An LSTM-Driven Differential Game Scheme for Formation and Configuration of Tethered Space Net Robot

Past research on the Tethered Space Net Robot (TSNR) was confined to satellite-based passive control due to its unique flexible structure, and consequently, the flexible net configuration in the forward direction could not be effectively managed during formation maneuvers. Besides, its entanglement with the target introduces additional challenges. To address these issues, a formation control framework is presented that utilizes neural networks and differential game theory for active control of flexible underactuated systems. A refined variable, termed the envelope depth, is proposed to characterize the 3D configuration of the flexible net. This variable establishes a critical bridge between satellite-level control and net-level manipulation. Moreover, an LSTM-MLP (Long Short-Term Memory-Multi-Layer Perceptron) neural network is applied to capture temporal features. It learns the nonlinear dynamic model of the envelope depth. Thereby, a coupling relationship between the flexible-net motion and the satellite dynamics is established. Furthermore, a neural game-theoretic formation configuration controller (NGT-FCC) based on differential game theory is developed to achieve cooperative control of satellite formation and 3D configuration. The effectiveness of proposed controller is demonstrated by numerical simulation results. The results show that, by actively controlling the envelope depth, it effectively suppresses the disturbance and limits the oscillation, reducing the envelope depth amplitude by 82.89%.