We propose a novel scheme that jointly addresses the problems of powering and coordinating a population of mini-robots for collective construction. In our setting, a population of simple mobile robots must push blocks into desired polygonal shapes. Each robot performs only simple phototaxis. Coordination is purely open-loop: a global light field guides and powers the robots. We demonstrate this concept in simulation and explore a series of dynamic light field design strategies that robustly result in assembled shapes including nonconvex polygons.