Catching a Robot Intruder with Limited Information

Abstract

This paper provides solutions and insight into a new set of problems of catching a mobile robot intruder using limited information about the intruder's location. The information about the intruder's location, which is termed a snapshot, is only available upon request. We formulate the problem of tracking and catching an intruder with limited number of snapshots, which we termed the Moving Target Search with Snapshots (MTSWS). In the MTSWS problem a mobile guard A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> is chasing a mobile intruder At in R2. Here, A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> knows the location of At either from a requested snapshot or if A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> is sufficiently close to A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> . The objective is to reduce the number of required snapshots and/or to reduce the distance travelled by A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> . We compute the number of snapshots that are necessary and sufficient to catch an intruder in the worst case. We also provide algorithmic solutions under a number of assumptions on the intruder's behaviour (e.g., intruder's random motion where At is oblivious to the actions taken by A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> . Last we provide solution to the problem when A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> is allowed to use k snapshots and determine the locations and the time that A <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> should take the snapshot.