Stochastic event capturing with a single mobile robot in rectangular perimeters

Abstract

In this paper, we are interested in a single robot detecting intrusions across a rectangular perimeter. We build a stochastic model to analyze the detection quality achieved by a single robot moving along the rectangular perimeter, based on the velocity and the mobility pattern. We define the following intrusion event mode: intrusions occur at a random point along the rectangular perimeter, and stay at that point for a random length of time. In our model, a robot is set to periodically move along a certain route at a variable speed. We derive the general expression for intrusion loss probability. Under the reasonable assumption that, once an intrusion takes place at a random point in the rectangular perimeter, it stays there for a random length of time, which follows an exponential distribution, we then derive the solution to the above problem.