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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 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 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 solution space searching method to study the initial design of interplanetary low thrust gravity assist trajectory.

For reducing the complexity and nonlinearity of the initial design problem, a sixth degree inverse polynomial shape based approach is brought. Then some improvements are provided for solving the parameters in the shape function and a quasi‐lambert solver is brought through the shape based method, the thrust profile can be generated under the given time of flight, boundary states including positions and velocities for low thrust phase. Combining gravity assist model, the problem is summarized and an improved pruning technique is used for searching the feasible solution space for low thrust gravity assist trajectory.

Using the solution space searching method, the feasible solution region would be generated under the given mission condition. The treatment about gravity assist demonstrates more accurate than previous method. Also another advantage is that the searching method can be used to design different types of mission trajectory, including flyby and rendezvous trajectories.

The method can be used as an efficient approach to search the feasible region for the complex low thrust gravity assist trajectory, and it can provide appropriate initial guesses for the low thrust gravity assist trajectory in mission design phase.

Feasible solution space would be obtained through the searching method. The quasi‐Lambert solver in the paper is found under the shape‐based method and relative improvement, and it shows its availability during the searching process. Through mission trajectory design, the effectiveness of the method is shown.

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.

Under this heading are published regularly abstracts of all Reports and Memoranda of the Aeronautical Research Council, Reports and Technical Memoranda of the United States National Advisory Committee for Aeronautics and publications of other similar Research Bodies as issued.

This paper aims to investigate, a new optimization algorithm for complex orbit transfer missions with low‐thrust propulsion system, which minimizes the drawbacks of traditional optimization methods, such as bad convergence, difficulty of initial guesses and local optimality.

First, the trajectory optimization problem comes down to a nonlinear constraint parameter optimization by using the concept of traditional hybrid method. Then, one utilizes genetic algorithm (GA) to solve this parameter optimization problem after treating the constraints with the simulated annealing (SA) and random penalty function. Finally, one makes use of localized optimization to improve the precision of the final solutions.

This algorithm not only keeps the advantages of traditional hybrid method such as high precision and smooth solutions, but also inherits the merits of GA which could avoid initial guess work and obtain a globally optimal solution.

Further, research is required to reduce the computational complexity when the transfer trajectory is very complex and/or has many adjustable variables.

By using this method, the globally optimal solutions of some complex missions, which could not be obtained by traditional method, could be found.

This method combines the GA with traditional hybrid method, and utilizes SA and random penalty functions to treat with constraints, and then gives out a super convergence way to find the globally optimal low‐thrust transfer orbit.

Building on the broaden-and-build theory and incorporating a self-regulatory perspective, this study examines the relationship between trait gratitude and subjective career success and investigates the mediating roles of growth mindset of work and career network breadth.

Time-lagged data were collected in three waves from a sample of 314 employees in China. Hypotheses were tested using structural equation modeling.

The findings demonstrate that trait gratitude is positively related to SCS, mediated by growth mindset of work as an indicator of psychological resources and career network breadth as an indicator of social resources. Trait gratitude is more strongly associated with network breadth (i.e., social resources) than with growth mindset (i.e., psychological resources).

Organizations may find trait gratitude an applicable addition to the selection criteria during the recruitment process.

By identifying trait gratitude as an antecedent of SCS and revealing its underlying mechanisms, the current study points to a new perspective on the study of career success.

In this paper, an online convex optimization method for the exoatmospheric ascent trajectory of space interceptors is proposed. The purpose of this paper is to transform the original trajectory optimization problem into a sequence of convex optimization subproblems.

For convenience in calculating accuracy and efficiency, the complex nonlinear terminal orbital elements constraints are converted into several quadratic equality constraints, which can be better computed by a two-step correction method during the iteration. First, the nonconvex thrust magnitude constraint is convexified by the lossless convexification technique. Then, discretization and successive linearization are introduced to transform the original problem into a sequence of one convex optimization subproblem, considering different flight phases. Parameters of trust-region and penalty are also applied to improve the computation performance. To correct the deviation in real time, the iterative guidance method is applied before orbit injection.

Numerical experiments show that the algorithm proposed in this paper has good convergence and accuracy. The successive progress can converge in a few steps and 3–4 s of CPU time. Even under engine failure or mission change, the algorithm can yield satisfactory results.

The convex optimization method presented in this paper is expected to generate a reliable optimal trajectory rapidly in different situations and has great potential for onboard applications of space interceptors.

The originality of this paper lies in the proposed online trajectory optimization method and guidance algorithm of the space inceptors, especially for onboard applications in emergency situations.

The purpose of this paper was to determine the effect of route optimization on travel distance, travel time and fuel consumption of municipal solid waste (MSW) collection trucks.

The study modeled the existing waste collection routes in three local authorities in Ghana and proposed optimal routes using Esri’s ArcGIS Network Analyst Extension. The system generated optimal distances and times were validated by subjecting collection trucks to the optimal routes. Paired sample t-test was used to analyze the differences in means of the existing and optimal outcomes. The collected data were subjected to correlation and uncertainty analyses.

Results from the study indicated that weekly travel distance reduced by 81.27 km, translating into saving of 4.79 percent when trucks used the optimal routes. Travel time and fuel consumption reduced by 853.59 min and 145.86 L, making savings of 14.21 and 10.81 percent, respectively. Significant differences occurred between the means of the existing and optimal routes for travel time and fuel consumption, for each of the three local authorities.

The study was conducted in Ghana using data collected from three local authorities.

Significant reduction of MSW collection cost can be achieved by waste management practitioners through route optimization.

The effect of route optimization on travel distance, travel time and fuel consumption has been established. Statistical analyses of the existing and optimal outcomes of the three local authorities have been provided. The findings from this study support the hypothesis that optimal routes reduce operating cost through savings in travel distance, travel time and fuel consumption.