Spiral Sweeping Protocols for Detection of 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. The feasibility of completing these tasks depends on geometric and dynamic constraints that impose a lower bound on the speed that the agents' formation must have. This speed is derived to ensure the satisfaction of the confinement task and increasing it above the lower bound enables sweepers to complete the full search task as well. We present two spiral line formation search processes for smart evaders, that address current limitations in search against smart evaders and 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.