Search Results (8)

The Lunar Gateway is a planned small space station that will orbit the Moon and serve as a central hub for NASA’s Artemis program to return humans to the lunar surface and to prepare for Mars missions. This work presents a hybrid optimization strategy for designing minimum-fuel transfers from an Earth orbit to a Lunar Near-Rectilinear Halo Orbit. The corresponding optimal control problem—crucial for missions to NASA’s Lunar Gateway—is characterized by a high-dimensional, non-convex solution space due to the multi-body gravitational environment. To tackle this challenge, a two-stage hybrid optimization scheme is employed. The first stage uses a Genetic Algorithm heuristic as a global search strategy, to identify promising feasible trajectory solutions. Subsequently, the initial solution guess (or guesses) produced by GA are improved by a local optimizer based on a Sequential Quadratic Programming method: from a suitable initial guess, SQP rapidly converges to a high-precision feasible solution. The proposed methodology is applied to a representative cargo mission case study, demonstrating its efficiency. Our numerical results confirm that the hybrid optimization strategy can reliably generate mission-grade quality trajectories that satisfy stringent constraints while minimizing propellant consumption. Our analysis validates the combined GA-SQP optimization approach as a robust and efficient tool for space mission design in the cislunar environment. Full article

This study focuses on the nonlinear departure dynamics of spacecraft from the Near Rectilinear Halo Orbit (NRHO) to the outer regions of Selenocentric Space. By carefully selecting the combination of orbital parameters and the order of the evaluation process, it becomes possible to precisely identify the divergence moment and to reliably classify the subsequent dynamical space. An empirical divergence detection algorithm is proposed by integrating multiple parameters derived from multi-body dynamical models, including gravitational potentials and related quantities. In an applied analysis using this method, it is found that the majority of perturbed trajectories diverge into the outer Earth–Moon Vicinity, while transfers into the inner Earth–Moon Vicinity are relatively limited. Furthermore, transfers to Heliocentric Space are found to be dependent not on the magnitude of the initial perturbation but on the geometric configuration of the Sun, Earth, and Moon during the transfer phase. The investigation of the Sun’s initial phase reveals a rotationally symmetric structure in the perturbation distribution within the Sun–Earth–Moon system, as well as localized conditions under which the destination space varies significantly depending on the initial state. Identifying the divergence moment allows for comparative evaluation of the spacecraft’s nonlinear dynamical state, providing valuable insights for the development of safe and efficient transfer strategies from selenocentric orbits, including those originating from the NRHO. Full article

With the increasing number of cislunar space missions, real-time and reliable navigation and communication services have become critical. It is necessary to develop the navigation constellations dedicated to cislunar space services. However, there are plenty of orbits in cislunar space providing alternative orbits, which makes constellation design a challenging task. To address this, this paper proposes a method for a cislunar navigation constellations configuration design via orbits with resonant periods. First, a periodic orbit catalog for the Earth–Moon system is constructed. Baseline orbits are selected from different orbital families, and all resonant orbits with periods proportional to the baseline orbits are compiled into a resonant orbit set. Second, a Dilution of Precision (DOP) model for navigation performance and a spatial zoning model are established. Then, resonant orbital combinations are screened based on orbital type composition, followed by resonance constellation generation according to predetermined constellation scales. All constellation configurations are categorized by orbital type to obtain a full resonant constellation set. Finally, the proposed method is applied to design optimal configurations providing navigation services for near-Earth and lunar regions. The simulation results shows that constellations combining L2 southern/northern Near-Rectilinear Halo Orbits (NRHOs) with vertical orbits at L4/L5 points deliver the optimal navigation performance in cislunar regions. The relationships between orbital radius and DOP values in target areas, as well as the DOP evolution patterns over constellation periods, are analyzed. The mean DOP values of the optimal constellation in both the near-Earth region and the lunar region increase as the spatial radius expands. Full article

Accurate orbit determination (OD) for spacecraft with impulsive maneuvers in a multi-body system is a challenging task, because the unknown magnitudes and epochs of the maneuvers make dynamic modeling difficult, disrupting the symmetry of state deviations before and after the maneuvers. This paper proposes an Adaptive State Noise Compensation (ASNC) algorithm for the OD of spacecraft with impulsive maneuvering in a three-body dynamics frame, which does not rely on maneuver parameters and can adaptively estimate state noise. Firstly, a decoupled matching factor is developed, which can be used to identify the maneuvering and non-maneuvering epochs of the target spacecraft. Next, based on the matching factor, a position state noise estimation method is presented. Moreover, a method for estimating velocity state noise through inverse mapping of the state transition matrix is formulated, and the compensated state noise is incorporated into the Kalman framework to achieve precise OD of maneuvering spacecraft. Finally, the proposed method is applied to solve the OD problem of a Near Rectilinear Halo Orbit (NRHO) near the Earth–Moon L2 point. Simulation results demonstrated that the proposed method improved accuracy by at least an order of magnitude compared to competitive methods, while effectively restoring the symmetry of the OD system. Full article

Gateway represents a key element of the Artemis program for the upcoming lunar exploration aimed at establishing a sustainable presence by the mid-2030s. This paper investigates minimum-fuel bi-impulsive orbit transfers from Gateway to low lunar orbits (LLOs) with a maximum time of flight of 48 h. Two distinct scenarios are analyzed: (i) target orbits with free right ascension of the ascending node (RAAN), and (ii) target orbits with specified RAAN. For case (i), a global optimization technique based on a heuristic algorithm is exploited to obtain the minimum-fuel transfer. Several inclinations of the target orbit are considered. For case (ii), two distinct techniques are proposed: (a) a purely heuristic approach, and (b) a semi-analytical method based on local refinement of a Lambert-based solution. Numerical propagations are conducted in all scenarios in a high-fidelity framework that includes all relevant perturbations. A comparison between the different strategies and the related numerical results is provided. Full article

The reachable set of controlled dynamical systems is the set of all reachable states from an initial condition over a certain time horizon, subject to operational constraints and exogenous disturbances. In astrodynamics, rapid approximation of reachable sets is invaluable for trajectory planning, collision avoidance, and ensuring safe and optimal performance in complex dynamics. Leveraging the connection between minimum-time trajectories and the boundary of reachable sets, we propose a sampling-based method for rapid and efficient approximation of reachable sets for finite- and low-thrust spacecraft. The proposed method combines a minimum-time multi-stage indirect formulation with the celebrated primer vector theory. Reachable sets are generated under two-body and circular restricted three-body (CR3B) dynamics. For the two-body dynamics, reachable sets are generated for (1) the heliocentric phase of a benchmark Earth-to-Mars problem, (2) two scenarios with uncertainties in the initial position and velocity of the spacecraft at the time of departure from Earth, and (3) a scenario with a bounded single impulse at the time of departure from Earth. For the CR3B dynamics, several cislunar applications are considered, including L1 Halo orbit, L2 Halo orbit, and Lunar Gateway 9:2 NRHO. The results indicate that low-thrust spacecraft reachable sets coincide with invariant manifolds existing in multi-body dynamical environments. The proposed method serves as a valuable tool for qualitatively analyzing the evolution of reachable sets under complex dynamics, which would otherwise be either incoherent with existing grid-based reachability approaches or computationally intractable with a complete Hamilton–Jacobi–Bellman method. Full article

The paper describes the preliminary design of a phasing trajectory in a cislunar environment, where the third body perturbation is considered non-negligible. The working framework is the one proposed by the ESA’s Heracles mission in which a passive target station is in a Near Rectilinear Halo Orbit and an active vehicle must reach that orbit to start a rendezvous procedure. In this scenario the authors examine three different ways to design such phasing maneuver under the circular restricted three-body problem hypotheses: Lambert/differential correction, Hohmann/differential correction and optimization. The three approaches are compared in terms of $\mathrm{\Delta }V$ consumption, accuracy and time of flight. The selected solution is also validated under the more accurate restricted elliptic three-body problem hypothesis. Full article

The paper presents the development of a fully-safe, automatic rendezvous strategy between a passive vehicle and an active one orbiting around the Earth–Moon L2 Lagrangian point. This is one of the critical phases of future missions to permanently return to the Moon, which are of interest to the majority of space organizations. The first step in the study is the derivation of a suitable full 6-DOF relative motion model in the Local Vertical Local Horizontal reference frame, most suitable for the design of the guidance. The main dynamic model is approximated using both the elliptic and circular three-body motion, due to the contribution of Earth and Moon gravity. A rather detailed set of sensors and actuator dynamics was also implemented in order to ensure the reliability of the guidance algorithms. The selection of guidance and control is presented, and evaluated using a sample scenario as described by ESA’s HERACLES program. The safety, in particular the passive safety, concept is introduced and different techniques to guarantee it are discussed that exploit the ideas of stable and unstable manifolds to intrinsically guarantee some properties at each hold-point, in which the rendezvous trajectory is divided. Finally, the rendezvous dynamics are validated using available Ephemeris models in order to verify the validity of the results and their limitations for future more detailed design. Full article