Motion synthesis for the self-reconfiguring molecule

In this paper we present a geometric approach to specifying and planning the motion of robotic molecules on a substrate of molecules in O(n) time, where n is the number of molecules in the substrate. We describe a language for specifying the molecule motion. We give algorithms for performing global translations, rotations, and stacking of molecular structures. We show that these motions are sufficient to guarantee certain classes of motion for molecular structures. We also examine a geometric approach to synthesizing language expressions for moving a molecule on a substrate of other molecules