Path planning algorithm is the key problem of Unmanned Aerial Vehicles (UAVs) mission planning. In the general case, the patrol UAV will calculate an optimal path to ensure the completion of the task, but in the adversarial and complex situations, the problem becomes more difficult. This paper presents a UAV path planning method using chaotic for border surveillance and patrol. The method uses Hénon map based on discrete memristor (DM-based Hénon map) to generate paths that are difficult to predict. To cope with complex and changing environments and possible obstacles, we combine the Rapidly-Exploring Random Trees star (RRT*) algorithm with the Artificial Potential Field (APF) method to ensure obstacle avoidance and efficient navigation in complex environments. This method enhances the adaptability and stealth of UAVs, ensuring safe and efficient operations.