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We propose that an important aspect of human-robot interaction is perspective-taking. We show how perspective-taking occurs in a naturalistic environment (astronauts working on a collaborative project) and present a cognitive architecture for performing perspective-taking called Polyscheme. Finally, we show a fully integrated system that instantiates our theoretical framework within a working robot system. Our system successfully solves a series of perspective-taking problems and uses the same frames of references that astronauts do to facilitate collaborative problem solving with a person.