  Occupancy grids are the most common framework when it comes to creating a map
of the environment using a robot. This paper studies occupancy grids from the
motion planning perspective and proposes a mapping method that provides richer
data (map) for the purpose of planning and collision avoidance. Typically, in
occupancy grid mapping, each cell contains a single number representing the
probability of cell being occupied. This leads to conflicts in the map, and
more importantly inconsistency between the map error and reported confidence
values. Such inconsistencies pose challenges for the planner that relies on the
generated map for planning motions. In this work, we store a richer data at
each voxel including an accurate estimate of the variance of occupancy. We show
that in addition to achieving maps that are often more accurate than tradition
methods, the proposed filtering scheme demonstrates a much higher level of
consistency between its error and its reported confidence. This allows the
planner to reason about acquisition of the future sensory information. Such
planning can lead to active perception maneuvers that while guiding the robot
toward the goal aims at increasing the confidence in parts of the map that are
relevant to accomplishing the task.
