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The purpose of this paper is to propose a modified fuel-balanced formation keeping strategy based on actively rotating satellites in the formation in the J2 perturbed environment.

Based on the relative orbital elements theory, the J2 perturbed relative motions between different satellites in the formation are analyzed, and then, the method to estimate fuel required to keep the in-plane and out-of-plane relative motions is presented, based on which a modified fuel-balanced formation keeping strategy is derived by considering both in-plane and out-of-plane J2 perturbations.

Numerical simulations demonstrate that the modified fuel-balanced formation keeping strategy is valid, and the modified fuel-balanced formation keeping strategy requires less total fuel consumption than original Vadali and Alfriend’s method.

The modified fuel-balanced formation keeping strategy is valid for formation flying mission whose member satellite is in circular or near-circular orbit.

The modified fuel-balanced formation keeping strategy can be used to solve formation flying keeping problem, which involves multiple satellites in the formation.

The modified fuel-balanced formation keeping strategy is proposed by considering both in-plane and out-of-plane J2 perturbations, which further reduce the fuel consumption than the original Vadali and Alfriend’s method.

The purpose of this paper is to evaluate the safety of formation flying satellites, and propose a method for practical collision monitoring and collision avoidance manoeuvre.

A general formation description method based on relative orbital elements is proposed, and a collision probability calculation model is established. The formula for the minimum relative distance in the crosstrack plane is derived, and the influence of J2 perturbation on formation safety is analyzed. Subsequently, the optimal collision avoidance manoeuvre problem is solved using the framework of linear programming algorithms.

The relative orbital elements are illustrative of formation description and are easy to use for perturbation analysis. The relative initial phase angle between the in‐plane and cross‐track plane motions has considerable effect on the formation safety. Simulations confirm the flexibility and effectiveness of the linear programming‐based collision avoidance manoeuvre method.

The proposed collision probability method can be applied in collision monitoring for the proximity operations of spacecraft. The presented minimum distance calculation formula in the cross‐track plane can be used in safe configuration design. Additionally, the linear programming method is suitable for formation control, in which the initial and terminal states are provided.

The relative orbital elements are used to calculate collision probability and analyze formation safety. The linear programming algorithms are extended for collision avoidance, an approach that is simple, effective, and more suitable for on‐board implementation.

The purpose of this paper is to propose a fuel‐optimal virtual centre selection method for formation flying maintenance in the J2 perturbed environment.

Based on the relative orbital elements (ROE) theory, the J2 perturbed relative motions between different satellites in the formation are analyzed, and then the fuel‐optimal virtual centre selection issue for formation flying maintenance are parameterized in terms of ROE. In order to determine the optimal virtual centre, two theories are proposed in terms of ROE.

Numerical simulations demonstrate that the fuel‐optimal virtual centre selection method is valid, and the control of the ROE of each satellite with respect to a virtual optimal centre of the formation is more efficient regarding the fuel consumption than the control of all satellites with respect to a satellite belonging to the formation.

The fuel‐optimal virtual centre selection method is valid for formation flying mission whose member satellite in circular or near circular orbit.

The fuel‐optimal virtual centre selection approach can be used to solve formation flying maintenance problem which involves multiple satellites in the formation.

The paper proposes a fuel‐optimal virtual centre selection method in terms of ROE, and shows that keeping the formation with respect the optimal virtual centre is more fuel efficient.

The purpose of this paper is to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft.

Based on the concept of fractionated spacecraft, orbit design requirements for cluster flight in the case of fractionated spacecraft are proposed, and categorized into three requirements: stabilization requirement, passive safety requirement, and the maximum inter‐satellite distance requirement. These design requirements are then reformulated in terms of relative eccentricity and inclination vectors (E/I vectors) using a relative motion model based on relative orbital elements (ROEs). By using ROEs theory, the cluster flight orbit design issue is modelled as the distribution of relative E/I vectors for each member satellite in the cluster, and solved by combining three different heuristic search methods and one nonlinear programming (NLP) method.

The simulation results show that the NLP method is valid and efficient in solving the cluster flight orbit design problem and that for some cluster flight scenarios, the heuristic search methods can be adopted to give feasible solutions without the NLP method.

The cluster flight scenario in this paper is limited because the cluster should be in the near‐circular low earth orbit (LEO), and the relative distance between the member satellites should be small enough to satisfy the relative motion linearization assumption.

The cluster flight orbit design method proposed in this paper can be applied by fractionated spacecraft mission designers to propose potential cluster flight orbit solutions.

In this paper, the relative E/I vectors method is adopted to propose an intuitive and effective cluster flight orbit design method for fractionated spacecraft.

The purpose of this paper is to propose a new fuel-balanced formation keeping reference trajectories planning method based on selecting the virtual reference center(VRC) in a fuel-balanced sense in terms of relative eccentricity and inclination vectors (E/I vectors).

By using the geometrical intuitive relative E/I vectors theory, the fuel-balanced VRC selection problem is reformulated as the geometrical problem to find the optimal point to equalize the distances between the VRC and the points determined by the relative E/I vectors of satellites in relative E/I vectors plane, which is solved by nonlinear programming method.

Numerical simulations demonstrate that the new proposed fuel-balanced formation keeping strategy is valid, and the new method achieves better fuel-balanced performance than the traditional method, which keeps formation with respect to geometrical formation center.

The new fuel-balanced formation keeping reference trajectories planning method is valid for formation flying mission whose member satellite is in circular or near circular orbit in J2 perturbed orbit environment.

The new fuel-balanced formation keeping reference trajectories planning method can be used to solve formation flying keeping problem, which involves multiple satellites in the formation.

The fuel-balanced reference trajectories planning problem is reformulated as a geometrical problem, which can provide insightful way to understand the dynamic nature of the fuel-balanced reference trajectories planning issue.

This paper aims to investigate the problem of on-line orbit planning and guidance for an advanced upper stage.

The double impulse optimal transfer orbit is planned by the Lambert algorithm and the improved particle swarm optimization (IPSO) method, which can reduce the total velocity increment of the transfer orbit. More specially, a simplified formula is developed to obtain the working time of the main engine for two phases of flight based on the theorem of impulse. Subsequently, the true anomalies of the start position and the end position for both two phases are planned by the Newton iterative algorithm and the Kepler equation. Finally, the first phase of flight is guided by a novel iterative guidance (NIG) law based on the true anomaly update with respect to the geometrical relationship. Also, a completely analytical powered explicit guidance (APEG) law is presented to realize orbital injection for the second phase of flight.

Simulations including Monte Carlo and three typical orbit transfer missions are carried out to demonstrate the efficiency of the proposed scheme.

A novel on-line orbit planning algorithm is developed based on the Lambert problem, IPSO optimization method and Newton iterative algorithm. The NIG and APEG are presented to realize the designed transfer orbit for the first and second phases of flight. Both two guidance laws achieve higher orbit injection accuracies than traditional guidance laws.

The purpose of this paper is to obtain the reachable domain (RD) for spacecraft with a single normal impulse while considering both time and impulse constraints.

The problem of RD is addressed in an analytical approach by analyzing for either the initial maneuver point or the impulse magnitude being arbitrary. The trajectories are considered lying in the intersection of a plane and an ellipsoid of revolution, whose family can be determined analytically. Moreover, the impulse and time constraints are considered while formulating the problem. The upper bound of impulse magnitude, “high consumption areas” and the change of semi-major axis and eccentricity are discussed.

The equations of RD with a single normal impulse are analytically obtained. The equations of three scenarios are obtained. If normal impulse is too large, the RD cannot be obtained. The change of the semi-major axis and eccentricity with large normal impulse is more obvious. For long-term missions, the change of semi-major axis and eccentricity leaded by multiple normal impulses should be considered.

The RD gives the pre-defined region (all positions accessible) for a spacecraft under a given initial orbit and a normal impulse with certain magnitude.

The RD for spacecraft with normal impulse can be used for non-coplanar orbital transfers, emergency evacuation after failure of rendezvous and docking and collision avoidance.