目的回顾性分析股骨近端骨巨细胞瘤患者的手术方式,验证GTOC临床评分系统的有效性。方法2011年1月至2022年12月,共收集浙江大学医学院附属第二医院股骨近端骨巨细胞瘤患者45例,根据中国骨巨细胞瘤协作组成成员(Member of the Chinese As...目的回顾性分析股骨近端骨巨细胞瘤患者的手术方式,验证GTOC临床评分系统的有效性。方法2011年1月至2022年12月,共收集浙江大学医学院附属第二医院股骨近端骨巨细胞瘤患者45例,根据中国骨巨细胞瘤协作组成成员(Member of the Chinese Association for Giant Cell tumor of Bone,GTOC)临床评分系统进行评分,统计分析GTOC临床评分系统与手术方式、术后并发症、下肢功能的关系,采用MSTS93下肢功能评分系统评估患肢术后功能,分析影响股骨近端骨巨细胞瘤手术方式选择的因素,对扩大刮除术与大段切除术进行对比分析,从而验证GTOC临床评分系统的有效性。结果45例患者随访时间12~86个月,平均25.7个月。共出现13例并发症,总的发生率28.9%,复发2例,总复发率为4.4%。单因素及多因素Cox回归分析显示影响手术方式选择的因素是病理性骨折和病变部位(P<0.05)。统计资料分析显示,高分组与低分组的手术方式差异有统计学意义(χ^(2)=8.557,P<0.05),呈正相关关系(Pearson相关系数R=0.436,P=0.003)。对扩大刮除术与瘤段切除重建术进行对比分析,两种手术方式的术后MSTS功能评分、手术时间有明显差异(P<0.05)。结论GTOC临床评分系统涵盖了手术方式选择的主要影响因素,对于股骨近端骨巨细胞瘤患者在临床治疗手术方案的选择中具有指导价值。展开更多
Establishing a sustainable mining expedition for the asteroids of the main belt over the 2035–2050 horizon is the visionary problem of the 12th Global Trajectory Optimisation Competition. A fleet of mining ships must...Establishing a sustainable mining expedition for the asteroids of the main belt over the 2035–2050 horizon is the visionary problem of the 12th Global Trajectory Optimisation Competition. A fleet of mining ships must rendezvous twice with asteroids to deploy miners and collect minerals. In this paper, we describe the approach of the CS Group team, OptimiCS, to solve this challenging problem. We present the symmetrical construction of upstream and downstream semi-sequences of asteroids, maximizing the mining time expectancy via a beam search with tabu iterations, and the composition of these semi-sequences into complete fleet routes, maximizing the total collected mass via simulated annealing. While representative Earth–asteroid legs are precomputed, the delta-V costs of the asteroid-to-asteroid hops composing the sequences are initially approximated during exploration via a method that refines the accuracy of the maximum initial mass. The resulting high-fidelity trajectories are adjusted and optimized via a direct method and nonlinear programming.展开更多
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 su...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 tofind 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 formulationfinds 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 thefinal score is extracted using a genetic algorithm.Ourfinal submitted solution placedfifth with a score of 15,489.展开更多
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...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.展开更多
This paper presents the results and design methods of team Nanjing University of Aeronautics and Astronautics in the 12th edition of the Global Trajectory Optimization Competition. To address the problem of sustainabl...This paper presents the results and design methods of team Nanjing University of Aeronautics and Astronautics in the 12th edition of the Global Trajectory Optimization Competition. To address the problem of sustainable asteroid mining, we focus on the following: analyzing the constraints and asteroids involved;selecting a candidate set of asteroids for which mining missions can be performed easily;establishing an algorithmic flow using phasing indicators, multiobjective beam search, and a genetic algorithm to determine the sequence of asteroid visits for mining ships;and optimizing low-thrust trajectories via an indirect method and global optimization. In addition, a central-node method is proposed to simplify the design process and reduce the computational cost of performing repetitive asteroid-rendezvous missions. The methods developed in the competition enable the mining of 161 asteroids via 20 mining ships, with a total collected mass of 11,513 kg.展开更多
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 mi...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.展开更多
Asteroid mining is a potentially lucrative method for extracting resources from space. Water resources found on asteroids can serve as fuel supplies for spacecrafts in deep space, and some asteroids are rich in precio...Asteroid mining is a potentially lucrative method for extracting resources from space. Water resources found on asteroids can serve as fuel supplies for spacecrafts in deep space, and some asteroids are rich in precious metals, offering immense potential economic value. The 12th Global Trajectory Optimization Competition, held in 2023, introduced a challenge to trajectory design for sustainable asteroid mining. Participating teams were tasked with maximizing the mining quantity over a 15-yr period by utilizing as many mining ships as possible to depart from the Earth, deploy miners on multiple asteroids, recover minerals, and return to the Earth. Σ team devised a strategy in which one ship completes one sequence, enabling the collection of minerals from 203 asteroids using 26 mining ships. This paper outlines the design methodology and outcomes of this approach, encompassing a preliminary analysis of the problem, optimization for the Earth departure and return, flight sequence search, and low-thrust conversion and optimization. Through methods such as asteroid selection and clustering, database building for Earth–asteroid transfers, global search with an impulsive model, local optimization with a low-thrust model, and conversion of remaining fuel into mining time, the computational efficiency was significantly enhanced, fuel consumption per unit mineral collection was reduced, and mining quantity was improved. Finally, the design outcomes of this approach are presented. The proposed trajectory design method enables the completion of multiple asteroid rendezvouses in a short time, providing valuable insights for future missions involving a single spacecraft conducting multiple rendezvouses with multiple asteroids.展开更多
Tsinghua University and the Shanghai Institute of Satellite Engineering organized the 12th edition of the Global Trajectory Optimization Competition (GTOC12) on June 19, 2023. The problem for GTOC12, entitled “Sustai...Tsinghua University and the Shanghai Institute of Satellite Engineering organized the 12th edition of the Global Trajectory Optimization Competition (GTOC12) on June 19, 2023. The problem for GTOC12, entitled “Sustainable Asteroid Mining”, explores how spacecraft can be dispatched from the Earth to various asteroids for resource extraction. The primary challenge involves designing coupled trajectories for multiple spacecraft to maximize the collected mineral mass. A novel game model is introduced to encourage the mining of rarely mined asteroids. GTOC12 saw significant participation, with 102 teams registered. By the end of the competition, 28 teams provided feasible solutions, highlighting a growing interest in the field. This study describes the design process of the GTOC12 problem and presents a review and analysis of the results from the participating teams.展开更多
The 8th edition of the Global Trajectory Optimization Competition(GTOC8)presented a novel concept of a space-based very-long-baseline interferometry(VLBI)telescope in cislunar space for observing selected radio source...The 8th edition of the Global Trajectory Optimization Competition(GTOC8)presented a novel concept of a space-based very-long-baseline interferometry(VLBI)telescope in cislunar space for observing selected radio sources in cosmos.It requires designing a three-spacecraft triangular formation with changeable sizes and orientations such that observation can be scheduled as efficiently as possible.We first review the problem,and then describe the methods employed by representative teams participating in the competition.Subsequently,we present the design techniques employed by the team from the Chinese Academy of Sciences,which are primarily based on orbital-geometry analysis.Two efficient trajectory patterns are summarized:million-kilometer triangular formations with symmetric circular orbits,and consecutive-lunar-flyby trajectories with Moon-to-Moon transfer orbits.These two trajectory patterns enable establishing and reconfiguring the triangular formation with sufficiently different sizes so that a number of radio sources can be observed,thus maximizing the performance index.Finally,we present a solution with the best currently known score of J=158 million km.展开更多
This paper presents the crucial method for obtaining our team's results in the 8th Global Trajectory Optimization Competition(GTOC8).Because the positions and velocities of spacecraft cannot be completely determin...This paper presents the crucial method for obtaining our team's results in the 8th Global Trajectory Optimization Competition(GTOC8).Because the positions and velocities of spacecraft cannot be completely determined by one observation on one radio source,the branch and bound method for sequence optimization of multi-asteroid exploration cannot be directly applied here.To overcome this diculty,an optimization method for searching the observing sequence based on nominal low-thrust trajectories of the symmetric observing con guration is proposed.With the symmetric observing con guration,the normal vector of the triangle plane formed by the three spacecraft rotates in the ecliptic plane periodically and approximately points to the radio sources which are close to the ecliptic plane.All possible observing opportunities are selected and ranked according to the nominal trajectories designed by the symmetric observing con guration.First,the branch and bound method is employed to nd the optimal sequence of the radio source with thrice observations.Second,this method is also used to nd the optimal sequence of the left radio sources.The nominal trajectories are then corrected for accurate observations.The performance index of our result is 128,286,317.0 km which ranks the second place in GTOC8.展开更多
文摘目的回顾性分析股骨近端骨巨细胞瘤患者的手术方式,验证GTOC临床评分系统的有效性。方法2011年1月至2022年12月,共收集浙江大学医学院附属第二医院股骨近端骨巨细胞瘤患者45例,根据中国骨巨细胞瘤协作组成成员(Member of the Chinese Association for Giant Cell tumor of Bone,GTOC)临床评分系统进行评分,统计分析GTOC临床评分系统与手术方式、术后并发症、下肢功能的关系,采用MSTS93下肢功能评分系统评估患肢术后功能,分析影响股骨近端骨巨细胞瘤手术方式选择的因素,对扩大刮除术与大段切除术进行对比分析,从而验证GTOC临床评分系统的有效性。结果45例患者随访时间12~86个月,平均25.7个月。共出现13例并发症,总的发生率28.9%,复发2例,总复发率为4.4%。单因素及多因素Cox回归分析显示影响手术方式选择的因素是病理性骨折和病变部位(P<0.05)。统计资料分析显示,高分组与低分组的手术方式差异有统计学意义(χ^(2)=8.557,P<0.05),呈正相关关系(Pearson相关系数R=0.436,P=0.003)。对扩大刮除术与瘤段切除重建术进行对比分析,两种手术方式的术后MSTS功能评分、手术时间有明显差异(P<0.05)。结论GTOC临床评分系统涵盖了手术方式选择的主要影响因素,对于股骨近端骨巨细胞瘤患者在临床治疗手术方案的选择中具有指导价值。
文摘Establishing a sustainable mining expedition for the asteroids of the main belt over the 2035–2050 horizon is the visionary problem of the 12th Global Trajectory Optimisation Competition. A fleet of mining ships must rendezvous twice with asteroids to deploy miners and collect minerals. In this paper, we describe the approach of the CS Group team, OptimiCS, to solve this challenging problem. We present the symmetrical construction of upstream and downstream semi-sequences of asteroids, maximizing the mining time expectancy via a beam search with tabu iterations, and the composition of these semi-sequences into complete fleet routes, maximizing the total collected mass via simulated annealing. While representative Earth–asteroid legs are precomputed, the delta-V costs of the asteroid-to-asteroid hops composing the sequences are initially approximated during exploration via a method that refines the accuracy of the maximum initial mass. The resulting high-fidelity trajectories are adjusted and optimized via a direct method and nonlinear programming.
文摘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 tofind 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 formulationfinds 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 thefinal score is extracted using a genetic algorithm.Ourfinal submitted solution placedfifth with a score of 15,489.
文摘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.
基金supported by the National Natural Science Foundation of China(Nos.12372046 and 12102177)the Natural Science Foundation of Jiangsu Province(No.BK20220130).
文摘This paper presents the results and design methods of team Nanjing University of Aeronautics and Astronautics in the 12th edition of the Global Trajectory Optimization Competition. To address the problem of sustainable asteroid mining, we focus on the following: analyzing the constraints and asteroids involved;selecting a candidate set of asteroids for which mining missions can be performed easily;establishing an algorithmic flow using phasing indicators, multiobjective beam search, and a genetic algorithm to determine the sequence of asteroid visits for mining ships;and optimizing low-thrust trajectories via an indirect method and global optimization. In addition, a central-node method is proposed to simplify the design process and reduce the computational cost of performing repetitive asteroid-rendezvous missions. The methods developed in the competition enable the mining of 161 asteroids via 20 mining ships, with a total collected mass of 11,513 kg.
文摘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.
基金supported by the Space Debris and Near-Earth Asteroid Defense Research Project(KJSP2023020303)Youliang Wang is grateful to the Youth Innovation Promotion Association of the Chinese Academy of Sciences(2022146).
文摘Asteroid mining is a potentially lucrative method for extracting resources from space. Water resources found on asteroids can serve as fuel supplies for spacecrafts in deep space, and some asteroids are rich in precious metals, offering immense potential economic value. The 12th Global Trajectory Optimization Competition, held in 2023, introduced a challenge to trajectory design for sustainable asteroid mining. Participating teams were tasked with maximizing the mining quantity over a 15-yr period by utilizing as many mining ships as possible to depart from the Earth, deploy miners on multiple asteroids, recover minerals, and return to the Earth. Σ team devised a strategy in which one ship completes one sequence, enabling the collection of minerals from 203 asteroids using 26 mining ships. This paper outlines the design methodology and outcomes of this approach, encompassing a preliminary analysis of the problem, optimization for the Earth departure and return, flight sequence search, and low-thrust conversion and optimization. Through methods such as asteroid selection and clustering, database building for Earth–asteroid transfers, global search with an impulsive model, local optimization with a low-thrust model, and conversion of remaining fuel into mining time, the computational efficiency was significantly enhanced, fuel consumption per unit mineral collection was reduced, and mining quantity was improved. Finally, the design outcomes of this approach are presented. The proposed trajectory design method enables the completion of multiple asteroid rendezvouses in a short time, providing valuable insights for future missions involving a single spacecraft conducting multiple rendezvouses with multiple asteroids.
基金supported by the National Natural Science Foundation of China(Grant Nos.12022214,U21B2050,and 12302058)the Young Elite Scientists Sponsorship Program of CAST(Grant No.2023QNRC001).
文摘Tsinghua University and the Shanghai Institute of Satellite Engineering organized the 12th edition of the Global Trajectory Optimization Competition (GTOC12) on June 19, 2023. The problem for GTOC12, entitled “Sustainable Asteroid Mining”, explores how spacecraft can be dispatched from the Earth to various asteroids for resource extraction. The primary challenge involves designing coupled trajectories for multiple spacecraft to maximize the collected mineral mass. A novel game model is introduced to encourage the mining of rarely mined asteroids. GTOC12 saw significant participation, with 102 teams registered. By the end of the competition, 28 teams provided feasible solutions, highlighting a growing interest in the field. This study describes the design process of the GTOC12 problem and presents a review and analysis of the results from the participating teams.
基金supported by the National Natural Science Foundation of China(No.11372311)the Key Research Program of the Chinese Academy of Sciences(No.ZDRW-KT-2019-1).
文摘The 8th edition of the Global Trajectory Optimization Competition(GTOC8)presented a novel concept of a space-based very-long-baseline interferometry(VLBI)telescope in cislunar space for observing selected radio sources in cosmos.It requires designing a three-spacecraft triangular formation with changeable sizes and orientations such that observation can be scheduled as efficiently as possible.We first review the problem,and then describe the methods employed by representative teams participating in the competition.Subsequently,we present the design techniques employed by the team from the Chinese Academy of Sciences,which are primarily based on orbital-geometry analysis.Two efficient trajectory patterns are summarized:million-kilometer triangular formations with symmetric circular orbits,and consecutive-lunar-flyby trajectories with Moon-to-Moon transfer orbits.These two trajectory patterns enable establishing and reconfiguring the triangular formation with sufficiently different sizes so that a number of radio sources can be observed,thus maximizing the performance index.Finally,we present a solution with the best currently known score of J=158 million km.
基金the National Natural Science Foundation of China(Grant Nos.11672146 and 11432001)The authors thank the organizer of GTOC8.
文摘This paper presents the crucial method for obtaining our team's results in the 8th Global Trajectory Optimization Competition(GTOC8).Because the positions and velocities of spacecraft cannot be completely determined by one observation on one radio source,the branch and bound method for sequence optimization of multi-asteroid exploration cannot be directly applied here.To overcome this diculty,an optimization method for searching the observing sequence based on nominal low-thrust trajectories of the symmetric observing con guration is proposed.With the symmetric observing con guration,the normal vector of the triangle plane formed by the three spacecraft rotates in the ecliptic plane periodically and approximately points to the radio sources which are close to the ecliptic plane.All possible observing opportunities are selected and ranked according to the nominal trajectories designed by the symmetric observing con guration.First,the branch and bound method is employed to nd the optimal sequence of the radio source with thrice observations.Second,this method is also used to nd the optimal sequence of the left radio sources.The nominal trajectories are then corrected for accurate observations.The performance index of our result is 128,286,317.0 km which ranks the second place in GTOC8.
