  For mobile robots to operate autonomously in general environments, perception
is required in the form of a dense metric map. For this purpose, we present the
stochastic triangular mesh (STM) mapping technique: a 2.5-D representation of
the surface of the environment using a continuous mesh of triangular surface
elements, where each surface element models the mean plane and roughness of the
underlying surface. In contrast to existing mapping techniques, a STM map
models the structure of the environment by ensuring a continuous model, while
also being able to be incrementally updated with linear computational cost in
the number of measurements. We reduce the effect of uncertainty in the robot
pose (position and orientation) by using landmark-relative submaps. The
uncertainty in the measurements and robot pose are accounted for by the use of
Bayesian inference techniques during the map update. We demonstrate that a STM
map can be used with sensors that generate point measurements, such as light
detection and ranging (LiDAR) sensors and stereo cameras. We show that a STM
map is a more accurate model than the only comparable online surface mapping
technique$\unicode{x2014}$a standard elevation map$\unicode{x2014}$and we also
provide qualitative results on practical datasets.
