The operational environments in which a mobile robot executes its missions often exhibit non-flat terrain characteristics, encompassing outdoor and indoor settings featuring ramps and slopes. In such scenarios, the conventional methodologies employed for localization encounter novel challenges and limitations. This study delineates a localization framework incorporating ground elevation and inclination considerations, deviating from traditional 2D localization paradigms that may falter in such contexts. In our proposed approach, the map encompasses elevation and spatial occupancy information, employing Gridmaps and Octomaps. At the same time, the perception model is designed to accommodate the robot's inclined orientation and the potential presence of ground as an obstacle, besides usual structural and dynamic obstacles. We have developed and rigorously validated our approach within Nav2, and esteemed open-source framework renowned for robot navigation. Our findings demonstrate that our methodology represents a viable and effective alternative for mobile robots operating in challenging outdoor environments or intrincate terrains.

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