The analysis and understanding of human-robot joint spatial behaviour (JSB) - such as guiding, approaching, departing, or coordinating movements in narrow spaces - and its communicative and dynamic aspects are key requirements on the road towards more intuitive interaction, safe encounter, and appealing living with mobile robots. This endeavours demand for appropriate models and methodologies to represent JSB and facilitate its analysis. In this paper, we adopt a qualitative trajectory calculus (QTC) as a formal foundation for the analysis and representation of such spatial behaviour of a human and a robot based on a compact encoding of the relative trajectories of two interacting agents in a sequential model. We present this QTC together with a distance measure and a probabilistic behaviour model and outline its usage in an actual JSB study. We argue that the proposed QTC coding scheme and derived methodologies for analysis and modelling are flexible and extensible to be adapted for a variety of other scenarios and studies. © 2012 IEEE.
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