  This paper introduces mathematical models of \sensors\ for mobile robots
based on visibility. Serving a purpose similar to the pinhole camera model for
computer vision, the introduced models are expected to provide a useful,
idealized characterization of task-relevant information that can be inferred
from their outputs or observations. Possible tasks include navigation,
localization and mapping when a mobile robot is deployed in an unknown
environment. These models allow direct comparisons to be made between
traditional depth sensors, highlighting cases in which touch sensing may be
interchangeable with time of flight or vision sensors, and characterizing
unique advantages provided by touch sensing. The models include contact
detection, compression, load bearing, and deflection. The results could serve
as a basic building block for innovative touch sensor designs for mobile robot
sensor fusion systems.
