  When robot manipulators decide how to reach for an object, hand it over, or
obey some task constraint, they implicitly assume a Euclidean distance metric
in their configuration space. Their notion of what makes a configuration closer
or further is dictated by this assumption. But different distance metrics will
lead to different solutions. What is efficient under a Euclidean metric might
not necessarily look the most efficient or natural to a person observing the
robot. In this paper, we analyze the effect of the metric on robot behavior,
examining both Euclidean, as well as non-Euclidean metrics -- metrics that make
certain joints cheaper, or that correlate different joints. Our user data
suggests that tasks on a 3DOF arm and the Jaco 7DOF arm can typically be
grouped into ones where a Euclidean metric works well, and tasks where that is
no longer the case: there, surprisingly, penalizing elbow motion (and sometimes
correlating the shoulder and wrist) leads to solutions that are more aligned
with what users prefer.
