Chapter 3. Sensor Area Coverage Abstract Sensor networks normally have redundancy for sensing coverage. Some sensors are allowed to sleep while preserving network functionality. Sensors which are randomly placed in an area should decide which of them should be active and monitor an area, and which of them may sleep, and become active at a later time. The connectivity is important so that the measured data can be reported to a monitoring center. Sensor area coverage problem has been considered for both the unit disk graph and physical layer based sensing models. Actuators may similarly run a protocol to decide about their service areas, releasing some of them from particular duty. Operational range assignment for both sensor and actuators nodes is also discussed. 3.1. Problems, models, and assumptions One of the fundamental issues in wireless sensor networks is the sensor coverage problem. It is to deploy a set of sensor nodes in an area of interest for monitoring and/or tracking. Sensor nodes are normally densely deployed in wireless sensor networks. To prolong the network lifetime, sensors should sleep as much as possible. Ideally, they should wakeup only when they are really needed. However, this may not be possible, since additional hardware may be required for such ability. For example, a radiotriggered hardware component was introduced by Gu and Stankovic [GS04]. Since the events of interest often contain energy, their energy can be used to trigger the added hardware component which then in turn initiates the transition of the system from sleep mode to wake-up mode. Existing sensors however are not equipped with such hardware. In these cases, when sensors decide to enter sleep-mode, they set their clock for waking at predetermined time, regardless of events nearby. WSNs and WSANs employ collaborative mechanisms for scheduling wake-up and sleep periods. Wake-up and sleep periods exist for both sensing and communication hardware components. Normally a portion of nodes is required to be active (with respect to certain hardware) to perform given tasks while other nodes could sleep to save energy. Both sensor and actuator networks have node redundancies for communication and/or sensing, since only some nodes are needed for traffic forwarding, monitoring or servicing. Activity scheduling is to decide which nodes should be active and which may be allowed to sleep. The decisions are periodically reevaluated, and the problem is also known as duty cycling. There are different levels of activity. Sensor nodes may turn off both sensing and communication hardware and therefore be in a fully sleep mode. A set of sensor nodes that together fully cover a given area are frequently referred to as the area-dominating set, or as the sensing backbone for the network. The communication backbone is normally built on top of the sensing backbone. That is, some of sensors may have active sensing device but passive transmitter and receiver hardware. Their communication needs can be fulfilled by their neighbors in the communication backbone (whose communication hardware is always turned on). We have discussed communication backbone construction techniques in the previous chapter. While this chapter refers to the sensor area coverage

1

problem, actuators can similarly be considered for the analogous actuator coverage problem, deciding which of them are needed to service sensors in their areas, while allowing others to rest or perform other duties. This problem occurs when/if the actuator network is dense and has redundancies. The chapter focuses on the design of the wake-up/sleep schemes for area coverage problems in WSNs and WSANs. In a typical area coverage problem, a set of sensors is distributed over a given area. Each sensor is able to cover a small area which is normally assumed to be a circle with radius centered at it. The problem is to find a subset of sensors that are connected and still cover the same area, such that these sensors alone are able to perform monitoring task. Full coverage, maximum network lifetime, and connectivity are critical requirements of any area coverage protocol. There is a variety of problem statements, assumptions, and solution approaches for the problem of sensor area coverage. The chapter focuses on the area coverage problem in which each point in a given geographic area should be covered by at least one sensor. The main objective of area coverage protocol is to achieve full area coverage by a subset of sensors with the minimal possible number of sensors in the subset. Assumptions about sensing radii may vary. In most articles, sensing radius of nodes is assumed to be fixed and same for all sensors (e.g. [TG02]). A more general case is when sensing radii are fixed for each sensor, but are not same. Sensing radius is assumed to be adjustable in some articles (e.g. [WY04]).

Fig. 3.1. The shaded area is 2-covered but not 2-layer covered. The area coverage problem can be generalized by requesting multiple coverage for each point in the area. The most straightforward generalization is k-coverage problem. An area is k-covered if every point of the area is covered by at least k distinct sensors. A more restrictive generalization is k-layer coverage problem, which requires k disjoint subsets of sensors so that each of these k subsets provides 1-coverage (fully covers the area). A k-layer coverage is also a k-cover, but converse may not hold. In the example in

2

Fig. 3.1, the shaded area centered at O is 2-covered since every point in the area is covered by at least 2 circles. However, we can not find 2 distinct subsets of sensors, so that each one fully covers the area. Sensing and communication are normally modeled as unit disk graphs (UDGs), with the corresponding sensing and communication radii. Let CR and SR denote the communication radius and sensing radius, respectively, in the rest of the chapter. In the unit-disk graph model, a sensor is able to monitor location of an event if and only if the location is within SR of the sensor. In reality, sensing ability decreases with distance, which can be exploited in a physical layer model, where the probability of sensing an event depends on the distance from the sensor to the event. Two nodes are communication neighbors if they are within distance CR from each other. Sensing neighbors are two nodes whose corresponding sensing areas overlap. If their sensing areas are disks then they are sensing neighbors if the distance between them is less than the sum of their corresponding sensing ranges. The sensor network may operate with or without time synchronization among sensor nodes. In a synchronous protocol, all sensor nodes maintain a common clock by applying some synchronization protocols [LR04, RBM05]. The sensor nodes coordinate with each other to make their activity schedules according to the common clock. All decisions are made in rounds. That is, all nodes could wake up at the same time, exchange messages, and then decide which of them will be active. The ZigBee standard requires sensor nodes to be time synchronized. Synchronous behavior provides advantages for energy efficient communication in addition to efficient area coverage protocols. In an asynchronous protocol, sensor nodes do not follow a common clock. Each node makes its own decision to be active or to sleep for a period of time based on its individual clock. Each node in asynchronous protocols may wake up at its predetermined time and decide whether it needs to be active based on a message exchange with currently active neighbors. It has been proven that finding the minimum number of connected working nodes that cover the area of interest is NP-hard [KAR00] [GDG03]. Since it is NP-hard for even centralized algorithms, finding localized algorithms to achieve good performance is an even more challenging task. 3.2. Coverage and connectivity criteria Coverage and connectivity criteria serve as building blocks in area coverage algorithms, by providing computationally efficient ingredients. The choice of criteria depends on the ratios of sensing and transmission radii and their uniformity. If the sensing and transmission radii are equal, the coverage property can be tested by verifying whether or not the whole perimeter of the sensing circle is covered by other circles. In the example in Fig. 3.2 (a), sensing area of node O is not fully covered by two other circles since there are two uncovered segments. The correctness of the criterion follows from the following observation. If two sensing circles intersect then each center is inside the other circle. If a point A on the perimeter of circle O is covered by a circle centered at P, all points on the line segment from A to center O are covered by same circle since both O and A are inside circle centered at P and sensing area of any circle is

3

convex. Therefore, instead of testing the whole line segment OA for inclusion in other circle, only endpoint A on the circle perimeter needs to be checked. Note that this (and the following) criteria assume that no two sensors are placed at the same location.

u

(a) Fig. 3.2. Perimeter based coverage test.

(b)

This criterion can be generalized to the case of k-coverage. The monitoring region is k-covered if and only if the perimeter of each sensor is covered by at least k distinct sensors [HT03]. This criterion is not applicable if the communication radius is larger than the sensing radius. In the example in Fig. 3.2 (b) (for k=1), suppose all nodes are within communication radius of node u. Although the perimeter of circle u is covered by other circles, sensing area of u is not fully covered. Wang et al [WXZLPG03] and Zhang and Hou [ZH05] introduced a covering criterion to decide whether or not a sensing area is fully covered by other sensing areas. It does not require the uniform sensing radius of nodes. Furthermore, it does not depend on ratio of the communication radius and the sensing radius. It also generalizes to sensing areas of arbitrary shape (not just disks) and is applied on the corresponding boundaries. Theorem 3.1. Coverage of circle centered at O by circles centered at C1, …, Cm can be reduced to coverage of intersection points of two covering circles Ci and Cj, or of O and one covering circle Ci, that is inside the sensing area of O, as follows. If there are at least two covering circles and any such intersection point is covered by a distinct covering circle Ck, then the sensing area is fully covered. Proof. The basic idea of proof (as given in [GCSS08]) is illustrated in Fig. 3.3 (a). Suppose that there is a point P which is not covered by any sensor in the region. P lies in an uncovered patch which is bounded by only exterior arcs of a collection of sensing circles and/or boundary of the sensing area. In Fig. 3.3 (a), the uncovered patch is the shadow area Q-R-S-T-U. Travel (in any direction) from P to the boundary of the uncovered patch and follow the boundary until it meets an intersection point (e.g. point Q in Fig. 3.3 (a)) of two covering circles C and D (or intersection point U of covering circle D and central circle O) on the boundary. Q is not covered by any third covering circle. It contradicts to the condition of the theorem. ♦

4

The central grey circle in Fig. 3.3 (b) is fully covered since any intersection point of two circles inside the grey area is covered by a third circle. For instance, intersection point P of circle A and circle C is covered by circle B and intersection point T of circle A and circle D is covered by circle C.

B

A P

R S

Q T O

U D

C

(a) (b) Fig. 3.3. The grey circle is fully covered if all intersection points are covered. The criterion in Theorem 3.1 provides an efficient method for testing full coverage of a sensing area. However, it does not provide direct information about the possible size of the uncovered region if the region is not fully covered. One possible estimate is to randomly generate a certain number of points and test coverage of each point with existing circles. The uncovered region could be estimated by the percentage of uncovered points. Alternative is to make an estimate based on the area of the polygon with same vertices (e.g. polygon QRSTU in Fig. 3.3 (a)). There exists a need for designing more accurate and fast-coverage size-estimation protocols. Theorem 3.1 can be extended to the 3-dimension scenarios. In [ONSCS06] it is used for the broadcasting protocol in 3D, where each node has the same transmission radius. This corresponds to the scenario for sensor volume coverage where CR=SR (details are in Chapter 2). In this case, the coverage criterion can be expressed as follows. Theorem 3.2. [ONSCS06] Suppose that sphere A is intersected by spheres C1, C2,…, Cm. Consider all intersection points X on the 3D perimeters of the spheres centered at the A, Ci and Cj. If there exists at least one such intersection point and every such intersection point X is located inside at least one of the remaining spheres (centered at Ck for some k) then the sphere centered A is fully covered by the spheres centered at C1, C2,…, Cm.

5

In case of arbitrary ratios of CR/SR, and sensing volumes of arbitrary shapes (for simplicity, spherical volumes are only stated in the criterion), the following generalization holds. Again no two sensors are assumed to be in the same location. Theorem 3.3. Suppose that sphere A is intersected by spheres C1, C2,…, Cm. Consider all intersection points X of spheres Ci, Cj, Ck (or by Ci, Cj, and A) located inside sphere A. If there exists at least one such intersection point and every such intersection point X is located inside at least of one of the remaining spheres (centered at Cp for some p) then the sphere centered A is fully covered by the spheres centered at C1, C2,…, Cm. Proof. The proof of Theorem 3.3 is similar to the proof of Theorem 3.1. Suppose that the volume centered at A is not fully covered by other volumes. Let P be one of uncovered points. It is located inside a 3D uncovered patch. ‘Travel’ from P until a boundary is met. It could be boundary of one of covering circles, or boundary of A. Traverse further that boundary until a line of intersection of two spheres is met. Traverse that line until a point of intersection with a third sphere is encountered. This point is not covered (it is not inside) any other sphere, which contradicts the assumptions in the theorem.♦ Both the coverage and connectivity criteria were studied in [ZH05] and [WXZLPG03]. It is proved that if the transmission radius is at least twice the sensing radius, and the area to be covered is convex, then the area coverage also implies connectivity of the covering sensors. Any two nodes whose sensing circles intersect are then neighbors within communication radius. Tian [T04] generalized the proof by eliminating the convexity condition. Theorem 3.4. If the transmission radius is at least twice the sensing radius then the area coverage also implies connectivity of the covering sensors. Proof. The proof [T04] is as follows. If a network is not connected then there are at least two connected components in the network. The distance of any pair of nodes that are selected from two components, respectively, is larger than CR. Since CR>2SR, there is no intersection between coverage area of nodes in two components. Therefore, the whole region is not fully covered since the region is continuous [T04]. ♦ The relationship between the degree of coverage and connectivity was further studied in [WXZLPG03]. A graph is k-connected if it remains connected when any k-1 vertices are deleted form the graph. Theorem 3.5. [WXZLPG03] A set of nodes that k-cover a convex region forms a kconnected communication graph if the communication radius is at least twice of the sensing radius (CR>2SR). Several centralized sensor area coverage algorithms are surveyed in [SSW05]. Since centralized algorithms are inefficient due to their communication overhead to gather

6

information, they are suitable only for very small networks. We will discuss here only localized algorithms. The presented algorithms all assume that each sensor is aware of its own location (geographic coordinates). 3.3. Area dominating set based sensor area coverage algorithm Sheu, Tu and Yu [STY07] proposed a localized protocol to find a set of connected sensor nodes to cover the required region in heterogeneous sensor networks. Sensor nodes may have different SR and CR. A sensor may need multiple hops to reach its sensing neighbors if SR>CR. This case is of theoretical interest only since in practice CR>SR. The protocol consists of three phases: neighbor discovery, self-pruning and active sensing neighbors discovery. Each sensor collects information on its sensing neighbors by ‘hello’ messages (neighbor discovery). The node information includes a node’s ID, sensing range, location and priority. The priority could be residual energy, sensing range or communication degree, or a combination of several metrics (priorities are assumed to be distinct among nodes). Note that flooding is required for a node to learn its sensing neighbors if SR>CR. Only this phase requires message exchanges among nodes. The remaining two are decisions made by each node without communicating with others. In the self-pruning phase, each node determines whether or not to be active. It decides to be active if its sensing area is not completely covered by the union of sensing areas of its sensing neighbors which have higher priority than the node. After this phase, the required region is fully covered by the active sensing nodes. In the active sensing neighbor discovery phase, each sensing node A determines active sensing neighbors. Several sensing neighbors may cover the same segment of A’s perimeter. A recognizes a sensing neighbor B as active if a segment of its perimeter is covered by B and B has the highest priority among all sensing neighbors that cover the same segment of the perimeter. A S1

S2

B F

E S3

D C S5

G

S4

Fig. 3.4. Area dominating set based coverage.

7

Suppose the sensing range is the priority and a node with a larger sensing range has a larger priority value. In the example in Fig. 3.4, suppose the order of priorities of nodes is as follows: A