In this study, we investigate the challenge of detecting smart mobile evaders initially located inside a predefined planar circular region from which they try to escape without being detected by a line formation of sweeping agents. We propose spiral sweeping protocols designed to successfully carry out the task by setting specific conditions on both the speed and trajectory of the sweeping formation. These protocols are crafted to ensure that evaders, constrained by a set speed limit, cannot elude the formation’s agents. At first, the focus is on containing these evaders within a designated area. Achieving this is contingent upon certain geometric and dynamic prerequisites, which determine the minimum speed threshold for the sweepers. If the sweepers’ speed surpasses this lower bound, they are not only capable of confinement but also of complete detection, suggesting that with the right strategy, they can detect every smart evader. We present two new spiral line formation search protocols tailored for the detection of smart evaders, overcoming existing gaps in search methodologies. In addition, we conduct a comprehensive analysis comparing previously designed circular line formation sweep protocols with our newly devised protocols. Our comparative study is based on two key metrics: the duration required to detect all evaders and the minimal critical speed essential for a successful search. By evaluating these different strategies, we prove that our proposed protocols achieve a critical speed that is only slightly larger than the theoretical lower bound and that the total search time required is considerably shorter compared with previous approaches.

Suppose in a given planar region, there are smart mobile evaders and we want to detect them using sweeping agents. We assume that the agents have line sensors of equal length. We propose procedures for designing cooperative sweeping processes that ensure successful completion of the task, thereby deriving conditions on the sweeping velocity of the agents and their paths. Successful completion of the task means that evaders with a known limit on their velocity cannot escape detection by the sweeping agents. A simpler task for the sweeping swarm is the confinement of the evaders to their initial domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the velocity the sweeping agent must have. This critical velocity is derived to ensure the achievement of the confinement task. Increasing the velocity above the lower bound enables the agents to complete the search task as well. We present results on the total search time for two types of novel pincer-movement search processes, circular and spiral, for any even number of sweeping agents. The proposed spiral process allows detection of all evaders while sweeping at velocities that approach the theoretical lower bound.