Parallel Permutation for Linear Full-resolution Reconfiguration of Heterogeneous Sliding-only Cubic Modular Robots

Abstract

This paper presents a parallel permutation algorithm that achieves linear full-resolution reconfiguration of sliding-only cubic modular robots. We assume the use of a cubic module that can only slide across other modules’ surfaces. The idea of a cubic modular robot with sliding-only motion primitive is a new concept that has advantages in simplifying the mechanisms of module hardware and space saving in its heterogeneous operations compared with previously studied cubic modules, such as those with sliding and convex motion primitives, or rotating motion primitives. However, because of its limited mobility, there are difficulties in managing the connectivity and scalability of the heterogeneous reconfiguration algorithm for it. To overcome these disadvantages, we introduce a parallel heterogeneous permutation method with linear operating time cost that can be incorporated into our previous full-resolution reconfiguration algorithm. We prove the correctness and completeness of the proposed algorithm. Simulation results show that the full-resolution reconfiguration algorithm that incorporates the proposed permutation algorithm reconfigures the robot structure with sliding-only cubic modules in linear operating-time cost.