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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]

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]

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]

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]

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]

On-orbit service (OOS) technologies, applied to provide essential maintenance to prolong the lifetime of spacecraft and to extend their function, have received widespread attention recently. The hovering formation, as one of the core technologies, enables the relative motion state between an active spacecraft and chief spacecraft within a specified range. In this study, we proposed a teardrop hovering formation, which is suitable for elliptical reference orbit with a J 2 perturbation. We formulated a mathematical model of the teardrop hovering formation maintained by the impulse control and presented a rapid method based on the state transition matrix. With the triangles of the three tangent lines solved by the rapid method, we estimated the envelope of the multi-loop hovering formation. Furthermore, we analyzed the influence of the reference orbital elements and formation parameters on the hovering formation by numerical simulations, which demonstrated the efficiency of the proposed method and provided a reference for the preliminary design of hovering formations. [ABSTRACT FROM AUTHOR]