# Multi-Robot Formation Control Based on CVT Algorithm and Health Optimization Management
###### Abstract  
In view of the low formation redundancy in the traditional rigid formation algorithm and its difficulty in dynamically adapting to the external environment, this study considers the use of the CVT (centroidal Voronoi tessellation) algorithm to control multiple robots to form the desired formation. This method significantly increases the complexity of the multi-robot system, its structural redundancy, and its internal carrying capacity. First, we used the CVT algorithm to complete the Voronoi division of the global map, and then changed the centroid position of the Voronoi cell by adjusting the density function. When the algorithm converged, it could ensure that the position of the generated point was the centroid of each Voronoi cell and control the robot to track the position of the generated point to form the desired formation. The use of traditional formations requires less consideration of the impact of the actual environment on the health of robots, the overall mission performance of the formation, and the future reliability. We propose a health optimization management algorithm based on minor changes to the original framework to minimize the health loss of robots and reduce the impact of environmental restrictions on formation sites, thereby improving the robustness of the formation system. Simulation and robot formation experiments proved that the CVT algorithm could control the robots to quickly generate formations, easily switch formations dynamically, and solve the formation maintenance problem in obstacle scenarios. Furthermore, the health optimization management algorithm could maximize the life of unhealthy robots, making the formation more robust when performing tasks in different scenarios. C 202211  
The following leader method is one of the earliest solutions for multi-robot formation control. In [4; 5], leader selection is described as an optimization problem; it adjusts the position of the follower based on the position of the leader, forming the desired formation. To maintain the required formation shape of spacecraft, [PERSON] set up virtual spring dampers between the spacecraft and realized a formation control method based on the artificial potential field [6]. In [7; 8], based on the principle of the virtual structure method, the formation control problem is described as a synchronous control problem, and a decentralized trajectory tracking controller was designed with the position error as feedback information to complete the functions of describing behavior and assigning tasks. In the above-mentioned formation control method, task-oriented, efficient cooperation between robots is used to improve the efficiency in completing tasks. In order to be more in line with the actual environment and enhance the robustness and anti-interference ability of the system, [PERSON] specified the communication diagram between robots to make the input speed constrain multiple mobile robots to converge to the desired formation, which improved the overall obstacle avoidance performance of the system. The amount of feedback was used as the control, based on the differences in neighbor behavior, thereby reducing communication loss and computing cost [9]. [PERSON] used a distributed control protocol to solve the problem of multi-mobile-robot formation considering sampling data and time delay [10]. [PERSON] solved the formation control problem of a heterogeneous multi-robot system under the premise of considering the robot kinematics uncertainty and communication delay, and used the Lyapunov function to prove the stability of the adaptive sliding mode controller [11]. Taking into account the complexity of the robot's task execution scenarios, [PERSON] designed a distributed formation optimization control framework for UAVs based on the hierarchical learning behavior of a pigeon flock, which transformed the multi-objective optimization problem into a single UAV, solving the multi-objective optimization problem to achieve stable formation flying in a complex obstacle environment [12].