We present a system for generating and understanding of dynamic and static spatial relations in robotic interaction setups. Robots describe an environment of moving blocks using English phrases that include spatial relations such as "across" and "in front of". We evaluate the system in robot-robot interactions and show that the system can robustly deal with visual perception errors, language omissions and ungrammatical utterances.
 Grounding language in sensorimotor spaces is an important and difficult task. In order, for robots to be able to interpret and produce utterances about the real world, they have to link symbolic information to continuous perceptual spaces. This requires dealing with inherent vagueness, noise and differences in perspective in the perception of the real world. This paper presents two case studies for spatial language and quantification that show how cognitive operations – the building blocks of grounded procedural semantics – can be efficiently grounded in sensorimotor spaces. In this article, principles involving the intrinsic, deictic, and extrinsic use of spatial prepositions are examined from linguistic, psychological, and AI approaches. First, I define some important terms. Second, those prepositions which permit intrinsic, deictic, and extrinsic use are specified. Third, I examine how the frame of reference is determined for all three cases. Fourth, I look at ambiguities in the use of prepositions and how they can be resolved. Finally, I introduce the natural language dialog system CITYTOUR, which can cope with the intrinsic, deictic, and extrinsic use of spatial prepositions, and compare it with the approaches dealt with in the previous sections as well as to some other AI systems. The paper presents a new model for context dependent interpretation of linguistic expressions about spatial proximity between objects in a natural scene. The paper discusses novel psycholinguistic experimental data that tests and verifies the model. The model has been implemented, and enables a conversational robot to identify objects in a scene through topological spatial relations (e.g. "X near Y"). The model can help motivate the choice between topological and projective prepositions. In conversation, people often use spatial relationships to describe their environment, e.g., "There is a desk in front of me and a doorway behind it," and to issue directives, e.g., "go around the desk and through the doorway." In our research, we have been investigating the use of spatial relationships to establish a natural communication mechanism between people and robots, in particular, for novice users. In this paper, the work on robot spatial relationships is combined with a multimodal robot interface. We show how linguistic spatial descriptions and other spatial information can be extracted from an evidence grid map and how this information can be used in a natural, human-robot dialog. Examples using spatial language are included for both robot-to-human feedback and also human-to-robot commands. We also discuss some linguistic consequences in the semantic representations of spatial and locative information based on this work.