Abstract. In recent work [4] , capillary forces between tiles floating on a liquidliquid interface are used to direct a self-assembly process. By carefully arranging the wetabilities of the edges of the tiles, regular arrays of various shapes spontaneously form when the tiles are gently shaken. It is difficult, however, to avoid flaws in the assembled aggregates and to assemble terminating and asymmetric structures. In this paper, we suppose that the wetability properties of the tiles, and therefore the capillary forces , can be controlled. In particular, we introduce a simple model of a "waterbug" shaped tile and derive the equations of motion for a system of such tiles from a model of the lateral forces between two floating colloidal particles. We then explore the possibilities for control in this setting and present some initial forays into addressing the above difficulties.
A simple dynamical model of the physics of tile assembly has been described REF .
Toward the Control of Self-Assembling Systems
Control Problems in Robotics
Engineering Computer Science