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.

This paper proposes an optimal, robust, and efficient guidance scheme for the perturbed minimum-time low-thrust transfer toward the geostationary orbit. The Earth’s oblateness perturbation and shadow are taken into account. It is difficult for a Lyapunov-based or trajectory-tracking guidance method to possess multiple characteristics at the same time, including high guidance optimality, robustness, and onboard computational efficiency. In this work, a concise relationship between the minimum-time transfer problem with orbital averaging and its optimal solution is identified, which reveals that the five averaged initial costates that dominate the optimal thrust direction can be approximately determined by only four initial modified equinoctial orbit elements after a coordinate transformation. Based on this relationship, the optimal averaged trajectories constituting the training dataset are randomly generated around a nominal averaged trajectory. Five polynomial regression models are trained on the training dataset and are regarded as the costate estimators. In the transfer, the spacecraft can obtain the real-time approximate optimal thrust direction by combining the costate estimations provided by the estimators with the current state at any time. Moreover, all these computations onboard are analytical. The simulation results show that the proposed guidance scheme possesses extremely high guidance optimality, robustness, and onboard computational efficiency.

In this study, a real-time optimal control approach is proposed using an interactive deep reinforcement learning algorithm for the Moon fuel-optimal landing problem. Considering the remote communication restrictions and environmental uncertainties, advanced landing control techniques are demanded to meet the high requirements of real-time performance and autonomy in the Moon landing missions. Deep reinforcement learning (DRL) algorithms have been recently developed for real-time optimal control but suffer the obstacles of slow convergence and difficult reward function design. To address these problems, a DRL algorithm is developed using an actor-indirect method architecture to achieve the optimal control of the Moon landing mission. In this DRL algorithm, an indirect method is employed to generate the optimal control actions for the deep neural network (DNN) learning, while the trained DNNs provide good initial guesses for the indirect method to promote the efficiency of training data generation. Through sufficient learning of the state-action relationship, the trained DNNs can approximate the optimal actions and steer the spacecraft to the target in real time. Additionally, a nonlinear feedback controller is developed to improve the terminal landing accuracy. Numerical simulations are given to verify the effectiveness of the proposed DRL algorithm and demonstrate the performance of the developed optimal landing controller.

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 difficulty, an optimization method for searching the observing sequence based on nominal low-thrust trajectories of the symmetric observing configuration is proposed. With the symmetric observing configuration, 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 configuration. First, the branch and bound method is employed to find the optimal sequence of the radio source with thrice observations. Second, this method is also used to find 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.