Qualitative Analysis of Visibility-Based Game with Constrained Attack Range

This study addresses the visibility-based game be-tween a pursuer with constrained attack range and an evader in multi-obstacle environments. The pursuer is considered as a pivotal actor tasked with maintaining surveillance over the evader while also initiating attacks when necessary, and the evader's objective is to escape the pursuer's surveillance as quickly as possible. This represents a variant of pursuit-evasion game, wherein the game concludes if the pursuer loses sight of the evader or if their distance falls below a certain threshold. By introducing Cartesian ovoids, it becomes more intuitive and convenient to conduct qualitative analysis, obtain analytical solutions, and thereby propose the optimal strategy for the pursuer in complex environments. This study delves into effective attack strategies for the pursuer without compromising their surveillance capabilities. Additionally, it conducts simulations to validate the effectiveness of the proposed theories.