An active energy management distributed formation control for tethered space net robot via cooperative game theory

The current studies for Tethered Space Net Robot (TSNR) typically treat the tension force induced by the net as a disturbance and employ passive suppression for compensation. However, these approaches not only result in excess fuel consumption but also overlook the intrinsic nature of the net dynamics. When one Maneuverable Unit (MU) maneuvers, it generates a tension force on the net that is transmitted to other MUs. This force not only affects the control accuracy of other MUs but also has a positive effect. In this paper, an Active Energy Management Distributed Formation Control (AEMC) strategy is proposed to reveal this kind of interaction and maximize its advantage. Firstly, an energy recovery framework is established, allowing each MU can effectively utilize the tension force due to the net. Specifically, a neural network estimator is designed to capture the hysteresis relationship in which MUs influence each other by transmitting forces through the net. Furthermore, to achieve the cooperative completion of tasks, a game based control scheme is proposed to optimize the control input and tension force collectively. Through prediction and optimization, MUs actively manage their impacts on each other, thereby controlling the influence of tension force on the tracking errors of others. Finally, numerical simulations are conducted to showcase the effectiveness of the proposed approach.