Formation-flying Spacecraft Research Articles

Comparison of Relative Motion Models for Spacecraft Flying in Formation

Comparison of Relative Motion Models for Spacecraft Flying in Formation

In-orbit target tracking by flyby and formation-flying spacecraft

In-orbit target tracking by flyby and formation-flying spacecraft

Curlometer Technique and Applications

AbstractWe review the range of applications and use of the curlometer, initially developed to analyze Cluster multi‐spacecraft magnetic field data; but more recently adapted to other arrays of spacecraft flying in formation, such as MMS small‐scale, 4‐spacecraft configurations; THEMIS close constellations of 3–5 spacecraft, and Swarm 2–3 spacecraft configurations. Although magnetic gradients require knowledge of spacecraft separations and the magnetic field, the structure of the electric current density (for example, its relative spatial scale), and any temporal evolution, limits measurement accuracy. Nevertheless, in many magnetospheric regions the curlometer is reliable (within certain limits), particularly under conditions of time stationarity, or with supporting information on morphology (for example, when the geometry of the large scale structure is expected). A number of large‐scale regions have been covered, such as: the cross‐tail current sheet, ring current, the current layer at the magnetopause and field‐aligned currents. Transient and smaller scale current structures (e.g., reconnected flux tube or dipolarisation fronts) and energy transfer processes. The method is able to provide estimates of single components of the vector current density, even if there are only two or three satellites flying in formation, within the current region, as can be the case when there is a highly irregular spacecraft configuration. The computation of magnetic field gradients and topology in general includes magnetic rotation analysis and various least squares approaches, as well as the curlometer, and indeed the added inclusion of plasma measurements and the extension to larger arrays of spacecraft have recently been considered.

Comparative estimation of the accuracy of methods of autonomous navigation of small spacecraft in formation flying

The results of comparative estimation of the accuracy of autonomous navigation of small spacecraft in formation flying are presented. To carry out the research, the zenith method and the method of navigation by orbital references were chosen. These methods are based on measurements of the angular position of the Earth and an orbital reference point relative to navigational stars. Assumptions concerning the central terrestrial gravitational field and the normality of errors of the on-board navigation measurements with known constant variability were introduced in the studies. The studies were carried out using the theory of analytical estimation of the accuracy of spacecraft autonomous navigation methods. The use of this theory makes it possible to obtain the covariance error matrix of the required vector of navigation parameters and to estimate the potential (maximum achievable) characteristics of the accuracy of the navigation methods used. A dimensionless navigation error coefficient was chosen as an indicator of the accuracy of small spacecraft navigation method. The coefficient is associated with the elements of the main diagonal of the covariance matrix, it characterizes the precision properties of the method, is integrated by nature and does not depend on the volume and accuracy of the results of navigation measurements. The criterion of expediency of applying the method of determining the parameters of motion of the spacecraft center of mass is based on the comparison of navigation error rates. The presented results allow us to make reasonable choice of the method of autonomous navigation and of the composition of the onboard control of small spacecraft in formation flying.

Relative positioning of formation-flying spacecraft using single-receiver GPS carrier phase ambiguity fixing

In recent years, differential carrier phase-based relative positioning (or “baseline determination”) with precision at the millimeter and submillimeter levels has been demonstrated for the GRACE, TanDEM-X and Swarm missions in offline processing. Specific features of such missions have included the use of spacecraft of similar shapes placed in almost identical orbits as well as the use of consistent geodetic-class GPS receivers. These elements have proven to be advantageous for the computation of baseline solutions with such precision levels. Particularly, they have allowed to fully leverage the use of differential GPS techniques, including the estimation and use of carrier phase integer ambiguities. Similarly, the aforementioned spacecraft and orbit characteristics have made it possible to tightly constrain the relative dynamics of formations in the generation of reduced-dynamic solutions. Other than the former examples, prospective formation-flying mission proposals, such as SAOCOM-CS and PICOSAR, may comprise spacecraft with very different characteristics, including dissimilar GPS/GNSS receivers. Such cases may no longer provide favorable conditions for relative orbit determination strategies. As an alternative, absolute orbit solutions may be computed individually for each spacecraft and used for the generation of precise baseline products. This study aims at the assessment of the potential of single-receiver ambiguity fixing for the generation of precise baseline solutions. Results using flight data from the GRACE, TanDEM-X and Swarm missions exhibit baseline accuracy better than 5 mm (3D RMS) for a one-month test period in June 2016. As such, the presented solutions may be considered for prospective formation-flying remote sensing missions with baseline precision requirements at the subcentimeter level. Likewise, the method is considered of particular interest for future multi-spacecraft formations and swarms that require efficient determination of a large number of individual baselines.

Improvement in the Recovery Accuracy of the Lunar Gravity Field Based on the Future Moon-ILRS Spacecraft Gravity Mission

This study mostly concentrates on the sensitivity analysis regarding the future dedicated Moon-ILRS spacecraft gravity mission. Firstly, the new single and combined analytical error models for the cumulative lunar geoid height impacted by the major error sources comprising the inter-spacecraft range-rate of the interferometric laser ranging system (ILRS), the spacecraft orbital position tracked by the deep space network (DSN) and the non-conservative force of the drag-free control system (DFCS) are developed on the basis of the spacecraft-to-spacecraft tracking in the low–low mode (SST-LL) from the future twin Moon-ILRS spacecraft. Secondly, the correctness of the new single and combined analytical error models is proved according to the compliance of the cumulative lunar geoid height errors among the inter-spacecraft range-rate, orbital position and non-conservative force. Finally, in comparison with the past gravity recovery and interior laboratory (GRAIL) program, the preferred design for the future Moon-ILRS mission is achieved in this paper. We recommend that the future twin Moon-ILRS formation-flying spacecraft had better adopt the new-type space-borne instruments involving the ILRS and DFCS. We demonstrate the compatible accuracy indexes of the key sensors (e.g., 10−9 m/s in the inter-spacecraft range-rate, 1 m in the orbital position and 3 × 10−13 m/s2 in the non-conservative force) and the optimal orbital parameters (e.g., 25-km orbital altitude, 100-km inter-spacecraft range and 1-s sampling interval) in the future Moon-ILRS twin-spacecraft mission.

A Fault Detection and Diagnosis Technique for Spacecraft in Formation Flying

The objective of this paper is to develop Fault Detection and Diagnosis (FDD) algorithms for spacecraft attitude control system actuators. In particular, the FDD algorithms are developed for an Attitude Control System (ACS) actuator in the Japan Canada Joint Collaboration Satellite Formation Flying mission (JC2Sat-FF). The main issue of this research concerns with the detection and diagnosis of actuator faults in momentum wheels, which are the main ACS actuators of the satellites in the mission. The fault detection and diagnosis are accomplished by using an Interacting Multiple Model (IMM) approach. The effectiveness and the efficiency of the fault detection and diagnosis algorithm are shown through simulation results in a high-fidelity nonlinear simulator based on the JC2Sat-FF mission. The proposed FDD algorithm can be readily extended for momentum wheels in other space missions.

Effect of J2 Perturbations on Relative Spacecraft Position in Near-Circular Orbits

F ORMATION flying, in which several spacecraft maintain their relative positionswith each other, has attractedmuch attention in recent years, and various missions for Earth and astronomical observations using spacecraft flying in formation have been proposed [1,2]. A spacecraft that moves in a reference orbit is called the chief spacecraft, and a spacecraft flying in formation with the chief spacecraft is called the deputy spacecraft. The relative equations of motion for a circular reference orbit are given by the well-known Hill–Clohessy–Wiltshire (HCW) equations [3]. The HCWequations are a set of linearized equations that describe themotion of the deputy relative to the chief under the assumption that the Earth is perfectly spherical. Because the effects of the Earth’s oblateness (as described by the J2 term in the Earth’s gravitational potential) are ignored in the derivation of the HCWequations, they cannot be used to accurately predict relative motion over a long time period. Many studies have incorporated the effects of the J2 perturbation. Schweighart and Sedwick extended the HCWequations to include the effect of J2 and derived a set of constant-coefficient linearized equations of motion [4,5]. Ross [6] and Roberts and Roberts [7] derived a set of timevarying coefficient linearized equations of motion using the gradient of acceleration due to J2. Even when the chief orbit is nominally circular, a small eccentricity usually occurs because of J2. In general, the relative equations of motion for a chief with an elliptic orbit are known as the Tschauner–Hempel equations [8]. The relative motion in an elliptic orbit becomes much more complicated because of J2. Gim and Alfriend derived a state transition matrix for the relative motion under such conditions with the effects of J2 [9]. Hamel and Lafontaine also derived a state transition matrix for the relative motion. They approximated the time variation in the difference between the osculating orbit elements of the chief and deputy by using the difference between the mean orbit elements and obtained a simple form of the matrix [10]. In addition, Humi and Carter focused on cases in which the chief follows an equatorial orbit and a polar orbit and derived relative equations of motion under J2 [11]. An averaged solution of the relative motion when the chief is in an elliptical orbit with the J2 perturbation was also obtained [12]. Moreover, a method to modify the initial conditions of a formation through numerical integration of the equations ofmotion by using the Gaussian least-square method was proposed [13]. In this study, we use the solutions to the HCWequations to focus on two formations in which the relative distance between the chief and deputy is constant: an along-track formation and a circular formation. We analyze the relative distance variation due to J2. This distance variation is particularly crucial when formation flying is used to create a telescopewith a long focal distance. In relation to the distance variation caused by J2, Sabatini et al. used a genetic algorithm and examined the conditions required to minimize the deviation from a circular formation; they found that the chief orbit had two special inclinations at which the deviation becomes extremely small [14]. Moreover, the condition for the agreement of in-plane and outof-plane fundamental frequencies of the relative motion under the effects of J2 is reduced to the same inclinations as that of the chief orbit [15]. The main objective of this study is to analyze the relative distance variation within one orbit period for a mission in which the relative distance is precisely maintained. For this purpose, we take a novel approach to derive a state transition matrix without using the mean orbit elements of the chief, assuming that the eccentricity of the chief is small, i.e., of the same order of magnitude as J2. From this state transition matrix, we obtain the relative distance variation occurring in one orbit period in an analytical form. Furthermore, we also derive the relation between the initial values of the deputy and the relative distancevariation. The new formulation of the deputy initial values in terms of the osculating orbit elements is derived to reduce the distance variation. Finally, numerical simulations are carried out to validate the analytical results.

Cryogenic Heat Pipe for Cooling High-Temperature Superconducting Coils

An emerging method of propellantless formation flight is the use of electromagnets coupled with reaction wheels called electromagnetic formation flight. To create a large magnetic field necessary for actuating formation-flying spacecraft, electromagnetic formation flight uses high-temperature superconducting wire. To achieve superconductivity, the high-temperature superconducting wire requires a consumable-free cryogenic thermal control system to maintain the wire temperature below the critical temperature throughout the entire electromagnetic formation-flight coil, which could be as large as 2 m in diameter. The research in this paper investigates a consumable-free method of maintaining isothermalization for a large-scale high-temperature superconducting coil. The high-temperature superconducting coil resides inside a thermally conductive jacket that is used for isothermalization. Both a solid conductor and a heat pipe were investigated for use as the thermally conductive jacket. In this paper, a proof-of-concept circular cryogenic heat pipe was tested in a 2-m-diam toroidal vacuum chamber. This system showed the potential for high-temperature superconducting cooling. The experiments in this paper demonstrate the feasibility of operating large high-temperature superconducting coils for future formation-flying missions.

Optimization of Low-Thrust Reconfiguration Maneuvers for Spacecraft Flying in Formation

In this work, the problem of optimization of low-thrust reconfiguration maneuvers for spacecraft flying in formation is addressed. The problem is stated as the solution of an optimal control problem in which an objective function related to controls is minimized, satisfying a series of constraints on the trajectory that are both differential and algebraic. The problem has been faced by transcribing the differential constraints into a nonlinear programming problem with a parallel multiple-shooting method. The resulting problem has been solved with an interior point method. The method that has been developed is particularly suited for the solution of problems in which the trajectory is constrained with a great number of inequalities on both states and controls. The method has been applied to the design of reconfiguration maneuvers for spacecraft flying in formation, for which the collision avoidance issue leads to the imposition of a large number of inequalities on states derived from the minimum distance constraint.

Computation and Applications of an Orbital Dynamics Symplectic State Transition Matrix

This paper presents a numerical method for deriving a symplectic state transition matrix for an arbitrary Hamiltonian dynamical system. It provides the exact solution-space mapping of the linearized Hamiltonian systems, preserving the symplectic structure that all Hamiltonian systems should possess by nature. The symplectic state transition matrix can be applied to accurate, yet computationally efficient, dynamic filters, long-term propagations of the motions of formation-flying spacecraft, eigenstructure/manifold analysis of N-body dynamics, etc., when the exact structure-preserving property is crucial. We present the derivation and key characteristics of the symplectic state transition matrix and apply it to the two-body dynamics, the circular restricted three-body problem, and an Earth orbit with perturbation forces based on the real ephemeris. These numerical examples reveal that this numerical symplectic state transition matrix shows improvements in preserving the structural properties of the state transition matrix as compared with the conventional linear state transition matrix with Euler or Runge―Kutta integrations.

Autonomous navigation of formation flying spacecrafts in deep space exploration and communication by hybrid navigation utilizing neural network filter

Autonomous navigation of spacecrafts is a difficult task, however, which is a must in future deep space exploration. With multiple spacecrafts flying in space, this aim can be achieved by formation flying spacecraft (FFS) utilizing inverse time difference of arrival (ITDOA) and inverse difference Doppler (IDD) methods, which can locate the position of earth-station from one-way uplink signals in the FFS coordinate, and by way of conversion of coordinates, the position of FFS is achieved in earth-centered earth-fixed (ECEF) coordinate. The ability of neural network (NN) filter in navigation to extract position of spacecrafts from random measuring noise of signal arrival time and Doppler shift is studied with different radius of FFS and surveying parameters. The NN filter used by spacecraft group is new way of unidirectional autonomous navigation and is of high precision of hybrid navigation.

Neighboring Optimum Feedback Control Law for Earth-Orbiting Formation-Flying Spacecraft

Thispaperdevelopsafeedbackcontrollawthatguaranteesneighboringfuel-optimalityofthereconfigurationofa formation of Earth-orbiting formation-flying spacecraft. It aims for the case in which a specific formation is to be achieved at a specific true anomaly. It guarantees neighboring fuel-optimality of such a reconfiguration maneuver, assuming that the formation evolves in the vicinity of an uncontrolled reference trajectory. It is in the semi-analytic form,as onlyone time-varyinggain matrixneedstobecomputed beforethe maneuver. Itallows afuel consumption/ formation accuracy tradeoff with the selection of only one scalar gain. Simulations compare the performance of this controller with the linear-quadratic regulator and the mean orbit elements controller in the context of a 1 km size formation reconfiguration. Simulations show that this neighboring optimum controller can perform the maneuver with better accuracy while spending as much or less propellant than the other controllers.

Non‐diagonal MIMO QFT controller design reformulation

AbstractThis paper presents a reformulation of the full‐matrix quantitative feedback theory (QFT) robust control methodology for multiple‐input–multiple‐output (MIMO) plants with uncertainty. The new methodology includes a generalization of previous non‐diagonal MIMO QFT techniques; avoiding former hypotheses of diagonal dominance; simplifying the calculations for the off‐diagonal elements, and then the method itself; reformulating the classical matrix definition of MIMO specifications by designing a new set of loop‐by‐loop QFT bounds on the Nichols Chart, which establish necessary and sufficient conditions; giving explicit expressions to share the load among the loops of the MIMO system to achieve the matrix specifications; and all for stability, reference tracking, disturbance rejection at plant input and output, and noise attenuation problems. The new methodology is applied to the design of a MIMO controller for a spacecraft flying in formation in a low Earth orbit. Copyright © 2008 John Wiley & Sons, Ltd.

Carrier-Phase Differential Global Positioning System Navigation Filter for High-Altitude Spacecraft

A new navigation Kalman filter has been developed which uses carrier-phase differential Global Positioning System techniques in a framework that includes integer ambiguities to estimate the relative states of high-altitude, formation-flying spacecraft. This model-based approach to relative navigation allows spacecraft formations to use carrier-phase techniques above the Global Positioning System constellation. The filter uses dynamics models for the spacecraft orbits, receiver clocks, ionospheric total electron content, and Global Positioning System satellite residual position and clock errors. The process noise driving the orbital dynamics is separated into a common-mode part and lower intensity differential-mode part to better model how disturbances influence formations. The ionospheric total electron content model contains information that allows the filter to decide when to use the dual-frequency measurements to correct for the ionosphere and when to use them to aid in integer ambiguity resolution. The filter tracks undifferenced carrier-phase ambiguities, but still resolves the double-differenced integer ambiguities for use in the relative navigation solution. Monte Carlo simulations are used to evaluate the filter's performance. In geostationary scenarios, the filter's mean relative position error magnitude is 1.2 cm, and its maximum error magnitude is 6 cm. In high-Earth-orbit scenarios at an apogee distance of 18 Earth radii, the filter's mean error magnitude is 11 cm, and its maximum error magnitude is 54 cm. The correct integer ambiguities are resolved in one or two 30 s measurement steps in most cases.

Design of optimal spacecraft‐asteroid formations through a hybrid global optimization approach

PurposeThe purpose of this paper is to present a methodology and experimental results on using global optimization algorithms to determine the optimal orbit, based on the mission requirements, for a set of spacecraft flying in formation with an asteroid.Design/methodology/approachA behavioral‐based hybrid global optimization approach is used to first characterize the solution space and find families of orbits that are a fixed distance away from the asteroid. The same optimization approach is then used to find the set of Pareto optimal solutions that minimize both the distance from the asteroid and the variation of the Sun‐spacecraft‐asteroid angle. Two sample missions to asteroids, representing constrained single and multi‐objective problems, were selected to test the applicability of using an in‐house hybrid stochastic‐deterministic global optimization algorithm (Evolutionary Programming and Interval Computation (EPIC)) to find optimal orbits for a spacecraft flying in formation with an orbit. The Near Earth Asteroid 99942 Apophis (2004 MN4) is used as the case study due to a fly‐by of Earth in 2029 leading to two potential impacts in 2036 or 2037. Two black‐box optimization problems that model the orbital dynamics of the spacecraft were developed.FindingsIt was found for the two missions under test, that the optimized orbits fall into various distinct families, which can be used to design multi‐spacecraft missions with similar orbital characteristics.Research limitations/implicationsThe global optimization software, EPIC, was very effective at finding sets of orbits which met the required mission objectives and constraints for a formation of spacecraft in proximity of an asteroid. The hybridization of the stochastic search with the deterministic domain decomposition can greatly improve the intrinsic stochastic nature of the multi‐agent search process without the excessive computational cost of a full grid search. The stability of the discovered families of formation orbit is subject to the gravity perturbation of the asteroid and to the solar pressure. Their control, therefore, requires further investigation.Originality/valueThis paper contributes to both the field of space mission design for close‐proximity orbits and to the field of global optimization. In particular, suggests a common formulation for single and multi‐objective problems and a robust and effective hybrid search method based on behaviorism. This approach provides an effective way to identify families of optimal formation orbits.

Formation flying of multiple spacecraft with autonomous rendezvous and docking capability

The idea of incorporating autonomous rendezvous and docking (ARVD) capability into spacecraft flying in formation is explored. The situations where it is advantageous to incorporate ARVD capability into spacecraft formations are identified. Attention is focused on various potential problems pertaining to the control of multiple spacecraft with ARVD capability. Multiple-model-based control laws for formation acquisition and ARVD are developed using generic spacecraft models. In particular, the use of such control laws for simultaneous docking of multiple spacecraft in formation acquisition and reconfiguration is studied. Various optimal formation reconfiguration problems are briefly discussed. The effectiveness of the developed control laws is studied via computer simulation using a six-spacecraft formation model.

Kalman Filtering for Relative Spacecraft Attitude and Position Estimation

In this paper a novel approach is developed for relative state estimation of spacecraft flying in formation. The approach uses information from an optical sensor to provide multiple line-of-sight vectors from one spacecraft to another. The line-of-sight measurements are coupled with gyro measurements and dynamical models in an extended Kalman filter to determine relative attitude, position, and gyro biases. The quaternion is used to describe the relative kinematics, whereas general relative orbital equations are used to describe the positional dynamics. Three different attitude formulations are presented. The first estimates the relative attitude and individual gyro biases for the chief and deputy spacecraft. The second estimates the relative attitude, and the relative velocity bias and the deputy gyro bias. The third estimates the relative attitude, and the relative velocity bias and the chief gyro bias. Simulation results indicate that the combined sensor/estimator approach provides accurate relative attitude and position estimates.

Low-cost relative navigation sensing: GNSS-like devices hosted on deployed tethers

Currently, the possibility to perform very precise GNSS-based relative navigation determination among two or more spacecraft in rendezvous, docking and/or formation flying scenarios is deemed as the baseline for several current and future missions. Due to the required centimetre-level accuracy, the pseudorange measurements accuracy is not sufficient, and carrier phase measurements shall be employed. Those algorithms making exclusive use of carrier phase measurements are usually called “kinematic” algorithms, and require for dedicated integer ambiguity resolution algorithms. Obviously, this relative navigation determination concept is only suitable when the spacecraft is in the range of the GNSS constellations coverage. In situations where the GNSS constellations do not provide coverage (from MEO/GEO orbits to non-Earth planetary orbits and passing through inter-planetary missions), systems based on radio frequency (RF) signal combining emitters and receivers on-board the same platform have been proposed and are currently being studied (i.e. DARWIN RF subsystem). Nevertheless, DARWIN scenario takes advantage of the multi-spacecraft scenario characteristic (four, at least, spacecraft hosting an emitter are required to provide three-dimensional navigation). Innovative approaches are required when considering three or just two spacecraft in formation flying. This paper illustrates the concept and supplies simulation-based accuracy results of a full GNSS-like-based relative navigation determination with RF emitters/receivers hosted on board two spacecraft flying in close formation or performing a RDV and docking manoeuvre, a target and a chaser respectively named. To fulfil concept requirements, at least three RF pseudolites shall be placed on-board or around the target spacecraft so to provide the required RF coverage meant for the chaser spacecraft. A key point to achieve the required system performance is related to the relative geometry between the emitting pseudolites and the receiving antennas. The ideal being the emitters uniformly distributed in the receiver antenna field of view. It is analysed how to achieve this spatial distribution, that cannot be accomplished by placing multiple emitters on-board the same vehicle structure (characteristic spacecraft dimension will be much smaller than the inter-spacecraft distance) by using a tether-based deployed pseudolites system. Tether deployment mechanisms, particularly gravity gradient assisted, are assessed in the paper, in order to achieve the best RF emitter pseudolites distribution for a maximum formation flying navigation determination accuracy.

Trajectory Planning of a Spacecraft based on the Modified Hill's Equation

Trajectory planning of a spacecraft in formation flying is considered in this paper. Based on the equations of motion of the spacecraft that incorporate effects of J2 geopotential disturbance, time-periodic realtive equations of motion are derived. Using the Floquet theorem to periodic terms due to J2 disturbance, approximate solutions for eigenvalues and eigenvectors of the state transition matrix of the linearized equations are obtained by perturbation calculation and characteristics of relative motion are discussed. A correction term of an initial velocity of formation flying to suppress the effects of J2 disturbance is obtained based on the approximate solutions. Numerical studies are conducted to verify the proposed trajectory planning.