This paper addresses the issue of grounding spatial relations in natural language for human-robot interaction and robot control. The problem is approached by identifying two set of spatial relations, the image space-based and object-centered, and expressing them as fuzzy sets to capture the ambiguity inherent to the linguistic expressions for the relations. The sizes and shades of the scene objects have also been modeled as fuzzy sets for conditioning the spatial relations. To verify the validity of our approach and test its feasibility in a natural language-based interface, we have considered the typical scenarios of using the spatial relations in simple declarative and imperative sentences and designed simple grammars for parsing such sentences. Our experiment has shown that fuzzy spatial relation analysis provides a useful way for modeling the ambiguity or imprecision of the natural language in describing spatial relations and that it is possible to use the spatial relation models to support robot control and human-robot interaction in a natural language-based interface.
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