  Human-centered environments are rich with a wide variety of spatial relations
between everyday objects. For autonomous robots to operate effectively in such
environments, they should be able to reason about these relations and
generalize them to objects with different shapes and sizes. For example, having
learned to place a toy inside a basket, a robot should be able to generalize
this concept using a spoon and a cup. This requires a robot to have the
flexibility to learn arbitrary relations in a lifelong manner, making it
challenging for an expert to pre-program it with sufficient knowledge to do so
beforehand. In this paper, we address the problem of learning spatial relations
by introducing a novel method from the perspective of distance metric learning.
Our approach enables a robot to reason about the similarity between pairwise
spatial relations, thereby enabling it to use its previous knowledge when
presented with a new relation to imitate. We show how this makes it possible to
learn arbitrary spatial relations from non-expert users using a small number of
examples and in an interactive manner. Our extensive evaluation with real-world
data demonstrates the effectiveness of our method in reasoning about a
continuous spectrum of spatial relations and generalizing them to new objects.
