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We study the problem of pursuit-evasion for a single pursuer and an evader in polygonal environments where the players have visibility constraints. The pursuer is tasked with catching the evader as quickly as possible while the evader tries to avoid being captured. We formalize this problem as a zero-sum game where the players have private observations and conflicting objectives.One of the challenging aspects of this game is due to limited visibility. When a player, for example, the pursuer does not see the evader, it needs to reason about all possible locations of the evader. This causes an exponential increase in the size of the state space as compared to the arena size. To overcome the challenges associated with large state spaces, we introduce a new learning-based method that compresses the game state and uses it to plan actions for the players. The results indicate that our method outperforms the existing reinforcement learning methods, and performs competitively against the current state-of-the-art randomized strategy in complex environments.
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Usable boundary for visibility-based surveillance-evasion games
Abstract We consider a surveillance-evasion game in an environment with obstacles. In such an environment, a mobile pursuer seeks to maintain visibility with a mobile evader, who tries to hide from the pursuer in the shortest time possible. In this two-player zero-sum game setting, we study the discontinuities of the value of the game near the boundary of the target set, where the players cannot see each other (the non-visibility region). In particular, we describe the transition between the usable part of the boundary of the target (where the value vanishes) and the non-usable part (where the value is positive). We show that the value exhibits different behaviour depending on the regularity of the obstacles. Namely, we prove that the boundary profile is continuous in the case of smooth obstacles and that it exhibits a jump discontinuity when the obstacle contains corners. Moreover, we prove that, in the latter case, there is a semi-permeable barrier emanating from the interface between the usable and the non-usable part of the boundary of the target set.
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- Award ID(s):
- 2110895
- PAR ID:
- 10599424
- Publisher / Repository:
- Springer Science + Business Media
- Date Published:
- Journal Name:
- Research in the Mathematical Sciences
- Volume:
- 12
- Issue:
- 3
- ISSN:
- 2522-0144
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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