Efficient constant-velocity reconfiguration of crystalline robots

Abstract

SUMMARYIn this paper, we propose novel algorithms for reconfiguring modular robots that are composed ofnatoms. 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 constant velocity and can displace at most a constant number of other atoms. We assume that one of the atoms has access to the coordinates of atoms in the target configuration.Our algorithms involve a total ofO(n2) atom operations, which are performed inO(n) parallel steps. This improves on previous reconfiguration algorithms, which either useO(n2) parallel steps or do not respect the constraints mentioned above. In fact, in the settings considered, our algorithms are optimal. A further advantage of our algorithms is that reconfiguration can take place within the union of the source and target configuration space, and only requires local communication.