Reconfiguration of 3D Pivoting Modular Robots

Hugo A. Akitaya; Frederick Stock

Reconfiguration of 3D Pivoting Modular Robots

Computational Geometry 2023-04-21 v1

Authors: Hugo A. Akitaya , Frederick Stock

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.

Cite

@article{arxiv.2304.09990,
  title  = {Reconfiguration of 3D Pivoting Modular Robots},
  author = {Hugo A. Akitaya and Frederick Stock},
  journal= {arXiv preprint arXiv:2304.09990},
  year   = {2023}
}