Coordinated Search With Multiple Robots Arranged in Line Formations

In this paper, we address the problem of detecting intruders in complex bidimensional environments with a team of robots arranged in line formations called sweep lines. Sweep lines are used to coordinate the motion of multiple robots and guarantee the detection of any number of arbitrarily fast intruders, even when each robot has a limited sensor footprint. We present a formalization of the problem, coined Line-Clear, which requires the computation of sweep schedules to coordinate the motion of multiple sweep lines using the fewest robots possible. We provide a proof of NP-hardness of the general Line-Clear problem based on results from graph searching. An algorithm to compute sweep schedules for simply connected environments, which additionally guarantees that the cleared area is connected and not recontaminated, is then presented. We analyze its complexity formally and in simulation experiments and present solutions for a number of subproblems required for an implementation of the algorithm. The analysis provides a formal criterion for when the algorithm runs in polynomial time and the experiments indicate that this criterion may be satisfied for most environments in practice.