Configuration Space Metrics

Abstract

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.