To address the problem of training oscillation and difficulty in convergence caused by environmental non-stationarity in turn-based pursuit-evasion games, this paper proposes a decision-making method for turn-based pursuit-evasion game based on multi-timescale learning (MTL). Initially, a turn-based pursuit-evasion game environment model was constructed, with both the evader and pursuer configured as reinforcement learning-based agents for training. Subsequently, to alleviate the negative impact of frequent multi-agent policy updates and asynchronous maneuvers on convergence speed, agents were alternately updated with periodically varying learning rates to mitigate environmental non-stationarity. Finally, simulation comparative analysis demonstrated that the proposed MTL method is more conducive to training convergence compared to standard learning (SL) methods, thereby validating the effectiveness of this approach.

With the rapid development of cislunar space activities, space situational awareness (SSA) has become a core capability for cislunar space security. However, traditional cislunar constellation designs are mostly coverage-driven, suffering from abstract threat scenarios and insufficient optimization for robust orbit determination (OD) against dynamic transfer targets. To address this, we propose a unified analysis framework covering transfer orbit scenario construction, angular measurement OD evaluation and multi-objective constellation optimization. Under the Earth-Moon Circular Restricted Three-Body Problem (CR3BP), we develop a transfer orbit generation method based on parking orbit elements (i, Ω, u) and Lunar Sphere of Influence (SOI) entry region classification, generating 92 valid orbits covering four typical entry regions via a ”real seed search + local extension” strategy. We further establish an NSGA-III multi-objective optimization model integrating orbit family selection, satellite allocation and sensor level, and conduct simulations within the 2–6 satellite design space. The results demonstrate that a complete and continuous cost-accuracy Pareto front is obtained, spanning a proxy cost interval of [78.0, 229.2] and a 95th-percentile robust terminal position error interval of [0.538, 2.950 km]. L5-Axial, L1-Vertical, and Distant Retrograde Orbit (DRO) emerge as the three dominant backbone orbit families across the solution set. Furthermore, constellation performance is found to depend more strongly on inter-orbit geometric complementarity and payload synergy than on a simple increase in satellite quantity. This work extends existing coverage-oriented constellation design approaches by incorporating dynamic transfer scenarios and OD-driven optimization, and provides a theoretical basis and engineering references for future cislunar situational awareness constellations targeting direct transfer threats.

Owing to the chaotic and non-integrable nature of three-body dynamics, the conventional Keplerian elements are rendered inadequate for cataloging cislunar space objects. Currently, there has been a conspicuous absence of universally recognized parameters for the characterization and cataloging of such objects, thereby posing an urgent challenge to cislunar space situational awareness. This paper proposes a novel approach to parameterize the orbits of Earth-Moon collinear libration points by leveraging the theoretical frameworks of canonical transformations. First, under the Hamiltonian-form dynamical equations of the libration point, symplectic transformations are employed to extract 3 modes of motion from locally linearized part. A subsequent canonical transformation then decouples the hyperbolic invariant manifold from the center manifold within the nonlinear remainder. Finally, 6 characteristic parameters obtained via action-angle variables are established in a bijective correspondence with the state variables, where two parameters characterize the motion of the invariant manifold and four parameters characterize the motion of the central manifold. Furthermore, a distribution map of the Earth-Moon libration point orbits is drawn utilizing Poincaré sections, which can be used to describe the distribution of libration point object. Simulation results demonstrate that the proposed parameters are not only applicable to orbit identification and object cataloging but also exhibit remarkable consistency and robustness against variations in observation arc length and observational errors.

To address the nonconvexity and energy optimization in spacecraft attitude maneuver path planning under complex pointing constraints, an adaptive convex model predictive control algorithm is proposed. The Hessian matrix of the attitude geometric constraints is constructed, demonstrating the nonconvex nature of these constraints. By introducing sequential convex programming, the nonconvex geometric constraints are adaptively convexified using first-order Taylor expansions. A predictive control strategy is then designed, in which the reference trajectory is continuously updated over the prediction horizon to approximate the optimal solution of the original nonconvex problem. Simulation results show that, compared to the convexification method based on the positive definite Hessian matrix, the proposed approach strictly satisfies complex attitude constraints while effectively reducing the energy consumption during the attitude maneuver process.

Space Surveillance Network (SSN) faces inherent challenges in coordinating space and ground-based sensors tasks to maintain the catalog of Resident Space Objects (RSOs). To address operational silos between autonomous scheduling centers, this work introduces a holonic organizational framework that systematically decouples SSN scheduling into two hierarchical process: RSO allocation to scheduling centers and intra-center task scheduling. Based on this framework, an SSN Heterogeneous Resource Joint Scheduling (SSN-HRJS) model is established, including the decision variables, objective function and constraints. Given the complexity of SSN-HRJS, a Data-driven Three-phase Joint Scheduling (DTJS) methodology is proposed. First, A Graph Convolutional Network (GCN) is employed to generate RSO-to-center allocations scheme and probability matrices by learning orbital and resource characteristics. Next, a Hierarchical Combination Optimization (HCO) produces sensor task scheduling plans using the allocation scheme. Subsequently, an Adaptive Simulated Annealing with Priori Search (ASAPS) algorithm leverages the probability matrix and initial scheduling plan to achieve global optimization. Extensive experiments and comparative studies are conducted to verify the efficiency of SSN-HRJS model and DTJS algorithm.

With the rapid increase in the number of spacecraft in low Earth orbit, Space Situational Awareness (SSA) capabilities are facing increasingly severe challenges. Traditional ground-based detection resources are limited by the Earth's curvature, detection range, and fixed geographical locations, leading to observation blind spots and discontinuous temporal coverage. In response, major spacefaring nations are actively developing space-based space object surveillance systems, with optical surveillance satellites being a key representative. Against this backdrop, how to plan trajectories for in-orbit spacecraft clusters that can effectively evade continuous surveillance by space-based optical sensors has become a critical technical challenge in the field of space security. To address this issue, this paper proposes a closed-loop trajectory planning and control method that integrates real-time situational updates and autonomous decision-making. First, a continuous-time optimal control model is formulated, incorporating cluster dynamics, collision avoidance, and sensor line-of-sight constraints. The model is then discretized and approximated using Bezier curves, transforming it into a tractable nonlinear programming problem. To enhance robustness and real-time performance, the solution is embedded within a receding horizon control framework equipped with a state error correction mechanism, forming a complete closed-loop control system. Simulation results demonstrate that the proposed method can successfully plan trajectories for spacecraft clusters that avoid the sensor fields of view of optical surveillance satellites, strictly satisfy inter-spacecraft collision avoidance constraints, and maintain high computational efficiency. These findings validate the reliability and effectiveness of the method as a solution for low-observability cooperative maneuvers of spacecraft clusters. This research provides key technical support for the intelligent planning of cooperative stealth maneuvers for spacecraft clusters in complex space situational awareness scenarios.

Research on the safe operation of on-orbit spacecraft is increasingly shifting from single-spacecraft scenarios to those involving multiple spacecraft. Based on the Multi-Agent Deep Deterministic Policy Gradient algorithm, this paper addresses the problem of cooperative pursuit of a target spacecraft by multiple interacting spacecraft with communication-based coordination. The orbital pursuit-evasion games is formulated as a partially observable Markov games, with carefully designed observation and action spaces. To leverage cooperative advantages among pursuers, a communication target allocation mechanism is designed, enabling the formation of a dynamic ring topology during action execution. A hybrid reward structure combining global and local rewards is proposed. Local rewards incorporate dynamic characteristics to differentiate contributions of individual spacecraft, while global rewards are designed based on an ideal encirclement configuration with its associated constraints. For network architecture, an Encoder-Head structure is adopted: the Encoder, implemented with Long Short-Term Memory networks, effectively captures temporal patterns in the observation space, while the Head, composed of Multi-Layer Perceptron networks, maps encoded latent features into actions. Simulations first investigate a scenario with six pursuers under observational noise, and comparisons against three communication mechanisms and two distinct evader strategies demonstrate that the proposed approach effectively enhances pursuit performance and exhibits generalization capability.

The Distant Retrograde Orbits(DROs) have become strategic targets for various countries due to their unique orbital configuration and specific properties. Therefore, providing a rapid and accurate initial orbit determination(IOD) scheme for DROs is a critical step in Earth-Moon space situational awareness. Given the instability of traditional IOD methods when simultaneously addressing the challenges of DROs and very short arcs(VSA), this paper proposes an IOD method based on constructing an Admissible Region(AR) from DRO characteristic parameters. This method sequentially constructs ARs based on characteristic parameters in both the inertial coordinate system and the synodic coordinate system to constrain the solution space. Within the final AR, an optimization algorithm based on observation-minus-computation(OC) residuals is utilized, integrating and predicting solutions while minimizing residuals, ultimately producing accurate DRO orbital data. By reducing the reliance on orbital integration typical of traditional methods, this approach lowers computational costs and enhances the simplicity and efficiency of solving the IOD problem for DRO.

This paper investigates the problem of orbital pursuit-evasion games under bounded distance constraints. The objective function is designed based on the relative distance and continuously processed using an exponential function to facilitate solution via two-player zero-sum differential game theory. Further, the necessary conditions for saddle-point strategies are derived and transformed into a nonlinear optimization problem solved through using the shooting method. Simulation results demonstrate that the designed optimized objective function can effectively maintain the relative distance within the bounded region while avoiding excessively close proximity between the two spacecraft. Additionally, extra simulation cases numerically verify the bilateral optimality of the computed strategies.

This study addresses multi-sensor task scheduling for Geostationary Orbit (GEO) spacecraft observation, developing a model incorporating visibility, task, and resource constraints. To enhance computational efficiency, an Improved Contract Net Protocol Algorithm with Up-Bottom mechanism (UB-ICNPA) is proposed, employing hierarchical computation distribution to reduce solution space complexity. Experimental comparisons with Rapid-Time Dynamic Scheduling (RTDS) demonstrate UB-ICNPA’s superior performance: 70-80% higher Profit Completion Rate (PCR) with reduced computation time and enhanced stability. The algorithm’s layered architecture effectively balances workload across nodes while maintaining scheduling precision, offering significant advancements for space-based sensor networks in managing increasing geostationary orbit surveillance demands.

The Earth–Moon libration points no longer exhibit the dynamical characteristics of “equilibrium points” due to perturbation effects when applying the ephemeris model. By decoupling the forced motions within the ephemeris model and computing the dynamical substitute trajectories, we can reconstruct a dynamical system that recovers the “equilibrium points” feature. Diverging from the conventional analytical approach rooted in the framework of Newtonian mechanics, this paper presents a novel method for calculating dynamical substitute based on the Hamiltonian mechanics framework. First, the Hamiltonian equations for the ephemeris model are formulated. Subsequently, the problem of decoupling forced motions is reformulated as solving a nonautonomous differential equation through canonical transformations. Then, an iterative method based on frequency analysis is employed for the computation. Eventually, approximate analytical solutions for five libration points over a 360 yr period are provided. Simulation results demonstrate that the computed approximate analytical solutions are in excellent agreement with the numerical integration results derived from the ephemeris model, thereby validating the efficacy of the proposed method. The Hamiltonian dynamical system derived herein enables the analysis of nonlinear central manifold motions via canonical transformations, facilitating the construction of higher-order analytical solutions for libration point orbits. This framework also provides a robust foundation for exploring characterization parameters of libration point orbits within the real Earth–Moon system.

This study proposed an efficient approach to address the boundary constraints in the context of rendezvous with the noncooperative target within the vicinity of elliptical orbits. The problem was transformed into a two- point boundary value problem (TPBVP) constituted by series of boundary constraints and differential equation constraints by deriving the necessary conditions for the saddle-point strategy. The switching functions embedded with the boundary constraints equations were derived through the Theory of Functional Connections (TFC) to deal with the boundary constraints. Subsequently, the nested function structure with two levels was applied to be the free functions, which was involved in the constrainted expressions together with switching functions to treate the differential equation constraints. Simulation outcomes confirmed the superior computational efficiency of this method when compared to previous studies. Furthermore, a comprehensive analysis was undertaken to explore the impact of orbital eccentricity and true anomaly on the game's results, offering critical insights for enhancing spacecraft safety during on-orbit operations.

This manuscript examines the spacecraft rendezvous pursuit-evasion scenario, employing the relative fuel consumption between two spacecraft as the optimization objective. Anchored in Pontryagin's Minimum Principle, the saddle point control strategy is deduced, revealing that the control laws converge to be identical at the saddle point. Considering the difficulty caused by discontinuities due to the potential glider coast phase of the aircraft, the time-optimal solution is leveraged as a preliminary solution to enhance the resolution of this issue, followed by the application of the L-BFGS-B algorithm to facilitate further optimization. The simulation outcomes substantiate the efficacy of this approach in addressing the challenge effectively. Additionally, the study elucidates that, when considering relative fuel consumption, one can optimally harness the gliding phase subsequent to the shutdown of propulsion system realizing fuel conservation alongside the attainment of mission goals.

This paper studies many-to-one orbital pursuit-evasion games under impulsive propulsion. A multi-agent environment is designed using Clohessy-Wiltshire (CW) dynamics, where pursuers observe only partial states (self and evader), differing critically from globally observable Markov decision process. The evader follows the maneuvers against all pursuers inspired by on the optimal one-to-one game maneuvers, while pursuers employ maneuvers given by MADDPG with two enhancements: (1) dense rewards based on relative dynamics, and (2) imitation learning for policy initialization and convergence. Simulations show 85% interception success despite the evader’s maneuver advantage, proving the method’s efficacy.

Due to the chaotic nature of the Earth-Moon multi-body dynamical environment and various errors in practical applications, spacecraft often face difficulty in maintaining the nominal orbit without effective control. This study addresses the problem of orbit maintenance control for the DRO (Distant Retrograde Orbit) under the ephemeris model and proposes a dynamic target method for DRO maintenance control. The method primarily employs a differential evolution optimization algorithm to improve the target position, thus achieving the maintenance of the quasi-periodic DRO. Simulation results for the one-year quasi-periodic DRO maintenance show that using two target points yields the best orbit control performance. Compared to the traditional target method, the dynamic target method reduces the maneuvering cost (fuel consumption) by approximately half and decreases the number of maneuvers by 25%.

The multi-body dynamics of cislunar space is an important research direction of spacecraft motion in nowadays. DRO (Distant Retrograde Orbit) is a high value orbit in cislunar space. The initial value of the plane DRO at CR3BP (Circular Restricted Three-Body Problem) includes the x-component position, y-component velocity, and period. Under the traditional differential correction method, if the x-component position is fixed, the y-component velocity and period need to be input as the variables to be corrected. In this case, the approximate value of the y-component velocity and the period need to be calculated in advance. An improved method for cislunar space DRO calculation based on differential correction is proposed. This method calculates the period by setting the orbital integral event, and updates the period in each correction, so as to obtain the exact value of the period in the process of correcting the y-component velocity. This method reduces the input of the period to be corrected so that reduces reliance on the period. Under the condition of fixed x-component position, the initial value and period of the orbit can be calculated by inputting only one parameter (y-component velocity) while traditional differential correction needs two (y-component velocity and period). In this study, the stability, Jacobi energy, precision and other indexes are analyzed between traditional differential correction and improved differential correction.

To address the challenges posed by highly time-sensitive targets with uncertainty and unpredictability in multi-satellite cooperative observation, conventional intelligent optimization algorithms often suffer from time-consuming and unstable issues. This paper presents a novel dynamic mission planning method that cleverly incorporates waiting time for tracking and tracked time as heuristics to guide task assignment. Furthermore, plannable and robustness indicators are introduced to facilitate global trade-offs in resource conflicts among multiple targets. Initially, the constraints specifically suitable for time-sensitive target observation are analyzed, followed by the modeling of the planning problem. Subsequently, a dynamic mission planning approach is proposed that utilizes dynamic priorities, offering a linear time solution for task assignment. Through simulation verification, the efficacy of the proposed method is demonstrated, showcasing its ability to enhance multi-satellite cooperative observation effectively. Additionally, it maximizes resource utilization in the face of diverse conflicts.

The domain of astrodynamics is witnessing a surge in scholarly interest, particularly concerning the spacecraft pursuit-evasion games. This treatise introduces an analytical methodology designed to deduce the optimal impulsive thrust game-theoretic strategies for spacecraft, considering both mass variation and the sensory limitations inherent in systems. The methodology commences by computationally delineating the relative reachable domain difference from a spatial geometry standpoint. Then, each spacecraft computes a threat index predicated on its perceptive faculties and the prevailing engagement geometry, then it strategically deploys thrust to precipitously diminish this index. The efficacy of the proposed analytical technique is corroborated by the simulation experiment. Given the analytical nature of the computations entailed, the approach holds significant promise for on-board application.

In real world, the relationship between experimental input and output has become more and more complex, which brings great challenges to the sensitivity analysis. This paper proposes a decision fusion based global sensitivity analysis method for complicated experiments, which not only provides quantitative evluation of the input factor influence on experimental results, but also mines the correlation and form the explicit criteria in IF-THEN fomation for further guidance. The theory of decision information system and continuous attribute discretization is presented first for transforming the experimental input and output into a decision table. In order to calculate the sensitivity of the factors and extract valid correlation criterions between conditional attributes and decision attributes simultaneously, the discrimination matrx is utilized for attribute reduction. Then a sensitivity analysis method based on decision fusion is proposed by organically assembling experiment design, attribute discretization, the discrimization matrix, and attribute reduction. Finally, the effectiveness and practicality of the proposed method were verified by the application of sensitivity analysis in hypersonic vehicle re-entry trajectory experiment.

Qualitative spacecraft pursuit-evasion problem which focuses on feasibility is rarely studied because of high-dimensional dynamics, intractable terminal constraints and heavy computational cost. In this paper, A physics-informed framework is proposed for the problem, providing an intuitive method for spacecraft threat relationship determination, situation assessment, mission feasibility analysis and orbital game rules summarization. For the first time, situation adjustment suggestions can be provided for the weak player in orbital game. First, a dimension-reduction dynamics is derived in the line-of-sight rotation coordinate system and the qualitative model is determined, reducing complexity and avoiding the difficulty of target set presentation caused by individual modeling. Second, the Backwards Reachable Set (BRS) of the target set is used for state space partition and capture zone presentation. Reverse-time analysis can eliminate the influence of changeable initial state and enable the proposed framework to analyze plural situations simultaneously. Third, a time-dependent Hamilton-Jacobi-Isaacs (HJI) Partial Differential Equation (PDE) is established to describe BRS evolution driven by dimension-reduction dynamics, based on level set method. Then, Physics-Informed Neural Networks (PINNs) are extended to HJI PDE final value problem, supporting orbital game rules summarization through capture zone evolution analysis. Finally, numerical results demonstrate the feasibility and efficiency of the proposed framework.