A recent arXiv preprint tackles a pursuit-evasion problem with a kinematic twist: the pursuer is a Reeds-Shepp vehicle, meaning it moves like a car with a minimum turning radius, and it can only detect the evader within a forward conic field of view. The evader, by contrast, is omnidirectional, able to move in any direction instantly. The question is how the evader can escape the pursuer's cone in minimum time.
The paper considers the case where the evader is slower or equally fast as the pursuer, parameterized by a speed ratio ν and the cone's half-angle. For this regime, the authors derive a classification of the game and compute its value—the minimal escape time under optimal play from both sides. The abstract indicates that the analysis covers the full range of cone angles and speed ratios for the slower-or-equal case, though the exact conditions are truncated in the announcement.
The contribution is a complete game-theoretic solution for this specific class of pursuit-evasion, which could inform path planning or surveillance scenarios where a limited-sensor pursuer chases a more agile but slower target. The work is theoretical and appears to be newly announced on arXiv, with the full details pending in the manuscript.