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 Proceedings of the 18th Annual International Symposium on Algorithms and Computation (ISAAC 2007), December 17–19, 2007, pages 208–219.

Abstract:

In this paper we propose a novel algorithm that, given a source robot S and a target robot T, reconfigures S into T. Both S and T are robots composed of $n$ atoms arranged in 2 × 2 × 2 meta-modules. The reconfiguration involves a total of O(n) atom operations (expand, contract, attach, detach) and is performed in O(n) parallel steps. This improves on previous reconfiguration algorithms [1–3], which require O(n²) parallel steps. Our algorithm is in place; that is, the reconfiguration takes place within the union of the bounding boxes of the source and target robots. We show that the algorithm can also be implemented in a synchronous, distributed fashion.

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