Reconfiguration Algorithms for Cubic Modular Robots with Realistic Movement Constraints

TL;DR

This work advances reconfiguration theory for cubic modular robots by incorporating realistic movement constraints: loose sliding that requires local clearance and a framework where most modules may be passive, carried by a robot. It proves two universality results in the $2$-accessible setting: (i) with linear extra scaffolding, any connected polycube can be formed from a line via a plane-sweep; (ii) with no extras, any structure whose external feature size is at least $2$ can be reconfigured to a line using a monotone, slice-based process. The paper also establishes a fundamental limitation: a 3-loose model does not admit universal reconfiguration for all shapes, via a counterexample; and it provides a practical, monotone construction for rearranging structures without extra modules. Collectively, these results connect realistic hardware considerations to algorithmic universality, with implications for ARMADAS-like programmable-matter systems and scalable assembly from passive components.

Abstract

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.

Figures (10)

• Figure 1: The two moves in the sliding-cubes model. Left: straight slide. Right: corner slide.
• Figure 2: The two moves in the pivoting-cubes model. Left: straight pivot. Right: corner pivot.
• Figure 3: Photograph of ARMADAS robot attempting to place a module between two modules and failing due to collisions of mechanical alignment features (red arrows).
• Figure 4: Valid (green) and invalid (red) moves of the green module in the loose-sliding model.
• Figure 5: Valid moves in the loose-sliding model. Left: straight slide move and the corresponding $2\times 2\times 2$ empty cube. Middle and right: corner slide move and the corresponding translation (indicated by the orange paths) of the $2\times 2\times 2$ empty cube.

Theorems & Definitions (15)

• Lemma 2
• Theorem 3
• Lemma 4
• Theorem 5
• Lemma 6
• Lemma 8
• Lemma 9
• Lemma 10
• Corollary 11
• Corollary 12