This paper investigates the global optimization of multispacecraft successive rendezvous trajectories, which is divided here into three subproblems: target assignment, sequence optimization, and rendezvous time optimization. A method consisting of two novel algorithms is proposed to solve these subproblems. First, a multitree search framework is developed to assign multiple targets to each spacecraft and simultaneously optimize the rendezvous sequence for every single spacecraft. Specifically, a novel algorithm of local search combined with beam search is proposed. Second, this paper converts the rendezvous time optimization problem into a multistage decision problem. Based on a critical rendezvous-epoch-dependent characteristic found in this subproblem, the number of state variables is thereby reduced. A novel dual dynamic programming algorithm is proposed and combined with dynamic programming to solve for the globally optimal rendezvous epochs efficiently. Global optimality is guaranteed by Bellman’s principle of optimality, which is the first time in such a problem to our knowledge. The proposed method achieves state-of-the-art performance in several typical fuel-optimal scenarios of active debris removal. This open-sourced method is non-database-dependent and contains only one design stage, which is expected to be adopted in other successive rendezvous missions.

Space-based gravitational wave (GW) detection at low frequencies is of great scientific significance and has received extensive attention in recent years. This work designs and optimizes the low-energy transfer of the heliocentric formation of GW detectors, which starts from a geosynchronous transfer orbit and targets an Earth-like orbit. Based on the example of the Laser Interferometer Space Antenna (LISA), the transfer is first designed in two-body dynamical models and then refined in simplified high-fidelity dynamical models that only consider the major orbital perturbations evaluated here. The main contributions of this work are to present an adaptive model continuation technique and to exploit the lunar swingby technique to reduce the problem-solving difficulty and velocity increment of orbital transfer, respectively. The adaptive model continuation technique fully reveals the effect of perturbations and rapidly iterates the solutions to the simplified models. The simulation results show that the lunar swingby does reduce the energy needed to escape the Earth’s sphere of influence. It is found that the gravitation of the Earth–Moon system has a significant contribution to reducing the velocity increment. The solution of low-energy transfer in the simplified models is that the duration is 360.6615 days and the total velocity increment is 0.8468 km/s.

Compared with launching new satellites, it is an economic scheme to use on-orbit satellites to maneuver to meet users' particular needs for Earth observation. This article studies the mission design method of on-orbit satellite maneuver for observing large-scale ground targets within a given duration. This article divides the original large-scale sequence optimization problem into two small-scale subproblems that are easy to optimize: short-sequence trajectory generation and multitrajectory combination optimization. The multitrajectory combination framework, including database generation, multitrajectory combination selection, trajectory patching, and trajectory keeping, is adopted to optimize the observation sequence and design the satellite's trajectory. In two specific scenarios, the fuel-optimal scenario and accurate revisit observation scenario, the proposed framework shows competitive optimization performance compared with the existing tree search algorithms. In addition, this article provides a known optimal result for the 11th China Trajectory Optimization Competition problem.

In this paper, the methods and results from Tsinghua University and Shanghai Institute of Satellite Engineering for the 11th Global Trajectory Optimization Competition (GTOC11) are presented. To deal with the complicated “Dyson Sphere” building problem, a three-stage procedure is conducted. First, the pre-analysis is performed to reduce search space. It is found that two-impulse maneuvers between asteroid flybys are near-optimal, the semi-major axis of the “Dyson Ring” should be better at 1.0–1.5 AU, and the larger arrival mass asteroids tend to be selected. Second, the globally optimal trajectory design problem is further divided into two sub-problems, the mothership trajectory design and the asteroid assignment to the “Dyson Ring” power stations. For the first problem, beam search is used to obtain numerous single mothership trajectories based on a pre-constructed flyby trajectory database of 3–8 asteroids. The overall trajectories and asteroids visited are obtained by selecting 10 mothership trajectories with a genetic algorithm. For the second problem, we build a database of optimal rendezvous times for all the 83,453 asteroids at different phase angles to reach power stations of different radii and phase angles, then a greedy algorithm is proposed to obtain the asteroid arrival schedule based on all the asteroids visited by motherships. Finally, local optimization of asteroid sequence and flyby epochs is conducted. The activation time adjustment in combination with indirect continuous-thrust trajectory optimization is used based on the global optimization result. In the final submission, motherships fly by 388 asteroids, and the minimum mass of twelve power stations reaches 94% of the theoretical upper bound, which is defined using the minimum-time orbital transfers with free initial and target phases.

Computing the visibility of remote sensing satellites on an area target is an important basic satellite observation mission. The calculational accuracy and efficiency are then very important for satellite imaging scheduling. This paper presents a fast, semi-analytical algorithm for predicting satellite-area target visibility. First, geometric relations are used to define the boundaries of all the area targets described by ordinary arcs with the algorithm then determining the intersections. Then, the cone characteristics and the rectangular field of view of the satellite are used with a fast judgement condition for the visibility. The visibility at each discrete time step is determined analytically with a binary search which is then used to quickly predict the time for the visible window. Numerical examples show that this method is accurate and efficient. The relative error in the visibility duration is 0.1% relative to the predictions of the commercial software STK while the calculational speed is 105 times faster than the brute force method and almost 1 000 times faster than the average speed of the existing fast calculation algorithms.

Rapid and responsive Earth observation satellites enable the evaluation of disaster risk, improve relief effectiveness, and reduce suffering and fatalities in the event of sudden disaster events. One promising method for responsive space satellites is orbital maneuvering. This article describes a multitree search framework for multisatellite responsiveness scheduling considering orbital maneuvering, where multiple ground targets are cooperatively observed by multiple observation satellites over a short period of time. Based on the traditional tree search, the proposed method constructs multiple trees and distributes all the targets to multiple satellites, allowing the observation sequence of a single satellite to be optimized. To apply the tree search algorithm, a tree node collection (TNC) composed of the corresponding nodes in multiple trees is used to represent the state of each satellite. Before the expansion phase, one specific node in the TNC is determined for later expansion. A beam search is then used to optimize the observation sequence. Ground-track adjustment techniques using impulse maneuver are considered for visiting a given target. The proposed framework is more effective than other algorithms and achieves a better performance than the previous best method in a typical multisatellite responsiveness scheduling scenario.

No AccessEngineering NotesTwo-Stage Dynamic-Assignment Optimization Method for Multispacecraft Debris RemovalNan Zhang, Shiyu Chen, Zhong Zhang and Hexi BaoyinNan Zhang https://orcid.org/0000-0002-9782-9282Tsinghua University, 100084 Beijing, People's Republic of China, Shiyu ChenBeijing Institute of Spacecraft System Engineering, 100094 Beijing, People's Republic of China, Zhong Zhang https://orcid.org/0000-0003-0728-3202Tsinghua University, 100084 Beijing, People's Republic of China and Hexi BaoyinTsinghua University, 100084 Beijing, People's Republic of ChinaPublished Online:9 Jun 2022https://doi.org/10.2514/1.G006602SectionsRead Now ToolsAdd to favoritesDownload citationTrack citations ShareShare onFacebookTwitterLinked InRedditEmail About References [1] Kessler D. J. and Cour-Palais B. 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H., "Functional Stability Analysis of Numerical Algorithms," Ph.D. Thesis, Dept. of Computer Sciences, Univ. of Texas, Austin, 1990. Google Scholar Previous article Next article FiguresReferencesRelatedDetails What's Popular Volume 45, Number 9September 2022 CrossmarkInformationCopyright © 2022 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. All requests for copying and permission to reprint should be submitted to CCC at www.copyright.com; employ the eISSN 1533-3884 to initiate your request. See also AIAA Rights and Permissions www.aiaa.org/randp. TopicsAerospace EngineeringAerospace SciencesAsteroidsAstrodynamicsAstronauticsPlanetary Science and ExplorationPlanetsSpace DebrisSpace MissionsSpace OrbitSpace Science and Technology KeywordsAerospace EngineeringNonlinear ProgrammingPropellantAnt Colony Optimization AlgorithmsSpacecraft MissionElectrodynamic TetherTrajectory OptimizationSpacecraft LaunchingGenetic AlgorithmSpace DebrisAcknowledgmentThis research was supported by the National Natural Science Foundation of China (U21B2050).PDF Received30 November 2021Accepted11 May 2022Published online9 June 2022

With the increase of space debris, space debris removal has gradually become a major issue to address by worldwide space agencies. Multiple debris removal missions, in which multiple debris objects are removed in a single mission, are an economical approach to purify the space environment. Such missions can be considered typical time-dependent traveling salesman problems (TDTSPs). In this study, an intelligent global optimization algorithm called Timeline Club Optimization (TCO) is proposed to solve multiple debris removal missions of the TDTSP model. TCO adopts the traditional ant colony optimization (ACO) framework and replaces the pheromone matrix of the ACO with a new structure called the Timeline Club. The Timeline Club records which debris object to be removed next at a certain moment from elitist solutions and decides the probability criterion to generate debris sequences in new solutions. Two hypothetical scenarios, the Iridium-33 mission and the GTOC9 mission, are considered in this study. Simulation results show that TCO offers better performance than those of beam search, ant colony optimization, and the genetic algorithm in multiple debris removal missions of the TDTSP model.