Representing Spatial Object Relations as Parametric Polar Distribution for Scene Manipulation Based on Verbal Commands

Abstract

Understanding spatial relations is a key element for natural human-robot interaction. Especially, a robot must be able to manipulate a given scene according to a human verbal command specifying desired spatial relations between objects. To endow robots with this ability, a suitable representation of spatial relations is necessary, which should be derivable from human demonstrations. We claim that polar coordinates can capture the underlying structure of spatial relations better than Cartesian coordinates and propose a parametric probability distribution defined in polar coordinates to represent spatial relations. We consider static spatial relations such as left of, behind, and near, as well as dynamic ones such as closer to and other side of, and take into account verbal modifiers such as roughly and a lot. We show that adequate distributions can be derived for various combinations of spatial relations and modifiers in a sample-efficient way using Maximum Likelihood Estimation, evaluate the effects of modifiers on the distribution parameters, and demonstrate our representation's usefulness in a pick-and-place task on a real robot.