ESA's Hera mission aims to visit binary asteroid Didymos in late 2026, investigating its physical characteristics and the result of NASA's impact by the DART spacecraft in more detail. Two CubeSats on-board Hera plan to perform a ballistic landing on the secondary of the system, called Dimorphos. For these types of landings the translational state during descent is not controlled, reducing the spacecrafts complexity but also increasing its sensitivity to deployment maneuver errors and dynamical uncertainties. This paper introduces a novel methodology to analyse the effect of these uncertainties on the dynamics of the lander and design a trajectory that is robust against them. This methodology consists of propagating the uncertain state of the lander using the non-intrusive Chebyshev interpolation (NCI) technique, which approximates the uncertain dynamics using a polynomial expansion, and analysing the results using the pseudo-diffusion indicator, derived from the coefficients of the polynomial expansion, which quantifies the rate of growth of the set of possible states of the spacecraft over time. This indicator is used here to constrain the impact velocity and angle to values which allow for successful settling on the surface. This information is then used to optimize the landing trajectory by applying the NCI technique inside the transcription of the problem. The resulting trajectory increases the robustness of the trajectory compared to a conventional method, improving the landing success by 20 percent and significantly reducing the landing footprint.

翻译：欧空局赫拉任务计划于2026年末造访双小行星系统迪迪莫斯，旨在详细研究其物理特性及NASA DART撞击器造成的撞击结果。赫拉搭载的两颗立方星计划在该系统次级体迪莫弗斯表面执行弹道着陆。此类着陆过程中，下降阶段的平动状态不受控制，虽降低了航天器复杂度，但增加了其对部署机动误差和动力学不确定性的敏感度。本文提出一种新颖方法，用于分析这些不确定性对着陆器动力学的影响，并设计具有鲁棒性的弹道。该方法采用非侵入式切比雪夫插值（NCI）技术传播着陆器的不确定状态，通过多项式展开近似不确定动力学，并利用由多项式展开系数导出的伪扩散指标分析结果，该指标量化了航天器可能状态集合随时间增长的速率。本研究以此指标约束撞击速度与角度，使其满足成功着陆表面的条件。基于该信息，通过在问题离散化过程中应用NCI技术优化着陆弹道。与传统方法相比，所得弹道提升了20%的着陆成功率，并显著缩小了着陆足迹。