Reconfiguration of 3D Pivoting Modular Robots
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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.
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