Cooperative task execution, a hallmark of eusociality, is enabled by local interactions between the agents and the environment through a dynamically evolving communication signal. Inspired by the collective behavior of social insects whose dynamics is modulated by interactions with the environment, we show that a robot collective can successfully nucleate a construction site via a trapping instability and cooperatively build organized structures. The same robot collective can also perform de-construction with a simple change in the behavioral parameter. These behaviors belong to a two-dimensional phase space of cooperative behaviors defined by agent-agent interaction (cooperation) along one axis and the agent-environment interaction (collection and deposition) on the other. Our behavior-based approach to robot design combined with a principled derivation of local rules enables the collective to solve tasks with robustness to a dynamically changing environment and a wealth of complex behaviors. The solution of complex problems on scales much This naturally raises two questions: (i) how do we design larger than the size of an individual, in both natural [1-8] a set of microscopic behavioral rules at the level of an individual and artificial systems [9-12], often requires the cooperative agent that leads to the emergence of robust and effort of a collective. An example is the collective flexible task completion? One difficulty is derive a principled approach for the synthesis of a broader that the participating agents in a collective must interact class of cooperative behaviors: collective architecture.