This study is mainly focusing on the problem of spacecraft close-range proximity with obstacle avoidance in the presence of complex shape. A novel Gaussian mixture model–based nonsingular terminal sliding mode control (GMM-NTSMC) is proposed. This is achieved by developing GMM-based potential function with a switching surface of NTSMC. It is theoretically proved that the closed-loop system is globally stable. The main contribution of this study is that the GMM-based avoiding strategies, which include the GMM-based terminal sliding mode control (GMM-TSMC) and GMM-NTSMC, can solve the collision avoidance problem considering complex shape while the artificial potential function–based terminal sliding model control (APF-TSMC) fails. Moreover, the GMM-NTSMC and the GMM-TSMC require less energy with respect to the APF-TSMC. Furthermore, the GMM-NTSMC retains the advantage of the NTSMC and can avoid singularity problem while GMM-TSMC cannot. Finally, numerical simulations are performed to verify the effectiveness and superiority of the proposed GMM-NTSMC.

这项研究主要集中在存在复杂形状的情况下，避开障碍物的航天器近距离接近问题。提出了一种基于高斯混合模型的非奇异终端滑模控制（GMM-NTSMC）。这是通过使用NTSMC的开关表面开发基于GMM的电位函数来实现的。理论上证明了闭环系统是全局稳定的。这项研究的主要贡献在于，基于GMM的避免策略（包括基于GMM的终端滑模控制（GMM-TSMC）和GMM-NTSMC）可以解决考虑复杂形状的碰撞避免问题，而人工势能函数-基于终端的滑动模型控制（APF-TSMC）失败。此外，相对于APF-TSMC，GMM-NTSMC和GMM-TSMC所需的能量更少。此外，GMM-NTSMC保留了NTSMC的优势，可以避免奇异性问题，而GMM-TSMC则不能。最后，进行了数值模拟，以验证所提出的GMM-NTSMC的有效性和优越性。