  This paper formally defines a robot system, including its sensing and
actuation components, as a general, topological dynamical system. The focus is
on determining general conditions under which various environments in which the
robot can be placed are indistinguishable. A key result is that, under very
general conditions, covering maps witness such indistinguishability. This
formalizes the intuition behind the well studied loop closure problem in
robotics. An important special case is where the sensor mapping reports an
invariant of the local topological (metric) structure of an environment because
such structure is preserved by (metric) covering maps. Whereas coverings
provide a sufficient condition for the equivalence of environments, we also
give a necessary condition using bisimulation. The overall framework is applied
to unify previously identified phenomena in robotics and related fields, in
which moving agents with sensors must make inferences about their environments
based on limited data. Many open problems are identified.
