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
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 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 t...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.展开更多
Asteroids may contain valuable minerals.A method to exploit asteroid mines is to transfer them closer to the Earth for further mining processes.In this work,we optimally mount a set of fixed-angle spacecraft thrusters...Asteroids may contain valuable minerals.A method to exploit asteroid mines is to transfer them closer to the Earth for further mining processes.In this work,we optimally mount a set of fixed-angle spacecraft thrusters on the surface of an asteroid to conduct concurrent detumbling and redirecting to the desired orbit.The optimization objective reconciles the minimum duration of the mission with the minimum required fuel as well as the maximum uniformity of the fuel distribution required for all thrusters.Each thruster can respond to redirection and detumbling commands simultaneously.Redirection and detumbling are performed via the directional adaptive guidance method and PID controllers,respectively,and the weight factors for each orbital element and the gains of the rotational control channels are also optimized in the process.We use the particle swarm optimization algorithm to evaluate the objective function by simulating the entire mission to find the optimal design.The rotational control damps the tumbling of the asteroid without interfering with the simultaneous redirection process and eventually fixes the asteroid in the optimally selected orientation in the inertial reference frame.The rotational velocity and attitude of the asteroid are controlled via separate PID controllers,which are set robustly.We can effectively optimize the mission by collectively tuning both the system’s rotational and redirection behaviors as well as the thrusters’configuration and optimally selecting the final attitude of the asteroid.展开更多
For deep-space mission design,the gravity of the Sun and the Moon can be first considered and utilized.Their gravity can provide the energy change for launching spacecraft and retrieving spacecraft as well as asteroid...For deep-space mission design,the gravity of the Sun and the Moon can be first considered and utilized.Their gravity can provide the energy change for launching spacecraft and retrieving spacecraft as well as asteroids.Regarding an asteroid retrieval mission,it can lead to the mitigation of asteroid hazards and an easy exploration and exploitation of the asteroid.This paper discusses the application of the Sun-driven lunar swingby sequence for asteroid missions.Characterizing the capacity of this technique is not only interesting in terms of the dynamic insights but also non-trivial for trajectory design.The capacity of a Sun-driven lunar swingby sequence is elucidated in this paper with the help of the“Swingby-Jacobi”graph.The capacity can be represented by a range of the Jacobi integral that encloses around 660 asteroids currently cataloged.To facilitate trajectory design,a database of Sun-perturbed Moon-to-Moon transfers,including multi-revolution cases,is generated and employed.Massive trajectory options for spacecraft launch and asteroid capture can then be explored and optimized.Finally,a number of asteroid flyby,rendezvous,sample-return,and retrieval mission options enabled by the proposed technique are obtained.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
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
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(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.
文摘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.
文摘Asteroids may contain valuable minerals.A method to exploit asteroid mines is to transfer them closer to the Earth for further mining processes.In this work,we optimally mount a set of fixed-angle spacecraft thrusters on the surface of an asteroid to conduct concurrent detumbling and redirecting to the desired orbit.The optimization objective reconciles the minimum duration of the mission with the minimum required fuel as well as the maximum uniformity of the fuel distribution required for all thrusters.Each thruster can respond to redirection and detumbling commands simultaneously.Redirection and detumbling are performed via the directional adaptive guidance method and PID controllers,respectively,and the weight factors for each orbital element and the gains of the rotational control channels are also optimized in the process.We use the particle swarm optimization algorithm to evaluate the objective function by simulating the entire mission to find the optimal design.The rotational control damps the tumbling of the asteroid without interfering with the simultaneous redirection process and eventually fixes the asteroid in the optimally selected orientation in the inertial reference frame.The rotational velocity and attitude of the asteroid are controlled via separate PID controllers,which are set robustly.We can effectively optimize the mission by collectively tuning both the system’s rotational and redirection behaviors as well as the thrusters’configuration and optimally selecting the final attitude of the asteroid.
文摘For deep-space mission design,the gravity of the Sun and the Moon can be first considered and utilized.Their gravity can provide the energy change for launching spacecraft and retrieving spacecraft as well as asteroids.Regarding an asteroid retrieval mission,it can lead to the mitigation of asteroid hazards and an easy exploration and exploitation of the asteroid.This paper discusses the application of the Sun-driven lunar swingby sequence for asteroid missions.Characterizing the capacity of this technique is not only interesting in terms of the dynamic insights but also non-trivial for trajectory design.The capacity of a Sun-driven lunar swingby sequence is elucidated in this paper with the help of the“Swingby-Jacobi”graph.The capacity can be represented by a range of the Jacobi integral that encloses around 660 asteroids currently cataloged.To facilitate trajectory design,a database of Sun-perturbed Moon-to-Moon transfers,including multi-revolution cases,is generated and employed.Massive trajectory options for spacecraft launch and asteroid capture can then be explored and optimized.Finally,a number of asteroid flyby,rendezvous,sample-return,and retrieval mission options enabled by the proposed technique are obtained.
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.
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.
