Reconfiguration of 3D Pivoting Modular Robots

TL;DR

This paper explores the reconfiguration capabilities of 3D Rhombic Dodecahedral modular robots, establishing complexity results, limitations, and introducing a new class of configurations called super-rigid.

Contribution

It extends 2D reconfiguration results to 3D, proves PSPACE-hardness, and introduces super-rigid configurations unique to 3D models.

Findings

Reconfiguration is PSPACE-hard in restricted models.

RD configurations are not universally reconfigurable in 3D.

Introduction of super-rigid configurations that remain rigid in larger assemblies.

Abstract

We study a new model of 3-dimensional modular self-reconfigurable robots Rhombic Dodecahedral (RD). By extending results on the 2D analog of this model we characterize the free space requirements for a pivoting move and investigate the $\textit{reconfiguration problem}$, that is, given two configurations $s$ and $t$ is there a sequence of moves that transforms $s$ into $t$? We show reconfiguration is PSPACE-hard for RD modules in a restricted pivoting model. In a more general model, we show that RD configurations are not universally reconfigurable despite the fact that their 2D analog is [Akitaya et al., SoCG 2021]. Additionally, we present a new class of RD configurations that we call $\textit{super-rigid}$. Such a configuration remains rigid even as a subset of any larger configuration, which does not exist in the 2D setting.