity field solution is estimated at a longer time interval. Fine‐tuning the parameterization choices leads to significant reduction of the temporal aliasing effects. The investigations reveal that the parameterization technique in case of a Bender‐type SFF can successfully mitigate aliasing effects caused by undersampling of high‐frequency atmospheric and oceanic signals, since their most significant variations can be captured by daily coestimated solutions. This amounts to a “self‐dealiasing” method that differs significantly from the classical dealiasing approach used nowadays for Gravity Recovery and Climate Experiment processing, enabling NGGMs to retrieve the complete spectrum of Earth's nontidal geophysical processes, including, for the first time, high‐frequency atmospheric and oceanic variations.