# Collaborative Multi-Robot Formation Control and Global Path Optimization
## 1 Introduction  
In the context of the continuous development and improvement of artificial intelligence theory, mobile robots have become more intelligent and autonomous, capable of replacing or assisting humans to complete dangerous, complex, and boring work. Therefore, mobile robots are widely used in industrial production, military operations, medical services, construction, and other fields. As a crucial technology for mobile robots, navigation technology fundamentally affects the path planning capability of mobile robots, determines whether they can identify and avoid obstacles, and calculates the best route to complete the task in the current working environment, quickly and accurately [1]. With the rapid development of various industries, single robots are no longer able to meet the demands of enterprises in terms of production, cost, and service efficiency, etc. Therefore, people are improving the performance of single robots and working on the research of multi-robot formation control to accomplish tasks that cannot be done by a single robot. The working environment of mobile robots is divided into static and dynamic [2]. In the former, the start and end points and obstacles are known and unchanged; in the latter, the moving path has to be calculated in real time based on the feedback information from sensors, since the start and endpoints and obstacles are dynamically changed. Path planning is further divided into local and global, depending on how much information the robot has about the environment. For the former, the environmental information is opaque, and the robot acquires information through sensors such as the position and geometric properties of obstacles, which are processed and computed at high speeds to perform obstacle avoidance. In the case of the latter, a path for the robot is planned in a known environment, and its accuracy depends on the degree of environmental informationacquisition. The aim of this study is the application of multi-robot formations in global path planning in a static environment. Many scholars focus on mobile robot path planning, and, so far, a large number of control optimization methods have been proposed. These include the Dijkstra algorithm [3], genetic algorithm [4], firefly algorithm [5], A* algorithm [6], artificial potential field method [7], RRT algorithm [8], neural network algorithm [9], etc. However, due to their own defects, these heuristic algorithms often cannot complete the task satisfactorily. For example, it takes the A* algorithm a long time to find a better path by traversing all reachable nodes [10]. The RRT algorithm is overly stochastic and has a high number of redundant nodes and path inflection points [11]. The study of heuristic algorithm improvement strategies for path planning problems has become popular nowadays. The artificial potential field method is one of the classical algorithms applied to path planning, but suffers from the defects of not being able to reach the target point and easily falling into the local optimum [12]. In response, scholars have taken a series of measures to address the above issues. [PERSON] et al. [13] proposed a membrane-evolving APF to find parameters that can generate feasible safe paths. [PERSON] et al. [14] have extended the APF through the motion characteristics of animals to enhance the human-robot interaction. [PERSON] et al. [15] proposed an improved APF for solving the obstacle avoidance problem of multiple robots. [PERSON] et al. [16] introduced the distance between the robot and the target point into the repulsive field function, avoiding the local optimization problem. The ACO is also a classical path planning method with the advantages of good feedback information and distributed computation [17]. However, due to the limitation of its own mechanism, the computational overhead is large and the convergence speed is slow in the process of finding the optimal path [18]. [PERSON] et al. [19] used the sigmoid function to change the ant colony pheromone update mechanism and reduce the computational cost.