The purpose of this paper is to present a novel satellite layout optimization design (SLOD) approach based on the phi-function, which provides a simple, effective and simultaneously accurate way to handle the geometry constraints (including non-overlapping constraint and distance constraint) with an explicit mathematical expression. Firstly, an extended basic SLOD model concerning the system mass characteristics is formulated with the introduction of a generic minimum/maximum distance constraint between components. In the previous literature, most of the investigated SLOD applications only involve the planar circular and rectangular components with fixed orientation due to the lack of an effective and accurate overlap calculation method, let alone control the distance between them. Therefore, the idea of using phi-functions to prevent overlap and control distance between components is put forward to alleviate this difficulty. Furthermore, to effectively prevent the container protrusion from the components, the phi-function method is extended by our proposed finite-component-boundary (FCB) method. Despite its positive effects, the limitation of the phi-function is clearly discussed to provide a comprehensive view on this useful tool. Finally, the validity and the effectiveness of the proposed methodology are demonstrated by two numerical packing design examples, two typical 2D SLOD applications and one 3D cube-shaped SLOD application.

本文的目的是提出一种基于phi函数的新颖的卫星布局优化设计（SLOD）方法，该方法提供了一种简单，有效且同时准确的方式来处理几何约束（包括非重叠约束和距离约束）带有明确的数学表达式 首先，通过引入组件之间的通用最小/最大距离约束，制定了有关系统质量特性的扩展基本SLOD模型。在先前的文献中，由于缺乏有效且准确的重叠计算方法，大多数研究的SLOD应用仅涉及具有固定方向的平面圆形和矩形组件，更不用说控制它们之间的距离了。因此，提出了使用phi函数来防止重叠和控制组件之间的距离的想法，以减轻这一困难。此外，为了有效防止容器从组件中突出，我们建议的有限组件边界（FCB）方法扩展了phi函数方法。尽管它具有积极作用，但仍明确讨论了phi函数的局限性，以提供对该有用工具的全面了解。最后，通过两个数值包装设计实例，两个典型的2D SLOD应用程序和一个3D立方体形SLOD应用程序证明了所提出方法的有效性和有效性。phi函数方法由我们提出的有限分量边界（FCB）方法扩展。尽管它具有积极作用，但仍明确讨论了phi函数的局限性，以提供对该有用工具的全面了解。最后，通过两个数值包装设计实例，两个典型的2D SLOD应用程序和一个3D立方体形SLOD应用程序证明了所提出方法的有效性和有效性。phi函数方法由我们提出的有限分量边界（FCB）方法扩展。尽管它具有积极作用，但仍明确讨论了phi函数的局限性，以提供对该有用工具的全面了解。最后，通过两个数值包装设计实例，两个典型的2D SLOD应用程序和一个3D立方体形SLOD应用程序证明了所提出方法的有效性和有效性。