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The terrain acquisition problem deals with the acquisition of the complete obstacle terrain model by a mobile robot placed in an unexplored terrain. This is a precursory problem to many well-known find-path and related problems which assume the availability of the complete terrain model. In this paper, we present a method for terrain acquisition by a finite-sized robot operating in plane populated by an unknown (but, finite) number of polygonal obstacles; each obstacle is arbitrarily located and has unknown (but, finite) number of vertices. The robot progressively explores newer vertices of the obstacles using sensor equipment. We show that the complete terrain model will be built by the robot in a finite time. We also show that at any point of time the partially acquired terrain suffices for the navigation of the robot during the exploration. Hence we conclude that the navigation techniques for known terrains can be applied for the robot navigation during exploration.