# Virtual Streamline Traction: Formation Cooperative Obstacle Avoidance Based on Dynamical Systems
## 1 Introduction  
In recent years, the concept of unmanned systems has gained significant traction. Notably, unmanned surface vehicles (USVs) have experienced rapid advancement. As crucial elements of unmanned maritime systems, USVs offer advantages such as high-speed intelligence, compact size, maneuverability, and cost-effectiveness compared to traditional surface vessels [1]. With the diversification of marine operations, the limitations of single-vehicle operations necessitate research into the cooperative use of multiple USVs to enhance operational efficiency and expand operational scores [2]. The cooperation among multiple USVs finds applications in marine replenishment, waterway security, unmanned combat systems, hydrological and meteorological information gathering, and surface search and rescue. Such cooperation represents a collaborative approach enabling USVs to accomplish complex tasks. As a member of intelligent robots, the importance of obstacle avoidance cannot be overemphasized [3]. Formation cooperative obstacle avoidance is a foundational technology for achieving effective cooperation among multiple USVs [4; 5; 6]. The following are two practical scenarios in formation obstacle avoidance:  
1. During the initial stage of task execution by the formation, the primary step involves assembling individual vehicles into a formation--positioning each vehicle at its designated location to establish the shape of the formation. During this process, obstacles along the route of each vehicle and route conflicts between vehicles may lead to collisions. To enhance the efficiency of task execution by the formation, adynamic process is preferred, where formation assembly and task execution occur synchronously rather than waiting for all vehicles to come into formation before commencing task execution. 2. During the task execution by the formation, obstacles may be encountered along the route. Therefore, the formation should rationally avoid obstacles while ensuring a safe distance between vehicles. Following avoidance, the formation may be recovered. Given the surface motion characteristics of USVs, obstacle avoidance should be conducted without sacrificing formation robustness and efficiency. Thus, a robust and efficient virtual guidance structure is preferred [7; 8]. However, virtual structure patterns have apparent drawbacks: their poor adaptability is unfavorable for obstacle avoidance. The obstacle avoidance in the virtual structure formation method typically involves the entire formation avoiding obstacles, with members of high mobility cooperating with those of low mobility to maintain the formation. However, this cooperation reduces the flexibility of each member within the formation. Consequently, it may result in an increased total path for obstacle avoidance, particularly when dealing with small groups of obstacles. Members with high mobility can traverse such obstacle groups without detouring. To minimize unnecessary trips and enhance task efficiency, we seek a novel solution to address the limited flexibility inherent in the virtual deconstruction method. To address these drawbacks, a series of targeted explorations were conducted. Mainstream obstacle-avoidance solutions include the following:  
1. The most traditional approach is one based on geometry; among many categories, the more classic is the velocity obstacle (VO) method [9; 10; 11; 12]. 2. Model predictive control (MPC) [13; 14; 15], where [13] utilizes MPC for quadratic programming on intended velocities for obstacle avoidance, and [14] employs MPC to address collision-avoidance issues within formations. 3. Based on probability or Stochastic planning methods, rapidly exploring random trees (RRT) algorithm and its variants are common [16; 17]. 4. Artificial potential field (APF) methods [18; 19; 20], with [19; 20] using consensus algorithms alongside APF to achieve intra-formation collision avoidance and formation obstacle avoidance. 5. Methods based on machine learning, including deep learning and reinforcement learning [21; 22; 23].