1. I owa S tate U niversity Laboratory for Advanced Networks (LAN) Coverage and Connectivity Control of Wireless Sensor Networks under Mobility Qiang QiuAhmed E. Kamal Department of Electrical and Computer Engineering Iowa State University

2. Laboratory for Advanced Networks (LAN) Outline 1.Introduction 2.The Problem and System Model 3.The Movement Algorithm 4.Connectivity and Coverage 5.Simulation Results 6.Conclusions

3. I owa S tate U niversity Laboratory for Advanced Networks (LAN) Introduction WSNs have been used in a number of tactical applications. Recent researches focus on fixed wireless sensors, ad hoc. We propose a sensor movement strategy:  A commander controls a cluster of mobile sensors to monitor a square area at a certain distance ahead of him in his direction of movement.  Once the speed and direction of the commander are decided, the new positions of the sensors are identified by our movement control algorithm.  Our movement algorithm also determines the speed and direction of movement for the sensors.  After a certain time, which is upper bounded, the commander and the sensors will all arrive at their new positions and the commander monitors a new region by these sensors.  The connectivity during the movement is guaranteed.

4. I owa S tate U niversity Laboratory for Advanced Networks (LAN) The Problem and System Model  The separation between adjacent sensor nodes is one unit, and this unit is taken as min(communication radius, coverage radius)  We define the sensor which is closest to the commander as the cluster head S 1m, where m=  The information collected by these sensors is relayed to the cluster head, and finally delivered to the commander by multihop communication.  Communication from the commander to the sensors is actually a reverse procedure. We consider a network with a commander and a region of a square shape in which the commander will be in charge of monitoring

5. I owa S tate U niversity Laboratory for Advanced Networks (LAN) The Problem and System Model Three important performance metrics for such a network :  Mobility: The commander and sensors will not fix at one position; The commander will execute the movement algorithm.  Connectivity: Any sensor can communicate with its neighbor sensors; The commander can communicate with the cluster head at any time  Coverage: The sensors can cover the same size of the region at the desired location; During the movement to a new location, however, coverage gaps may occur, but the duration of gaps must be upper limited.

6. I owa S tate U niversity Laboratory for Advanced Networks (LAN) The Movement Algorithm We make following assumptions for our sensor network:  The commander knows all the information about the sensors.  We define two state: monitor state and movement state.  When in monitor state, the relative position of the commander and the monitored sensor field should be the same. For the monitor state, if the commander changes speed while not changing his direction, the sensors adjust their speed accordingly.  The network changes from movement mode to monitor mode as soon as possible, such that the duration of the movement state is upper bounded by a given time, T max.

7. I owa S tate U niversity Laboratory for Advanced Networks (LAN) The Movement Algorithm When a commander moves by an angle,, and with speed V c. We assume that the movement will be implemented in time T and the maximum value of T is T max. Since, setting and T =T max and considering S nn to move the maximum distance L ij = L nn and  ij =  nn then we combine equations (1) to (5), and solve Xs nn, Ys nn and Vs nn. This Vs nn will be the maximum speed of sensors (Vs max = Vs nn ). Proposition 1:For, a sensor, S ij, using a speed Vs max, moves to it new position, will do so in time T, where T T max. Proof:The proof is straightforward and is based on L ij L nn.

8. I owa S tate U niversity Laboratory for Advanced Networks (LAN) Connectivity and Coverage Proposition 2: Under the movement algorithm of previous slides, the following two conditions are satisfied: 1. The distance between the commander and the cluster head doest not exceed the cluster head’s transmission range. 2. The distance between any two neighboring sensors does not exceed one unit.

9. I owa S tate U niversity Laboratory for Advanced Networks (LAN) Connectivity and Coverage The distance between the commander and cluster head S 1m at time t is L cc (t). Let L cc2 (t)=L cc 2 (t). R c is the cluster head transmission range. Equivalently, we show that L cc 2 (t) never exceeds R c 2 during this time interval.  L cc2 (t) is a quadratic function of t, its curve is an open up quadratic curve L cc2 (t) has maximum values of R c 2 at times 0 and T, during (0, T), the value of L cc2 (t) will be less than R c 2  Then the distance between the commander and the cluster head will therefore never exceed R c in the interval [0, T], which proves the first part.

10. I owa S tate U niversity Laboratory for Advanced Networks (LAN) The distance between any sensor S a with its horizontal neighbor sensor S b at time t is L ss (t). Let L ss2 (t)=L ss 2 (t).  L ss2 (t) is a quadratic function of t, its curve is an open up quadratic curve L ss2 (t) has maximum values of 1 2 at times 0 and T, during (0, T), the value of L cc2 (t) will be less than 1 2. L ss (t) will be less than 1 during(0, T).  The proof for the connectivity between any sensor S a with its vertical neighbor sensor S a is similar to the above case. Connectivity and Coverage

11. I owa S tate U niversity Laboratory for Advanced Networks (LAN) Connectivity and Coverage Proposition 3:Under the movement algorithm, the commander can cover the same size of sensor field when it changes from one monitor mode to a new monitor mode. Proof: The proof is simple. Because the relative position of the commander and the sensors will be same, and every sensor will monitor the same size of grid area in its sensor range, the sensors will cover the same size of sensor field when they are in a new monitor mode.

12. I owa S tate U niversity Laboratory for Advanced Networks (LAN) Simulation Results We place 81 sensor nodes in a grid network with different scenarios, Vc=1. V c (unit/s)T max (s)V max (unit/s)T(s) 193.19912.9352 182.07575.4774 193.19916.0568 182.075711.7697 93.19912.9352 182.07575.4774 193.19916.0568 182.075711.7697 Given a fixed speed for the commander, the time for changing from one monitor state to a new monitor state will increase with the movement direction and the upper bound T max, and all changes can be made within T max.

13. I owa S tate U niversity Laboratory for Advanced Networks (LAN) Simulation Results Consider an example in which the commander moves in the direction of with speed of 1 unit/s, and T max =9. The sensor S 15 is the cluster head and Ls 15 (t) is the distance between the commander and S 15 at any time t. Time TLs 15 (t) d 23 d 32 d 34 d 43 061111 1 5.6878 0.9480 2 5.5490 0.9248 3 5.5965 0.9327 4 5.8256 0.9709 4.493561111 This result is consistent with Proposition 2, and guarantees the connectivity between the commander and the cluster head. It also shows that the distance between one sensor and its neighbor sensors is always below their initial value, and arrives at its maximum value at time 0 and T.

14. I owa S tate U niversity Laboratory for Advanced Networks (LAN) Simulation Results We simulate a simplified example with 25 sensors placed in grid network. The commander moves in the direction of with speed of 2 unit/s, and T max =10. Using our movement algorithm, we get the actual time T=4.5805 and Vs max =3.7947. Vs ij j=1j=2j=3j=4j=5 i=12.86822.95973.05773.16153.2705 i=23.01143.09873.19243.29203.3968 i=33.15703.24043.33013.42563.5265 i=43.30463.38443.47043.56213.6592 i=53.45393.53043.61293.70113.7947 j=1j=2j=3j=4j=5 i=10.16320.21120.25620.29830.3377 i=20.13390.18060.22450.2659 i=30.10730.15260.19550.23610.2744 i=40.08310.12700.16880.20850.2462 i=50.06090.10350.14420.18300.2199

15. I owa S tate U niversity Laboratory for Advanced Networks (LAN) Conclusions The paper has presented a strategy to change the direction of movement and speed of the sensors once the direction of the commander is changed. The sensors must arrive at their final position in which they provide coverage of the target area within an upper bounded time, T max. This upper bound was used to derive the speed of the sensors and their directions of movement. It was shown that during the movement of the sensors to their new locations, they stay connected, and also connected to the commander through a cluster head sensor. It was also shown that coverage gaps will not exceed T max.