Neural network-aided electromagnetic spacecraft formation flying attitude-orbit coupled control at the Sun-Earth L2 point

In response to the need for a supportive space structure for deep space exploration, this paper investigates a novel approach to designing and implementing an electromagnetic Spacecraft Formation Flying (SFF) at the Sun-Earth Lagrange point L2. To address the attitude-orbit coupling problem, two Neural Network (NN) structures are integrated: A Hermite polynomial-based NN (HeNN) to estimate the SFF relative orbital motion, and a Legendre polynomial-based NN (LeNN) for the attitude estimation. The two neural networks are further combined with a developed Nonlinear Control (NC) approach. Hence, assuming a quaternion-based uncertain attitude model, two NN-aided adaptive NC are derived based on the characteristics of the relative orbital model. The first approach assumes an uncertain relative orbital plant, resulting in the named HeNN&LeNN algorithm; that is, the proposed HeNN-aided adaptive NC controls the relative orbital motion, and the LeNN-aided adaptive NC controls the attitude. The second approach assumes a deterministic nonlinear relative orbital plant, resulting in the named NC&LeNN strategy; i.e., the nominal NC controls the relative orbital motion, and the LeNN-aided adaptive NC controls the attitude. The asymptotic stability and effectiveness of these approaches are demonstrated through the Lyapunov method. Moreover, an improved magnetic moment-based cost function is introduced to accomplish deep-space SFF attitude-orbit coupling control with a relatively low electromagnetic energy consumption. The simulation results corroborate the status of the NC&LeNN approach as an alternative to existing NN-based approaches, and the potential of the HeNN&LeNN approach as a general model-free control strategy for more complex or realistic scenarios. This research thereby holds a significant potential for advancing the application of intelligent control methods and electromagnetic technologies in deep-space exploration.