  Robots operating in households must find objects on shelves, under tables,
and in cupboards. In such environments, it is crucial to search efficiently at
3D scale while coping with limited field of view and the complexity of
searching for multiple objects. Principled approaches to object search
frequently use Partially Observable Markov Decision Process (POMDP) as the
underlying framework for computing search strategies, but constrain the search
space in 2D. In this paper, we present a POMDP formulation for multi-object
search in a 3D region with a frustum-shaped field-of-view. To efficiently solve
this POMDP, we propose a multi-resolution planning algorithm based on online
Monte-Carlo tree search. In this approach, we design a novel octree-based
belief representation to capture uncertainty of the target objects at different
resolution levels, then derive abstract POMDPs at lower resolutions with
dramatically smaller state and observation spaces. Evaluation in a simulated 3D
domain shows that our approach finds objects more efficiently and successfully
compared to a set of baselines without resolution hierarchy in larger instances
under the same computational requirement. We demonstrate our approach on a
mobile robot to find objects placed at different heights in two 10m$^2 \times
2$m regions by moving its base and actuating its torso.
