An axis map (AM) represents the orientations of planar surfaces in an environment and is void of positional information. Three-dimensional axis mapping (3DAM) is a graph-based optimization algorithm that generates an AM, while carefully addressing the parameterization of axes (i.e., normal vectors). 3DAM exploits the lack of positional information to form a densely connected graph. This paper provides a detailed description of the parameterization of axes, an outline of the 3DAM algorithm, as well as outdoor experimental results showing the usefulness of AMs as a tool for mobile autonomous geotechnical mapping.

This paper introduces two-dimensional axis mapping, which estimates axis maps (AMs) based on LiDAR measurements. An AM describes the dominant orientations of surfaces in an environment and is void of positional information. As a consequence of the directional nature of the map, there are significant differences compared with traditional mapping algorithms. Experimental results are presented from simulated, indoor, outdoor, and underground environments. One major application of AMs is for heading estimation. An example of this application is shown to effectively bound the growth of heading error in both an indoor and an outdoor environment.