# Distributed Weighted Coverage for Multi-Robot Systems in Non-Convex Environment
## 1 Introduction  
Swarm robots are composed of simple single agents, which have certain autonomous, local communication, and perception abilities. By imposing some simple rules, the entire system exhibits complex group behavior characteristics, such as self-organization and cooperation [1]. Swarm robots are inspired by many biological species in nature that exhibit collective behaviors [2; 3]. Technological advances and cost reductions in communication, computing, control, and sensing devices for intelligence, as well as the advantages of multi-intelligent body systems over single intelligence, collaborative control of multi-agent systems, and mobile sensor networks, have attracted considerable attention in recent years. Particularly, a group of agents is deployed to desired locations according to different task scenarios and requirements. The execution of different tasks in the same environment is the principal application scenario in collaborative multi-agent systems. However, based on different scenarios, these distributed tasks may vary. Some examples of distributed tasks include forest fire monitoring and detection [4; 5; 6], environmental monitoring [7; 8], pollution source monitoring and control [9; 10], and environmental coverage [11; 12]. However, multi-robot systems are also robust and scalable for area coverage. Ref. [13] proposed an overlay control law that moves each mobile sensor to the centroid of its Voronoi cell. Ref. [14] solved the problem of distribution neutralization during the two-dimensional diffusion of toxic substances by a distributed agent control method, where the location of the agent is optimized by centroidal Voronoi tessellation (CVT). [PERSON] et al. [15] introduced distributed control laws using non-smooth analysis andcomputational geometry, which have applications in network robot coordination problems. [PERSON] [16] drove a multi-intelligent system into a static Chebyshev structure by proposing a new chance-constrained model predictive control algorithm-based on-state estimation, where each agent is located at the Chebyshev center of its Voronoi cell, and the noise problem in the system model is effectively solved. [PERSON]. [17] proposed a distributed control scheme for the coverage of Voronoi-based discrete-time multi-agent dynamic systems in a multi-dimensional static convex polyhedron environment. By using a local control law to steer each robot toward the Chebyshev center of its associated time-varying Voronoi neighborhood, the mechanism by which subsets of robots agree on intra-neighbor distances was revealed. Distributed coordination algorithms for increasing the coverage sensing range of non-identical mobile sensor networks are provided in Refs. [18,19]. In [20], an algorithm was developed to maximize the contribution of each mobile robot to the overall coverage by adding several mobile sensors to a static sensor network and positioning them appropriately in the required field. Although the abovementioned studies and related contributions can enhance the effective application of multi-robots for environmental coverage, they are all based on some hypothetical premises. These include the assumption that the robots can communicate mutually, they operate in an obstacle-free environment, and factors such as localization errors and robots' sizes in real systems are negligible. For covering problems in non-convex environments, [PERSON] [21] and [PERSON] [22] mapped a class of connected regions in non-convex environments to convex regions via a diffeomorphism. By combining with the [PERSON] algorithm, the coverage problem in a simple non-convex environment can effectively be solved. However, this method has limitations in covering problems with multiple obstacles or complex non-convex environments. [PERSON] [23] replaced the traditional Euclidean distance with the geodesic distance. However, the collision avoidance performance of this method in complex environments is not reflected. Moreover, obstacles have significant implications on the robot's trajectory.