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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 adoi:10.5772/57293 fatcat:iy6666wcdjdvfabkwyzebdmis4