Pursuit-evasion dynamics for multi-USV with heading angle limits and random noises

Unmanned Surface Vehicles (USVs) have significantly advanced marine technology, offering substantial potential for various applications. This study introduces an innovative random pursuit-evasion framework for USVs, addressing critical gaps by simultaneously incorporating heading angle constraints and environmental noise. By integrating heading angle limits with Gaussian noise to model environmental uncertainties, we establish a robust analytical foundation for examining pursuit-evasion dynamics across varying group sizes. This framework is based on distinct evasion strategies, including Weighted Collective Avoidance and Nearest-Pursuer Avoidance. Our primary metric, mean capture time (CT), is used to evaluate scenarios with varying numbers of pursuers and a single evader. Through numerical simulations and theoretical analyses, we explore how noise intensities and heading limitations jointly affect CTs and evasion effectiveness. Our findings reveal that both environmental disturbances and kinematic constraints significantly impact the dynamics of pursuit-evasion interactions. This research advances the theoretical understanding of random pursuit-evasion dynamics and provides potential applications for enhancing the operational capabilities of USVs in complex and uncertain maritime environments.