# Search for Smart Evaders with Sweeping Agents

## TL;DR

This paper develops sweeping strategies for line-formations of agents to detect or confine smart evaders in a planar region, deriving velocity conditions and analyzing search times based on geometric and dynamic constraints.

## Contribution

It introduces procedures for designing sweeping processes with velocity bounds to ensure evader detection or confinement, considering geometric and dynamic factors.

## Key findings

- Derived critical velocity bounds for successful search and confinement.
- Provided formulas relating search time to sweeping velocity and initial conditions.
- Demonstrated how increasing velocity improves search success probability.

## Abstract

Suppose that in a given planar circular region, there are some smart mobile evaders and we would like to find them using sweeping agents. We assume that the sweeping agents are in a line formation whose total length is 2r. We propose procedures for designing a sweeping process that ensures the successful completion of the task, thereby deriving conditions on the sweeping velocity of the linear formation and its path. Successful completion of the task means that evaders with a given limit on their velocity cannot escape the sweeping agents. A simpler task for the sweeping formation 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 that the sweeper line formation must have. This critical velocity is derived to ensure the satisfaction 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 as a function of the sweeping velocity of the formation given the initial conditions on the size of the search region and the maximal velocity of the evaders.