Astrodynamics最新文献

The 2:1 resonant distant retrograde orbit (DRO), known for its long-term stability and global accessibility, holds strategic significance in current Earth-Moon space mission explorations. This paper conducts a comprehensive analysis of the problem of low-energy transferring into 2:1 DRO using the weak stability boundary (WSB) and lunar gravity assist (LGA) in the planar bi-circular restricted four-body problem (BCR4BP). The transfer process is categorized into three phases: the Earth-Moon transfer, Sun-Earth weak stability boundary transfer, and DRO low-energy capture. Addressing key questions, our study investigates: (1) Under what LGA conditions can the spacecraft reach the approximate area where the WSB region is situated? (2) How do trajectories, upon reaching the region where the WSB is located, return to the vicinity of 2:1 DRO, potentially facilitating low-energy DRO insertion? Our study involved a comprehensive analysis of the spacecraft’s changes in Earth-Moon mechanical energy and Jacobi energy during the entire transfer process. This analysis yielded the energy and geometric conditions necessary for potential low-energy DRO insertion, effectively filtering out numerous impractical candidate trajectories and enhancing computational effciency. In this paper, the geometric condition is referred to as the low-energy transfer gateway (LETG). Using the LEGT as the stitching interface, a significant number of feasible solutions were obtained effectively for bi-impulse DRO transfer trajectories through differential correction, some of which were previously undiscovered.

This study employed a quantum-annealing framework to solve spacecraft trajectory optimization problems. Quantum annealing belongs to the field of quantum computing and is a promising technique for tackling hard binary optimization problems by employing quantum annealers. To address the optimal control of a trajectory using quantum annealing, a transcription procedure was introduced to express the problem in the binary optimization form required. The proposed procedure leverages the pseudospectral method to discretize the trajectory and represents the dynamical constraints as algebraic equality constraints at specific nodes. Subsequently, both a linearization procedure and binary representation strategy for the real-valued variables of the problem were presented, leading to the quadratic binary unconstrained optimization form. The quantum-annealing-based method was tested in the context of an interplanetary low-thrust transfer from the Earth to Mars. First, we discussed which instances of the problem, especially in terms of their dimensions, are implementable on currently available quantum annealers; then, a solution was sought by employing annealers from D-Wave systems. Solutions from hybrid solvers that combine classical and quantum resources, and fully quantum solvers were explored. The results demonstrate the validity of the transcription approach, demonstrate the ability of the hybrid solver to tackle the case-study problem, and highlight the promising features and current limitations of practical trajectory optimization with quantum annealing.

The desire to fly small spacecraft close together has been a topic of increasing interest over the past several years. This paper presents the development and analysis of a model predictive control based framework that is used with the D’Amico relative orbital elements (ROEs) to maintain the desired trajectories of a cluster of spacecraft while also allowing freedom to maneuver within some allowable bounds. Switching surfaces based on the ROE constraints contain the full state of the system, allowing for fuel reduction over other approaches that use the Hill—Clohessy—Wiltshire equations. The formation and boundary constraints are designed such that no two agents have overlapping regions, allowing the vehicles to maintain safety of fl ight without continually maintaining the trajectories of other agents. This framework allows for a scalable method that can support clusters of satellites to safely achieve mission objectives while minimizing fuel usage. This paper provides simulated results of the framework for a three spacecraft formation that demonstrates a 67% fuel reduction when compared to previous approaches.

The accuracy of angles-only initial orbit determination (IOD) is significantly compromised when only a short-arc orbit is observed. The ill-conditioned problem in matrices due to weak geometric constraints caused by short arcs and observation errors typically causes significant errors in the estimated ranges and thus unsatisfactory IOD. This paper presents a critical analysis of the ill-conditioned problem using the Gooding algorithm and proposes several techniques to improve it. On the basis of multiple observations, a least-squares method is proposed to solve the ranges at the first and last epochs. For the short-arc case, the ridge estimation technique is applied to mitigate the ill-conditioned problem. To determine whether an orbit is eccentric, a procedure to assess orbit eccentricity is developed via the range-search method, which aims to provide reasonably accurate initial ranges to the Gooding algorithm. Finally, an eccentricity-constraint technique for the Gooding algorithm is proposed for cases where the orbit is determined to be nearly circular. The performances of these techniques on space-based simulation data are assessed, and an improved Gooding algorithm (I-Gooding) suitable for various observation conditions is proposed. The I-Gooding algorithm is subsequently applied to process actual ground-based observations. The results show that its accuracy in estimating the semimajor axis is 47% higher than that afforded by the standard Gooding algorithm.

The removal of large space debris from a geostationary orbit to a disposal orbit via an ion beam shepherd spacecraft was considered in this study, with attention given to the electrostatic effect. The generation of an ion force, which provides contactless thrust, occurs because of the transfer of momentum from the ions of the engine plume of the spacecraft to the space debris. This process is accompanied by the transfer of a positive charge to the space debris. As a result, electrostatic interactions occur between the spacecraft and space debris. The goals of this study were to assess the influence of this effect on the dynamics of space debris during contactless ion beam-assisted removal and to develop hybrid contactless transportation schemes based on the use of an ion beam and electrostatic interactions. A mathematical model describing the motion of space debris and spacecraft under the influence of ionic and electrostatic forces and torques was developed. The concepts of electrostatic ion beam shepherd, electrostatic tractor with ion beam, and charged ion beam shepherd were proposed and compared. The results of numerical simulations revealed that the electrostatic ion beam shepherd scheme is preferable from the perspective of minimizing fuel costs when solving the problem of removing space debris from a geostationary orbit. A control law for the spacecraft charge needed for space-debris detumbling during ion-beam transportation is proposed. A numerical simulation of space debris removal was performed via a hybrid scheme.

This paper presents the solutions and results of the 12th edition of the Global Trajectory Optimization Competition (GTOC12) of the National University of Defense and Technology. To address the complex interstellar mining problem proposed by GTOC12, our solution is divided into two stages. The first stage focuses on preliminary work, including the target selection, the establishment of departure and return databases, and the development of methods to estimate transfer costs, with the aim of enhancing planning efficiency during the global planning phase. The second stage involves trajectory optimization for multiple mining ships, including single-mining-ship trajectory optimization and a multiship iterative process. For single-mining-ship trajectory optimization, the method involves three steps: first, employ a heuristic method for planning the first rendezvous sequences; second, utilize an ant colony optimization (ACO) algorithm for planning the second rendezvous sequences; and third, apply a differential evolution (DE) algorithm alongside an indirect method to refine rendezvous times and low-thrust trajectories. Through the implementation of a multiship iterative strategy, the team accomplished trajectory optimization for multiple mining ships that met the constraints. The final score submitted by the team was 15,160.946, which achieved the sixth place in the competition.

In 2023, the 12th edition of Global Trajectory Competition was organized around the problem referred to as “Sustainable Asteroid Mining”. This paper reports the developments that led to the solution proposed by ESA’s Advanced Concepts Team. Beyond the fact that the proposed approach failed to rank higher than fourth in the final competition leader-board, several innovative fundamental methodologies were developed which have a broader application. In particular, new methods based on machine learning as well as on manipulating the fundamental laws of astrodynamics were developed and able to fill with remarkable accuracy the gap between full low-thrust trajectories and their representation as impulsive Lambert transfers. A novel technique was devised to formulate the challenge of optimal subset selection from a repository of pre-existing optimal mining trajectories as an integer linear programming problem. Finally, the fundamental problem of searching for single optimal mining trajectories (mining and collecting all resources), albeit ignoring the possibility of having intra-ship collaboration and thus sub-optimal in the case of the GTOC12 problem, was efficiently solved by means of a novel search based on a look-ahead score and thus making sure to select asteroids that had chances to be re-visited later on.

We present the solution approach developed by the team “TheAntipodes” during the 12th edition of the Global Trajectory Optimization Competition (GTOC12). An overview of the approach is as follows: (1) generate asteroid subsets, (2) chain building with beam search, (3) convex low-thrust trajectory optimization, (4) manual refinement of rendezvous times, and (5) optimal solution set selection. The generation of asteroid subsets involves a heuristic process to find sets of asteroids that are likely to permit high-scoring asteroid chains. Asteroid sequences “chains” are built within each subset through a beam search based on Lambert transfers. Low-thrust trajectory optimization involves the use of sequential convex programming (SCP), where a specialized formulation finds the mass-optimal control for each ship’s trajectory within seconds. Once a feasible trajectory has been found, the rendezvous times are manually refined with the aid of the control profile from the optimal solution. Each ship’s individual solution is then placed into a pool where the feasible set that maximizes the final score is extracted using a genetic algorithm. Our final submitted solution placed fifth with a score of 15,489.

The 12th Global Trajectory Optimization Competition challenged teams to design trajectories for mining asteroids and transporting extracted resources back to the Earth. This paper outlines the methods and results of the runner-up team, BIT-CAS-DFH, highlighting an overall analysis of the approach as well as detailed descriptions of the methods used. The approach begins with building databases to reduce computational costs in trajectory design. Then, asteroid sequences are determined. A segmentation-based approach was adopted to efficiently handle the large dataset. Each sequence was divided into four time-based segments. Segments 1 and 4 were generated forward and backward, respectively, using a breadth-first beam search. Candidates for these segments were refined using genetic and greedy algorithms. Segments 2 and 3 were then generated and selected forward and backward based on the results of Segments 1 and 4. Following this, a matching process paired candidates from Segments 2 and 3. With the asteroid sequences established, low-thrust trajectories were optimized using indirect methods. A local optimization strategy was employed to maximize the collected mass by fine-tuning rendezvous timings. The final solution is presented, with comparative analyses against other teams’ approaches.