We present an algorithm for self-reconfiguration of admissible 3D configurations of pivoting modular cube robots with holes of arbitrary shape and number. Cube modules move across the surface of configurations by pivoting about shared edges, enabling configurations to reshape themselves. Previous work provides a reconfiguration algorithm for admissible 3D configurations containing no non-convex holes; we improve upon this by handling arbitrary admissible 3D configurations. The key insight specifies a point in the deconstruction of layers enclosing non-convex holes at which we can pause and move inner modules out of the hole. We prove this happens early enough to maintain connectivity, but late enough to open enough room in the enclosing layer for modules to escape the hole. Our algorithm gives reconfiguration plans with O(n2)\mathcal {O}({n^2}) moves for nn modules.

中文翻译：

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重新配置旋转模块化立方体机器人中的非凸孔


我们提出了一种算法，用于对具有任意形状和数量的孔的旋转模块化立方体机器人的可接受的 3D 配置进行自重构。立方体模块通过围绕共享边缘旋转在配置表面上移动，从而使配置能够重塑自身。先前的工作为不包含非凸孔的可接受的 3D 配置提供了一种重新配置算法；我们通过处理任意可接受的 3D 配置来改进这一点。关键的见解指定了包围非凸孔的层解构中的一个点，在该点我们可以暂停并将内部模块移出孔。我们证明这种情况发生得足够早以维持连接，但也足够晚以在封闭层中打开足够的空间以便模块逃脱漏洞。我们的算法给出了 nn 个模块的 O(n2)\mathcal {O}({n^2}) 次移动的重新配置计划。