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This paper aims to address the problem of formation control for spacecraft formation in elliptic orbits by using local relative measurements.

A decentralized formation control law is proposed to solve the aforementioned problem. The control law for each spacecraft uses only its relative state with respect to the neighboring spacecraft it can sense. These relative states can be acquired by local relative measurements. The formation control problem is converted to n stabilization problems of a single spacecraft by using algebraic graph theories. The resulting relative motion model is described by a linear time-varying system with uncertain parameters. An optimal guaranteed cost control scheme is subsequently used to obtain the desired control performance.

Numerical simulations show the effectiveness of the proposed formation control law.

The proposed control law can be considered as an alternative to global positioning system-based relative navigation and control system for formation flying missions.

The proposed decentralized formation control architecture needs only local relative measurements. Fuel consumption is considered by using an optimal guaranteed cost control scheme.

Spacecraft formation flying is a key technology for future astronautics. The relative dynamics of formation flying in eccentric orbits is studied, and the relative motion between spacecrafts is analyzed in this paper. Based on the two‐body problem, the extension of Hill equations is achieved and used in relative dynamics of eccentric orbits. Moreover, the transformation of differential variables is applied, and the algebraic solution of the relative motion is obtained, which can be generally used for spacecraft formation flying in eccentric orbits. In addition, the analysis and numerical simulations are given for the relative motion of spacecraft formation flying. The results demonstrate that each spacecraft in eccentric orbits can run in a periodic motion surrounding the master spacecraft under some conditions. And multiple spacecraft can also set up some special formations according to missions.

The purpose of this paper is to present a methodology and experimental results on using global optimization algorithms to determine the optimal orbit, based on the mission requirements, for a set of spacecraft flying in formation with an asteroid.

A behavioral‐based hybrid global optimization approach is used to first characterize the solution space and find families of orbits that are a fixed distance away from the asteroid. The same optimization approach is then used to find the set of Pareto optimal solutions that minimize both the distance from the asteroid and the variation of the Sun‐spacecraft‐asteroid angle. Two sample missions to asteroids, representing constrained single and multi‐objective problems, were selected to test the applicability of using an in‐house hybrid stochastic‐deterministic global optimization algorithm (Evolutionary Programming and Interval Computation (EPIC)) to find optimal orbits for a spacecraft flying in formation with an orbit. The Near Earth Asteroid 99942 Apophis (2004 MN₄) is used as the case study due to a fly‐by of Earth in 2029 leading to two potential impacts in 2036 or 2037. Two black‐box optimization problems that model the orbital dynamics of the spacecraft were developed.

It was found for the two missions under test, that the optimized orbits fall into various distinct families, which can be used to design multi‐spacecraft missions with similar orbital characteristics.

The global optimization software, EPIC, was very effective at finding sets of orbits which met the required mission objectives and constraints for a formation of spacecraft in proximity of an asteroid. The hybridization of the stochastic search with the deterministic domain decomposition can greatly improve the intrinsic stochastic nature of the multi‐agent search process without the excessive computational cost of a full grid search. The stability of the discovered families of formation orbit is subject to the gravity perturbation of the asteroid and to the solar pressure. Their control, therefore, requires further investigation.

This paper contributes to both the field of space mission design for close‐proximity orbits and to the field of global optimization. In particular, suggests a common formulation for single and multi‐objective problems and a robust and effective hybrid search method based on behaviorism. This approach provides an effective way to identify families of optimal formation orbits.

A decentralized dynamic neural network (DNN)-based fault detection (FD) system for the reaction wheels of satellites in a formation flying mission is proposed. The paper aims to discuss the above issue.

The highly nonlinear dynamics of each spacecraft in the formation is modeled by using DNNs. The DNNs are trained based on the extended back-propagation algorithm by using the set of input/output data that are collected from the 3-axis of the attitude control subsystem of each satellite. The parameters of the DNNs are adjusted to meet certain performance requirements and minimize the output estimation error.

The capability of the proposed methodology has been investigated under different faulty scenarios. The proposed approach is a decentralized FD strategy, implying that a fault occurrence in one of the spacecraft in the formation is detected by using both a local fault detector and fault detectors constructed specifically based on the neighboring spacecraft. It is shown that this method has the capability of detecting low severity actuator faults in the formation that could not have been detected by only a local fault detector.

The nonlinear dynamics of the formation flying of spacecraft are represented by multilayer DNNs, in which conventional static neurons are replaced by dynamic neurons. In our proposed methodology, a DNN is utilized in each axis of every satellite that is trained based on the absolute attitude measurements in the formation that may nevertheless be incapable of detecting low severity faults. The DNNs that are utilized for the formation level are trained based on the relative attitude measurements of a spacecraft and its neighboring spacecraft that are then shown to be capable of detecting even low severity faults, thereby demonstrating the advantages and benefits of our proposed solution.

This paper aims to investigate the problem of finite-time consensus tracking control without unwinding for formation flying spacecraft in the presence of external disturbances.

Two distributed finite-time controllers are developed using the backstepping sliding mode. The first robust controller can compensate for external disturbances with known bounds, and the second one can compensate for external disturbances with unknown bounds.

Because the controllers are designed on the basis of rotation matrix, which represents the set of attitudes both globally and uniquely, the system can overcome the drawback of unwinding, which results in extra fuel consumption. Through introducing a novel virtual angular velocity, exchange of control signals between neighboring spacecraft becomes unnecessary, and it is able to reduce the communication burden.

The two robust controllers can deal with unwinding that may result in fuel consumption by traveling a long distance before returning to a desired attitude when the closed-loop system is close to the desired attitude equilibrium.

Two finite-time controllers without unwinding are proposed for formation flying spacecraft by using backstepping sliding mode. Furthermore, exchange of control signals between neighboring spacecraft is unnecessary.

This paper aims to investigate the decentralised strategy to coordinate the reconfiguration of multiple spacecraft.

The system of interest consists of multiple spacecraft with independent subsystem dynamics and local constraints, but is linked through their coupling constraints. The proposed method decomposes the centralised problem into smaller subproblems. It minimises the fuel consumption of multiple spacecraft performing a reconfiguration manoeuvre through an iterative computation. In particular, each agent optimises its individual cost function using the most recently available local solution for the other agents.

The simulation scenarios include spacecraft formation reconfiguration and close manoeuvres around obstacles were conducted. The simulation results showed the fast convergence of the proposed algorithm, while local and inter-vehicle constraints were maintained.

The main advantage of this approach is that it adopts a linear form of the objective function. This allows the local optimisation problem to be formulated as a mixed-integer, linear programming problem, most of which can be quickly solved with resort to commercial software.

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.

Recent spacecraft attitude control systems tend to use wireless communication for cost-saving and distributed mission purposes while encountering limited communication resources and data exposure issues. This paper aims to study the attitude control problem with low communication frequency under the sampled-data.

The authors propose constructive control system structures based on quantization and event-triggered methods for intra-spacecraft and multi-spacecraft systems, and they also provide potential solutions to shield the control system's data security. The proposed control architectures can effectively save communication resources for both intra-spacecraft and multi-spacecraft systems.

The proposed control architectures no longer require sensors with trigger-ing mechanism and can achieve distributed control schemes. This paper also provides proposals of employing the public key encryption to secure the data in control-loop, which is transmitted by the event-triggered control mechanism.

Spacecraft attempts to use wireless communication, yet the attitude control system does not follow up promptly to accommodate these variations. Compared with existing approaches, the proposed control structures can save communication resources of control-loop in multi-sections effectively, and systematically, by rationally configuring the location of quantization and event-triggered mechanisms.

This paper presents several new control schemes and a necessary condition for the employment of encryption algorithms for control systems based on event-based communication.

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.