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Hovering technology, as one of the core technologies in on-orbit service (OOS) missions, enables the relative position between an active spacecraft and chief spacecraft to be maintained within a given range, and it has received widespread attention in recent years. In this study, for an elliptical reference orbit, we proposed a series of control strategies to maintain a teardrop hovering formation with a J 2 perturbation. First, we formulated a mathematical model of the teardrop hovering formation maintained by the impulse control and presented a rapid method based on a relative-position correction method. Based on the sensitivity matrix, a strategy for maintaining a hovering formation using constant-thrust control was obtained. Furthermore, based on the proposed fast iterative method, an improved strategy was developed to satisfy a magnitude constraint. Finally, we analyzed the influence of the reference orbital elements and formation parameters on the hovering formation using numerical simulations, which demonstrated the efficiency of the proposed method. This provides a reference for the preliminary design of hovering formations. • The constant-thrust strategies for maintaining teardrop formation are proposed. • The magnitude constraint of engine is considered in the constant-thrust strategy. • Compared with traditional way, the proposed constant-thrust strategies save fuel. • The influence of the parameters on total impulse for maintenance are analyzed. [ABSTRACT FROM AUTHOR]

Satellite formation plays an important role in space missions such as on-orbit services and distributed space facilities. In these missions, hovering in a bounded range is one of the core tasks, but hovering technologies for the chief satellite in an elliptical orbit have been rarely investigated. Given the boundary constraints of relative motion between the chief and deputy satellites, this paper proposes two models for the design and control of hovering formation near an elliptical reference orbit through impulse: (1) the revisiting hovering formation model, which forces the deputy satellite to revisit the same relative position and maintains the formation via impulses; (2) the sequential-impulse-control hovering formation model, which uses a sequence of impulses to ensure the deputy satellite flies within the given boundary. Unlike the revisiting hovering formation model, this model does not require a fixed revisiting point, so the satellite's trajectory is more flexible. The geometrical properties, formation maintenance strategy, and impulse-control solution for both models are investigated in detail. Finally, numerical simulations are conducted to verify the advantages of the proposed methods over other conventional methods, suggesting their wide applications in practical space missions. • Two impulsive-control models are proposed for bounded hovering formation in elliptical orbit. • The proposed methods support in-plane, out-of-plane, and three-dimension hovering formations. • The in-plane and out-of-plane controls are decoupled to decrease control complexity and difficulty. • Different factors on the fuel cost are analyzed to provide a reference for practical engineering. [ABSTRACT FROM AUTHOR]

Fly-around technology, as applied to maintain a chasing spacecraft flying periodically around the chief spacecraft, has received widespread attention in recent years. The conventional impulsive or continuous-thrust control approaches for maintaining non-natural formations put a high demand on the engine and limit the applicability of engineering. In this study, which is based on the relative orbital elements, we propose a series of analytic natural fly-around formations for the two-body case, which can revisit specific points or be maintained within a certain range. In addition to maintaining the fly-around formation when considering the J2 perturbation, we present a two-stage constant thrust control method solved with the linearized sensitive matrix. Furthermore, based on this method, we present several maintaining strategies that guarantee a periodic revisit to a specified relative position. We conduct numerical simulations to demonstrate the efficacy of these proposed methods. • A series of analytic natural fly-around formations are proposed. • The reference orbit is elliptical orbit, which can also be applied to circular orbit. • A two-stage constant thrust control method solved through the linearized sensitive matrix is presented. • Several maintaining strategies are presented to guarantees periodic revisit specified relative position. [ABSTRACT FROM AUTHOR]

For the visibility optimization problem of satellite constellations, this paper presents an efficient hybrid optimization method taking multiple constraints into account. To reduce the time needed for the optimization, the satellite constellation is assumed to have a specific configuration. The optimization includes two steps. The first step searches for optima over a large scale, while the second step is designed to obtain the accurate optimal solution based on the result of the first-step optimization. Based on the analysis of the coverage performance function, a linear adaptive population method is proposed for the first step. When compared with the traditional optimization method, calculation time can be efficiently reduced while ensuring an accurate optimization. Several numerical simulations are conducted for validation. It proves to be a practical choice for engineering applications. • Different types of satellite load sensors and different coverage performance indices are considered. • Constraints of double- or more-level coverage are discussed. • The trend of the number of local maximum points of one-level coverage to the ground point are analyzed. • A novel hybrid two-step optimization method is proposed. [ABSTRACT FROM AUTHOR]

The goal of this paper is to investigate the on-orbit servicing (OOS) of geosynchronous satellites based on low-thrust transfers while considering the different demands of the satellites and the effects of perturbations. One or more servicing spacecraft start from a parking orbit and service the satellites in sequence via low-thrust orbit transfers, and return to the parking orbit in the end. The different demands lead to different service requirements of time and mass, while the perturbations affect the control solution of servicing spacecraft during each transfer, and induce orbit drifts of uncontrolled target satellites during the mission. An analytical method that can efficiently calculate the fuel consumption of low-thrust transfer is proposed, and methods for evaluating the orbit drifts of uncontrolled satellites are presented. The impact of perturbations on OOS mission is investigated in detail, showing that non-negligible factors include lunisolar attraction and tessral harmonic. Based on the dynamic models, a string-based simulated annealing algorithm is adopted to schedule the OOS mission. The efficiency of the proposed dynamic models and optimization method are verified through ample simulations. Results show that it is much more efficient and reasonable to take orbit drift calculations as corrections on the scheduling result assuming no orbit drifts. The proposed models and methods make it possible to schedule the OOS mission with low-thrust transfers, while achieving high accuracy under the effects of J2 perturbation, lunisolar attracion, tesseral harmonic and solar radiation pressure. • On-orbit servicing (OOS) of GEO satellites via low-thrust transfers is studied. • Analytical transfer solution is developed to calculate the fuel consumption. • J2, lunisolar attraction and tesseral harmonic affect fuel consumption of OOS. • Various servicing demands lead to different requirements of time and cargo mass. • A string-based simulated annealing algorithm is designed to schedule the OOS mission. [ABSTRACT FROM AUTHOR]

Abstract When compared with Cartesian coordinates, curvilinear coordinates have shown significant superior accuracy when applied to a linear model for relative motion in a circular reference orbit. Experts assume the same superiority for an elliptical reference orbit. However, the curvilinear model in an elliptical reference orbit has not been established, and the superiority has not been proved. After a strictly theoretical derivation this paper establishes a linear model with spherical coordinates for relative motion in an elliptical reference orbit. The differential equation has the same form as the Lawden or Tschauner-Hempel equation and can be easily solved with the solutions from the literature. In addition both the theoretical derivation and the numerical examples prove the model's superior accuracy in leader-follower formation and formations with a large along-track distance. The proposed model reduces the approximate limits of close relative motion, and it is expected to be applied in the propagation, guidance, and control for longer term relative motion with large along-track distances. [ABSTRACT FROM AUTHOR]

The magnetically suspended momentum wheel (MSMW) expands its fresh functions through deflecting the rotary shaft. An improved nonsingular terminal sliding-mode control (NTSMC) method is proposed to achieve high precision tracking of shaft deflection for the MSMW under coupled disturbance and saturated amplifier. A novel structure designed for this MSMW is introduced initially. Its magnetic torque model and coupled disturbance are analyzed, and a tracking error dynamic model is established. Then a NTSMC method is applied to shaft tracking control. As the saturation of amplifier influences tracking performances, an improved NTSMC is designed to deal with saturation problem. Finally, several simulations are performed to validate the effectiveness of the proposed method. The results indicate the proposed method improves the tracking precision and velocity compared with the conventional integral sliding-mode method, and solves the saturation problem compared with existing NTSMC method. [ABSTRACT FROM AUTHOR]

A novel instantaneous GNSS ambiguity resolution approach which makes use of only single-frequency carrier phase measurements for ultra-short baseline attitude determination is proposed. The Monte Carlo sampling method is employed to obtain the probability density function of ambiguities from a quaternion-based GNSS-attitude model and the LAMBDA method strengthened with a screening mechanism is then utilized to fix the integer values. Experimental results show that 100% success rate could be achieved for ultra-short baselines. [ABSTRACT FROM AUTHOR]

For out-of-plane relative equilibrium of a two-spacecraft formation achieved by internal forces, this paper proposes a scheme which complies with the characteristics of angular momentum conservation to analyze such a formation over the entire parameter space. By purposely rewriting one of the equilibrium condition, this paper defines a modification of the set of equations for the out-of-plane equilibrium configurations. Thereby, the relative equilibrium can be solved analytically in the whole multidimensional real number field through these equations. Numerical examples are also included to provide some insight about the equilibrium conditions. Moreover, the results from derivation and illustrative examples disclose a novel picture of the out-of-plane relative equilibrium. [ABSTRACT FROM AUTHOR]

Abstract: A new set of relative orbit elements is strictly defined through spherical geometry. The exact transformation equations between the new relative orbit elements and classical-orbital elements are derived. A new relative motion model with no singularity problem is derived based on the relative orbit elements, which are suitable for both elliptical and circular reference orbits. The in-plane and out-of-plane relative motion can be completely decoupled based on the new model. The inverse transformation of state transfer matrix is obtained to analyze perturbation effects and control strategy. The geometric characteristics of relative motion can be easily described using the relative eccentricity/inclination vector method. The proposed method and conclusions are validated by simulation through some typical examples. This paper improves the basic theory of relative orbit elements and unifies the expressions of the elliptical and near-circular close relative motion. [Copyright &y& Elsevier]

Maneuvering to a free return trajectory is a vital abort means for crewed lunar missions. A novel method of solving the fuel optimization of free return abort trajectory for Earth-Moon transfer by two-stage transformation on optimization model and Bayesian optimization is documented. Two new design variables—perilune altitude and transfer time from earth to perilune, instead of the original injection velocity vector, are introduced to transform the general model into a two-dimensional model. Each feasible abort trajectory is determined by a numerical method including initial estimate and exact solution. Then the characteristics of the relationship between the new variables and the fuel objective of impulse maneuver are applied to further transform the model into a one-dimensional model. Based on the Bayesian optimization method, fuel optimization is successfully and efficiently implemented for the free return abort trajectory at multiple abort moments during the Earth-Moon transfer. Furthermore, the influence of the initial Earth-Moon phase on the result of fuel optimization is presented. Numerical simulations are conducted to demonstrate the efficacy of the proposed method. • Fuel optimization of free return abort trajector. • y for Earth-Moon transfer is studied. • We propose a two-stage transformation method to overcome the difficulty of optimization model. • Bayesian Optimization method is applied to solve the optimization efficiently based on problem's characteristics. • The time window of abort trajectory and influence of the initial Earth-Moon phase is discussed. [ABSTRACT FROM AUTHOR]

This paper proposes a geometrical multi-satellite discontinuous-coverage analysis method for arbitrary fields that considers the J 2 perturbation. First, to calculate the single-satellite discontinuous coverage performance, the concept of single-satellite field mapping is introduced. Additionally, based on the geometric relationship between any two satellites, relative field mapping is proposed, which can transform the double-satellite coverage problem into an equivalent single-satellite coverage problem. Furthermore, by extending the concept of the relative field mapping, the constellation field mapping and its mapping regions are presented, which can be used to analytically calculate the revisit time of the constellation. The proposed method is verified by simulations under different conditions such as altitude, inclination, target latitudes, the field parameters of the sensor, sunlight, and the constellation configuration. The simulation results show that the maximum revisit time can be accurately obtained and intuitively displayed with the proposed method, which provides a valuable reference for Earth observation constellation design. • The analytical constellation field mapping with translation property is presented for the first time. • The proposed constellation field mapping is time-invariant and suitable for any field of view. • The discontinuous coverage can be obtained rapidly, and the sunlight constraint is considered. • Other characteristics of the constellation coverage are obtained through this analysis approach. [ABSTRACT FROM AUTHOR]

Abstract Three Dimensional Magnetically Suspended Wheel (3-DMSW) is a new kind of inertia actuator for spacecraft attitude control, which can provide a 3 degrees of freedom torque. On account of the constraint characteristics of 3-DMSW such as a small deflection saturation angle of rotor shaft and the saturation of rotor's variable rotational speed, an anti-saturation steering law based on weighted pseudo inverse is proposed for 3-DMSW cluster. A new weight adjustment method is proposed to adjust the weights of shaft deflections dynamically. A specially designed exponential function with current deflection angle and angular velocity information on the exponent position is adopted as the evaluation criterion of current torque output ability of shaft deflection. Thus the torque command can be distributed dynamically with no angle saturation. The weight adjustment method is demonstrated theoretically and the effectiveness of the anti-saturation steering law is validated by conducting several numerical simulations of attitude agile maneuver. Comparing with the 3-DMSW cluster and flywheel cluster using the traditional steering law, the results show that the 3-DMSW cluster using the proposed method makes the process of agile maneuver more rapid and accurate and the saturation angles of 3-DMSW cluster will not be reached. Highlights • The Three Dimensional Magnetically Suspended Wheel (3-DMSW) is applied in attitude control. • The saturation of rotor shaft deflection angle and rotor's variable rotational speed isconsidered. • A novel anti-saturation steering law for 3-DMSW cluster is proposed. • A new weight adjustment method for the steering law is specially designedand demonstrated theoretically. [ABSTRACT FROM AUTHOR]

An innovative orbit determination method which makes use of gravity gradients for Low-Earth-Orbiting satellites is proposed. The measurement principle of gravity gradiometry is briefly reviewed and the sources of measurement error are analyzed. An adaptive hybrid least squares batch filter based on linearization of the orbital equation and unscented transformation of the measurement equation is developed to estimate the orbital states and the measurement biases. The algorithm is tested with the actual flight data from the European Space Agency’s Gravity field and steady-state Ocean Circulation Explorer (GOCE). The orbit determination results are compared with the GPS-derived orbits. The radial and cross-track position errors are on the order of tens of meters, whereas the along-track position error is over one order of magnitude larger. The gravity gradient based orbit determination method is promising for potential use in GPS-denied spacecraft navigation. [ABSTRACT FROM AUTHOR]