Abstract
The pursuit-evasion problem is widespread in nature, engineering, and societal applications. It is commonly observed in nature that predators often exhibit faster speeds than their prey but have less agile maneuverability. Over millions of years of evolution, animals have developed effective and efficient strategies for both pursuit and evasion. In this paper, we provide a dynamic framework for the pursuit-evasion problem of unicycle systems, drawing inspiration from nature. First, we address the scenario involving one pursuer and one evader by proposing an Alert-Turn control strategy, which consists of two efficient ingredients: a sudden turning maneuver and an alert condition for starting and maintaining the maneuver. We present and analyze the escape and capture results at two levels: a lower level of a single run and a higher level with respect to parameters' changes. In addition, we provide a theorem with sufficient conditions for capture. The Alert-Turn strategy is then extended