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.
A high-precision online trajectory optimization method combining convex optimization and Radau pseudospectral method is presented for the large attitude flip vertical landing problem of a starship-like vehicle. During the landing process, the aerodynamic influence on the starship-like vehicle is significant and non-negligible. A planar landing dynamics model with pitching motion is developed considering that there is no extensive lateral motion modulation during the whole flight. Combining the constraints of its powered descent landing process, a model of the fuel optimal trajectory optimization problem in the landing point coordinate system is given. The nonconvex properties of the trajectory optimization problem model are analyzed and discussed, and the advantages of fast solution and convergence certainty of convex optimization, and high discretization precision of the pseudospectral method, are fully utilized to transform the strongly nonconvex optimization problem into a series of finite-dimensional convex subproblems, which are solved quickly by the interior point method solver. Hardware-in-the-loop simulation experiments verify the effectiveness of the online trajectory optimization method. This method has the potential to be an online guidance method for the powered descent landing problem of starship-like vehicles.
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