Spiral Sweeping Search for Smart Evaders

Consider a given planar circular region, in which there is an unknown number of smart mobile evaders. We wish to detect evaders using a line formation of sweeping agents whose total sensing length is predetermined. We propose procedures for designing spiral sweeping protocols that ensure the successful completion of the task, thus deriving conditions on the sweeping speed of the linear formation and its path. Successful completion of the task implies that evaders with a given limit on their speed cannot escape the sweeping agents. A simpler task for the sweeping formation is the confinement of evaders to a desired region, such as their original domain. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the speed that the sweeping agents must have. This critical speed is derived to ensure the satisfaction of the confinement task. Increasing the speed above the lower bound enables the sweepers to complete the search task as well. We develop two spiral line formation search processes for smart evaders, that address current limitations in search against smart evaders. Additionally, we present a quantitative and qualitative comparison analysis between the total search time of circular line formation sweep processes and spiral line formation processes. We evaluate the different strategies by using two metrics, total search time and the minimal critical speed required for a successful search.