This paper addresses the problem of copying an unknown assembly of primitives with known shape and appearance using information extracted from a single photograph by an off-the-shelf procedure for object detection and pose estimation. The proposed algorithm uses a simple combination of physical stability constraints, convex optimization and Monte Carlo tree search to plan assemblies as sequences of pick-and-place operations represented by STRIPS operators. It is efficient and, most importantly, robust to the errors in object detection and pose estimation unavoidable in any real robotic system. The proposed approach is demonstrated with thorough experiments on a UR5 manipulator.