Model predictive control for close-proximity maneuvering of spacecraft with adaptive convexification of collision avoidance constraints

This study investigated model predictive control (MPC) for close-proximity maneuvering of spacecraft. It is essential for a designed MPC to effectively handle collision avoidance between the servicer spacecraft and the client spacecraft, especially while the client is rotating. The rotating motion of the client leads to dynamic changes in the collision avoidance constraints, which increases the difficulty of optimizing the control input in the MPC framework. Therefore, this study presents a method to improve the performance and computational efficiency of MPC for rendezvous and docking with a nonrotating or rotating client. An ellipsoid is adopted to model the client’s keep-out zone (KOZ). Given the spherical KOZ of the servicer, an expanded ellipsoid is introduced to describe the KOZ for the center of mass of the servicer and modeled as a nonlinear constraint. The linearization method for reference points located at the expanded ellipsoid is adopted to convexify the nonlinear constraints. The reference points are adaptively determined according to the positions of the servicer, client, and expanded ellipsoidal KOZ. The resulting hyperplanes are then used to describe the collision avoidance constraints. By utilizing the aforementioned strategies, combined with the calculated reference points, an adaptive convex programming algorithm suitable for real-time implementation of MPC is derived. The performance of the proposed method is demonstrated through numerical simulations.     

负电子亲和半导体的二次电子发射

根据0.8keV≤Epomax≤5keV的负电子亲和(negative electron affinity,NEA)半导体二次电子发射(secondary electron emission,SEE)的特性，初级电子产额R，现有的次级电子产额δ的通用公式和实验数据，分别推导并实验证明了NEA金刚石的δ在0.5Epomax≤Epo≤10Epomax, GaN在2keV≤Epomax≤5keV, NEA金刚石的δ在08keV≤Epo≤3keV, GaN在08keV≤Epomax≤2keV的特殊公式;其中Epomax为δ达到最大值时的Epo, Epo为初级电子入射能。推导出了08keV≤Epomax≤5keV时NEA半导体的内部二次电子到达发射极表面后逃逸到真空中的概率B。还提出了计算08keV≤Epomax≤5keV NEA半导体1/α的方法;其中1/α为二次电子的平均逃逸深度。分析结果表明，B和1/α的理论研究有助于研究不同样品制备方法对NEA半导体中SEE的定量影响，从而生产出理想的NEA发射体，如NEA金刚石。