Bounding the Energy Consumption of Mobile Sensor Nodes For Triangulation-based Coverage

In a Triangulation-based coverage scheme, a group of three mobile sensor nodes (MSN) position themselves to form an equilateral triangle for a desired period of time. Such a scheme has several applications in localization, environmental monitoring and coordinated target tracking. In this work, we introduce an efficient mobile traversal algorithm (MTA) that profides a triangulation-based coverage of a field that can be approximated as a rectangle. We analyze the energy consumption of the MTA interms of the distance and time taken to complete the full coverage of the field. The bounds on the minimum total and individual energy consumption per MSN is determined. A prior knowledge about the energy consumption can be useful to charge the mobile seeds with the required amount needed for the particular application. I. I NTRODUCTION A fundamental issue in sensor network is the coverage problem, which addresses how well sensors observe or monitor a region. Due to the energy constraints of sensor nodes, an energy-efficient coverage scheme is viable for the lifetime of In this work, we propose a mobile traversal algorithm (MTA) that employs three MSNs, equipped with location devices such as GPS, to cover a field that can be approximated by a rectangle. The MSNs can be deployed at a random initial position in the field, and with the knowledge of their current location with respect to the field to be covered, they will form an equilateral triangle near the deployment site. Each side of the triangle is assumed to be r units, where r is an application dependant parameter, often limited by the sensing and communication ranges of the MSNs. After forming such a triangle for a pre-determined (constant) period of time, they will coordinate with each other, and according to the proposed MTA algorithm, move to form another triangle to cover another part of the field. A MSN(or MSNs) can enter the sleep mode to conserve energy as the new triangle is being formed. The proposed algorithm enables the MSNs to minimize their (total and individual) travel distance or time needed to provide a full coverage of the field. Note that since the MSNs spent a constant amount of time performing sensing or sending beacon signals (depending on the application) while they are positioned as a triangle, the energy consumed by the MSNs is proportional to the total distance or time taken to complete the traversal. Accordingly, the proposed algorithm and its performance bound are also useful in minimizing and bounding the energy consumption of the MSNs. This paper is organized as follows. In Section II, we for- mulate the problem. The proposed mobile traversing algorithm (MTA) is presented in Section III. In Section IV, bounds on the total distance and time required to complete the traversal process is derived. The minimum and maximum distance travelled by any individual MSN to complete the traversal is determined in Section V. Section VI concludes the paper.