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Title: Enumeration of Polyominoes & Polycubes Composed of Magnetic Cubes
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.  more » « less
Award ID(s):
1932572 1553063 1849303
PAR ID:
10439808
Author(s) / Creator(s):
; ; ; ;
Date Published:
Journal Name:
2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)
Page Range / eLocation ID:
6977 to 6982
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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