Realistic reconfiguration of Crystalline and Telecube robots

Abstract: In this paper we propose novel algorithms for reconfiguring modular robots that are composed of n atoms. Each atom has the shape of a unit cube and can expand/contract each face by half a unit, as well as attach to or detach from faces of neighboring atoms. For universal reconfiguration, atoms must be arranged in 2 × 2 × 2 modules. We respect certain physical constraints: each atom reaches at most unit velocity and (via expansion) can displace at most one other atom. We require that one of the modules can store a map of the target configuration. Our algorithms involve a total of O(n2) such atom operations, which are per-formed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n2) parallel steps [7, 9, 4] or do not respect the constraints men-tioned above [1]. In fact, in the setting considered, our algorithms are optimal, in the sense that certain reconfigurations require Ω(n) parallel steps. A further advan-tage of our algorithms is that reconfiguration can take place within the union of the source and target configurations. ∗ Charge ́ de Recherches du FNRS