994 IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 28, NO. 7, SEPTEMBER 2010 Simple Movement Control Algorithm for Bi-Connectivity in Robotic Sensor Networks Hai Liu, Xiaowen Chu, Yiu-Wing Leung, and Rui Du Abstract—Robotic sensor networks are more powerful than sensor networks because the sensors can be moved by the robots to adjust their sensing coverage. In robotic sensor networks, an important problem is movement control: how the robots can autonomously move to the desired locations for sensing and data collection. In this paper, we study a new movement control problem with the following essential requirements: i) an initial and possibly disconnected network is self-organized into a bi-connected network, ii) only 1-hop information is used for movement control, iii) the coverage of the network is maximized while the total moving distance in the movement process is minimized. We propose a simple movement control algorithm for this problem. This algorithm emulates the attractive force (such as the force in a stretched spring) and the repulsive force (such as the electrostatic force between electric charges) in nature, such that each robot simply follows the resultant virtual force to move. We theoretically prove that this algorithm guarantees bi-connected networks under a mild condition and derive bounds on the maximum coverage and the minimum moving distance. We conduct extensive simulation experiments to demonstrate that the proposed algorithm is effective. Index Terms—Robotic sensor networks, movement control, topology control, localized algorithms. I. I NTRODUCTION A ROBOTIC SENSOR NETWORK consists of a set of mobile robots that collaborate with each other to gather, process and exchange information. Each robot is equipped with a wireless transceiver and one or more sensors. The sensors provide the sensing functions, the robots move the sensors to the desired locations (e.g., for adjusting their sens- ing coverage in response to the changing environments), and the wireless transceivers provide the communication functions (e.g., for coordination and data exchange among the sensors). With movable sensors, robotic sensor networks are more pow- erful than sensor networks and they can be used in many ap- plications, such as surveillance, monitoring, unmanned space exploration, data collection and military missions [6]. In robotic sensor networks, an important problem is move- ment control: how the robots can autonomously move to estab- lish a network for sensing and data collection while realizing some given objectives and requirements (e.g., maximizing Manuscript received 1 May 2009; revised 16 February 2010. This work is supported in part by grants from Research Grants Council of Hong Kong [Project No. HKBU211009] and FRG/08-09/II-41 of Hong Kong Baptist University. The authors are with the Department of Computer Science, Hong Kong Baptist University, Hong Kong (e-mail: hliu@comp.hkbu.edu.hk, chxw@comp.hkbu.edu.hk, ywleung@comp.hkbu.edu.hk). Digital Object Identifier 10.1109/JSAC.2010.100904. the sensing coverage and achieving fault-tolerance) 1 . This movement control problem has been studied in the literature where different studies consider different requirements. These requirements are described in the following. Initial connectivity: If any robot can communicate with any other robot either directly (if they are within their com- munication range) or indirectly (through other intermediate robot(s)), the robotic sensor network is connected; otherwise, the network is disconnected. Some studies assume that the initial network is connected [1] [3] [6] [21], while other studies do not need this assumption and the initial network can be disconnected [10] [13] [17]. In practice, it is desirable not to make this assumption for wider applicability. Final connectivity: A basic requirement of movement con- trol is to make the network connected. Some studies aim at re- alizing this requirement [10] [13] [17]. Other studies consider the possible communication faults (e.g., caused by hardware failure or damage, energy depletion, malicious attacks, harsh environmental conditions, etc.) and aim at making the network bi-connected for fault-tolerance [3] [6], where a bi-connected network has at least two node-disjoint paths between any pair of nodes [12]. In practice, bi-connectivity is desirable because robots and sensors are typically simple devices used in possibly harsh environments. Information required: If two robots can communicate with each other directly, we say that they are 1-hop away from each other. The movement control algorithm in [10] requires only 1-hop information, while other algorithms [3] [6] [17] require more than 1-hop information (e.g., the centralized algorithm in [3] requires global information of the entire network). In practice, it is desirable to use only 1-hop information for smaller communication overhead and better responsiveness. Sensing range and communication range: Let each robot have a communication range R c and a sensing range R s . The study in [10] assumes that R c ≥ √ 3R s , while the study in [17] does not need any assumption about R c and R s . It is desirable that R c and R s can take any positive values for wider applicability. Objectives: The study in [10] and [21] aims at maximizing the coverage, the study in [6] aims at minimizing the moving distance, and the study in [17] aims at maximizing the coverage and minimizing the moving distance. In practice, it 1 In the recent literature, movement control is also exploited for replacing failed sensors [19], balancing the workload of sensors [20], and routing in robotic sensor networks (specifically, energy-efficient routing [11], localized mobility control routing [11], broadcast routing [15], routing for maximizing the probability that robots can detect a strategic site of sensing [5]). In our study, movement control is used to establish a network while realizing some objectives and requirements (stated in section II) 0733-8716/10/$25.00 c  2010 IEEE