# Multi-UAV Cooperative Anti-Submarine Search Based on a Rule-Driven MAC Scheme
## 1 Introduction  
In the past decade, UAVs have been widely used in surveillance, search, target tracking, damage assessment, and other fields. Multi-UAV cooperative anti-submarine research has received increasing attention from academics and the national defense industry [1, 2, 3]. Because UAV cooperative anti-submarine technology has the characteristics of good concealment and strong maneuvering search ability, it can realize reconnaissance coverage of the mission area to discover the target and obtain information. Therefore, a considerable amount of research on multi-UAV cooperative search submarine technology has been carried out [4, 5, 6]. Collaborative search is a probabilistic detection task, which requires updating of the probability of dynamic targets according to the observations of multi-UAVs in order to describe the position of the target in a probabilistic way and help UAVs to make increasingly accurate decisions to find the target. To achieve the probability update of dynamic targets, it is necessary to establish a search environment model. To date, significant research has been conducted in this field; among the important topics is to establish an environmental grid search map [4, 7, 8, 9, 10], which can be divided into a target probability map, digital pheromone map, return rate map, etc. For example, in [7], a search map method based on a target probability map was proposed, which can update the target existence probability in real time based on a collaborative search framework and effectively improve search efficiency. A UAV collaborative search method based on a digital pheromone model was designed in [8]; the search environment was modeled by abstracting the concept of digital pheromones, which was used to coordinate a swarm of UAVs into biological swarms, which can adapt to dynamic changes in the environment. In [9], a digital pheromone map was extended and combined with a genetic algorithm to solve the coordination problem of multi-UAVs with respect to the area coverage problem. In [10], an integrated targetprobability map and an certainty map were proposed based on the concept of a \"territorial awareness information map\", which can efficiently coordinate the tracks of multi-UAVs in the face of clustered targets. In [4], a method of dynamic asset allocation was designed in an uncertain task environment, whereby each asset is allocated to a specific area, and, with the movement of the target, the assets are periodically reallocated, which optimizes the search space and improves the search efficiency. However, the establishment of the above search grid probability does not consider the correlation between the targets. In particular, in anti-submarine missions, the target submarine cooperates with other warships or submarines in a certain tactical formation [11]; that is, the submarine maintains a certain position in relation to the surrounding warships to form a protective formation. Therefore, it is necessary to study the correlation between target submarines and ships, as well as the formation characteristics of mutual cover, and to establish an association rule-driven target probability map model. This remains an open and challenging problem and is the research object of this paper. On the other hand, extensive research has also been carried out on search algorithms for multi-UAV dynamic targets. Intelligent algorithms have received increasing attention as a means solving path-planning problems in complex dynamic environments. Intelligent algorithms [12; 13; 14; 15] include particle swarm algorithms, immune genetic algorithms, bee swarm algorithms, neural network algorithms, etc. For example, in [12], the search problem was transformed into an optimization problem of detecting the target probability by using the Bayesian theorem, and a motion-coding particle swarm optimization algorithm was proposed to generate the motion path of UAVs.