## 1 Introduction  
Based on the technological development of industry 4.0 [1], robots can accomplish many tasks in smart factories. Therefore, many workers in smart factories have been replaced by robots. A single robot can accomplish some tasks, but others with high complexity and/or in large spaces may require multiple robots to work together [2]. Decreasing transit time, increasing system reliability, path planning, and collision avoidance are challenging problems for cooperative multi-robot groups. Path planning is one of the challenges, and it can be divided into single-robot path planning [3, 4] and multi-robot path planning [5, 6]. In this paper, we deal with the problem of path planning for multiple robots in a dynamic environment. There have been a lot of papers studying the problem of single-robot or multi-robot path planning. For the path planning of a single robot, [PERSON] [7] created a robot navigation system that presented a path generation method within a maze of arbitrary complexity and optimized the generated path with the appropriate boundary conditions. An immunity algorithm is proposed by [8], in which the robot could perform its task through optimal path planning and minimal rotation angle efficiency. Traditional and heuristic approaches to path planning were proposed, such as the potential field method and A* algorithm, as seen in papers [9, 10]. [PERSON] [11] chose the roadmap method and utilized a Voronoi diagram to calculate the optimal path between a single source and a single destination with some polygonal obstacles. [PERSON] [12] proposed a jump point search (JPS) A* algorithm to improve computational time and path optimality and compared it with other algorithms like basic Theta*, Phi*, and A* in different scenarios. A modified genetic algorithm (MGA) based on the Bezier curve method was proposed by [13], in which the robot's path is dynamically determined based on the obstacles' locations and improved the exploration capabilities. In the study of multi-robot path planning, [PERSON] [14] proposed an improved gravitational search algorithm (IGSA) in a dynamic environment to optimize path trajectories for multiple robots. An improved particle swarm optimization (IPSO) algorithm and an improved gravity search algorithm (IPSA) are combined to achieve a collision-free smooth optimal path from the beginning position to the end position in [15]. A hierarchical model predictive (HMP) control was introduced by [16; 17] to address the heuristic search methods that cannot provide path stability through theoretical guarantees for multiple robots. [PERSON] [18] emphasized a team of robots in formation control mode for robot navigation in two-dimensional and three-dimensional spaces with mobile obstacles. Recently, there have been some works on coverage path planning, which has become a relevant topic. In paper [19], a flock of unmanned aerial vehicles (UAVs) was used to reconstruct rough terrains to plan safe trajectories for an unmanned ground vehicle (UGV). [PERSON] [20] used UAV to identify terrain morphology and unstructured vineyards to develop an algorithm for generating a path for UGV. The preliminary idea used in this study is a Voronoi diagram [21], which uses multiple points as the cores to divide a flat space into several areas for the path planning of the robot's moving. Although the Voronoi diagram is not a new concept used in path planning for robots' cooperation and exploration, it still plays a critical role in improving various algorithms for different purposes. For instance, [PERSON] [22] used a Voronoi diagram and the particle swarm optimization algorithm to achieve multi-robot navigation and obstacles avoidance. In paper [23], the Voronoi diagram divides farmland into several areas for multiple robots to perform agriculture tasks. For multi-robot exploration problems, paper [24] used the distributed Voronoi partition to disperse the robot and then used the parametric algorithms to further control the robot's dispersion behavior to achieve the maximum area exploration.