Searching and mapping among indistinguishable convex obstacles

We present exploration and mapping strategies for a mobile robot moving among a finite collection of convex obstacles in the plane. The obstacles are unknown to the robot, which does not have access to coordinates and cannot measure distances or angles. The robot has a unique sensor, called the gap sensor, that tracks the direction of the depth discontinuities in the robot's visibility region. Furthermore, the robot can only move towards depth discontinuities. As the robot moves, the depth discontinuities split and merge, and these changes are encoded in a Gap Navigation Tree. We present a strategy for this robot that is guaranteed to explore the whole environment, but that cannot decide whether the exploration has been completed. If in addition it is assumed that the robot has access to a pebble, which is an identifiable point that the robot can manipulate, then we prove that the robot can decide (in polynomial time in the number of obstacles) whether the environment has been completely explored. For this, the robot is able to distinguish every obstacle using only the gap sensor and a single pebble. These results are a continuation of our previous work on gap sensing for multiply connected environments, in which we reduce the sensing requirements for the robot by constraining the shape of the obstacles.