Abstract:
Pursuit-evasion problems arise in many contexts, such as cooperative encirclement by autonomous robots, defense operations, and collective behavior in biological systems. They are important for understanding how multiple agents make decisions and cooperate in uncertain environments. In reality, both pursuers and evaders are affected by random environmental factors. However, most existing analytical models either add noise only to the evader or treat the pursuer as fully deterministic, which makes it difficult to characterize the system behavior when both sides are uncertain. To address this issue, this paper studies a multi-pursuer pursuit-evasion system in a two-dimensional continuous space with random disturbances. A dynamical model is developed that includes random perturbations on both the pursuer and evader sides, and allows the evader to actively escape based on relative position information. For the single-pursuer case, we derive an analytical expression for the mean capture time (MCT) using the theory of mean first-passage time for stochastic differential equations, and obtain the scaling relation between the velocities and the noise intensities. Numerical simulations are used to verify the quantitative accuracy of the analytical results and their ability to capture the main features of the dynamics. For systems with one, two, and multiple pursuers, we then study how the MCT and the distributions of capture times depend on the number of pursuers, the noise intensities of both sides, and the velocity ratio between pursuers and evader. The results show several effects: the disappearance of critical behavior, a change in the role of noise from delaying capture to generally accelerating capture, and an increase in system robustness as the number of pursuers grows. Under ideal assumptions of a two-dimensional unbounded domain, isotropic white noise, and instantaneous sensing, these results provide a clear and testable theoretical framework for designing multi-pursuer cooperative capture strategies and choosing parameters in uncertain environments. They also lay a foundation for future work on more complex settings, such as bounded domains, complex boundaries, and learning-based strategies.
