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.

翻译：考虑一个给定的平面圆形区域，其中存在数量未知的智能移动逃逸者。我们期望利用一支感知总长度预先确定的线列扫描编队来检测逃逸者。本文提出了设计螺旋扫描策略的流程，以确保任务成功完成，并由此推导出线列编队的扫描速度及其路径所需满足的条件。任务成功完成意味着速度受限于给定值的逃逸者无法逃脱扫描编队。对于扫描编队而言，一个更简单的任务是将逃逸者限制在期望区域内（例如其初始区域）。这些任务的可行性取决于几何与动力学约束，这些约束对扫描编队所需的速度施加了下界。我们推导出这一临界速度以确保限制任务的实现。当速度提升至该下界之上时，扫描者即可同时完成搜索任务。针对智能逃逸者，我们开发了两种螺旋线列编队搜索流程，以解决当前针对智能逃逸者搜索中存在的局限性。此外，我们对圆形线列编队扫描流程与螺旋线列编队流程的总搜索时间进行了定量与定性比较分析。我们采用总搜索时间及成功搜索所需的最小临界速度这两个指标来评估不同策略。