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The National University of Defense Technology and the Xi'an Satellite Control Center organized the 11th edition of the Global Trajectory Optimization Competition (GTOC11) in 2021. The GTOC11 problem was created as a link between the ninth and tenth editions of the Global Trajectory Optimization Competition to bridge the gap between the planetary and galactic civilizations by introducing an intermediate stellar civilization scenario. The problem involves the construction of a Dyson sphere, a theoretical mega-structure that encircles a star with platforms orbiting in a tight formation to capture the maximum energy from it. Challenges in astrodynamics including the construction-orbit selection, combinatorial flyby of multiple asteroids, and mass distribution among stations were considered in the Dyson sphere design. A total of 94 teams registered for the competition, of which 25 teams provided solutions and passed automatic verification on the website. In this article, we describe the selection of the problem and its design process. In addition, an overview of the entire competition and an analysis of its results are presented. • NUDT and XSCC organized the 11th edition of the GTOC. • The problem of the GTOC-11 was designed to build a preliminary "Dyson Sphere". • A total of 94 teams registered this competition, and 25 of them returned solutions. [ABSTRACT FROM AUTHOR]

An indirect optimization procedure is presented to minimize the propellant consumption for finite-burn transfers with two practical thrust control models, namely, inertially fixed thrust and fixed-plane linearly varying thrust direction. The optimality equations are derived with theory of optimal control and the consequent boundary value problem is solved with a procedure based on Newton's method. A homotopic approach is used to find suitable tentative solutions and assure convergence. The method is applied to the optimization of Moon escape trajectories with accurate dynamic models and proves to be fast and accurate. • Indirect optimization with inertially fixed or rotating thrust. • Techniques to assure convergence are developed. • Moon return trajectories are computed with complex dynamics. • High speed and efficient optimization. [ABSTRACT FROM AUTHOR]

Abstract The ninth edition of the China Trajectory Optimization Competition (CTOC9) considered the problem of navigation augmentation over a set of Chinese cities, wherein the competitors were expected to design a suitable LEO constellation to obtain the required navigation performance with the aim of minimizing overall system cost. In addition, an economical deployment strategy was also considered. The synthesis methods used by the Xi'an Satellite Control Center (XSCC) are described, along with the promising solution found by the team. Firstly, two techniques, feasible region based reduction and coverage region based reduction, are applied in sequence to narrow the search space. Then, the optimal constellation configuration is obtained through an Differential Evolution Algorithm (DE). Finally, a series of maneuver strategies are searched to inject each navigation satellite from a given initial carrying orbit to its target location. The solution obtained during the competition ranked third, and the improved one, found after the deadline, got the outstanding prize. [ABSTRACT FROM AUTHOR]

We present a study of the transfer orbits connecting landing points of irregular-shaped asteroids. The landing points do not touch the surface of the asteroids and are chosen several meters above the surface. The ant colony optimization technique is used to calculate the multiple-hopping trajectories near an arbitrary irregular asteroid. This new method has three steps which are as follows: (1) the search of the maximal clique of candidate target landing points; (2) leg optimization connecting all landing point pairs; and (3) the hopping sequence optimization. In particular this method is applied to asteroids 433 Eros and 216 Kleopatra. We impose a critical constraint on the target landing points to allow for extensive exploration of the asteroid: the relative distance between all the arrived target positions should be larger than a minimum allowed value. Ant colony optimization is applied to find the set and sequence of targets, and the differential evolution algorithm is used to solve for the hopping orbits. The minimum-velocity increment tours of hopping trajectories connecting all the landing positions are obtained by ant colony optimization. The results from different size asteroids indicate that the cost of the minimum velocity-increment tour depends on the size of the asteroids. [ABSTRACT FROM AUTHOR]

The optimization problem of fuel-optimal trajectories from a low circular Moon orbit to a target hyperbolic excess velocity vector using finite-thrust propulsion is solved. The ability to obtain the most accurate satisfaction of necessary optimality conditions in a high-accuracy dynamic model is the main motivation of the current study. The solutions allow attaining anytime-return Earth-interface conditions from a low lunar orbit. Gravitational effects of the Sun, Earth, and Moon are included throughout the entire trajectory. Severe constraints on the fuel budget combined with high-accuracy demands on the endpoint conditions necessitate a high-fidelity solution to the trajectory optimization problem and JPL DE405 ephemeris model is used to determine the perturbing bodies' positions. The optimization problem is solved using an indirect method. The optimality of the solution is verified by an application of Pontryagin's maximum principle. More accurate and fuel-efficient trajectories are found for the same mission objectives and constraints published in other research, emphasizing the advantages of this technique. It is also shown that the thrust structure consists of three finite burns. In contrast to previous research, no singular arc is required in the optimal solutions, and all the controls appear bang-bang. [ABSTRACT FROM AUTHOR]

This paper addresses the scheduling problem arising from refueling multiple geosynchronous (GEO) satellites with multiple servicing vehicles [many-to-many (M2M) refueling]. The problem is defined by a set of potential fuel tanker locations, a homogeneous fleet of servicing vehicles with limited capacities, and a set of fuel-deficient GEO satellites with known fuel demands. The objective is to open a subset of fuel tankers, to assign GEO satellites to these tankers and to design vehicle servicing sequences, in order to minimize the total mission costs. To achieve such an economical refueling strategy, the fuel tanker location and routing decision are required to be determined simultaneously. It is shown that this problem can be formulated as a location-routing problem (LRP) which is obviously NP-hard. In order to solve it, an ant colony optimization (ACO) metaheuristic that features a special solution representation scheme is proposed. The proposed algorithm is then tested on two types of instances depending on whether the cost for opening a fuel tanker is considered or not. Numerical experiments show that both the consideration of the fuel tanker opening costs and their locations do affect the refueling schedule. Furthermore, the proposed algorithm outperforms the existing approaches in the M2M refueling mission design, and it is able to detect the optimal refueling strategy on all instances containing 85 GEO targets with 15 potential fuel tankers while previous works stopped at 15 satellites and 2 fuel tankers. • Scheduling of the multiple satellites refueling mission is presented. • Servicing vehicle routing and the fuel tanker location are considered simultaneously. • An ant colony optimization based solving methodology is proposed. • A special solution presentation scheme is applied to improve the computational burden. [ABSTRACT FROM AUTHOR]