A Dynamics Perspective of Pursuit-Evasion: Capturing and Escaping When the Pursuer Runs Faster Than the Agile Evader

Pursuit-evasion is fascinating in both nature and artificial world. Typically, a pursuer runs faster than its targeted evader while with less agile maneuverability. Naturally, there is a wonder that how an evader escapes from a faster pursuer or how faster a pursuer is able to capture an agile evader? This is not yet answered from the dynamics (i.e., Lagrangian or Newtonian) perspective. In this paper, we first provide a concise dynamics formulation from a bio-inspired perspective, in which the evader's escape strategy consists of two simplest possible yet efficient ingredients integrated as an organic whole, i.e., the suddenly turning-left or turning-right propelling maneuver, together with the early alert condition for starting and maintaining this maneuver. Then, we characterize the dynamic properties of the system at two different levels: 1) the maneuvers and non-trivial escape of the evader, at the level of individual runs of the system; and further 2) the non-trivial escape zones, the sharp phase-transitions and the phase-transition lines of the gaming outcome, at the level of the running results with respect to different ranges of the system parameters. The results are consistent with natural observations and may disclose some clues of natural laws, as well as imply applications in competition of autonomous mobile robots.