In the past decades, space missions to small bodies (Galileo, OSIRIS‐REx, Hayabusa, Hayabusa2, Chang'e 2, Rosetta, etc.) have enriched us greatly with voluminous new knowledge on our solar system. In situ observations by these missions have revealed the extreme complexity and remarkable diversity of the spatial environment around their target asteroids. A study on the motion of objects in such complex environments is of great importance for understanding the evolution history of surface/subsurface materials on the asteroids. Establishing a reasonable dynamic model is obviously a crucial step. This paper proposes a method for tracking the motion of an object near the surface of an arbitrary asteroid. This method combines the irregular shape, an unlimited rotational state and asymmetric gravitational field, which are three key factors that dominate the complex movement of an object on and off the asteroid's surface. The gravitational attraction and potential are computed using the polyhedral method with corrections for the possible singularities. The asteroid's surface is then approximated using a continuous and differentiable surface, and the parametric representation forms of the body are derived based on polynomial series. An event‐driven scheme is designed, so that the orbital motion and surface motion are processed separately by checking the triggering events. The algorithm was implemented using C++. Benchmarking tests are organized on a local cluster, showing a satisfactory performance in both accuracy and efficiency. This method was further applied to improve the control accuracy of the landing spot of an asteroid surface lander.

中文翻译：

---

参数形状模型用于追踪小行星附近物体的迁移

在过去的几十年中，对小型物体（伽利略，OSIRIS-REx，Hay鸟，Hay鸟2，Chang娥二号，罗塞塔等）的太空飞行使我们对太阳系有了大量的新知识，极大地丰富了我们。这些任务的实地观测表明，其目标小行星周围的空间环境极为复杂，且具有明显的多样性。在如此复杂的环境中进行物体运动的研究对于理解小行星表面/地下物质的演化历史非常重要。建立合理的动态模型显然是至关重要的一步。本文提出了一种跟踪任意小行星表面附近物体运动的方法。这种方法结合了不规则形状，无限旋转状态和不对称重力场，这是控制物体在小行星表面上下移动的复杂运动的三个关键因素。使用多面体方法对重力引力和势进行计算，并对可能的奇点进行校正。然后，使用连续且可微的表面对小行星的表面进行近似，然后根据多项式级数推导出物体的参数表示形式。设计了事件驱动方案，因此可以通过检查触发事件来分别处理轨道运动和表面运动。该算法是使用C ++实现的。基准测试在本地群集上进行组织，显示出令人满意的准确性和效率表现。进一步应用该方法来提高小行星表面着陆器着陆点的控制精度。