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Real-Time Optimal Control for Spacecraft Orbit Transfer via Multiscale Deep Neural Networks

This study is motivated by the requirement of on-board trajectory optimization with guaranteed convergence and real-time performance for optimal spacecraft orbit transfers. To this end, a real-time optimal control approach is proposed using deep learning technologies to obtain minimum-time trajectories of solar sail spacecraft for orbit transfer missions. First, the minimum-time two-dimensional orbit transfer problem is solved by an indirect method, and the costate normalization technique is introduced to increase the probability of finding the optimal solutions. Second, by making novel use of deep learning technologies, three deep neural networks are designed and trained offline by the obtained optimal solutions to generate the guidance commands in real time during flight. Consequently, the long-standing difficulty of on-board trajectory generation is resolved. Then, an interactive network training strategy is presented to increase the success rate of finding optima by supplying good initial guesses for the indirect method. Moreover, a multiscale network cooperation strategy is designed to deal with the recognition deficiency of deep neural networks (DNNs) with small input values, which helps achieve highly precise control of terminal orbit insertion. Numerical simulations are given to substantiate the efficiency of these techniques, and illustrate the effectiveness and robustness of the proposed DNN-based trajectory control for future on-board applications.