We introduce and analyze a model for self-reconfigurable robots made up of
unit-cube modules. Compared to past models, our model aims to newly capture
two important practical aspects of real-world robots. First, modules often do
not occupy an exact unit cube, but rather have features like bumps extending
outside the allotted space so that modules can interlock. Thus, for example,
our model forbids modules from squeezing in between two other modules that are
one unit distance apart. Second, our model captures the practical scenario of
many passive modules assembled by a single robot, instead of requiring all
modules to be able to move on their own.
We prove two universality results. First, with a supply of auxiliary modules,
we show that any connected polycube structure can be constructed by a
carefully aligned plane sweep. Second, without additional modules, we show
how to construct any structure for which a natural notion of external feature
size is at least a constant; this property largely consolidates
forbidden-pattern properties used in previous works on reconfigurable modular
robots.