'Institute of Electrical and Electronics Engineers (IEEE)'
Abstract
This paper considers what can be accomplished
using a mobile robot that has limited sensing. For navigation
and mapping, the robot has only one sensor, which tracks the
directions of depth discontinuities. There are no coordinates, and
the robot is given a motion primitive that allows it to move toward
discontinuities. The robot is incapable of performing localization
or measuring any distances or angles. Nevertheless, when dropped
into an unknown planar environment, the robot builds a data
structure, called the Gap Navigation Tree, which enables it to
navigate optimally in terms of Euclidean distance traveled. In a
sense, the robot is able to learn the critical information contained
in the classical shortest-path roadmap, although surprisingly it is
unable to extract metric information. We prove these results for
the case of a point robot placed into a simply connected, piecewise-
analytic planar environment. The case of multiply connected
environments is also addressed, in which it is shown that further
sensing assumptions are needed. Due to the limited sensor given
to the robot, globally optimal navigation is impossible; however,
our approach achieves locally optimal (within a homotopy class)
navigation, which is the best that is theoretically possible under
this robot model
