Minimum-time Transfer Research Articles

Neural Network-Based Optimization of LEO Transfers

This study investigates the application of neural networks to the evaluation of minimum-time low-thrust transfers in low Earth orbit. The findings demonstrate the effectiveness of utilizing costates to regularize the training loss, significantly enhancing the accuracy of the predictions of the neural networks, even when working with limited datasets. Remarkably precise estimates of transfer times are achieved by training the regularized networks on datasets comprising one million samples. The incorporation of a warm-started guess strategy, involving simpler neural networks to provide transfer time and costates predictions for new transfers, accelerates the data collection process, making this approach highly practical for real-world applications. Overall, the methodology employed in this research study holds significant promise for low-thrust space missions, particularly when the evaluation of multiple minimum-time transfers is necessary in mission planning. In fact, the trained neural networks significantly speed up convergence when solving optimal control problems with indirect optimization methods. Furthermore, the remarkable accuracy in estimating both minimum transfer times and costates provides the flexibility of relying entirely on neural networks for determining minimum time.

Multi-Modal Urban Traffic Transfer Schedule Timetable Bi-Objective Optimization: Model, Algorithm, Comparison, and Case Study

The optimization of the connection between urban rail transit and the bus is an essential issue that benefits passenger travel and the urban structure and has social benefits, which can be realized by reasonably adjusting the bus departure schedule. This study is necessary because the development status quo of China’s urban transportation network planning is unreasonable, travel efficiency is not high, and operating costs are high. This paper sets up the decision variables of bus departure time and departure interval at each station, establishes a dual-objective optimization model with the minimum schedule change and the minimum transfer time, and studies the application of the augmented Chebyshev algorithm in the dual-objective optimization model. Secondly, based on the Shenzhen metro and public transportation integrated circuit card data, the case analysis uses the generalized Chebyshev algorithm and the non-dominated sorting genetic algorithm, respectively. The optimization results show that using the improved augmented and generalized Chebyshev algorithm in the bus schedule alteration time within a reasonable range can maximize the total transfer time, which compared with the original scheme is shortened by 68.06%. In contrast, genetic algorithms will make the complete bus schedule alteration prominent, and the whole transfer time is substantially increased. The results show that the improved augmented generalized Chebyshev algorithm is more suitable for solving the dual-objective rail transit connection problem.

An ILP approach for tactical flight rescheduling during airport access mode disruptions

AbstractAirport access mode disruptions, such as a subway shutdown, threaten the whole passenger door‐to‐door journey. When such a disruptive event occurs, knowledge of passengers' delays would help the airport operation centre to decide if a departure flight should be delayed. This paper proposes a tactical flight rescheduling at an airport to minimise the number of stranded passengers while considering operational constraints. An integer linear programming formulation of the problem is presented. Constraints such as terminal capacities, maximal runway throughput, minimum turnaround time or minimum transfer time for connecting passengers are considered. An exact and heuristic resolution is proposed and compared to a study case around Paris‐Charles de Gaulle airport. The new schedule satisfies the operational constraints and reduces up to 60% of the number of stranded passengers with moderate deviation from the initial planning.

Perturbed low-thrust geostationary orbit transfer guidance via polynomial costate estimation

This paper proposes an optimal, robust, and efficient guidance scheme for the perturbed minimum-time low-thrust transfer toward the geostationary orbit. The Earth's oblateness perturbation and shadow are taken into account. It is difficult for a Lyapunov-based or trajectory-tracking guidance method to possess multiple characteristics at the same time, including high guidance optimality, robustness, and onboard computational efficiency. In this work, a concise relationship between the minimum-time transfer problem with orbital averaging and its optimal solution is identified, which reveals that the five averaged initial costates that dominate the optimal thrust direction can be approximately determined by only four initial modified equinoctial orbit elements after a coordinate transformation. Based on this relationship, the optimal averaged trajectories constituting the training dataset are randomly generated around a nominal averaged trajectory. Five polynomial regression models are trained on the training dataset and are regarded as the costate estimators. In the transfer, the spacecraft can obtain the real-time approximate optimal thrust direction by combining the costate estimations provided by the estimators with the current state at any time. Moreover, all these computations onboard are analytical. The simulation results show that the proposed guidance scheme possesses extremely high guidance optimality, robustness, and onboard computational efficiency.

Optimal interplanetary trajectories for Sun-facing ideal diffractive sails

A diffractive sail is a solar sail whose exposed surface is covered by an advanced diffractive metamaterial film with engineered optical properties. This study examines the optimal performance of a diffractive solar sail with a Sun-facing attitude in a typical orbit-to-orbit heliocentric transfer. A Sun-facing attitude, which can be passively maintained through the suitable design of the sail shape, is obtained when the sail nominal plane is perpendicular to the Sun–spacecraft line. Unlike an ideal reflective sail, a Sun-facing diffractive sail generates a large transverse thrust component that can be effectively exploited to change the orbital angular momentum. Using a recent thrust model, this study determines the optimal control law of a Sun-facing ideal diffractive sail and simulates the minimum transfer times for a set of interplanetary mission scenarios. It also quantifies the performance difference between Sun-facing diffractive sail and reflective sail. A case study presents the results of a potential mission to the asteroid 16 Psyche.

Comparison of Learning Spacecraft Path-Planning Solutions from Imitation in Three-Body Dynamics

Spacecraft path-planning approaches that are capable of producing not only autonomous but also generalized solutions promise to open new modalities for robotic exploration and servicing in orbit environments characterized by epistemic uncertainty. Our hypothesis is that, in face of large systemic uncertainties, learning control policies from human demonstrations may offer a pathway to spacecraft guidance solutions that are more generalizable and complementary of baseline-dependent methods. In this context, the performance discrepancy between spacecraft path-planning policies trained from human demonstrations and optimal baseline solutions has not been characterized. We define a low-thrust, minimum-time transfer problem with predefined boundary constraints, across a wide range of binary asteroid systems, which form a “sandbox” environment for complex, highly variable, and poorly known orbit environments. Trajectories generated using optimal control theory (both indirect and direct methods) and human demonstrations (from a gamified version of the baseline environment) are collected. We test different implementations of behavioral cloning to analyze both feed forward and stateless long short-term memory regressions. As a result, we collect initial empirical evidence of performance degradation during cloning (compared to precisely optimal behavior) and performance stability across variations of the environment parameters. Such evidence informs the selection and improvement of the behavioral cloning architecture in future studies.

Optimum, Suboptimal and Solar Sailing Orbital Maneuvers for a Spacecraft Orbiting the Earth

The present research performs numerical studies to search for the best maneuvers, from the point of view of minimum time, to make adjustments in the semi-major axis, eccentricity and inclination of a spacecraft traveling around the Earth. For those maneuvers, low thrust propulsion is used under optimal and sub-optimal assumptions, to verify the main differences in terms of transfer time. In addition, solar sail dynamics is used. The spacecraft is assumed to have a propulsion with a fixed magnitude and that the control is based on choosing the direction of the propulsion. It is found that optimal control gives the minimum transfer time, while sub-optimal control restricted the control to follow a predescribed function, which is assumed to be a constant or linear function in time. Finally, solar sails present themselves as an option where fuel is a critical factor, given their much longer maneuver duration, but with a zero fuel consumption. The numerical-analytical modeling of optimization methods developed in this study can break any type of symmetry in the solutions. In turn, they can increase their energetic efficiency. The present research compares those results in detail, in particular looking at the transfer time in all cases studied.

Refined MagSail thrust model for preliminary mission design and trajectory optimization

A magnetic sail is an advanced propellantless propulsion system concept for deep space missions, proposed by Dana Andrews and Robert Zubrin about 30 years ago. The thrust is generated by the electromagnetic interaction between the solar wind charged particles and an artificial magnetic field obtained through a large current-carrying coil made of superconducting material. This paper discusses an up-to-date single-loop magnetic sail thrust model based on the numerical and experimental results obtained in the last decade. In particular, a particle model is initially used to evaluate the performance of a reference configuration in terms of thrust components in a body reference frame. Then, some scaling relationships are used to estimate the magnetic sail performance as a function of the design parameters. The proposed thrust model is used to analyze the minimum-time transfer problem between two circular and coplanar heliocentric orbits. Minimum flight times necessary to complete ephemeris-free Earth-Venus and Earth-Mars transfers are calculated as a function of the magnetic sail characteristic size in a parametric way.

GTOC 11: Results found at Beijing Institute of Technology and China Academy of Space Technology

This paper presents the crucial method for the results found at Beijing Institute of Technology and China Academy of Space Technology in the 11th Global Trajectory Optimization Competition (GTOC-11). To build 12 solar-power stations placed in the “Dyson Ring” orbit around the Sun, GTOC-11 focuses on the flyby trajectory design, low-thrust trajectory optimization, and target assignment problem. The mission with time and state constraints causes many difficulties in the design and optimization, which is performed in the following four steps. The first step is to design the orbital elements of the “Dyson Ring” by the grid search method. An approximate model is utilized to evaluate the minimum transfer time for each candidate at first, and the accurate solutions are obtained by the indirect method. The second step involves the Mother Ship trajectories design. A large quantity of earth-to-asteroid and asteroid-to-asteroid subsequences are generated by parallel beam search. The complete trajectories of Mother Ship are designed by connecting the subsequences using beam search. The third step involves the station assignment problem, which is required to design the asteroid transfer device activation epoch and the target station assignment. Based on the results above, the last step involves the rendezvous trajectories optimization to obtain the accurate thrust direction profile. Finally, the submitted and post-competition results are reported.

Quantum transfer through small networks coupled to phonons: Effects of topology versus phonons.

Particle or energy transfer through quantum networks is determined by network topology and couplings to environments. This study examines the combined effect of topology and external couplings on the efficiency of directional quantum transfer through quantum networks. We consider a microscopic model of qubit networks coupled to external vibrations by Holstein and Peierls couplings. By treating the positions of the network sites and the site-dependent phonon frequencies as independent variables, we determine the Hamiltonian parameters corresponding to minimum transfer time by Bayesian optimization. The results show that Holstein couplings may accelerate transfer through suboptimal network configurations but cannot accelerate quantum dynamics beyond the limit of the transfer time in an optimal phonon-free configuration. By contrast, Peierls couplings distort the optimal networks to accelerate quantum transfer through configurations with less than six sites. However, the speed-up offered by Peierls couplings decreases with the network size and disappears for networks with more than seven sites. For networks with seven sites or more, Peierls couplings distort the optimal network configurations and change the mechanism of quantum transfer but do not affect the lower limit of the transfer time. The machine-learning approach demonstrated here can be applied to determine quantum speed limits in other applications.

Exploiting manifolds of [formula omitted] halo orbits for end-to-end Earth–Moon low-thrust trajectory design

In this work, end-to-end low-thrust transfers from a GTO orbit to a low-altitude lunar orbit by exploiting the manifolds of a chosen Earth–Moon L1 halo orbit has been studied. The practicality of piece-wise, minimum-time transfers that exploit halo orbit manifolds is demonstrated, which offers more flexibility to meet mission objectives. It is known that the structure of the manifolds varies substantially due to the presence of the Sun and its contribution has to be considered to obtain more realistic trajectories. To incorporate Sun’s perturbation, we study (1) manifolds’ behavior within a Bi-Circular Problem (BCP) dynamics and (2) Sun’s impact on the previously converged trajectories obtained using the standard Circular Restricted Three-Body Problem (CR3BP). Comparisons of the resulting trajectories using the CR3BP and BCP are presented.

Characterizing Minimum-Time Solar Sail Geostationary Orbit Transfers Using Pseudospectral Optimal Control

This work examines the problem of planet-centered orbit transfers using solar sail propulsion. Though solar sails offer unlimited , they place coupled time-dependent restrictions on thrust magnitude and direction, and the multiple objectives of an orbit transfer can make locally optimal approaches inefficient; it is therefore advantageous to use optimal control to design such trajectories. This paper presents orbit-averaged equinoctial-element equations of motion for a solar sail under a discretized and interpolated control law. These equations are used to study transfer from a geostationary transfer orbit to geostationary orbit; a locally optimal control law is used to generate initial trajectories, and Gaussian pseudospectral optimal control is applied to yield minimum-time transfers. In the default case, with sail area–mass ratio of , optimization reduces the transfer time from 1222 to 293 days. Finally, sail area per mass, sail reflectivity, and initial sun–Earth orientation are varied to explore their effects, and to provide general design guidelines for planet-centered solar sail transfers. Distinct performance regimes are observed for transfers taking longer or shorter than one year, and for reflectivities greater or less than 0.4. Additionally, initial solar position was found to drastically affect the behavior of transfers in the fast regime.

Multi-fidelity and multi-objective optimization of low-thrust transfers with control strategy for all-electric geostationary satellites

To reduce the transfer time and radiation damage of all-electric geostationary satellites, this article develops a metamodel based multi-objective optimization scheme for low-thrust geostationary Earth orbit transfers. A multi-stage control strategy is employed to convert the optimal Earth orbital transfer problem into a parameterized multi-objective optimization problem with minimum total transfer time and proton displacement dose objectives. Based on the notion of multi-model fusion, the multi-fidelity system dynamics and radiation damage models are established to reduce the optimization cost. Furthermore, a novel adaptive Co-Kriging based multi-objective optimization method is proposed to effectively solve the multi-objective optimization problem with multi-fidelity models. In this approach, Co-Kriging metamodels are constructed using the multi-fidelity data to approximate the time-consuming low-thrust transfer models for optimization. And the Co-Kriging metamodels are adaptively refined by the infill samples to explore the Pareto frontier efficiently. Finally, a real-world all-electric geostationary satellite transfer example is investigated. The results show that a number of non-dominated low-thrust trajectories are successfully obtained with limited computational budget. Moreover, the total transfer time and displacement damage dose are significantly reduced after optimization, which illustrates the effectiveness of the metamodel based multi-objective low-thrust transfer optimization scheme.

Research on Bus and Metro Transfer From Perspective of Hypernetwork—A Case Study of Xi’an, China (December 2020)

Aiming at the blank of hypernetwork in the empirical research field of the composite transportation network, taking Xi’an city as an example, this paper uses the “HyperEdge” to connect the bus network with the metro network and constructs a large-scale complex hypernetwork, hereinafter referred to as B-M hypernetwork. In this paper, the topological characteristics of a single hypernetwork are analogized to a complex hypernetwork, and the interaction mechanism among bus networks, metro networks, and B-M hypernetwork is studied. A multi-source least transferred algorithm based on the incidence matrix is proposed to solve any two nodes’ minimum transfer times in a large complex hypernetwork. The multi-source least transferred algorithm and matrix transfer algorithm is applied to the B-M hypernetwork, and the random attack and intentional attack analyze the robustness of the B-M hypernetwork. The results show that the improved multi-source minimum transmission algorithm based on the incidence matrix is feasible and effective and can obtain superior computing power for large and complex hypernetworks.

Road map to L4/L5 with a solar sail

This paper explores the capability of solar sails to transfer a probe from the displaced Sun-Earth L1 and L2 libration points to the region of practical stability (RPS) around the triangular equilibrium points L4 and L5. If the sailcraft arrives inside the RPS with zero synodical velocity, it will remain there with minor station keeping requirements. Moreover, the location of the RPS is ideal for space weather missions as the Sun can be observed from a different angle compared to spacecraft orbiting the L1 point. The unstable manifolds of the displaced L1 and L2 points come close to these regions providing opportunities for natural transfer trajectories. By varying the solar sail orientation along the manifold, the dynamics can be altered and simple transfer trajectories that reach the RPS with few sail maneuvers are enabled. However, these trajectories are not optimal from a transfer time perspective, but can serve as suitable initial guesses for a direct optimization method to find minimum-time transfers between the displaced L1 and L2 points and the RPS at L4 and L5.

Organizational and legal characteristics of the main Orthodox religious organizations in Ukraine and the specifics of their economic activity

For the most rational functioning, any religious organization should have the following organizational and legal structure, which will allow: to make changes, if necessary, adequately to the conditions of the activity of this public entity; to carry out the minimum time transfer of capital from one activity to another on the basis of assessing their effectiveness; provide the fastest possible transmission of accurate and reliable information at the levels of management from top to bottom and back for rapid decision-making to improve the effectiveness of a particular direction and the organization as a whole within the framework of existing legislation for such organizations.Today in Ukraine there are two organizational and legal types of RO: hierarchical and rhizome. The hierarchical type are those organisational structure which have a clear hierarchy and a hierarchy of statuses (to him we belong, the Orthodox RO). Such structures are a giant Corporation, uniting under a single name tens of thousands of independent or semi-independent economic agents, and “feeding” form the basis of the administrative management system of these RO (the lowest link in the organizational structure allocates funds to the highest, requests permission for certain types of economic activities, etc.). The sources of income at the various organizational levels of such structures differ not only in scope but also in scale. The current scale of economic activity of structures of this organizational and legal type, estimated by observers in the hundreds of millions of dollars, its scope and relative stability now allow us to talk about the formation of a special sector of the post-Soviet economy – the Church, which develops in accordance with its inherent logic. In this regard, it is necessary to further develop the legislative support for the economic activities of the RO not only in our country, but also in the entire post-Soviet space.

Development of General-Purpose Root-Finding Module for General Mission Analysis Tool

A general-purpose root-finding module for designing spacecraft trajectories is developed to have similar accuracy to that of other well-known root-finding modules, and greater speed. Three quasi-Newton root-finding algorithms are implemented: the Newton–Raphson method, the Broyden’s method and the Generalized Broyden’s method. Based on the proposed root-finding module, General Mission Analysis Tool (GMAT) of National Aeronautics and Space Administration’s Goddard Space Flight Center (NASA/GSFC) is functionally extended by integrating the Broyden’s method and the Generalized Broyden’s method into its differential corrector module. Non-trivial spacecraft trajectory design problems, such as Lambert’s problem for trans-lunar trajectory and minimum-time transfer problem to the Mars are solved to analyze the performance of the proposed module. The numerical performances of each root-finding algorithm are quantitatively analyzed by the total number of function evaluations, the total number of iterations, convergence error, mean convergence rate, and running time. The overall comparative analysis shows that the Broyden’s method and the Generalized Broyden’s method are about 20–40% faster than the Newton–Raphson method and solutions from each algorithm have similar numerical accuracy. We also show that for selected test problems, the Generalized Broyden’s method converges in less running time than others with similar numerical accuracy in GMAT. The updated differential corrector module was released in R2014a version of GMAT.

Methodology for calculation of minimum transfer time in the transport hub

The most important element in railway passenger transport is a customer – traveller, who requires the transport from one place to another. A basic precondition for accomplishing the main requirement – transport, is making the complete offer which provides not only transport, but also other associated services. Practically, there are many associated criteria of transport, for example safety, duration, price, reliability, comfort and complementary services. Passenger transport is generally considered as an activity, which arises as the consequence of spatial division of places, where people are in exact time and their need to move. Motivators for moving could be commuting – job or education, dealing with personal or working matters, travelling for vacation – hiking, sport, health, cultural and social facilities, visiting relatives and friends. Requirements for transport of passengers originate in the need to move, while the passenger transport is dependent on the willingness of travelling. In passenger transport, there are mostly individual passengers, so it is difficult to determine all transport requirements. The paper is focused on one of the key factors of passenger transportation - connectivity of trains. Connectivity of passenger trains and other means of transport can be distinguished also from temporal and spatial point of view. Temporal connectivity is such sequence of arrivals and departures of different passenger trains and other means of transport, which allows changing the different passenger vehicles easily in regard to necessary time. Spatial connectivity means the distance between two passenger vehicles, among which the passenger is moving. In the paper, there is described the general methodology for calculation of minimum transfer time in the railway station. Railway passenger station is some kind of transport hub – a starting and finishing point for flows of passengers. Passengers have the opportunity to change the train type from long-haul train to regional train or contrariwise or simply enter or leave the system of railway transport. In the methodology, all necessary aspects are taken into account.

Statistical analysis of passenger-crowding in bus transport network of Harbin

Passenger flow data is indispensable but rare in the study of public transport networks. In this study, we focus on the passenger-crowding characteristics of the bus transport network of Harbin (BTN-H) based on passenger flow investigation. The three frequency histograms for all the uplinks and downlinks in Harbin are presented, including passengers on the bus at each section, crowding coefficients, and position parameters of crowded sections. The differences in crowding position are analyzed on each route. The distributions of degree and crowding degree (in directed space L) follow an exponential law. The new finding indicates that there are many stations with few crowded sections and a few stations with many crowded sections. The distributions of path length and crowded length (in directed space P) are presented based on the minimum transfer times, and it is found that they can be fitted by a composite Gaussian function and a Gaussian function, respectively. The stations and paths can be divided into three crowd levels. We conclude that BTN-H is crowded from a network-based perspective.

A star-photon sailcraft mission in the Alpha Centauri system

The recent findings of exoplanets have renewed interest in exploration missions of extra-solar star systems. In this context the binary star system of Alpha Centauri A/B plays a scientifically important role. The current paper aims at investigating the capture and the transfer trajectories from A to B performed by a stellar-photon sailcraft, which gives the best performance in long duration missions. The mission has been divided into four phases and minimum transfer time trajectories have been obtained by using a direct optimisation approach. Finally, a preliminary analysis in terms of Zero Velocity Curves has been carried out.