Pei-Ling Chiu Mobile Sensor Networks

Pei-Ling Chiu2 Outline Research Framework Paper: ”Movement-Assisted Sensor Deployment” Related Work Discussion

Movement-Assisted Sensor Deployment Guiling Wang, Guohong Cao, and Tom La Porta Department of Computer Science & Engineering The Pennsylvania State University IEEE INFOCOM 2004

Pei-Ling Chiu4 Introduction In this paper, the authors design and evaluate three distributed self-deployment protocols for sensor networks. The problem statement is: given the target area, how to maximize the sensor coverage with less time, movement distance and message complexity. The proposed distributed self-deployment protocols 1. To discover the existence of coverage holes 2. The proposed protocols calculate the target positions of these sensors. They use Voronoi diagrams to discover the coverage holes and design three movement-assisted sensor deployment protocols. Performance metrics: coverage, deployment time, moving distance, scalability to initial deployment and communication range, etc.

Pei-Ling Chiu5 Voronoi Diagram The Voronoi diagram of a collection of nodes partitions the space into polygons. Every point in a given polygon is closer to the node in this polygon than to any other node. Fig. 1 Voronoi polygon of point O : G p (O)=( p (O), E p (O)) p (O) is the set of Voronoi vertices of O. E p (O) is the set of Voronoi edges of O. N(O) denotes the set of Voronoi neighbors of O. The Voronoi edges of O are the vertical bisectors of the line passing O and its Voronoi neighbors, e.g., V 5 V 1 is OA ’s bisector.

Pei-Ling Chiu6 Voronoi Diagram and Voronoi Polygon Neighbors N(O)={A, B, C, D, E} Vertices (O)={V 1, V 2, V 3, V 4, V 5 } Edges E(O)={V 1 V 2, V 2 V 3, V 3 V 4, V 4 V 5, V 5 V 1 } Point O→sensor node

Pei-Ling Chiu7 Voronoi Diagram These Voronoi polygons together cover the target field. The points inside one polygon are closer to the sensor inside this polygon than the sensors positioned elsewhere. Each sensor is responsible for the sensing task in its Voronoi polygon. In this way, each sensor can examine the coverage hole locally. To construct the Voronoi polygon, each sensor only needs to know the existence of its Voronoi neighbors, which reduces the communication complexity.

Pei-Ling Chiu8 Movement-Assisted Sensor Deployment Protocols The sensor deployment protocol runs iteratively until it terminates or reaches the specified maximum round. In each round, sensors 1. To broadcast their locations 2. To construct their local Voronoi polygons based on the received neighbor information 3. The Voronoi polygons are examined to determine the existence of coverage holes. 4. If any coverage hole exists, sensors decide where to move to eliminate or reduce the size of the coverage hole; otherwise, they stay.

Pei-Ling Chiu9 Three Movement-Assisted Sensor Deployment Protocols The VECtor-based Algorithm (VEC) The virtual forces will push sensors from the densely covered area to the sparsely covered area. The VORonoi-based Algorithm (VOR) The Minimax Algorithm (Minimax)

Pei-Ling Chiu10 The Deployment Protocol (5) VEC() / VOR() / Minimax()

Pei-Ling Chiu11 The VECtor-based Algorithm VEC is motivated by the attributes of electro-magnetic particles: when two electro-magnetic particles are too close to each other, an expelling force pushes them apart. Assume d(s i, s j ) is the distance between sensor s i and sensor s j. d ave is the average distance between two sensors when the sensors are evenly distributed in the target area. d ave can be calculated beforehand since the target area and the number of sensors to be deployed are known. The virtual force exerted by s j on s i is denoted as F ij, with the direction from s j to s i.

Pei-Ling Chiu12 Virtual Force The virtual force between two sensors s i and s j will push them to move (d ave - d(s i, s j ))/2 away from each other. In case one sensor covers its Voronoi polygon completely and should not move, the other sensor will be pushed d ave - d(s i, s j ) away. The field boundary also exert forces, denoted as F b, to push sensors too close to the boundary inside. F b exerted on s i will push it to move d ave / 2 - d b (s i ) d b (s i ) is the distance of s i to the boundary. d ave /2 is the distance from the boundary to the sensors closest to it when sensors are evenly distributed. The final overall force on sensors is the vector summation of virtual forces from the boundary and all Voronoi neighbors.

Pei-Ling Chiu13 Virtual Force Local coverage The coverage of the local Voronoi polygon The intersection of the polygon and the sensing circle Movement-adjustment scheme Sensor checks whether the local coverage will be increased by its movement. If the local coverage is increased at the new target location, the sensor will move; otherwise, it will stay.

Pei-Ling Chiu14 The VECtor-based Algorithm

Pei-Ling Chiu15 Snapshot of the Execution of VEC 35 sensors in a 15m by 15m space Sensing range = 6m Coverage: (a) 75.7%, (b) 92.2%, (c) 94.7%

Pei-Ling Chiu16 The VORonoi-based Algorithm VOR algorithm pulls sensors to their local maximum coverage holes. In VOR, if a sensor detects the existence of coverage holes, it will move toward its farthest Voronoi vertex (denoted as V far ). Fig. 5 shows VOR works. Point A is the farthest Voronoi vertex of s i and d(A, s i ) is longer than the sensing range. Sensor s i moves along line s i A to Point B, where d(A,B) is equal to the sensing range.

Pei-Ling Chiu17 Maximum Moving Distance local view of Gp(s i ) is not correct s i is not aware of the existence of s j because of communication limitations. if si moves toward point A and stops at a distance d(A,B) (sensing range), si has moved more than needed. We limit the maximum moving distance to be at most half of the communication range to avoid the situation.

Pei-Ling Chiu18 Oscillation Control Moving oscillations may occur if new holes are generated due to sensor’s leaving. To deal with this problem, we add oscillation control which does not allow sensors to move backward immediately. Each time a sensor wants to move, it first checks whether its moving direction is opposite to that in the previous round. If yes, it stops for one round.

Pei-Ling Chiu19 The VORonoi-based Algorithm

Pei-Ling Chiu20 Snapshot of the Execution of VOR Coverage: (a) 75.7%, (b) 89.2%, (c) 95.6%

Pei-Ling Chiu21 The Minimax Algorithm Minimax does not move as far as VOR to avoid the situation that the vertex which was originally close becomes a new farthest vertex. Minimax chooses the target location as the point inside the Voronoi polygon whose distance to the farthest Voronoi vertex (V far ) is minimized. We call this point the Minimax point, denoted as O m. Minimax can reduce the variance of the distances to the Voronoi Vertices, resulting in a more regular shaped Voronoi polygon, which better utilizes sensor’s sensing circle.

Pei-Ling Chiu22 The Minimax Algorithm A circle centered at point O with radius r is denoted C(O, r). The circumcircle of three points V u, V v, V w is denoted as C(V u, V v, V w ). Definition 1: Minimax circle C m (O m, r m ) is the circle centered at the Minimax point O m, with radius r m = d(O m, V far ). Lemma 1: C m (O m, r m ) must pass at least two Voronoi vertices.

Pei-Ling Chiu23 The Minimax Algorithm Definition 2: The circumcircle of two point V u and V w (C(V u, V w )) is defined as the circle whose center is the midpoint of V u and V w and whose radius is d(V u, V w )/2. Lemma 2: If C m (O m, r m ) passes exactly two Voronoi vertices:V u and V w, then C m (O m, r m ) = C(V u, V w ). In other words, if the Minimax circle passes only two Voronoi vertices, it must be centered at the midpoint of these two vertices.

Pei-Ling Chiu24 The Minimax Algorithm If the Minimax circle passes more than two Voronoi vertices, it is the circumcircle of these vertices. To find the Minimax point, to find all the circumcircles of any two and any three Voronoi vertices Among those circles, the one with the minimum radius covering all the vertices is the Minimax circle. The center of this circle is the Minimax point. Theorem 1: Let Γ = {C(V u, V v ) | C(V u, V v ) covers all vertices in V p, and V u, V v  V p }  { C(V u, V v, V w ) | C(V u, V v, V w ) covers all vertices in V p, and V u, V v, V w  Vp}, then C m (O m, r m )  Γ and  C(O, r)  Γ, r  r m.

Pei-Ling Chiu25 The Minimax Algorithm

Pei-Ling Chiu26 Snapshot of the Execution of Minimax Coverage: (a) 75.7%, (b) 92.7%, (c) 96.5%

Pei-Ling Chiu27 Termination The local coverage increase of one sensor does not affect the local coverage of another sensor. Thus, sensors will stop naturally when the best coverage is obtained. In some applications, the coverage requirement is not that high. To terminate the deployment procedure earlier, we use a threshold , defined as the minimum increase in coverage below which a sensor will not move. With a larger , the deployment will finish earlier.

Pei-Ling Chiu28 Optimizations In some cases, the initial deployment of sensors may form clusters, as shown in Fig. 10. In this case, sensors located inside the clusters can not move for several rounds, since their Voronoi polygons are well covered initially. This problem prolongs the deployment time. To reduce the deployment time in this situation, we propose an optimization which detects whether too many sensors are clustered in a small area. The algorithm “explodes” the cluster to scatter the sensors apart, if necessary.

Pei-Ling Chiu29 Optimizations Each sensor compares its current neighbor number to the neighbor number it will have if sensors are evenly distributed. The explosion algorithm The sensor chooses a random position within an area centered at itself which will contain the same number of sensors as its current neighbors in the even distribution. only runs in the first round. It scatters the clustered sensors and changes the deployment to be close to random.

Pei-Ling Chiu30

Pei-Ling Chiu31 Performance Evaluation Performance metrics Deployment Quality Sensor coverage Time → the number of rounds Deployment Cost The sensors cost→the number of sensor Energy consumption→moving distance

Pei-Ling Chiu32 Parameters Fields size: 50m  50m, 150m  150m Sensor density: 30,35, 40, 45 sensors/50mx50m Initial deployments: random distribution, normal distribution Sensor communication range: 10m~28m, (20m) Sensor sensing range: 10m  =0

Pei-Ling Chiu33 Coverage and Sensor Cost 85 sensors, 98% coverage

Pei-Ling Chiu34 Coverage and Sensor Cost In the first round, VOR is better than Minimax. VEC is sensitive to the initial deployment.

Pei-Ling Chiu35 Moving Distance Minimax, VOR: moving distance are larger under lower density VEC: the moving distance is similar under different sensor densities

Pei-Ling Chiu36 Impact of Topology Normal distribution With as high as 80 sensors, the coverage cannot reach 80% even when  is 10.

Pei-Ling Chiu37 High-degree clustering  =1 n=40 VEC-O: VEC+optimization, VOR-O: VOR+optimization, Minimax-O : Minimax +optimization Optimization: explode algorithm Minimax can not increase the coverage as quickly as in the random case. Minimax surpasses VEC after the tenth round when σ = 1, and after the seventh round whenσ = 5. This again demonstrates that Minimax has advantage in coverage.

Pei-Ling Chiu38 Impact of Communication Range When the communication range is lower than 12m, the performance is reduced When the communication range is too low, most sensors do not know all their Voronoi neighbors, and the constructed Voronoi diagram is not very accurate.

Pei-Ling Chiu39 Discussion Optimal Movement vs. Communication Sensors move only once the centralized algorithms Simulated movement The three distributed algorithms only incur an approximately additional 20% movement overhead, compared to these algorithms. Although the centralized approach may minimize the sensor movement, a central server architecture may not be feasible in some applications. Simulated movement Poor performance under network partitions

Pei-Ling Chiu40 Discussion As the sensing range decreases with regard to the communication range, our protocols will perform very well because they can accurately construct the Voronoi diagrams. The protocols are not sensitive to the scale of the network and target field The performance of the algorithms depend on the density of sensors.

Pei-Ling Chiu41 Outline Research Framework Paper: ”Movement-Assisted Sensor Deployment” Related Work Discussion

Sameera Poduri and Gaurav S. Sukhatme In IEEE International Conference on Robotics and Automation, May 2004 Department of Computer Science University of Southern California, Los Angeles, California, USA Constrained Coverage for Mobile Sensor Networks

Pei-Ling Chiu43 Introduction In this paper the authors consider constrained coverage for a mobile sensor network. The constraint is node degree - the number of neighbors of each node in the network. More precisely, the authors require each node to have a minimum degree K, where K is parameter of the deployment algorithm. Motivation: Reliability: Sometimes a high degree is required for the sake of redundancy. Connectivity: Global network connectivity is strongly dependent on node degree.

Pei-Ling Chiu44 Introduction A global map of the environment is either unavailable or of little use because the environment is not static. They also assume that no global positioning system (GPS) is available. Approach: Based on virtual potential fields Force laws: Repulsive force: to maximum coverage Attractive force: to impose the constraint of K-degree

Pei-Ling Chiu45 Problem Formulation Problem: Given N mobile nodes with isotropic radial sensors of range Rs and isotropic radio communication of range Rc, how should they deploy themselves so that the resulting configuration maximizes the net sensor coverage of the network with the constraint that each node has at least K neighbors? Neighbors: if the Euclidean distance between two nodes is less than or equal to the communication range Rc. Assumptions: 1) The nodes are capable of omni-directional motion, 2) Each node can sense the exact relative range and bearing of its neighbors, 3) It follows a binary detection model.

Pei-Ling Chiu46 Problem Formulation The deployment algorithm: Distributed and scalable Not require a prior map or localization of nodes Performance metrics: 1) the normalized per-node coverage. Coverage =(Net Area Covered by the Network) / N  R s 2 2) the percentage of nodes in the network that have at least K neighbors. 3) the average degree of the network.

Pei-Ling Chiu47 The Deployment Algorithm

Pei-Ling Chiu48 Symmetrically Tiled Network The coverage of these Symmetrically Tiled networks is an upper bound on the coverage achievable by networks given the constraint of K-degree.

Pei-Ling Chiu49 Experiments

1. Zack Butler and Daniela Rus, “Controlling Mobile Sensors for Monitoring Events with Coverage Constraints”, ICRA ' IEEE International Conference on, Volume: 2, April 26-May 1, Zack Butler and Daniela Rus,“Event-Based Motion Control for Mobile-Sensor Networks,” IEEE Pervasive Computing, October-December Event-Based Motion Control

Pei-Ling Chiu51 Introduction Scenario: If the specific area of interest (within a larger area) is unknown during deployment. For example, if a network is deployed to monitor the migration of a herd of animals, the herd’s exact path through an area will be unknown beforehand. Event-based The sensors could converge on the event to get the maximum amount of data. The sensors could move such that they also maintain complete coverage of their environment while reacting to the events in that environment. In this way, at least one sensor still detects any events that occur in isolation, while several sensors more carefully observe dense clusters of events.

Pei-Ling Chiu52 Introduction The authors have developed distributed algorithms for mobile-sensor networks to physically react to changes or events in their environment or in the network itself. Assumptions: The sensor begin in a uniform distribution over the environment. The events can be represented discretely in space and time. At least one sensor can sense each event and broadcast the event location to the other sensors. Every sensor learns about each event location.

Pei-Ling Chiu53 History-Free Approach The approach uses only the current position of the sensor and the position of an event to determine the motion of the sensor. A sensor will move toward each event by the amount given by f, f(d)=  d  e -  d d: the distance between a sensor and an event. f(  )=0, 0  f(d)  d,  d, f(d 1 )-f (d 2 ) d 2

Pei-Ling Chiu54 History-free Approach

Pei-Ling Chiu55 History-based Approach The approach uses a small of history and more carefully analyzes the distribution of events. It uses a coarse histogram of the events as a basis for determining its correct position. Each sensor computes the cumulative distribution (CDF) of the scaled event distribution. The sensor then finds the point in the scaled CDF corresponding to its initial position, and moves to that location.

Pei-Ling Chiu56 History-based Approach

Pei-Ling Chiu57 History-Free and History-Based Approach Sensor network may lose network connectivity or sensor coverage.

Pei-Ling Chiu58 Maintaining Coverage The Authors instead have the sensors follow the event distribution exactly until required for coverage, so that they can achieve a good approximation to the event distribution in high density area and good coverage in low density area. Approaches: Complete Voronoi Algorithm Local Voronoi Algorithm

Pei-Ling Chiu59

Pei-Ling Chiu60 Outline Research Framework Paper: ”Movement-Assisted Sensor Deployment” Related Work Discussion