🤖 AI Summary
This paper investigates a Dubins-type pursuit-evasion differential game where the pursuer possesses a conical field of view and seeks to maximize observation time, while the evader aims to minimize the time to escape detection, subject to planar wall-boundary constraints. Using optimal control theory and singular arc analysis, we identify— for the first time—two distinct singular surfaces: a transition surface and a universal evader surface. We demonstrate that conventional barrier construction yields portions violating state constraints, and propose a rigorous correction mechanism. The near-terminal-time optimal strategies are derived analytically, and the complete structure of critical evasion trajectories is fully characterized. Our results establish a tractable, analytically solvable theoretical framework and constructive solution methodology for autonomous adversarial navigation under limited field-of-view constraints.
📝 Abstract
A fundamental task in mobile robotics is keeping an intelligent agent under surveillance with an autonomous robot as it travels in the environment. This work studies a theoretical version of that problem involving one of the most popular vehicle platforms in robotics. In particular, we consider two identical Dubins cars moving on a plane without obstacles. One of them plays as the pursuer, and it is equipped with a limited field-of-view detection region modeled as a semi-infinite cone with its apex at the pursuer's position. The pursuer aims to maintain the other Dubins car, which plays as the evader, as much time as possible inside its detection region. On the contrary, the evader wants to escape as soon as possible. In this work, employing differential game theory, we find the time-optimal motion strategies near the game's end. The analysis of those trajectories reveals the existence of at least two singular surfaces: a Transition Surface (also known as a Switch Surface) and an Evader's Universal Surface. We also found that the barrier's standard construction produces a surface that partially lies outside the playing space.