arXiv subjects

Shuyue Fu

Publications and source records attributed to Shuyue Fu.

14 recordsLinked to original sources

arXiv2026

Diffractive-Sail Single-Impulse Reachable Set for Interplanetary Transfer Design

Interest in planetary exploration has renewed, and the design of interplanetary transfers has attracted remarkable attention. This paper considers the interplanetary transfer design using a diffractive sail. Considering a nonzero departure hyperbolic excess velocity, the interplanetary transfer problem is transformed into the problem of computing single-impulse reachable sets. Then, based on previous work, a complementary computational method for reachable sets under arbitrary dynamics is proposed using differential algebra combined with adaptive grid refinement. The adaptive grid refinement considers two types of merit scores that reveal dynamical properties and the truncation error of the differential algebra propagation. The proposed method is applied to compute the diffractive-sail reachable sets, and the results verify the effectiveness of the method and merit scores. Finally, a preliminary design of the interplanetary transfers, specified as the Earth-Mars transfers, is performed based on the diffractive-sail reachable sets. The design results are presented. The effects of the corresponding parameters, including transfer time, diffractive angle, and type of diffractive sails, on transfer characteristics are analyzed, providing further insight into parameter selection for interplanetary transfer design.

astro-ph.EP↗

arXiv2026

Diffractive Sail H-Reversal Trajectory: Theoretical Feasibility, Design Strategies, and Applications

With the growing threat of near-Earth asteroid, planetary defense serves as a vital shield against catastrophic disasters. Kinetic impact utilizing an angular momentum reversal (H-reversal) trajectory of a solar sail is a highly advantageous defense approach. However, traditional reflective sails (RS) are constrained during these maneuvers by attitude-thrust coupling and a degradation of solar radiation pressure utilization at the high cone angles required for transverse acceleration. To enhance impact performance and simplify control, this paper proposes an H-reversal impact scheme utilizing a Sun-facing diffractive sail (SFDS) under a one-stage diffraction angle {\theta}d strategy and a two-stage {\theta}d strategy. The feasible parameter spaces for both strategies were mapped using the hodograph method. Tailored trajectory design methods were established for both strategies based on the feasibility analysis. Apophis impact scenario was considered, and the corresponding trajectories were constructed. Simulations demonstrate that the one-stage {\theta}d SFDS outperforms RS through a 21% increase in the impact velocity and a 35% decrease in the mission duration. Furthermore, the proposed two-stage {\theta}d strategy yields an additional 9km/s gain in impact velocity. By utilizing SFDS H-reversal trajectories, this research establishes an emergency planetary defense framework characterized by rapid response and high kinetic energy.

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arXiv2026

Three-Body Earth-Moon Transfers with Different Departure/Arrival Orbital Altitudes: New Phenomenon and Diffusion Model-Augmented Construction

Construction of Earth-Moon transfers is the basis of missions to explore the Moon and cislunar space. The traditional grid search method suffers from a relatively low convergence rate and computational efficiency, mainly focusing on the distribution of transfer characteristic parameters. Moreover, when constructing transfers with different departure/arrival orbital altitudes, the process of grid search and trajectory correction should be repeated with a low convergence rate and computational efficiency. To address these limitations of the traditional grid search method, this paper is devoted to exploring an effective way to augment the grid search method. Bi-impulsive Earth-Moon transfers from a circular Earth parking orbit to a circular Moon target orbit in the Earth-Moon planar circular restricted three-body problem are considered in this paper. Firstly, the transfers are constructed, and the corresponding solution space is explored in terms of construction parameters, including departure phase angle at the Earth parking orbit, initial-to-circular velocity ratio, and time of flight. An interesting phenomenon about the discontinuous behavior of the time-of-flight distribution with respect to departure phase angle is identified. This phenomenon is further used to train a diffusion model, which aims to augment the traditional grid search method and generate high-quality initial guesses for transfers with different departure/arrival orbital altitudes. The construction results of the proposed method are presented and analyzed. The proposed diffusion model-augmented grid search method improves the convergence rate by 47.34-56.25% and saves the wall-clock time by 39.39-40.52% over the traditional grid search method relatively, while ensuring comparable transfer characteristics.

math.OC↗

arXiv2026

Reflective-Sail Weak Stability Boundary Structure with the Locally Optimal Control Law

Escaping from the Earth is the first step of interplanetary transfers. Traditional ballistic escape trajectories in the Sun-Earth circular restricted three-body problem face limitations in relatively long time of flight and low hyperbolic excess velocity. To augment the construction of escape trajectories from the Earth, this Note proposes the concept of reflective-sail weak stability boundary structures and accordingly constructs and analyzes escape trajectories from the Earth in the context of the Sun-Earth planar circular restricted three-body problem with a reflective sail. Using an ideal reflective sail, the locally optimal control law to maximize the time derivative of the Keplerian energy with respect to the Earth is adopted. Levi-Civita regularization about the Earth is derived to address the singularity caused by the Earth. The configurations of reflective-sail weak stability boundary structures are calculated to provide initial states for constructing escape trajectories and information about regions where escape is facilitated. Then, the escape trajectories using a reflective sail are constructed based on the proposed weak stability boundary structures. The escape performance, including time of flight and estimated hyperbolic excess velocity, is analyzed. Comparison with ballistic escape trajectories in the Sun-Earth PCR3BP is also performed, indicating improved escape performance characterized by shorter time of flight and higher hyperbolic excess velocity.

astro-ph.EP↗

arXiv2026

Data Mining-Based Cislunar Escape-Family Analysis in The Multi-Body Models

Escape trajectories from the Earth-Moon system play an important role in interplanetary transfer. This paper focuses on the escape trajectories from a 167 km circular Earth orbit in the Earth-Moon planar circular three-body problem and the Sun-Earth/Moon planar bicircular four-body problem and is denoted to providing a comprehensive analysis on these escape trajectories. To achieve these purposes, the global maps of escape trajectories are constructed, and escape trajectories with one lunar gravity assist are pre-filtered. Then, an effective method to identification escape families is proposed based on dynamical analysis and data mining techniques. Once the escape families are identified, the corresponding characteristics are analyzed to provide insights into the construction of escape trajectories. Based on these escape families, the effects of the solar gravity perturbation on the number of escape trajectories, the emergence and disappearance of escape families, variation in generalized energy, and transfer characteristics are further summarized, providing insights into the model selection in the escape trajectory construction. This paper establishes an analysis methodology of escape trajectories from a perspective of escape families, deepening the understanding of escape dynamics.

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arXiv2025

Deep Neural Network-Based High-Precision Identification of Weak Stability Boundary Structures

Weak stability boundary structures have been widely applied to the analysis on ballistic capture and the construction of low-energy transfers. The first step of this application is to compute/identify weak stability boundary structures. Conventional numerical and analytical methods cannot simultaneously achieve computational efficiency and identification precision. In this paper, we propose an efficient and precise method to identify weak stability boundary structures based on deep neural network. The geometric and dynamical properties of weak stability boundary structures are firstly analyzed, which provides further insights into the training of the deep neural network models. Then, the optimal hyperparameter combinations are determined by examining the identification precision of the trained deep neural network models. The performance of the models with the optimal hyperparameter combinations is further validated using the representative test datasets, achieving the precision of 97.26-99.91%. The trained models are also applied to constructing weak stability boundary structures.

astro-ph.EP↗

arXiv2025

Discontinuous Behavior of Time-of-Flight Distribution for Bi-impulsive Earth-Moon Transfers in the Three-Body Model

As interest in the Earth-Moon transfers renewed around the world, understanding the solution space of transfer trajectories facilitates the construction of transfers. This paper is devoted to reporting a novel or less-reported phenomenon about the solution space of bi-impulsive Earth-Moon transfers in the Earth-Moon planar circular restricted three-body problem. Differing from the previous works focusing on the transfer characteristics of the solution space, we focus on the distribution of the construction parameters, i.e., departure phase angle at the Earth parking orbit, initial-to-circular velocity ratio, and time of flight. Firstly, the construction method of bi-impulsive transfers is described, and the solutions satisfying the given constraints are obtained from the grid search method and trajectory correction. Then, the distribution of the obtained solutions is analyzed, and an interesting phenomenon about the discontinuous behavior of the time-of-flight distribution for each departure phase angle is observed and briefly reported. This phenomenon can further provide useful insight into the construction of bi-impulsive transfers, deepening the understanding of the corresponding solution space.

math.OC↗

arXiv2025

Energy Transition Domain and Its Application in Constructing Gravity-Assist Escape Trajectories

This Note proposes the concept and theory of energy transition domain (ETD) defined by the mechanical energy of spacecraft in the Earth-Moon planar circular restricted three-body problem (PCR3BP) inspired by the pioneering work from Ano{\`e} et al. (2024) on the ETD defined by the two-body energy with respect to the secordary body in the PCR3BP. An effective construction method of gravity-assist escape trajectories is then proposed. Firstly, the concept of the ETD defined by the mechanical energy is presented, and its dependency on the Jacobi energy is analyzed. This dependency may provide prior knowledge about selecting the range of the Jacobi energy in the construction of escape trajectories. Then, gravity-assist escape trajectories departing from the 167 km low Earth orbit and 36000 km geosynchronous Earth orbit are constructed based on the ETD. The initial states are selected in the sphere of influence of the Moon, and the trajectories are searched from the forward and backward integration. Finally, the obtained solutions are presented and analyzed.

astro-ph.EP↗

arXiv2025

Families of Transfers from circular low Earth orbit to Distant Prograde Orbit around the Moon

Distant prograde orbits around the Moon exhibit remarkable potential for practical applications such as cislunar surveillance activities and low-energy transfers due to their instability. Previous works on transfers from circular low Earth orbit to distant prograde orbits mainly focused on construction methods based on dynamical structures, lacking a comprehensive analysis of the solution space of this transfer scenario. This paper investigates the solution space and identifies families of transfers from a 167 km circular low Earth orbit to a 1:1 distant prograde orbit. In particular, grid search and trajectory continuation are performed to construct these transfer trajectories. Initial guesses of the transfers are selected in the 1:1 distant prograde orbit through a backward propagation strategy and are then corrected to satisfy specified constraints. Based on the obtained solutions, a linear predictor is derived to predict more feasible solutions and a predictor-corrector continuation method is used to extend the solution space. Twelve transfer families are identified, most of which are new or previously underexplored. The distributions of construction parameters and transfer characteristics of these twelve families are analyzed and discussed, showing which families are applicable to which types of specific practical missions. Comparison between the obtained solution and solution developed by previous works is further performed to imply the effects of the selection of dynamical model on transfer construction.

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arXiv2025

Constructing Four-Body Ballistic Lunar Transfers via Analytical Energy Conditions

The current lunar exploration, particularly the regular large-scale cargo transportation in the Earth-Moon system proposes requirements for amount of low-energy lunar transfers. The conventional grid-search method to construct low-energy lunar transfers suffers from extensive computational effort and large-scale searches. To further improve the method, this paper focuses on one type of low-energy lunar transfers termed ballistic lunar transfers, and derives prior knowledge to narrow the scale of searches. The Sun-Earth/Moon planar bicircular restricted four-body problem (PBCR4BP) is adopted as the dynamical model to construct lunar transfers. First, the analytical conditions for ballistic capture are derived and summarized in form of exact ranges of the Jacobi energy at the lunar insertion point. Both sufficient and necessary condition and necessary condition are developed. These conditions suggest an important role of the Sun-Earth/Moon PBCR4BP rather than the Earth-Moon planar restricted three-body problem in achieving lunar ballistic capture. Then, a grid-search method combined with the analytical energy conditions is proposed to construct ballistic lunar transfers. Simulations shows that a high ballistic capture ratio is achieved by the proposed method (99.87% for direct insertion and 98.72% for retrograde insertion). Examining the obtained ballistic lunar transfers, the effectiveness of the analytical energy conditions is verified. Samples of our obtained lunar transfers achieves lower or comparable impulses compared to solutions obtained in the previous works. Solutions belonging to new or less-reported transfer families are also presented, and the potential engineering applications of these trajectories are briefly discussed.

astro-ph.EP↗

arXiv2025

Design and Continuation of Nonlinear Teardrop Hovering Formation along the Near Rectilinear Halo Orbit

This short communication is devoted to the design and continuation of a teardrop hovering formation along the Near Rectilinear Halo orbit and provides further insights into future on-orbit services in the cislunar space. First, we extend the concept of the teardrop hovering formation to scenarios along the Near Rectilinear Halo orbit in the Earth-Moon circular restricted three-body problem. Then, we develop two methods for designing these formations based on the nonlinear model for relative motion. The first method addresses the design of the teardrop hovering formations with relatively short revisit distances, while the second method continues hovering trajectories from short to longer revisit distances. In particular, new continuation method is developed to meet the design requirements of this new scenario. Simulation results verify the effectiveness of the proposed methods, and a near-natural teardrop hovering formation is achieved by considering the dynamical properties near the NRHO. Comparisons between design results obtained using linear and nonlinear models further strengthen the necessity of using the nonlinear model.

math.OC↗

arXiv2025

Analytical Strategies and Winning Conditions for Elliptic-Orbit Target-Attacker-Defender Game

This paper proposes an analytical framework for the orbital Target-Attacker-Defender game with a non-maneuvering target along elliptic orbits. Focusing on the linear quadratic game, we derive an analytical solution to the matrix Riccati equation, which yields analytical Nash-equilibrium strategies for the game. Based on the analytical strategies, we derive the analytical form of the necessary and sufficient winning conditions for the attacker. The simulation results show good consistency between the analytical and numerical methods, exhibiting 0.004$\%$ relative error in the cost function. The analytical method achieves over 99.9$\%$ reduction in CPU time compared to the conventional numerical method, strengthening the advantage of developing the analytical strategies. Furthermore, we verify the proposed winning conditions and investigate the effects of eccentricity on the game outcomes. Our analysis reveals that for games with hovering initial states, the initial position of the defender should be constrained inside a mathematically definable set to ensure that the attacker wins the game. This constrained set further permits geometric interpretation through our proposed method. This work establishes the analytical framework for orbital Target-Attacker-Defender games, providing fundamental insights into the solution analysis of the game.

math.OC↗

arXiv2024

Analytical Pursuit-Evasion Game Strategy in Arbitrary Keplerian Reference Orbits

This paper develops an analytical strategy for solving the linear quadratic pursuit-evasion game in arbitrary Keplerian reference orbits. The motion of the pursuer and evader is described using the controlled Tschauner-Hempel equations, and the optimal game strategies of the pursuer and evader are presented by the solution of the differential Riccati equation.The analytical solution of the differential Riccati equation is presented for elliptic, parabolic, and hyperbolic reference orbits, thereby enabling an analytical pursuit-evasion game strategy. Then, the procedure to solve the pursuit-evasion game using this analytical strategy is proposed. Simulations of pursuit-evasion game in elliptic, parabolic, and hyperbolic reference orbits validate the effectiveness of the developed analytical strategy. Results indicates that the analytical strategy saves the CPU time by more than 99.8$\%$ compared to the numerical one, highlighting the efficiency of the developed strategy. The developed analytical strategy is also applicable to pursuit-evasion game scenarios considering orbital disturbances. Compared to the conventional strategy, which succeed in only two out of six test scenarios, the developed strategy achieves success in all six cases, particularly demonstrating its effectiveness in high-eccentricity cases.

math.OC↗

arXiv2024

Interior transit orbits in the planar bicircular restricted four-body problem: classification and application

Low-energy transfers are advantageous for lunar exploration missions due to low fuel consumption and extended launch periods. This paper is devoted to the classification of interior transit orbits and their application on low-energy transfer in the Sun-Earth/Moon planar bicircular restricted four-body problem (PBCR4BP). First, the Lagrangian coherent structures (LCSs) are introduced to generate the interior transit orbits. The number of periapses about the Moon is selected as the classification parameter and mapped into the LCSs, achieving clear classification boundaries. Then, the evolution laws of the classifications with respect to energy and solar gravity perturbation are discussed and summarized. Construction strategies for low-energy transfer are proposed based on the classifications and their evolution laws. Numerical simulation of the transfer trajectories verifies the effectiveness of the proposed strategies. The dynamical behaviors and transfer characteristics of transit orbits and their families are revealed, and a direct link between transit orbit families and low-energy transfers is finally established.

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