Enumeration of Polyominoes & Polycubes Composed of Magnetic Cubes
Enumeration of Polyominoes & Polycubes Composed of Magnetic Cubes
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DOI：
10.1109/iros51168.2021.9636784
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
Yitong Lu;Anuruddha Bhattacharjee;Daniel Biediger;Min-Joo Kim;Aaron T. Becker
中科院分区：
文献类型：
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作者：
Yitong Lu;Anuruddha Bhattacharjee;Daniel Biediger;Min-Joo Kim;Aaron T. Becker
本文探讨了一个家庭的设计磁立方体和计数有多少配置是可能的，每个设计作为一个功能的模块的数量。磁性模块化立方体是在其表面上布置有磁体的立方体。磁体被定位成使得每个面具有向外的磁南极或磁北极。此外，我们要求立方体的净磁矩通过相对面的中心。当具有相反极性的立方体面被紧密靠近时，这些磁性布置使得能够耦合，并且使得能够通过控制全局磁场的取向来移动立方体。本文研究了可以由磁性模块立方体构造的2D和3D形状，并描述了所有可能的磁体布置，遵守这些规则。我们选择了十个磁性排列，并为每个排列指定了一个“颜色”，以便于可视化和参考。我们提供了一种方法来枚举的数量的唯一的polyominoes和polycubes，可以构造从一组给定的有色立方体。我们使用这种方法来枚举2D中多达20个模块和3D中多达16个模块的所有安排。我们提供了一个运动规划的2D装配，并通过模拟比较哪些安排需要更少的运动生成，哪些安排是更常见的。硬件演示探索这些模块在2D和3D中的自组装和拆卸。
This paper examines a family of designs for magnetic cubes and counts how many configurations are possible for each design as a function of the number of modules. Magnetic modular cubes are cubes with magnets arranged on their faces. The magnets are positioned so that each face has either magnetic south or north pole outward. Moreover, we require that the net magnetic moment of the cube passes through the center of opposing faces. These magnetic arrangements enable coupling when cube faces with opposite polarity are brought in close proximity and enable moving the cubes by controlling the orientation of a global magnetic field. This paper investigates the 2D and 3D shapes that can be constructed by magnetic modular cubes, and describes all possible magnet arrangements that obey these rules. We select ten magnetic arrangements and assign a "color" to each of them for ease of visualization and reference. We provide a method to enumerate the number of unique polyominoes and polycubes that can be constructed from a given set of colored cubes. We use this method to enumerate all arrangements for up to 20 modules in 2D and 16 modules in 3D. We provide a motion planner for 2D assembly and through simulations compare which arrangements require fewer movements to generate and which arrangements are more common. Hardware demonstrations explore the self-assembly and disassembly of these modules in 2D and 3D.