2023/04/19 by Hugo A. Akitaya, Frederick Stock, Akitaya, Hugo A. +1 · 1 citation
Engineering · Physics and Astronomy · #Advanced Materials and Mechanics #Computational Geometry (cs.CG) #FOS: Computer and information sciences #Micro and Nano Robotics #Modular Robots and Swarm Intelligence
paper · pdf · doi:10.48550/arxiv.2304.09990
openalex publication_date 2023/04/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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 super-rigid. Such a configuration remains rigid even as a subset of any larger configuration, which does not exist in the 2D setting.