Construction is one of the world’s largest and least automated industries, relying on the cooperation of multiple people with diverse skillsets in labor intensive, physical tasks. Since the 1980s, efforts to introduce robots into construction contexts have mostly focused on automating discrete tasks or monitoring site activities. In this paper, by contrast, we show how robots might be designed to adaptively support the cooperative work of construction teams. Following an indicative review of the state of the art in construction robotics, the paper shows how a detailed ethnographic study of construction workers shaped the design, development, and evaluation of a robot able to assist a team of carpentry workers by delivering tools and hardware during the installation of formwork panels. The resulting prototype is a building companion rover guided by state-of-the-art deep reinforcement learning (DRL) methods and an innovative social navigation stack. Through quantitative and qualitative evaluations in lab settings and on a construction site, we show how the rover can adaptively support carpentry workers taking their specific workflow into account. By documenting these technical and conceptual contributions, we hope to bring ”robotically-supported construction” into focus as a domain of interest for the construction robotics community.