A Neural Network Warm-Started Indirect Trajectory Optimization Method

Abstract

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.

Trajectory Optimization with Complex Obstacle Avoidance Constraints via Homotopy Network Sequential Convex Programming

“…The traditional method of fitting control variables and trajectories using supervised learning requires many samples [28][29][30][31][32][33], and the only way to obtain samples is to solve complex optimal control problems. Therefore, acquiring a large number of samples has become a challenge in neural network training.…”

“…As an auxiliary tool for trajectory optimization, the neural network can effectively improve the performance of traditional algorithms [28][29][30][31][32][33]. Yin [28] proposed a trajectory planning method based on a neural network, thus improving the indirect method's convergence rate.…”

“…The concept of the HNN is proposed for the first time. Compared with [28][29][30][31][32][33], training the HNN does not require solving optimal control problems. Only the MSD field is needed so that adequate samples can be generated efficiently and stably.…”

Optimal Circle-to-Ellipse Orbit Transfer for Sun-Facing E-Sail

“…It is assumed that the spacecraft departs from a circular parking orbit with the aim of reaching a coplanar target orbit of given eccentricity. Orbit-to-orbit transfers are analyzed in an optimal framework, where the total flight time is minimized with an indirect approach [42][43][44]. The novelty of the paper is to apply the optimal control theory to the special but important case when the direction of the E-sail propulsive acceleration vector is aligned with the Sun-spacecraft line.…”

Optimal Earth Gravity-Assist Maneuvers with an Electric Solar Wind Sail

“…The problem is addressed within an optimal framework [37], where the hyperbolic excess velocity relative to the Earth after a given flight time is maximized. The optimal control problem is solved by means of an indirect multiple shooting technique [38], which allows the time histories of the E-sail attitude and the grid voltage to be obtained. To simplify the analysis, the Earth's heliocentric orbit is assumed to be circular, the spacecraft motion is two-dimensional, and the dimensions of Earth's sphere of influence are neglected.…”