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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 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 solve the problem that the standard particle swarm optimization (PSO) algorithm has a low success rate when applied to the optimization of multi-dimensional and multi-extreme value functions, the authors would introduce the extended memory factor to the PSO algorithm. Furthermore, the paper aims to improve the convergence rate and precision of basic artificial fish swarm algorithm (FSA), a novel FSA optimized by PSO algorithm with extended memory (PSOEM-FSA) is proposed.

In PSOEM-FSA, the extended memory for PSO is introduced to store each particle’ historical information comprising of recent places, personal best positions and global best positions, and a parameter called extended memory effective factor is employed to describe the importance of extended memory. Then, stability region of its deterministic version in a dynamic environment is analyzed by means of the classic discrete control theory. Furthermore, the extended memory factor is applied to five kinds of behavior pattern for FSA, including swarming, following, remembering, communicating and searching.

The paper proposes a new intelligent algorithm. On the one hand, this algorithm makes the fish swimming have the characteristics of the speed of inertia; on the other hand, it expands behavior patterns for the fish to choose in the search process and achieves higher accuracy and convergence rate than PSO-FSA, owning to extended memory beneficial to direction and purpose during search. Simulation results verify that these improvements can reduce the blindness of fish search process, improve optimization performance of the algorithm.

Because of the chosen research approach, the research results may lack persuasion. In the future study, the authors will conduct more experiments to understand the behavior of PSOEM-FSA. In addition, there are mainly two aspects that the performance of this algorithm could be further improved.

The proposed algorithm can be used to many practical engineering problems such as tracking problems.

The authors hope that the PSOEM-FSA can increase a branch of FSA algorithm, and enrich the content of the intelligent algorithms to some extent.

The novel optimized FSA algorithm proposed in this paper improves the convergence speed and searching precision of the ordinary FSA to some degree.