A cooperative pursuit-evasion game in wireless sensor and actor networks

https://doi.org/10.1016/j.jpdc.2013.05.009Get rights and content

Highlights

  • A novel multi-step cooperative strategy for pursuit-evasion control is presented.

  • A pursuit control law with less state information is proposed to guarantee the line formation.

  • A Daisy-Chain Formation algorithm and a sliding mode-based method are presented to control the pursuit.

  • We present a cooperative pursuit approach where the evader can be static or dynamic.

Abstract

This paper studies the problem of the pursuit-evasion game under the wireless sensor and actor networks (WSANs). In order to plan paths for pursuers to capture an evader in the pursuit-evasion game, a novel multi-step cooperative strategy is presented. Under this strategy, the pursuit-evasion game is studied in two stages. In the first stage we assume that the evader is always static in the workplace, and in the second stage the evader will move once it senses the existence of pursuers. A Daisy-Chain Formation algorithm and a sliding mode-based method are presented to control the pursuit. Based on Lyapunov stability theory, the proposed algorithm is proved to be convergent. At last, simulation results are provided to demonstrate the effectiveness of the proposed method.

Introduction

Wireless sensor and actor networks (WSANs) are composed of a large number of sensor nodes and multiple mobile actors. The roles of sensor and actor nodes are to collect data from the environment and perform appropriate actions based on this collected data, respectively. Compared with traditional wireless sensor and actor networks (WSNs), WSANs not only have the capacity of monitoring the environment, but also can make decisions based on the observations and perform appropriate actions. Due to these characteristics, WSANs provide numerous applications in various practical fields, such as battlefield surveillance and microclimate control in buildings, nuclear, biological and chemical attack detection, home automation and environmental monitoring; see  [3] and references therein.

Generally, WSANs deal with three levels of coordination: sensor–sensor (SS), sensor–actor (SA), and actor–actor (AA). The SS coordination  [2], [1] is employed to gather information from the environment. The SA coordination  [23] is used to report new events and to transmit the characteristics of the events from the sensors to actors. In AA coordination, actors are required to execute a specific task through cooperation. Due to complexity and uncertainty of the task, AA coordination will directly impact the overall performance of WSANs. Therefore, the work to be described in this paper is mainly focused on AA coordination. For AA coordination, one critical and typical application is pursuit-evasion game (PEG), which can be posed as to determine a strategy for a team of pursuers (or actors) to capture an evader in a workplace.1 In recent years, considerable research has been reported on this topic. Based on the game model of “Lion and Man”, Ref.  [20] extended the Greedy and Lion strategies to Circumventer and Planes strategies, and a simple and natural strategy for lion to win the game was proposed. In  [11], a bearing-only pursuit strategy was provided, and hence each pursuer decreased the relative distance between pursuer and evader to a step-size. More recently, a sweep–pursuit–capture strategy for discrete-time PEG was proposed in  [6], where pursuers patrolled the environment to detect the existence of evader. However, this operation can and would increase energy consumption stored in pursuers during the SWEEPING phase. Besides, it makes designing a cooperative pursuit algorithm harder because of the lack of complete observability.

In  [7], [5], PEG was characterized as a cooperative Homicidal Chauffeur game, where one pursuer was selected as a leader to interact with the evader, and the other pursuers should keep a Daisy-Chain Formation with the leader. In this way, the path taken by the leader was traversed by the kth pursuer after a time delay of (k1)sip, where k{2,,N} and sip>0. However, these control strategies are designed based on an overall and static information acquisition. Thus pursuers cannot make a real-time motion adjustment associated with evader’s motion, especially when the motion of evader is approximately random. Accordingly, an unexpected situation may appear: evader stands in front of pursuers but pursuers cannot implement any effective capture strategy. Moreover, in other literatures  [17], [19], [9], [14], “neighbor rule” was widely used in the topology communication between pursuers, wherein each pursuer was required to communicate with its neighbors. Analyzing the action of “neighbor rule” in PEG, it is shown that many interactions between pursuers are unnecessary, which make the communication much more complex. In this way, if PEG is achieved with less information, it will be more attractive to decrease communication complexity and energy consumption between pursuers.

This paper attempts to overcome the above issues by designing a cooperative PEG under WSANs. Due to the well-known benefits such as good dynamic response, robustness against uncertainty, high insensitivity to noises, the slide mode-based method is applied to the pursuit algorithm design. With the application of sensor networks, complete visibility of the workplace and communication over a long radius is possible. Global pursuit strategy can then be used to efficiently find the desired path for pursuers, regardless of the level of intelligence of the evader. To achieve capture task, a novel multi-step cooperative strategy is proposed, i.e., PRE-CAPTURE and CAPTURE. In view of the advantages of string formation in  [16], [22], i.e., a global formation can be achieved with less information, we propose a line formation algorithm in the PRE-CAPTURE step, wherein each pursuer just needs to acquire its front pursuer’s information. In the CAPTURE step, two stages of the PEG are considered: in the first stage, the evader is unsmart and it keeps static state in the workplace; in the second stage, the evader is smart, i.e., the evader is initially static in the workplace and will move once it senses the existence of pursuers. According to different stages, corresponding capture control algorithms based on sliding mode-based method are designed. At last, system stability is analyzed by Lyapunov stability theory.

Section snippets

Problem formulation

The cooperative PEG in this paper is studied in a planar environment with a single evader and multiple pursuers (i.e., actors). Sensor networks, which provide sensing-at-distance to circumvent line-of-sight limitations of pursuers, are used to locate the pursuers and evader. With the assistant of sensor networks, each pursuer has its own roadmap of the workplace and is able to communicate with the other pursuers. At the same time, if sensor networks detect the evader, they will notify pursuers

Main results

In this section, we design a cooperative PEG, which is divided into two steps: PRE-CAPTURE and CAPTURE. In the PRE-CAPTURE step, a leader-following strategy is adopted, where one pursuer is designed as the leader and the other ones are followers. This leader-following strategy can also be known as “Single-Actor Case” in WSANs  [3], [14], where only one actor (i.e., pursuer) receives capture task. Moreover, it is assumed that pursuer 0 plays the role of “leader”. In the CAPTURE step, all

Simulation results

To evaluate the performance of the proposed approaches, some simulation results are illustrated in this section. The parameters are set as follows: r=10,v=50,h1=h2=6,δ1=δ1=0.02,μ=1, sampling period δ=0.001s,k1=50 and k2=30, wherein  k1 and k2 meet the requirements in Theorem 1. At time t=0, six pursuers are static in the workplace, and the initial states of pursuers are given as q0=[0,0,π/4]T,q1=[0.5,0,0]T,q2=[3,2,0]T,q3=[4,2,1]T,q4=[1,4,1.5]T,q5=[6,1,3]T. The state of the detected

Conclusion

This paper presents a novel multi-step cooperative strategy for pursuit-evasion control of mobile vehicles. A pursuit control law with less state information is proposed to guarantee the line formation of pursuers in the PRE-CAPTURE step. In the CAPTURE step, two stages are considered. According to different stages, Daisy-Chain Formation and Transition Pursuit algorithms are proposed to achieve the capture task, respectively. Moreover, the sliding mode approach is also used in the proposed

Acknowledgments

This paper was supported by the National Basic Research Program of China (973Program) (No. 2010CB731800), Key Project of National Science Foundation of China (No. 60934003), National Nature Science Foundation of China (No. 61074065), and the Science Foundation of Yanshan University for the Excellent Ph.D Students (No. 201204).

Jing Yan received the B.Eng. degree in automation from Henan University, Kaifeng, China, in 2008. He is currently working toward a Ph.D. degree in the Institute of Electrical Engineering, Yanshan University, Qinhuangdao, China.

His research interests focus on multiagent systems and wireless sensor networks, particularly in coordination control of mobile robots and distributed detection and estimation in sensor networks and their applications in industrial networks.

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    Jing Yan received the B.Eng. degree in automation from Henan University, Kaifeng, China, in 2008. He is currently working toward a Ph.D. degree in the Institute of Electrical Engineering, Yanshan University, Qinhuangdao, China.

    His research interests focus on multiagent systems and wireless sensor networks, particularly in coordination control of mobile robots and distributed detection and estimation in sensor networks and their applications in industrial networks.

    Xin-ping Guan received his M.Sc. Degree in applied mathematics from Harbin Institute of Technology, Harbin, China, in 1991, and his Ph.D. degree in electrical engineering from Harbin Institute of Technology, Harbin, China, in 1999. Since 1986, he has been at Yanshan University, where he is currently a professor. In 2007, he also joined Shanghai Jiao Tong University, Shanghai, China.

    His research interests include robust congestion control in communication networks, cooperative control of multiagent systems, and networked control systems.

    Xiao-yuan Luo received the M. Eng. and Ph.D. degrees from the Institute of Electrical Engineering, Yanshan University, Qinhuangdao, China, in 2001 and 2004, respectively. He is currently a professor in Yanshan University.

    His research interests include fault detection and fault tolerant control, multiagent and networked control systems.

    Cai-lian Chen received the B.Eng. and M.Eng. degrees from the Institute of Electrical Engineering, Yanshan University, Qinhuangdao, China, in 2000 and 2002, respectively, and the Ph.D degree in control and systems from City University of Hong Kong, Hong Kong, China, in 2006. She is currently an associate professor in Shanghai Jiaotong University, Shanghai.

    Her research interests include wireless sensor and actor network, and multiagent and nonlinear systems.

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