Linear reconfiguration of cube-style modular robots

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) atomic operations (expand, contract, attach, detach) and is performed in O(n) parallel steps. This improves on previous reconfiguration algorithms [D. Rus, M. Vona, Crystalline robots: Self-reconfiguration with compressible unit modules, Autonomous Robots 10 (1) (2001) 107–124; S. Vassilvitskii, M. Yim, J. Suh, A complete, local and parallel reconfiguration algorithm for cube style modular robots, in: Proc. of the IEEE Intl. Conf. on Robotics and Automation, 2002, pp. 117–122; Z. Butler, D. Rus, Distributed planning and control for modular robots with unit-compressible modules, Intl. J. Robotics Res. 22 (9) (2003) 699–715, doi:10.1177/ 02783649030229002], which require O(n[superscript 2]) 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.