We've described a scheme by which a swarm of robots can automatically assemble solid structures of square building blocks in two dimensions according to a high-level user-specified design. We discuss the use of extended stigmergy: augmenting the basic notion of stigmergy by increasing the capabilities of environmental elements. In this construction setting, the elements are the building blocks, the basic information they carry is the simple fact of their presence at a location, and extensions include cases where they can store additional information, perform computations, and/or communicate with physically attached neighbors. Benefits can include increased robustness and faster completion of a desired structure. We review three variants of that construction scheme that use extended stigmergy to different degrees. We focus on analysis of the algorithms and their comparative performance, mainly theoretical but also through simulation experiments.