We propose a new meta-module design for two important classes of modular robots. The new meta-modules are three-dimensional, robust and compact, improving on the previously proposed ones. One of them applies to so-called edge-hinged modular robot units, such as M-TRAN, SuperBot, SMORES, UBot, PolyBot and CKBot, while the other one applies to so-called central-point-hinged modular robot units, which include Molecubes and Roombots. The new meta-modules use the rotational degrees of freedom of these two types of robot units in order to expand and contract, as to double or halve their length in each of the two directions of its three dimensions, therefore simulating the capabilities of Crystalline and Telecube robots. Furthermore, in the edge-hinged case we prove that the novel meta-module can also perform the scrunch, relax and transfer moves that are necessary in any tunneling-based reconfiguration algorithm for expanding/contracting modular robots such as Crystalline and Telecube. This implies that the use of meta-meta-modules is unnecessary, and that currently existing efficient reconfiguration algorithms can be applied to a much larger set of modular robots than initially intended. We also prove that the size of the new meta-modules is optimal and cannot be further reduced.

我们为两类重要的模块化机器人提出了一种新的元模块设计。新的元模块是三维的、健壮的和紧凑的，改进了之前提出的元模块。其中一种适用于所谓的边缘铰链模块化机器人单元，例如 M-TRAN、SuperBot、SMORES、UBot、PolyBot 和 CKBot，而另一种适用于所谓的中心点铰链模块化机器人单元，包括 Molecubes 和 Roombots。新的元模块使用这两种机器人单元的旋转自由度来扩展和收缩，使其在其三个维度的两个方向中的每个方向上的长度都增加一倍或减半，从而模拟了 Crystalline 和长方体机器人。此外，在边缘铰链的情况下，我们证明了新的元模块还可以执行任何基于隧道的重新配置算法中必要的收缩、放松和转移动作，用于扩展/收缩模块化机器人，例如 Crystalline 和 Telecube。这意味着元元模块的使用是不必要的，并且当前存在的有效重新配置算法可以应用于比最初预期的更大的模块化机器人集。