Realistic Reconfiguration of Crystalline (and Telecube) Robots.
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 atoms can store a map of the target configuration. Our algorithms involve a total of O(n 2) such atom operations, which are performed in O(n) parallel steps. This improves on previous reconfiguration algorithms, which either use O(n 2) parallel steps [7, 9, 4] or do not respect the constraints mentioned above . In fact, in the setting considered, our algorithms are optimal, in the sense that certain reconfigurations require Ω(n) parallel steps. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configurations.
|Main Author:||Aloupis, Greg.|
|Other Authors:||Collette, Sebastien., Damian, Mirela., Demaine, Erik D., El-Khechen, Dania., Flatland, Robin., Langerman, Stefan., O'Rourke, Joseph., Pinciu, Val., Ramaswami, Suneeta., Sacristan, Vera., Wuhrer, Stefanie.|