arXiv subjects

Shengping Gong

Publications and source records attributed to Shengping Gong.

At least 19 recordsLinked to original sources

arXiv2026

Inversion Framework of Internal Mass Distribution Parameters of Asteroid Apophis from Dynamical Observations

The detection of the internal mass distribution of asteroids is of great significance for understanding their origin, evolution, and mission planning for exploration. Previous approaches rely on indirect density estimates or close-range spacecraft gravity inversion, which have limited applicability. This paper presents a proof-of-concept framework to infer the internal mass properties of asteroid (99942) Apophis during its close Earth flyby in 2029 using dynamical observations collected during the encounter. We establish a dynamical mapping from the evolution of orbital and rotational states to internal structural parameters, formulate it as an inverse problem, and solve it using Particle Swarm Optimization. The algorithm is first validated on a regular ellipsoidal model and then applied to three mass distribution models based on the actual shape of Apophis. Under ideal observation conditions, the relative error of the inverted moment of inertia ratios can be below 0.001%, and the absolute error of the center-of-mass position reaches the order of 10-5 meters. The algorithm successfully distinguishes among different internal structures. When realistic measurement noise is introduced, the inversion accuracy degrades. A sensitivity analysis reveals that the accuracy of the inertia tensor inversion is primarily limited by angular velocity measurement noise, whereas center-of-mass determination is highly sensitive to the precision of position and velocity data. This study provides a proof-of-concept for a technically feasible and cost-effective approach to infer asteroid internal structure during close encounters, and also highlights the critical data accuracy requirements for practical application, offering guidance for future observation campaigns.

astro-ph.EP↗

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

Dual-Thrust Switching Analytical Guidance Algorithm for Powered Landing with Attitude Smoothness Optimization

Traditional numerical guidance methods for powered landing of reusable rockets are typically constrained by high computational complexity and inadequate real-time performance. Moreover, insufficient consideration of attitude smoothness often induces severe fluctuations in control commands; meanwhile, most existing approaches are tailored for single-thrust scenarios, failing to accommodate the guidance requirements of multi-engine thrust switching. To mitigate these limitations, this paper proposes an analytical guidance method optimized for attitude smoothness, which supports dual-thrust-mode switching. First, a corresponding optimal control problem is formulated, and it is theoretically proven that the optimal attitude command takes a concise piecewise cubic function form. This transforms complex trajectory optimization into a parametric analytical optimization problem, yielding a substantial improvement in computational efficiency. Further, a three-phase guidance framework is designed to enable adaptive determination of the guidance activation point and thrust switching point; when integrated with an aerodynamic correction strategy, this framework enhances the method's adaptability in complex flight environments particularly under high lift-to-drag ratio conditions. Simulation results demonstrate that the attitude command profile generated by the proposed method aligns closely with the theoretical optimal solution, with an ultra-short computation time, confirming its strong potential for online real-time implementation. Even under stringent conditions (e.g., limited thrust adjustment range, high lift-to-drag ratios, and parameter deviations), the method consistently achieves high-precision landing, showcasing promising prospects for engineering applications.

math.OC↗

arXiv2026

Condensed PIPG Sequential Convex Optimization for Reusable-Rocket Powered Landing with Strong Aerodynamics

Reusable-rocket powered landing under strong aerodynamics couples variable mass, free final time, and bounded aerodynamic controls through nonlinear velocity-frame dynamics. This paper develops a condensed proportional--integral projected-gradient (PIPG) sequential-convex method whose principal contribution is an exact reduced-space inner architecture. Because the problem contains only six terminal hard equalities and no state path constraints, 217 nodal-state variables and 210 trapezoidal dynamics equalities are eliminated from the 31-node convex subproblem, leaving 101 primal variables and six terminal equalities. Row-orthogonal preconditioning, fixed-size matrix--vector products, and nodewise circular-epigraph projections then yield a customized PIPG kernel. Physical consistency of the angle-dependent axial force is maintained by gradually releasing drag sensitivity between the reference squared angle and an epigraph variable $A$, together with a convex tightness term. A pointwise Hamiltonian argument shows that the fully released limiting subproblem admits a tight optimum satisfying $A=\alpha^2+\beta^2$. Deterministic annealing, two-stage inner accuracy, and a rejected-on-failure threefold extrapolation are secondary outer-loop accelerators.

math.OC↗

arXiv2026

Submillisecond Sequential Convex Optimization for Powered Landing via Dynamics Condensation and xPIPG

Powered landing with variable mass, free final time, and quadratic aerodynamic drag requires the repeated solution of local convex subproblems, whose main online cost lies in the long dynamics-equality chain and the inner iterations. This paper develops a condensed sequential convex approximation designed for low latency. Exact block elimination removes 217 intermediate-state components and 210 interval equations from a 31-node model, leaving 100 primal variables coupled by six terminal equalities. A low-weight energy term and fixed quadratic proximal regularization make the ideal surrogate strongly convex with predictable curvature. The inner solver is an extrapolated proportional--integral projected gradient (xPIPG) implemented with fixed-size arrays, $3\times3$ interval solves, and a fused one-pass node map. The one-pass map is a deliberate low-cost approximation, not the exact joint proximal operator. We therefore evaluate the timed code by nonlinear trajectory residuals and independent physical checks rather than by a claim of exact KKT convergence. The single-precision C implementation completes one plan in four outer updates and 336 xPIPG updates. On an Intel Core i7-10875H, the median end-to-end solve time is \SI{374}{\micro\second} and the P99 value is \SI{512}{\micro\second}. All 100 common initial-state perturbations pass validation, and the median remains below \SI{0.7}{\milli\second} for 15--51 nodes. An independent high-accuracy first-order-hold integration gives a terminal position error of \SI{0.183}{\meter}. Within the stated model, hardware, stopping rule, and timing boundary, this is, to the authors' knowledge, the first submillisecond end-to-end sequential-convex solve for a single powered-landing trajectory.

math.OC↗

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.

astro-ph.EP↗

arXiv2026

Microsecond-Class Powered-Descent Optimization via Exact Condensation and Strong Convex Regularization

Fuel-dominant powered descent can be written as a convex program, but the usual full-state epigraph formulation still carries many state variables, fuel epigraph variables, and dynamics equalities. In addition, the pure-fuel objective provides no strong-convexity curvature. This paper combines three structural reductions. First, a dimensionally consistent low-weight energy term makes the control solution unique. Second, a terminal-state sensitivity recursion eliminates every intermediate state exactly; invertible row normalization turns the 30-node baseline with 300 primal variables and 174 equality multipliers into a problem with 90 control variables and six terminal multipliers. Third, the shared radial structure of the fuel norm and thrust ball gives an exact closed-form proximal operator consisting of group shrinkage followed by magnitude clipping. The condensed problem is solved with a fixed-budget extrapolated proportional--integral projected-gradient iteration implemented in fixed-size C17 arrays. In a Mars powered-descent case with energy weight 0.02 and relative reference-solution tolerance $10^{-3}$, the iteration count decreases from 2744 for the pure-fuel full-state epigraph baseline to 93, while the fuel metric increases by only 0.033\%. The mean end-to-end solve time is \SI{68.2}{\micro\second}, and P99 is \SI{128.1}{\micro\second}, on an Intel i7-10875H. Because the thrust set in this test case is already a convex ball, the contribution is fast solution of the convex core rather than a new lossless-convexification theorem.

math.OC↗

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.

astro-ph.EP↗

arXiv2025

Parameter Optimization in Trajectory Planning via Differentiable Convex Programming

Sequential convex programming has been established as an effective framework for solving nonconvex trajectory planning problems. However, its performance is highly sensitive to problem parameters, including trajectory variables, algorithmic hyperparameters, and physical vehicle parameters. This paper introduces a differentiable sequential convex programming framework that integrates differentiable convex optimization with sequential convex programming to enable end-to-end parameter optimization. By deriving first-order sensitivity relations of second-order cone programming solutions with respect to problem data, exact gradients of trajectory performance metrics with respect to arbitrary parameters are obtained and propagated through iterations. The effectiveness of the proposed framework is validated through three representative applications: optimal terminal-time prediction for powered landing, trust-region penalty optimization in subproblems, and surface-to-mass ratio optimization for hypersonic gliding vehicles. Simulation results show that the proposed framework enables reliable gradient-based parameter learning and significantly improves numerical performance, convergence behavior, and design efficiency. These results indicate that the differentiable sequential convex programming framework provides a powerful and general tool for vehicle design, mission optimization, and hyperparameter selection in aerospace trajectory planning.

math.OC↗

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

Sparse Kalman Identification for Partially Observable Systems via Adaptive Bayesian Learning

Sparse dynamics identification is an essential tool for discovering interpretable physical models and enabling efficient control in engineering systems. However, existing methods rely on batch learning with full historical data, limiting their applicability to real-time scenarios involving sequential and partially observable data. To overcome this limitation, this paper proposes an online Sparse Kalman Identification (SKI) method by integrating the Augmented Kalman Filter (AKF) and Automatic Relevance Determination (ARD). The main contributions are: (1) a theoretically grounded Bayesian sparsification scheme that is seamlessly integrated into the AKF framework and adapted to sequentially collected data in online scenarios; (2) an update mechanism that adapts the Kalman posterior to reflect the updated selection of the basis functions that define the model structure; (3) an explicit gradient-descent formulation that enhances computational efficiency. Consequently, the SKI method achieves accurate model structure selection with millisecond-level efficiency and higher identification accuracy, as demonstrated by extensive simulations and real-world experiments (showing an 84.21\% improvement in accuracy over the baseline AKF).

eess.SY↗

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

Recursive Inference for Heterogeneous Multi-Output GP State-Space Models with Arbitrary Moment Matching

Accurate learning of system dynamics is becoming increasingly crucial for advanced control and decision-making in engineering. However, real-world systems often exhibit multiple channels and highly nonlinear transition dynamics, challenging traditional modeling methods. To enable online learning for these systems, this paper formulates the system as Gaussian process state-space models (GPSSMs) and develops a recursive learning method. The main contributions are threefold. First, a heterogeneous multi-output kernel is designed, allowing each output dimension to adopt distinct kernel types, hyperparameters, and input variables, improving expressiveness in multi-dimensional dynamics learning. Second, an inducing-point management algorithm enhances computational efficiency through independent selection and pruning for each output dimension. Third, a unified recursive inference framework for GPSSMs is derived, supporting general moment matching approaches, including the extended Kalman filter (EKF), unscented Kalman filter (UKF), and assumed density filtering (ADF), enabling accurate learning under strong nonlinearity and significant noise. Experiments on synthetic and real-world datasets show that the proposed method matches the accuracy of SOTA offline GPSSMs with only 1/100 of the runtime, and surpasses SOTA online GPSSMs by around 70% in accuracy under heavy noise while using only 1/20 of the runtime.

stat.ML↗

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.

astro-ph.EP↗

arXiv2025

Learning-Based Stable Optimal Control for Infinite-Time Nonlinear Regulation Problems

Infinite-time nonlinear optimal regulation control is widely utilized in aerospace engineering as a systematic method for synthesizing stable controllers. However, conventional methods often rely on linearization hypothesis, while recent learning-based approaches rarely consider stability guarantees. This paper proposes a learning-based framework to learn a stable optimal controller for nonlinear optimal regulation problems. First, leveraging the equivalence between Pontryagin Maximum Principle (PMP) and Hamilton-Jacobi-Bellman (HJB) equation, we improve the backward generation of optimal examples (BGOE) method for infinite-time optimal regulation problems. A state-transition-matrix-guided data generation method is then proposed to efficiently generate a complete dataset that covers the desired state space. Finally, we incorporate the Lyapunov stability condition into the learning framework, ensuring the stability of the learned optimal policy by jointly learning the optimal value function and control policy. Simulations on three nonlinear optimal regulation problems show that the learned optimal policy achieves near-optimal regulation control and the code is provided at https://github.com/wong-han/PaperNORC

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