Chasing an intruder with limited information

Abstract

This paper provides solutions and insights 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 $G$ is chasing a mobile intruder $B$ in $R^{2}$. Here, $G$ knows the location of $B$ either from a requested snapshot or if $G$ is sufficiently close to $B$ by sensing it. Sensing is the ability of $G$ to detect $B$ directly (e.g., using a directional proximity sensor or a short range camera). The objectives are to determine the number of required snapshots in the worst case and to reduce the distance travelled by $G$ as it attempts to catch $B$ (i.e., getting close enough so that it can follow and catch $B$ without additional information). In this paper we present (1) Solution for computing the number of snapshots that are necessary and sufficient to catch an intruder in the worst case. (2) Algorithmic solutions when $G$ is limited to using k snapshots by determining the locations and the time that $G$ should take the snapshots. (3) Algorithmic solution when taking a snapshot is associated with a time penalty. Namely, when $G$ is taking a snapshot then $G$ must wait for a period of time before it can move again. The time penalty is applied either before or after taking a snapshot.