05859663

a

05859663 Aloupis, Greg Collette, S\'ebastien Damian, Mirela Demaine, Erik D. El-Khechen, Dania Flatland, Robin Langerman, Stefan O'Rourke, Joseph Pinciu, Val Ramaswami, Suneeta Sacrist\'an, Vera Wuhrer, Stefanie Realistic reconfiguration of crystalline (and telecube) robots. Chirikjian, Gregory S. (ed.) et al., Algorithmic foundations of robotics VIII. Selected contributions of the eighth international workshop on the algorithmic foundations of robotics (WAFR 2008), Guanajuato, M\'exico, December 7--9, 2008. Berlin: Springer (ISBN 978-3-642-00311-0/hbk978-3-642-00312-7/ebook). Springer Tracts in Advanced Robotics 57, 433-447 (2010). 2010 Berlin: Springer EN

doi:10.1007/978-3-642-00312-7_27

Summary: 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\times 2\times $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 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 $\Omega (n)$ parallel steps. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configurations.