The number of space debris has rapidly increased in the recent times with the rising number of space missions. Thus, to ensure the safety of any operating satellite, collision avoidance maneuvers must be performed. It is also practically impossible to make the state measurements and dynamic models completely error-free. So, this study deals with fuel-optimal collision avoidance maneuvers while also incorporating the effects of uncertainty on them. In this paper, one formulation for convex optimization and another formulation for non-convex optimization have been presented and compared. Effects that the choice of the optimization algorithms and the number of discretization points used have on the optimal Δv as well as on the computational speed have also been discussed.

近年来，随着太空任务数量的增加，空间碎片的数量迅速增加。因此，为确保任何运行中的卫星的安全，必须执行避碰机动。实际上也不可能使状态测量和动态模型完全没有错误。因此，本研究涉及燃料优化的避撞机动，同时还考虑了不确定性对它们的影响。在本文中，提出并比较了一种用于凸优化的公式和另一种用于非凸优化的公式。还讨论了优化算法的选择和使用的离散化点的数量对最佳 Δv 以及计算速度的影响。