Collective construction of environmentally-adaptive structures

We describe decentralized algorithms by which a swarm of simple, independent, autonomous robots can build two-dimensional structures using square building blocks. These structures can (1) exactly match arbitrary user-specified designs, (2) adapt their shape to immovable obstacles, or (3) form a wall of given minimum width around an environmental feature. These three possibilities span the range from entirely prespecified structures to those whose shape is entirely determined by the environment. Robots require no explicit communication, instead using information storage capabilities of environmental elements (a form of "extended stigmergy") to coordinate their activities. We provide theoretical proof of the correctness of the algorithms for the first two types of structures, and experimental support for algorithms for the third.