Paper by Erik D. Demaine

Reference:

Greg Aloupis, Sébastien Collette, Mirela Damian, Erik D. Demaine, Robin Flatland, Stefan Langerman, Joseph O'Rourke, Suneeta Ramaswami, Vera Sacristán, and Stefanie Wuhrer, “Linear Reconfiguration of Cube-Style Modular Robots”, in Abstracts from the 12th Encuentros de Geometría Computacional (EGC 2007), June 25–27, 2007, pages 19–34.

Abstract:

In this paper we propose a novel algorithm for both contracting and expanding cube-style modular robots which reconfigures any given source robot composed of n atoms into any given target robot with O(n) basic actions, improving on previous O(n²) algorithms. During reconfiguration, the robot forms one connected component at all times, and the reconfiguration takes place within the union of the bounding boxes of the initial and final robot configurations. The algorithm can be implemented using distributed control and allowing massive simultaneous parallel moves of the atoms.

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