Social distance augmented qualitative trajectory calculus for Human-Robot Spatial Interaction

In this paper we propose to augment a wellestablished Qualitative Trajectory Calculus (QTC) by incorporating social distances into the model to facilitate a richer and more powerful representation of Human-Robot Spatial Interaction (HRSI). By combining two variants of QTC that implement different resolutions and switching between them based on distance thresholds we show that we are able to both reduce the complexity of the representation and at the same time enrich QTC with one of the core HRSI concepts: proxemics. Building on this novel integrated QTC model, we propose to represent the joint spatial behaviour of a human and a robot employing a probabilistic representation based on Hidden Markov Models. We show the appropriateness of our approach by encoding different HRSI behaviours observed in a human-robot interaction study and show how the models can be used to represent and classify these behaviours using social distance-augmented QTC.