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 Ah is chasing a mobile intruder At in R2. Here, Ah knows the location of At either from a requested snapshot or if Ah is sufficiently close to At. The objective is to reduce the number of required snapshots and/or to reduce the distance travelled by Ah• 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 Ah• Last we provide solution to the problem when Ah is allowed to use $k$ snapshots and determine the locations and the time that Ah should take the snapshot.