This paper considers the problem of completing assemblies of passive objects in nonconvex environments, cluttered with convex obstacles of unknown position, shape and size that satisfy a specific separation assumption. A differential drive robot equipped with a gripper and a LIDAR sensor, capable of perceiving its environment only locally, is used to position the passive objects in a desired configuration. The method combines the virtues of a deliberative planner generating high-level, symbolic commands, with the formal guarantees of convergence and obstacle avoidance of a reactive planner that requires little onboard computation and is used online. The validity of the proposed method is verified both with formal proofs and numerical simulations. For more information: Kod*lab