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The purpose of this paper is to present a method to achieve small satellite formation keeping operations by using the differential lift and drag to control the drift caused by J2 perturbation in circular or near-circular low earth orbits (LEOs).

Each spacecraft is equipped with five large flat plates, which can be controlled to generate differential accelerations. The aerodynamic lift and drag acting on a flat plate is calculated by the kinetic theory. To maintain the formation within tracking error bounds in the presence of J2 perturbation, a nonlinear Lyapunov-based feedback control law is designed.

Simulation results demonstrate that the proposed method is efficient for the satellite formation keeping and better accuracy advantage in comparison with classical approaches via the fixed maximum differential aerodynamic acceleration.

Because the aerodynamic force will reduce drastically as the orbital altitude increases, the formation keeping control strategy for small satellites presented in this paper should be limited to the scenarios when satellites are in LEO.

The formation keeping control method in this paper can be applied to solve satellite formation keeping problem for small satellites in LEO.

This paper proposes a Lyapunov control strategy for satellite formation keeping considering both lift and drag forces, and simulation results show better performance with high accuracy under J2 perturbation.

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 present a novel high-precision relative navigation method for tight formation-keeping based on thrust on-line identification.

Considering that thrust acceleration cannot be measured directly, an on-line identification method of thrust acceleration is explored via the estimated acceleration of major space perturbation and the inter-satellite relative states obtained from space-borne acceleration sensors; then, an effective identification model is designed to reconstruct thrust acceleration. Based on the identified thrust acceleration, relative orbit dynamics for tight formation-keeping is established. Further, using global positioning system (GPS) measurement information, a modified extended Kalman filter (EKF) is suggested to obtain the inter-satellite relative position and relative velocity.

Compared with the normal EKF and the adaptive robust EKF, the proposed modified EKF has better estimation accuracy in radial and along-track directions because of accurate compensation of thrust acceleration. Meanwhile, high-precision relative navigation results depend on high-precision acceleration sensors. Finally, simulation studies on a chief-deputy formation flying control system are performed to verify the effectiveness and superiority of the proposed relative navigation algorithm.

This paper provides a reference in solving the problem of high-precision relative navigation in tight formation-keeping application.

This paper proposes a novel on-line identification method for thrust acceleration and shows that thrust identification-based modified EKF is more efficient in relative navigation for tight formation-keeping.

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 present a method to conduct small satellite rendezvous mission by using the differential aerodynamic forces under J2 perturbation in low earth orbit (LEO).

Each spacecraft is assumed to be equipped with two large flat plates, which can be controlled for generating differential accelerations in all three directions. Based on the kinetic theory, the aerodynamic lift and drag generated by a flat plate are calculated. To describe the relative dynamics under J2 perturbation, a modified model is derived from the high-fidelity linearized J2 equations proposed by Schweighart and Sedwick.

Simulation results demonstrate that the proposed method is valid and efficient to solve satellite rendezvous problem, and the modified model considering J2 effect shows better accuracy than the Horsley’s Clohessy–Wiltshire-based model.

Because aerodynamic force will reduce drastically as orbital altitude rises, the rendezvous control strategy for small satellites presented in this paper should be limited to the scenarios when satellites are in LEO.

The rendezvous control method in this paper can be applied to solve satellite rendezvous maneuver problem for small satellites in LEO.

This paper proposes a modified differential aerodynamic control model by considering J2 perturbation, and simulation results show that it can achieve higher rendezvous control accuracy.

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 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.

Keeping satellite position within close tolerances is key for the utilization of satellite formations for space missions. The presence of perturbation forces makes control inevitable if such mission objective is to be realised. Various approaches have been used to obtain feedback controller parameters for satellites in a formation; this paper aims to approach the problem of estimating the optimal feedback parameter for a leader–follower pair of satellites in a small eccentric orbit using nature-based search algorithms.

The chaotic artificial bee colony algorithm is a variant of the basic artificial bee colony algorithm. The algorithm mimics the behaviour of bees in their search for food sources. This paper uses the algorithm in optimizing feedback controller parameters for a satellite formation control problem. The problem is formulated to optimize the controller parameters while minimizing a fuel- and state-dependent cost function. The dynamical model of the satellite is based on Gauss variational equations with J2 perturbation. Detailed implementation of the procedure is provided, and experimental results of using the algorithm are also presented to show feasibility of the method.

The experimental results indicate the feasibility of this approach, clearly showing the effective control of the transients that arise because of J2 perturbation.

This paper applied a swarm intelligence approach to the problem of estimating optimal feedback control parameter for a pair of satellites in a formation.

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.

The purpose of this paper is to study the effect of J₃ perturbation of the Earth’s oblateness on satellite orbit compared with J₂ perturbation.

Based on the parametric variation method in the time domain, considering more accurate Earth potential function by considering J₃-perturbation effect, the perturbation equations about satellite’s six orbital elements (including semi-major axis, orbit inclination, right ascension of the ascending node, true anomaly, eccentricity and argument of perigee) has been deduced theoretically. The disturbance effects of J₂ and J₃ perturbations on the satellite orbit with different orbit inclinations have been studied numerically.

With the inclination increasing, the maximum of the semi-major axis increases weakly. The difference of inclination disturbed by the J₂ and J₃ perturbation is relative to orbit inclinations. J₃ perturbation has weak effect on the right ascension and argument of perigee. The critical angle of the right ascension and argument of perigee which decides the precession direction is 90° and 63.43°, respectively. The disturbance effects of J₂ and J₃ perturbations on the argument of perigee, right ascension and eccentricity are weakened when the eccentricity increases, simultaneously, the difference of J₂ and J₃ perturbations on argument of perigee, right ascension and argument of perigee decreases with eccentricity increasing, respectively.

In the future, satellites need to orbit the Earth much more precisely for a long period. The J₃ perturbation effect and the weight compared to J₂ perturbation in LEO can provide a theoretical reference for researchers who want to improve the control accuracy of satellite. On the other hand, the theoretical analysis and simulation results can help people to design the satellite orbit to avoid or diminish the disturbance effect of the Earth’s oblateness.

The J₃ perturbation equations of satellite orbit elements are deduced theoretically by using parametric variation method in this paper. Additionally, the comparison studies of J₂ perturbation and J₃ perturbation of the Earth’s oblateness on the satellite orbit with different initial conditions are presented.