Game theory based finite-time formation control using artificial potentials for tethered space net robot

The Tethered Space Net Robot (TSNR) is an innovative solution for active space debris capture and removal. Its large envelope and simple capture method make it an attractive option for this task. However, capturing maneuverable debris with the flexible and elastic underactuated net poses significant challenges. To address this, a novel formation control method for the TSNR is proposed through the integration of differential game theory and robust adaptive control in this paper. Specifically, the trajectory of the TSNR is obtained through the solution of a real-time feedback pursuit-evasion game with a dynamic target, where the primary condition is to ensure the stability of the TSNR. Furthermore, to minimize tracking errors and maintain a specific configuration, a robust adaptive formation control scheme with Artificial Potential Field (APF) based on a Finite-Time Convergent Extended State Observer (FTCESO) is investigated. The proposed control method has a key advantage in suppressing complex oscillations by a new adaptive law, thus precisely maintaining the configuration. Finally, numerical simulations are performed to demonstrate the effectiveness of the proposed scheme.