2 research outputs found
Equivalent Environments and Covering Spaces for Robots
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.Comment: 34 pages, 8 figure
Locally-Optimal Navigation in Multiply-Connected Environments without Geometric Maps
In this paper we present an algorithm to build a sensor-based, dynamic data structure useful for robot navigation in an unknown, multiply-connected planar environment. This data structure offers a robust framework for robot navigation, avoiding the need of a complete geometric map or explicit localization, by building a minimal representation based entirely on critical events in online sensor measurements made by the robot. There are two sensing requirements for the robot: it must detect when it is close to the walls, to perform wall-following reliably, and it must be able to detect discontinuities in depth information. It is also assumed that the robot is able to drop, detect and recover a marker. The navigation paths generated are optimal up to the homotopy class to which the paths belong, even though no distance information is measured