An Efficient Spatial Representation for Path Planning of Ground Robots in 3D Environments

For efficient path planning of ground robots in 3D environments with structures such as buildings or overhanging objects, an appropriate spatial representation of the environment is normally required. Some popular representations, such as elevation maps and multi-level surface maps, need to be projected into a 2D plane to extract traversibility maps for path planning. They cannot properly handle all complex situations, such as bridges. Some other predominant representations, such as 3D occupancy grid maps and 3D normal distributions maps, typically have high computational and storage demands. In this paper, we propose a 2.5D normal distributions transform map (NDT map) as an efficient and compact representation of 3D environments for path planning of ground robots. Our open-source work partitions the space evenly in $x-y$ direction and $z$ direction separately and transforms the 3D point clouds of environments into 2.5D representation based on the NDT. The 2.5D-NDT map only stores space surface patches that are potentially navigable for path planning of ground robots, and represents them with four parameters based on the NDT. Moreover, the map is efficiently organized by our proposed two-layer indexes to speed up the computation. We further present algorithms for a traversability analysis and path planning, which utilize the proposed map. Experiments on data sets, containing indoor and outdoor scenarios, demonstrate that our approach can represent 3D environments properly and compactly for path planning of ground robots. Paths suitable for navigation of ground robots can be planned efficiently in complex 3D environments based on our proposed algorithm.