C2AP: Coverage-aware and Connectivity-constrained Actor Positioning in Wireless Sensor and Actor Networks K. Akkaya Department of Computer Science Southern Illinois University Carbondale Carbondale, IL 62901
[email protected]
M. Younis Dept. of Comp. Science & Elect. Eng. University of Maryland Baltimore County Baltimore, MD 21250
[email protected] mines in the battlefield, and the NASA JPL miniaturized rover [3], are some examples of possible actor nodes. Coverage is one of the most important design goals in most applications of WSANs [4]. It is often required for the network to provide services at every part of the deployment area. For example in forest monitoring applications, actors such as fire trucks and flying aircrafts need to be engaged as rapidly as possible to control a fire and prevent it from spreading. Similarly for scientific studies or space applications actors should respond instantaneously to record rare phenomena, e.g. capture an image or record a weird behavior of a habitat. Therefore, a careful placement of actors in the area is crucial so that they can perform their duties appropriately while meeting applicationlevel constraints on the overall response time. Collaborative data processing and response planning is very popular in WSANs. An actor shares its collected data with other actors and coordinates with them on the best response and on the most appropriate set of actors that need to be involved. The selection of actors that need to be engaged can be based on many factors such as actor’s capabilities, actor’s proximity to the region/event to be handled, actor’s current load, etc. Such interaction among actors requires that they stay reachable to each other. Therefore, actor placement has to not only maximize the area coverage but also ensure inter-actor connectivity. In this paper we investigate the problem of actor placement for increased coverage while maintaining inter-actor connectivity. We present C2AP, an algorithm for Coverage-aware and Connectivityconstrained Actor Positioning in WSANs. C2AP strives to maximize the actors’ coverage without violating the connectivity requirement. C2AP is completely distributed; relying only actors’ interaction without external control. The main idea is to apply repelling forces among neighboring actors, similar to molecular particles in Physics, in order to spread them in the deployment area. However, the movement of each
Abstract In addition to the miniaturized sensor nodes, Wireless Sensor and Actor Networks (WSANs) employ significantly more capable actor nodes that can perform application specific actions to deal with events detected and reported by the sensors. Since these actions can be taken at any spot within the monitored area, the actors should be carefully placed in order to provide maximal coverage. Moreover, the actors often coordinate among themselves in order to arbitrate tasks and thus inter-actor connectivity is usually a requirement. In this paper, we propose a distributed actor positioning algorithm that maximizes the coverage of actors without violating the connectivity requirement. The approach applies repelling forces between neighboring actors, similar to molecular particles in Physics, in order to spread them in the region. However, the movement of each actor is restricted in order to maintain the connectivity of the inter-actor network. The performance of the approach is validated through simulations.
1. Introduction Wireless sensor and actor networks (WSANs) have started to receive a growing attention from the research and engineering communities in recent years. Potential applications of WSANs include urban search-andrescue, battlefield surveillance, lunar and planetary exploration, detecting and countering pollution in coastal areas, monitoring and guarding the environment against suspiciously active chemical/biological agents, etc. [1][5][8]. Such networks employ large number of miniaturized lowcost sensing nodes that are responsible for measuring ambient conditions and reporting such measurements to some actor nodes over wireless communication links. Actors have the capability for processing the sensed data, making decisions and then performing the appropriate actions. Robotic Mule [2], which is an autonomous robot designed for the Army to detect
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actor is restricted in order to prevent partitioning the inter-actor network. C2AP also handles the discovery of orphaned actors which are not initially in the communication range of other actors. C2AP is validated through simulations and is shown to be both effective in achieving high coverage and efficient in terms of incurred overhead at the individual actors. This paper is organized as follows. The next section describes the system model that we consider throughout the paper. The related work is discussed in section III. Section IV discusses the connected coverage problem in details and describes C2AP. The performance of the C2AP is evaluated trough simulation in section V. Section VI concludes the paper with a summary and mentions our future extensions.
The coverage problem has been studied in the literature in the context of multi-robot systems. The network in these systems consists of robots which have sensing, vision and motion capabilities. The issue is how to locate the robots so that every point in the region will be under the shadow of a particular robot [4]. We consider a different system model, in which actors need to stay available for extended time and thus have to conserve their energy. In addition, we strive to support inter-actor collaboration by ensuring connectivity among the deployed actors under communication range constraint. Similarly, in Wireless Sensor Networks (WSNs), the sensing coverage of the network has been considered as an important quality of service metric. Particularly, the recent works such as [6][7] studied the improvement of sensing coverage after the deployment of the sensors by assuming that the sensors can relocate. C2AP is mainly inspired from the approaches reported in [6][7]. The idea of repelling forces is similar. However, there are many differences: First, we apply the approach to actors rather than sensors. Second, we consider connectivity restriction when applying the forces on each actor. Third, the definition of forces is different and based on the transmission range of the actors. And forth, we handle orphaned actors which are initially disconnected. Unlike coverage, which has constantly been an objective or constraint for sensor node placement, connectivity was deemed a non-issue in most of the works for WSNs. This is because; having a strongly connected network is not essential in WSNs where data are usually gathered at the base-station. Therefore, ensuring the presence of a data route from a node to the base-station would be sufficient. In addition, the radio range of sensors is usually greater than the sensing range and thus when the coverage problem is solved, the connectivity is automatically ensured. Therefore, connectivity is usually considered to improve the fault tolerance by forming K-connected networks [9]. Since the area of WSANs is fairly new, there is not much work on coverage and connectivity problems in WSANs. One of the few projects that address specific problems for WSANs is reported in [5]. The authors mainly tackle the problem of picking appropriate actors for responding to an event in a particular region. The paper focused on the problem of actor assignment to overlapping areas with the least amount of energy and packet delay. Another recent work which considered improvement of coverage of actors is proposed in [8]. The idea of coverage in this work is exactly same as the one we consider in this paper. However, again it does not consider connectivity. Rather it focuses on improving end-to-end delay of sensor data.
2. System Model A set of sensors and actor nodes are spread throughout an area of interest to detect and track events and take necessary actions in that area. The sensors are battery-operated with diverse capabilities and types and are empowered with limited data processing engines. While sensors are deployed in abundance, the number of actor nodes is limited since robot-like nodes are usually used and they tend to be very expensive. The actors are both less-energy constrained and have larger transmission range than the sensors. The transmission range of actors is restricted and is significantly less than the dimensions of the deployment area. While an actor can in theory reach other actors through a satellite, the frequent inter-actor interaction required by the application would make the often-intermittent satellite links unsuitable. The action range of an actor, which is defined as the maximum distance it can cover, is limited and different than the radio range. In the paper, we assume that actors are randomly deployed. Actors discover each other in the area trough repeated beacons. Actors aggregate their individual set of neighbors in order to establish a core inter-actor network. Two possible scenarios are possible. In the first scenario, some actors become isolated from the core network, e.g. when they get placed away from the other actors. We call these actors orphaned. C2AP strives to integrate orphaned actors in the inter-actor network. The second scenario may yield multiple partitioned sub-networks of actors. Extending C2AP to handle that scenario is part of our future plan.
3. Related Work
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performed. Each actor node winning this competition can move as far as it can get without breaking its communication links to other actors. Those neighbors, that lost the competition, will stay stationary. To increase the degree of freedom in repositioning actors, C2AP applies link pruning in order identify a minimal set of links that ought to be maintained. Such pruning will enable less constrained actor’s motion. Spreading actors will also allow the discovery of orphaned nodes. An orphaned actor that remains isolated for long time will move to the center of the deployment area in order to increase the probability of joining the existing core inter-actor network.
4. Connectivity-Constrained Actor Positioning for Maximal Coverage We define the problem as follows: “Given n actors initially placed randomly in an area of interest, we are interested in repositioning actor nodes in order to form a connected inter-actor network that maximizes area coverage while imposing minimal overhead on the individual actors.” There are two variants of this problem depending on the post-deployment topology of the inter-actor network. The first applies when the initial placement of actors yields a connected network. In the second variant, actors form a partitioned network, i.e. multiple isolated sub-networks. Achieving maximal actor coverage and establishing a connected inter-actor network topology in such scenario is very challenging. In this paper we present, C2AP, a distributed algorithm that pursues controlled movement of actors in order to handle the first scenario. C2AP strives to maximize actor coverage while maintaining the inter-actor connectivity. We also consider a special case of the second variant where a core inter-actor network could be established for some of the actors leaving out one or multiple orphaned actor nodes. In other words, C2AP works with a single core connected network containing all or a subset of the actors in the area. Given the infinite solution space and the required inter-actor connectivity, finding optimal locations for the actor nodes is a very complex problem which has been proven to be NP-hard [10]. Therefore, we pursue heuristics. As we mentioned, C2AP moves actor nodes to extend their coverage while sustaining or even enhancing inter-actor connectivity. We adopt the principle of diffusion among molecular particles in Physics in order to spread actors in the area. An actor will apply repelling forces to move away from neighboring actors. To sustain inter-actor connectivity, actors’ spreading is constrained in order to maintain existing communication links. C2AP does so in a distributed manner relying only on inter-actor coordination. Since simultaneous relocations of actors may lead to violating the interactor network connectivity constraints, C2AP strives to maintain a global order of the relocation of the individual actors. C2AP still allows some actors to move at the same time if no conflicting (no exactly same) views of the state of the inter-actor network are used. The idea is to localize the decision making process for determining which actor to move first. In the context of C2AP an actor would only coordinate with its immediate neighbors, which are directly reachable to it. This takes the form of a competition among the neighboring actors before the relocation is
4.1. Self-Spreading of Connected Actors In order to solve the problem where the initial network is connected, we propose to use the principle of repulsion in Physics which happens when the molecules start diffusing in order to reach equilibrium [6][7]. In such a case, the molecules are spread through the medium by repelling each other until becoming so much apart that inter-molecule repulsion does not cause further motion. This process provides a uniform distribution of molecules. The repulsion between any two molecules is inversely proportional to the distance. Utilizing this idea, C2AP defines repelling forces on each actor based on its neighbors and the boundaries of the deployment area to move the actors for better area coverage. Thus, the repelling force on actor node i from actor node j is defined as follows:
( r − d ji ) , Fj = 2 0 ,
if r > d ji
i
(1)
if r ≤ d ji
where r is the transmission range and dji is the distance between i and j. Similar force can be defined from a particular edge e of the boundary of the deployment area to node i as follows:
( s − d ei ), i Fe = 0 ,
if s > d ei if
s ≤ d ei
(2)
where s is the action range of actor node i and dei is the distance from an edge to node i. Since there will be multiple forces acting on an actor node, the node should get the summation of these forces. The summation is performed based on vector addition. The magnitude of the composite force on a node and its direction will define the new location of an actor. This can be computed by using vector addition. We omit the description of vector addition here due to space constraints.
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Determining the new location: Once the composite force is defined, the actor node can move in the direction of that force a distance that is proportional to its magnitude. However, the travel distance will be restricted so that the links between the neighboring actor nodes are not broken. Such a distance obviously is limited to at most the transmission range of an actor; assuming neighbors will not simultaneously move. Therefore, the node picks a location which will be on the same line as the final destination and has a distance less than or equal to the transmission range to each of its neighbors. This location can easily be computed as we describe next. Assume that the coordinates of actors A, B and C are (a1, b1), (a2, b2) and (a3, b3) respectively, and that the new location of actor B is (a2new, b2new) as in shown in Fig. 1. Then, the equation of the line is: (3) y = mBx + c and c can be computed by applying one of the points to the equation. From (3),
b2 = m B a 2 + c
will pick the closest location among the alternatives since it will ensure that all its neighbors are less than a distance r away. Link Pruning: With the increasing number of neighbors the movement of an actor node will be restricted significantly which leads to poor spreading and hence less improvement in area coverage. Therefore, C2AP applies an optimization by eliminating redundant inter-actor links; basically identifying the least number of links for a node to stay connected to other actors. Such optimization mainly tries to remove some of the constraints on the distance that an actor can travel. The idea is to exchange the neighborhood tables among the actor nodes and try to check for multiple ways to reach a neighbor. If an actor determines that it can reach a neighbor through another actor, it can prune the existing link to that neighbor. This means, when determining the new location to move, the actor does not care for preserving connectivity with that neighbor since it can reach it as well as other nodes in the inter-actor network without using the link to that neighbor. In case there are multiple links which can be pruned, the actor will choose the longest links since those will be the first to be disconnected during the actor relocation, and thus will impose more stringent constraints. Obviously, link pruning cannot be performed simultaneously by all actors since it will lead to partitioning the network as every actor would base its decision on a varying network state. This also applies for the decision on the travel distance and direction for actor’s motion. In the next subsection, we address this issue and describe a coordination protocol for ensuring an ordered relocation of actors.
(4)
⇒ c = b2 − m B a 2
Applying (a2new, b2new) to (3) we get
b 2new = m B a 2 new + c
(5) The distance between (a2new, b2new) and (a1, b1) should be less than the actor communication range “r”.
(a 2 new − a1 ) 2 + (b2 new − b1 ) 2
