Chao Zhai·Zhaoxu Wang·Jie Dou

In recent years,cooperative coverage control of multi-agent system (MAS) has attracted plenty of researchers in various fields [1,2].Different from multi-agent consensus or synchronization,multi-agent coverage control cares about how to coordinate a team of agents for effectively monitoring or covering a given terrain,which inevitably gives rise to the interaction between individual dynamics and external environments.Nevertheless,environmental uncertainties that include static uncertainties and dynamic uncertainties and limited sensing capabilities of a single agent make it a great challenge to design control algorithms of MAS for achieving the desired coverage performance.

To tackle static uncertainties of environment,a series of control approaches have been developed.Therein,the divide-and-conquer methodology is widely adopted to design coverage control algorithms of MAS.The basic idea is to divide the whole region into multiple subregions,and each agent is only responsible to cover its own subregion.In this way,the global coverage goal is fulfilled when each agent accomplishes its own coverage task,and multi-agent conflicts can be reconciled with ease.As a classic example,Voronoi partition enables agents to decompose the coverage region into multiple polygons in a distributed manner,and its centroidal Voronoi tessellation can be employed to achieve the optimal placement of resources [3].Inspired by the property of such tessellation,a distributed control algorithm is proposed to drive mobile sensors with localization uncertainties to approach the configuration that optimizes an index of coverage performance [4].It is demonstrated that these mobile sensors converge to the weighted centroid of their convex uncertain Voronoi cells.Despite high computation burdens,the Voronoi partition-based control algorithms facilitate the asynchronous and distributed implementation in practical applications.Equal workload partition is another well-known scheme for multi-agent coverage design to handle static uncertainties of environment,and it attempts to assign equal workload to each agent by decomposing the coverage region into sub-regions.As a result,MAS is expected to complete all the workload in the minimum time.For instance,Zhai and Hong [5] proposed a decentralized control algorithm to cover an irregular region with unknown workload distribution.The coverage region is decomposed into several stripes,and an online algorithm is designed to further divide the stripe into sub-stripes with the equal workload,in parallel to cover its sub-regions by each agent.In coverage problems,multi-agent dynamics is normally designed for optimizing a specific coverage index,which could conflict with other objectives (e.g.,collision avoidance,network connectivity).The above coverage control algorithms enable decoupling agent dynamics with other conflicting objectives,thereby contributing to theoretical analysis and technical realization.

Besides partition-based approaches,some novel coverage control strategies of MAS are developed to deal with dynamic uncertainties of environment,including awareness control [6],heat equation-based control [7],swarm control[8],and so on.In the above problems,environment information (e.g.,workload distribution,heat flow and pheromone)is uncertain and dynamic,and it acts as a bridge that coordinates agents to accomplish the coverage mission.In other words,collective behaviors of MAS give rise to the dynamic change of external environments,and the ever-changing environment directly reshapes the dynamic behaviors of MAS.

Considering that the geohazard occurrence depends on multiple factors (e.g.,rainfall,lithology,and slope angle)and varies in spatial and temporal dimensions,geohazard monitoring and early warning can be investigated in the framework of multi-agent coverage control in dynamic uncertain environments.For example,a group of agents(e.g.,unmanned aerial vehicles) can be coordinated to scan each point of interest in order to identify the concerned target in a large uncertain terrain using sweep coverage,whose objective is to move the agents across a coverage area,while maintaining the balance between maximizing the detection efficiency and minimizing the area of missed detections[9].By treating the surface deformations at some points of the terrain as random events,a well-defined formulation of region coverage can be employed to deploy mobile sensors in the mountainous area for maximizing the probability of monitoring landslide hazards [10,11].In the above formulation,the probability distribution function of landslide hazards can be constructed and updated with the aid of latest data and sophisticated learning algorithms [12].

The applications of multi-agent coverage control for geohazard monitoring in dynamic uncertain environments will meet a series of grand challenges in the integration of remote sensing techniques [13],data analytics [14] and cooperative control design of MAS.In terms of coverage control design,airborne interferometric synthetic aperture radar (InSAR)is vulnerable to adverse meteorological conditions (e.g.,drastic air flow),which may result in flight deviation from preplanned routes,thereby reducing the accuracy of phase interferometry.How to coordinate multiple airborne InSARs in the coverage control design for eliminating motion errors and the flat earth effect is a great difficulty of practical significance.In addition,for a comprehensive observation of geohazards,it is indispensable to process multi-source heterogeneous data from a variety of static or mobile sensors that include InSAR,crack meter,inclinometer,rain gage,and so on [15].Thus,the effective synthesis of coverage control strategies for various sensors is a hard task to improve the quality of service of geohazard monitoring system for promptly identifying the geohazard precursor.

This letter briefly discussed some representative coverage control approaches of MAS in uncertain environments and demonstrated the prospect of their applications to geohazard monitoring.In addition,the main challenges were analyzed in terms of coverage control design for enhancing the monitoring level of geohazards.As a largely unexplored research area,plenty of technical issues with great practical values remains unsolved,which requires the development of novel coverage control approaches,practical spatial and temporal model of geohazards,and data fusion techniques to carry out real-time monitoring task in harsh geological environments.

AcknowledgementsThis work was supported by the Fundamental Research Funds for the Central Universities,China University of Geosciences (Wuhan).