The authors consider the problem of terrain model acquisition by a mobile point robot placed in an unexplored terrain populated by stationary polyhedral obstacles in two/three dimensions. The point robot autonomous machine (PRAM) is used as an abstract model for real-life mobile robots. An algorithm is presented that enables the PRAM to autonomously acquire the complete model of an unexplored obstacle terrain composed of an unknown (but finite) number of polyhedral obstacles in two/three dimensions. PRAM undertakes a number of traversals to explore the obstacle terrain with the sensor, and builds the complete obstacle terrain model. The latter is completely built with N sensor scanning operations and at most 2(N - 1) elementary traversals, where N is the total number of vertices of the obstacles. The complexities of the computational operations carried out by the PRAM are estimated.
