In this paper, we address the problem of mapping outdoor rough terrain environments for mobile robots. While uncertainties arising from multiple sources are considered explicitly and assumed to be unknownbut-bounded, a set-theoretic framework is proposed to construct the terrain model as a set-valued elevation map that extends the notion of the elevation map with elevation variation in each cell stored by intervals. The localization problem of the mobile robot is also considered and solved by a

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... set-membership filter in order to provide guaranteed bounded-pose estimation, which can be incorporated to the elevation map to improve the accuracy of the final terrain model. A more compact terrain representation can be obtained by the proposed algorithm with relatively low computational complexity, which makes it suitable for real-time applications. Furthermore, improved smoothness is achieved by the inherent conservativeness of the set-theoretic method without additional filtering or interpolation processes. Simulations as well as real-life experiments of a mobile robot operating in outdoor rough terrain environments with a 2D scanning laser rangefinder demonstrate the effectiveness and robustness of the proposed method.