Collision-free control of a nano satellite in the vicinity of China Space Station using Lorentz augmented composite artificial potential field

This study addresses the problem of trajectory control for a nano satellite flying very closely near China Space Station (CSS) with obstacle avoidance. The control law is designed based on a newly developed composite artificial potential field (APF) model combined with its induced artificial Lorentz force. The composite APF model could precisely and efficiently compute the total potential field contributed from each element that constitutes the whole body of CSS. Those elements are modeled as the common geometric entities such as cuboids and capsule bodies to facilitate distance calculation, so that their independent APFs can be easily modeled in analytical form. In this way, the nano satellite under the composite APF-based control could fly anywhere outside CSS, which cannot be easily achieved by other APF models. To solve the local minima problem which often occur in classical APF-based methods, an APF-induced artificial Lorentz force is added to the original control law. The stability of the closed-loop system with the control law is proved using Lyapunov theory. Finally, some numerical examples are designed to show the effectiveness of the proposed control law. Since the composite APF and its induced artificial Lorentz force only relies on CSS's partial structure near the nano satellite, the method is suitable in the practical missions where the obstacle's information cannot be fully and accurately known. The method here can be applied in the practical missions such as on-orbit ultra-close photographing of CSS by nano satellites in future.