A Neural Network Warm-Started Indirect Trajectory Optimization Method

The mission of spacecraft usually faces the problem of an unknown deep space environment, limited long-distance communication and complex environmental dynamics, which brings new challenges to the intelligence level and real-time performance of spacecraft onboard trajectory optimization algorithms. In this paper, the optimal control theory is combined with the neural network. Then, the state–control sample pairs and the state–costate sample pairs obtained from the high-fidelity algorithm are used to train the neural network and further drive the spacecraft to achieve optimal control. The proposed method is used on two typical spacecraft missions to verify the feasibility. First, the system dynamics of the hypersonic reentry problem and fuel-optimal moon landing problem are described and then formulated as highly nonlinear optimal control problems. Furthermore, the analytical solutions of the optimal control variables and the two-point boundary value problem are derived based on Pontryagin’s principle. Subsequently, optimal trajectories are solved offline using the pseudospectral method and shooting methods to form large-scale training datasets. Additionally, the well-trained deep neural network is used to warm-start the indirect shooting method by providing accurate initial costates, and thus the real-time performance of the algorithm can be greatly improved. By mapping the nonlinear functional relationship between the state and the optimal control, the control predictor is further obtained, which provides a backup optimal control variables generation strategy in the case of shooting failure, and ensures the stability and safety of the onboard algorithm. Numerical simulations demonstrate the real-time performance and feasibility of the proposed method.