In space systems, controlled dynamics are often modeled using linear time-varying (LTV) models due to the periodic orbital motion of spacecraft. When designing such models, it is advantageous to construct computationally feasible representations that exhibit clear controllability properties. Network modeling approaches are particularly effective in this context. This paper addresses the need for efficient rendezvous techniques in emerging orbital services, such as active debris removal and cargo delivery. To improve sustainability and extend satellite lifespans, a continuous-time feedback control framework is proposed for autonomous rendezvous operations, utilizing low-thrust propulsion based on relative orbit elements. Controllability is enhanced by deriving a periodic LTV model that incorporates J2 perturbations. Additionally, structural controllability is employed as a key design principle in the development of a control-oriented surrogate model that ensures persistent controllability throughout an entire orbital revolution while simultaneously minimizing modeling error. The proposed framework constructs a surrogate model that preserves the essential orbital dynamics while enforcing continuous controllability. The effectiveness of the framework is validated through numerical examples.
Low-energy capture via the weak stability boundary (WSB) is a critical technique for reducing the terminal orbit-insertion cost in planetary exploration missions. However, under the influence of multibody chaotic dynamics, the relationship between achievable propellant savings and high-dimensional design parameters remains inadequately characterized. Thus, identifying globally optimal capture opportunities is challenging, as large-scale numerical searches are computationally expensive and lack convergence guarantees. This paper presents a layered-bounded search (LBS) approach that incorporates analytical convergence conditions to efficiently identify the discrete globally optimal feasible solution under the prescribed discretization. The main contributions are threefold: First, a closed-form expression for the propellant savings of WSB capture relative to direct capture is derived, establishing an explicit correspondence between design parameters and propellant savings. Second, leveraging this expression, analytical optimality criteria for low-energy capture are developed, providing the theoretically optimal combination of design parameters. Finally, analytical convergence conditions are formulated, and the proposed LBS strategy initiates numerical refinement in the neighborhood of the theoretical optimum, rapidly locating the globally feasible optimum under real dynamics and substantially reducing computational cost. The proposed criteria and method are validated in the Sun–Jupiter and Sun–Venus systems, confirming their ability to provide a convergent, interpretable guide for designing low-energy capture trajectories.
Optical navigation plays a critical role in enabling challenging operations near small bodies. Existing techniques for processing optical data often depend on surface-related information, such as geological feature catalogs or shape models, which are limited by scale variations and low resolution of onboard datasets. To address these limitations, this study proposes a visual odometry-inspired method that uses motion direction observables extracted from the analysis of image pairs. These observables are used to constrain the spacecraft’s trajectory through a least-squares batch filtering approach. Leveraging deep learning models to reliably detect and match common features in partially overlapping images acquired at successive epochs, the proposed framework enables accurate spacecraft localization in the inertial reference frame. A comprehensive validation pipeline was developed to evaluate the network’s performance on datasets generated under varying illumination conditions and orbital configurations, demonstrating robustness in identifying correspondences between keypoints. This process supports the precise computation of the spacecraft’s estimated direction of motion. Numerical simulations in a synthetic environment, modeled on mission scenarios involving the Moon and the asteroid Vesta, provide an initial assessment of the achievable accuracy of the navigation solution and demonstrate its robustness to dynamical errors and camera pointing uncertainties representative of real mission conditions.
Hamiltonian mechanics provides the foundations for analytical approaches and geometric insights into solutions for a variety of mechanical systems that are difficult to capture through alternative approaches. These insights are particularly valuable for the development of perturbation methods in astrodynamics. While explicit symplectic integrators are well established for systems with separable Hamiltonians, their application to nonseparable Hamiltonian systems, such as the circular and elliptic restricted three-body problems, has traditionally been considered intractable until a recent breakthrough by the authors. This paper generalizes this explicit symplectic integrator framework by introducing a variable time-step implementation using time regularization transformations. Numerical experiments demonstrate excellent preservation of the geometric properties of the Hamiltonian flow through the time-regularized symplectic framework, while achieving robust long-term numerical performance. The proposed scheme compares favorably with conventional nonsymplectic adaptive stepping methods, achieving higher accuracy with fewer integration steps over long-duration propagations. In particular, the symplectic framework maintains bounded energy errors, ensuring that propagated trajectories remain on the correct energy surface, which is essential for reliable orbit prediction and mission design in cislunar space.
