# Multi-Robot Formation Control Based on CVT Algorithm and Health Optimization Management
###### Abstract
In summary, controlling multiple robots to maintain a fixed formation can result in completing the specified tasks more efficiently, and the formation control should be extended to a more efficient dynamic mode, that is, provided the robots maintain the corresponding formation as much as possible, to reduce the rigidity of the formation. Therefore, the question of how to achieve the formation with less energy consumption in a shorter time has also received considerable attention. [PERSON] used the distribution and neutralization of multi-robot clusters in the diffusion process of toxic substances as the background, and combined the CVT algorithm with multi-robot control for the first time [13]. [PERSON] proposed a discrete-time-based CVT algorithm that can use Euclidean metrics to achieve coverage of non-convex environments [14]. The algorithm was proved by solving the coverage of obstacles and exploration problems in non-convex indoor environments. In [15], a coverage algorithm is defined that is subject to differential constraints in a non-convex environment. The algorithm introduces a limited range of sub-divisions to limit the amount of communication between robots, and the convergence of the algorithm is verified in simulation. In [16], an adaptive control algorithm is designed to drive the robot to the weighted centroid of the corresponding Voronoi cell, and finally the Lyapunov function is used to prove that the robot network can converge to the optimal configuration. In the process of using the formation to complete the task, the completion of the overall task and the health of the robot are equally important. In past formation use, the user seldom considered the impact of various harsh environments on the health of the robot under real conditions. The impact of such environments may degrade the health of the robot or even cause it to fail to work, which will have a significant impact on the completion of the task and the performance of the robot [17]. Therefore, in an intelligent and efficient formation control system, these abnormal possibilities must be considered and the individual situation must be assessed, in order to maximize the formation performance and mission completion, and to achieve a higher level of overall mission performance than non-health-perception systems. In terms of the impact of individual health-degrading tasks, [18] proposed a task allocation system based on health management which can predict the impact of various abnormalities on the task status through dynamic programming and select measures to mitigate these effects. The authors in [19; 20; 21] investigated the impact of different robot driving capabilities in the team on the coverage task, using online and distributed methods to learn the changes in the relative driving performances of the robots, which can be a trade-off between time and the energy consumption of the robot, to ensure that the robots converged to the best configuration. In view of the above problems, an efficient and dynamic multi-robot formation algorithm should be developed that can form an efficient dynamic formation with the least cost and make flexible changes according to the obstacle environment. Most importantly, the impact of the environment on the health of robots must be taken into account, in order to be able to make real-time dynamic adjustments to the robots and to improve the performance and robustness of the robot formation. On this basis, this study combines the CVT (centroidal Voronoi tessellation) algorithm with multi-robot formation control. First, we used the CVT algorithm to complete the Voronoi division of the task map and designed the controller to control the robot to track the specified Voronoi cell centroid. When the CVT algorithm converged, it was guaranteed that the robots formed the specified desired formation in the specified area according to the optimal distribution.