Mobility increases the surface coverage of distributed sensor networks

Abstract

Coverage is a fundamental issue in sensor networks, which usually dictates the overall network performance. Previous studies on coverage issues mainly focused on sensor networks deployed on a 2D plane or in 3D space. However, in many real world applications, the target fields can be complex 3D surfaces where the existing coverage analysis methodology cannot be applied. This paper investigates the coverage of mobile sensor networks deployed over convex 3D surfaces. This setting is highly challenging because this dynamic type of coverage depends on not only sensors’ movement but also the characteristics of the target field. Specifically, we have made three major contributions. First, we generalize the previous analysis of coverage in the 2D plane case. Second, we derive the coverage characterization for the sphere case. Finally, we consider the general convex 3D surface case and derive the coverage ratio as a function of sensor mobility, sensor density and surface features. Our work timely fills the blank of coverage characterization for sensor networks and provides insights into the essence of the coverage hole problem. Numerical simulation and real-world evaluation verify our theoretical results. The results can serve as basic guidelines for mobile sensor network deployment in applications concerning complex sensing fields.

Introduction

Sensor networks are widely deployed in many commercial and military scenarios because of their unique advantages, such as low cost, ease of deployment and unattended operation. Typical applications include tracking wild animals [1], [2], forest fire detection [3], forest carbon monitoring [4], volcano surveillance [5] and environmental data reconstruction [6], [7].

Ensuring coverage is a fundamental problem in sensor networks and one of the main considerations for system designers [8]. The investigation of the coverage of a sensor network answers important questions, e.g., what are the traces of the moving objects? What are the chances that an abnormal event like an intrusion will be detected during its lifetime? How well can the sensor network monitor a target field? How accurate is it if the sampled data are used to virtually reconstruct the environmental conditions of the field? Furthermore, the coverage property closely relates to the surveillance quality of a sensor network, the monitoring ability of an intrusion detection system and the connectivity of a k-hop clustered mobile wireless network [9]. Thus, it is important to understand the relationship between coverage and system parameters including the sensor density, sensors’ mobility and the sensing field’s properties. This will help designers better deploy sensor networks for various practical applications concerning complex sensing fields.

Recent years have witnessed the increasing adoption of mobile sensor networks. Sensors can be mounted on autonomous robots, such as the Pioneer 3DX [10] and the Starburg [11], or be mounted on wild animals [1], [2]. System designers embrace mobile sensors since mobility enables self-deployment and adaptability. For example, in a hostile environment where sensors cannot be manually deployed, mobile sensors can move to the desired positions during the redeployment phase [12], [13], [14]; in ocean environments where sensors move with the surrounding ocean currents [11], mobile sensors can adapt to the floating water. Moreover, mobility can be exploited to compensate for the insufficient number of sensors, to improve the area coverage of a randomly deployed sensor network [18], [19] and to optimize the data collection operation [6]. Recent studies have already shown that mobility can increase communication capacity [20], network connectivity [9] and security [21] in ad hoc networks.

For coverage characterization, most existing works assume that the target field is a 2D plane or 3D space. However, in many real world applications, the fields of interest (FoIs) are complex 3D surfaces (Fig. 1a). Such examples appear in the ZebraNet project [1], the GreenOrbs project [4], and the Tungurahua volcano monitoring project [5]. In a 2D plane or 3D space, sensors can move freely within the whole FoI, but for 3D surfaces, sensors are restricted to move only on the surface. This implies that existing results derived under the 2D plane or 3D space model may be inappropriate when being applied to the 3D surface case.

Surface coverage is first introduced by Zhao et al. [22] and extended in [23]. They point out that coverage strategies derived on 2D planes do not work for 3D surfaces since they will encounter the coverage hole problem (Fig. 1b). In [22], [23], however, only the surface coverage of static sensor networks is studied. The coverage ratio is determined by the initial network configuration and remains unchanged over time. Liu et al. [18] have analyzed the coverage of mobile sensor networks, but they concentrate on the 2D plane case and their results cannot be directly applied to the 3D surface case since their analysis fails to take into account the properties of the FoI. As a result, it is still not clear how mobility affects the coverage of mobile sensor networks on 3D surfaces.

To fill this gap, we study the surface coverage of a mobile sensor network deployed over a convex 3D surface. Specifically, we are interested in the surface coverage ratio over a time period, which is achieved by the continuous movement of sensors. Unlike traditional approaches that aim to provide simultaneous coverage of all locations at each time instant, or exploit mobility to obtain a new stationary configuration that improves the coverage ratio after the sensors move to the desired positions, the surface coverage in mobile scenarios aims at covering the locations once during an event’s lifetime. This kind of surface coverage can be reduced to the scenario in [22], [23] by making the sensors move at zero speed. Characterizing the surface coverage ratio of a mobile sensor network requires comprehensive consideration of the initial network configuration, features of the convex 3D surface and dynamic aspects of the sensors’ movement. In contrast, the stationary 2D plane coverage, mobile 2D plane coverage and stationary surface coverage consider only one or two of those three aspects.

The main contributions in this paper are summarized as following:

• To the best of our knowledge, this is the first attempt at characterizing the surface coverage of distributed mobile sensor networks. We propose a theoretical analysis framework for coverage studies on general convex 3D surfaces.

• We derive theoretical results for 2D planes, spheres and general convex 3D surfaces under three mobility models. Our results show that mobility increases the surface coverage.

• Numerical simulation and real-world evaluation verify the accuracy of our theoretical results. Results using a 2D plane model perform poorly for 3D surfaces due to the coverage hole problem, which verifies our motivation.

• Our theoretical results provide insights into the essence of the coverage hole problem: the nonzero Gaussian curvature is the root cause for the invalidity of the 2D plane model for the surface coverage case.

The paper is organized as follows. Section 2 gives a brief review of related works, then in Section 3 we summarize our main results and give corresponding interpretations. The network model and coverage metrics are introduced in Section 4. Section 5 is devoted to considering the 2D plane case, while the sphere case is presented in Section 6. Section 7 shows our analysis framework for general surfaces, followed by our simulation and evaluation results in Section 8. In Section 9, we give a brief discussion, then conclude our work and point out possible directions for future work.