  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.
