On the Time to Search for an Intermittent Signal Source Under a Limited Sensing Range

A mobile robot with a limited sensing range is deployed to search for a stationary target that intermittently emits short duration signals. The searching mission is accomplished as soon as the robot receives a signal from the target. We propose the expected searching time (EST) as a primary metric to evaluate different robot motion plans under different robot configurations. To illustrate the proposed metric, we present two case studies. In the first case, we analyze two common motion plans: a slap method (SM) and a random walk (RW). The EST analysis shows that the SM is asymptotically faster than the RW when the searching space size increases. In the second case, we compare a team of n homogeneous low-cost robots with a super robot that has the sensing range equal to that of the summation of the n robots. Our analysis shows that the low-cost robot team takes Θ(1/n) time, while the super robot takes Θ(1/√n) time as n → ∞. Our metrics successfully demonstrate their ability in assessing the searching performance. The analytical results are also confirmed in simulation and physical experiments.