Efficient enumeration of modular robot configurations and shapes

A modular robot consists of a set of mechatronic modules that can be connected in many different ways, which makes it possible to build robots of many different shapes from the same basic set of modules. The main contribution of this work is an algorithm that, given the parameters of a module and the number of modules, efficiently can calculate how many different configurations and shapes can be built. These numbers are important because the first is a measure of the self-reconfigurability and the second, given there is a relationship between form and function, the versatility of a modular robot. As an experimental contribution, we enumerate the configuration and shape spaces of square, two-dimensional modules with all possible connector configurations. We proceed to three dimensions and enumerate the spaces of the theoretically interesting sliding cube module, and the M-TRAN and SuperBot modules. Several observations are made, an important one is that the shape spaces of the two physical modules are large even for a small number of modules (103 different shapes using 3 modules). This implies that it is not the lack of shape diversity that holds these modular robots back from being versatile. A result that suggests that if modules are designed right, versatility can potentially be reached even with few modules, which is contrary to the common belief in the community that more is better.