The goal of this research is to devise guaranteed defense policies that allow to protect a given region from the entrance of smart mobile invaders by detecting them using a team of defending agents equipped with identical line sensors. By designing cooperative defense strategies that ensure all invaders are detected, conditions on the defenders' speed are derived. Successful accomplishment of the defense task implies invaders with a known limit on their speed cannot slip past the defenders and enter the guarded region undetected. The desired outcome of the defense protocols is to defend the area and additionally to expand it as much as possible. Expansion becomes possible if the defenders' speed exceeds a critical speed that is necessary to only defend the initial region. We present results on the total search time, critical speeds and maximal expansion possible for two types of novel pincer-movement defense processes, circular and spiral, for any even number of defenders. The proposed spiral process allows to detect invaders at nearly the lowest theoretically optimal speed, and if this speed is exceeded, it also allows to expand the protected region almost to the maximal area.

Assume that inside an initial planar area there are smart mobile evaders attempting to avoid detection by a team of sweeping searching agents. All sweepers detect evaders with fan-shaped sensors, modeling the field of view of real cameras. Detection of all evaders is guaranteed with cooperative sweeping strategies, by setting requirements on sweepers' speed, and by carefully designing their trajectories. Assume the smart evaders have an upper limit on their speed which is a-priori known to the sweeping team. An easier task for the team of sweepers is to confine evaders to the domain in which they are initially located. The sweepers accomplish the confinement task if they move sufficiently fast and detect evaders by applying an appropriate search strategy. Any given search strategy results in a minimal sweeper's speed in order to be able to detect all evaders. The minimal speed guarantees the ability of the sweeping team to confine evaders to their original domain, and if the sweepers move faster they are able to detect all evaders that are present in the region. We present results on the total search time for a novel pincer-movement based search protocol that utilizes complementary trajectories along with adaptive sensor geometries for any even number of pursuers.