A Novel Greedy Forward Algorithm for Routing Data Toward a High Speed Sink in Wireless Sensor Networks

A Novel Greedy Forward Algorithm for Routing Data Toward a High Speed Sink in Wireless Sensor Networks Horacio A.B.F. Oliveira, Raimundo S. Barreto, Awdren L. Fontao, Antonio A.F. Loureiro, and Eduardo F. Nakamura Department of Computer Science Federal University of Amazonas, Brazil {horacio,rbarreto,awdren}@dcc.ufam.edu.br Department of Computer Science Federal University of Minas Gerais, Brazil loureiro@dcc.ufmg.br FUCAPI Analysis, Research, and Technological Innovation Center, Brazil eduardo.nakamura@fucapi.br Abstract Sink nodes are responsible for aggregating data gathered by a Wireless Sensor Network (WSN) and transmitting them to a monitoring facility. Usually, these are static nodes that serve as gateways to infrastructured networks. In some applications, these sink nodes move around the monitoring area, usually in lower speeds (e.g., robots, dirigibles). In this work, we go further and study WSN scenarios in which sink nodes can move at higher speeds, such as an Unmanned Aerial Vehicle (UAV) or even an airplane. In these cases, propagated queries cannot be answered by using the sink s position when the query was sent, since the sink will be elsewhere due to its high speed. Thus, we propose and evaluate the performance of three algorithms for data query in WSNs when the sink is moving at a high speed. Our results show clearly the need for new algorithms for these scenarios as well as the good performance of our proposed algorithms. Keywords-routing; high speed; wireless sensor networks. I. INTRODUCTION Wireless Sensor Networks (WSNs) [1] [3] are composed of a large number of small sensor devices that are able to sense and gather data from their surroundings, process the data gathered, and send them toward a sink node, using multihop wireless communication. The sink node is responsible for sending the data to a monitoring facility. Usually, sensor nodes, including the sink, are static nodes. Some proposals [] [6], however, have demonstrated the advantages of using mobile sinks to mitigate the process of collecting the data gathered by a WSN. In these cases, the sink node moves throughout the sensor field communicating with the sensor nodes. In all proposed scenarios, the sink node has low to medium mobility such as a robot, a airship, small remote controlled cars, or even a person carrying the sink node. The main challenge is basically how to keep the routing table of the sensor nodes updated, so they can forward the gathered data toward the current position of the sink node. This work was partially supported by the National Institute of Science and Technology Critical Embedded Systems (INCT-SEC), by the Brazilian National Council for Scientific and Technological Development (CNPq) under the processes 5571/6-1, 5587/6-5, 719/7-8, 57588/8- and 573963/8-8 and by the São Paulo Research Foundation (FAPESP) under the process 8/5787-9. More recent scenarios have demonstrated the need for collecting data from a WSN using sink nodes that move at high speeds. For instance, a sink node could be an Unmanned Aerial Vehicle (UAV) or even an airplane, in which case the aerial vehicle would be responsible for flying over the WSN sending queries and receiving replies from the sensor nodes. Due to the high speed nature of the sink node, the reply packets, sent by the sensor nodes in multiple hops, cannot be sent toward the position of the sink node when it sent the query packet, since the sink node will be elsewhere in the network. In this work, we propose a new Greedy Forward algorithm for sending data toward a high speed sink in WSNs: the Whisper (Wireless HIgh SPEed Routing) algorithm. Based on this algorithm, we also propose three different variations: Whisper, Whisper, and Whisper. The main idea of these Whisper algorithms is to recognize that the sink node is not at the location where the query packet was sent due to its high speed trajectory. Thus, to overcome this problem, the Whisper algorithm sends the reply packet towards a more updated location, or even a future location, of the sink node(figure 1). The performance of the proposed algorithms is evaluated using the NS- simulator. We present an extensive set of experiments that show the need for new algorithms in these high speed scenarios, and also clearly indicate the good performance of the proposed algorithms. The remaining of this paper is organized as follows. In the next section, we describe the related work regarding mobile sinks as well as communication at high speed WSNs. Section III shows some definitions used throughout this paper and our problem definition. The Whisper algorithm and its variants are presented in Section IV, which are evaluated in Section V. In section VI, we briefly discuss the applicability, advantages, and limitations of the proposed solution. Finally, in Section VII we present our conclusions. II. RELATED WORK A first attempt to tackle the problem of data delivery from sensor nodes toward a mobile sink in WSNs is the TTDD (Two-Tier Data Dissemination) []. In this algorithm,

Figure 1: A query sent to a WSN by a high speed sink. each node builds a grid structure that allows mobile sinks to receive data through controlled flooding limited to their local cells. Fordor and Vidacs [5] proposed an efficient routing algorithm that allows all nodes to reach the mobile sink. That algorithm tries to find an intermediate solution for good routes while minimizing the number of messages required to update them. At last, Shim and Park [6] proposed an algorithm based on locators. Those locators are uniformly distributed in the sensor field and are able to find the current position of the mobile sink. If a node tries to send data towards an outdated position of the sink, this node can get a more updated position using these locators. In [7], it is carried out experiments using an aerial device. In that work, n sensor nodes are randomly distributed in a circle or area R. The mobile sink can place itself at specified positions and height and send packets to sensor nodes. Results clearly demonstrate the possibility of communication with the sensor nodes. However, the increase in height affect the delivery ratio, communication range, and energy consumption. Khalid et al. [8] evaluated the sink speed by making the to sink move through the sensor field at a V i speed and an angle of θ degrees, regarding the axis X. The results also indicate the possibility of half duplex link communication even at high speeds. As shown in this section, the problem of data delivery toward a mobile sink has been basically studied at low to medium speeds. Othar proposals that use a mobile sink at high speeds focus only on single-hop communication. In this work, however, we propose a different and novel approach: multihop data delivery towards a high speed mobile sink. In ourproposedapproach,wealsomakeuseoffloodingtosend queries from the sink node to all sensor nodes. On the other hand, we do not try to update the position of the sink node using messages, since they would be outdated before the update packet reaches the destination. This will be further discussed below. III. PROBLEM DEFINITION In this section, we present some definitions used herein. Definition 1 (Wireless Sensor Networks): A WSNs can be seen as an Euclidean graph G = (V,E) with the following properties: n is the number of nodes; r, the communication range; Q = [,s] [,s] [,r] is the sensor field in 3-D; V = {v,v 1,...,v n } is the set of sensor nodes, v is the mobile sink node; (i,j) E iff the distance between v i and v j is at most r, i.e., v i reaches v j and vice-versa; v i V,(Xp i,yp i,zp i ) R 3 is the real position of node v i ; while (Xc i,yc i,zc i ) R 3 is the computed position of node v i (e.g., using a localization system). Definition (High Speed Mobile Sink): A high speed mobile sink, in this work, is defined as the node v capable of: mobility over 1 km/h; predefined trajectories (e.g., straight line, curves); continuously localization (e.g., equipped with GPS Global Positioning System); in which the main goal is to cross the sensor field collecting data. Definition 3 (Data Query Algorithm): Unlike normal routing algorithms that try to maintain routes between source and destination nodes, this work is focused mainly in routing algorithms for data query [9]. In these algorithms, the sink node sends a query to the sensor network, as if it was a distributed database system (i.e.,sensor databases [1]). This query is usually propagated by flooding. Sensor nodes that can respond to the query assemble a reply packet that is sent toward the sink node. Some proposed algorithms of this type include the Directed Diffusion [11] and the Received Signal Strength Routing [1]. IV. WHISPER - A NOVEL GREEDY FORWARD ALGORITHM FOR ROUTING DATA TOWARDS A HIGH SPEED SINK In this section, we propose a new Greedy Forward algorithm for sending data towards a high speed sink: the Whisper (Wireless High Speed Routing) algorithm. As mentioned before (and depicted in Figure 1), the main idea of Whisper is to recognize that the sink node is no longer at the location where the query packet was sent, due to its high speed trajectory. Then, if we send the reply packet toward the location where the query was sent, the reply message will not be able to reach the sink node. Thus, to overcome this problem, the Whisper algorithm sends the reply packet toward a more updated location, or even a future location, of the sink node. Such a location is recomputed at each hop for each intermediate node. Then, this node forwards the packet to its neighbor that is closer to the newly computed sink s position. Therefore, it is important that each node knows its own location, the location of its neighbors, and the Sink s Trajectory and Displacement (Definitions and 5). Definition (Sink s Trajectory T s ): this trajectory can be a line, a curve or any another trajectory that can be mathematically expressed. For the sake of simplification, and without any loss of generality, we consider that, while inside

the sensor field, the sink will maintain the trajectory of a straight line, which is common for objects at high speed. Thus, given an initial point (e.g., the sink s position when the query was sent) and a direction, this line can be easily computed as y = tan(θ)(x x )+y, where θ is the angle in relation to the x-axis and (x, y ) is the initial position. This sink s trajectory is sent along with the query packet. Definition 5 (Sink s Displacement S s (t)): can be defined as the position of the sink node along its trajectory in time t (measured in seconds). Such a displacement needs also to be described by an equation such as S s (t) = vt + 1 at where a is the constant acceleration and v the initial velocity. Again, for the sake of simplification and without any loss of generality, we will consider that the acceleration will be zero, i.e., there will be no changes on the sink s velocity while it is in the sensor field. Thus, its displacement will be simply S s (t) = v s t, where v s is the sink s velocity (km/h). The Whisper algorithm, shown and explained in Algorithm 1, starts when the sink node enters the sensor field and sends a query packet (lines -1). This query, among other information, contains the routing time (R i, initially zero Definition 6). Definition 6 (Routing Time R p ): in order to compute the sink s current location, we need to know its time of displacement. This time is the same as the routing time, whichisthetotaltimethequerypacketleftthesinknodeand arrived at the current node. It can be computed as the sum of all packet delays in all intermediate nodes, as depicted in Figure (a). To compute the delay of a single hop, we can use the delay measurement technique [13], which is commonly used by synchronization algorithms [1]. Basically it is the sum of all delays to send a packet from a sender to a receiver node, as depicted in Figure (b). Every node that receives the query (directly from the sink or through an intermediate node) estimates the delay of this packet, update its neighbor table, and forwards the packet to its neighbors (lines 11-). If the current node has any data to reply to the sink node, it assembles a reply packet with the data and sends it to the hop i node after time i seconds. The hop i and time i values are computed according to the Whisper algorithm Type. In this work, we propose three different variations of the Whisper Algorithm: the Whisper (Section IV-A), the Whisper (Section IV-B), and the Whisper (Section IV-C). At last, if an intermediate node receives a reply packet, it will compute the new values for hop i and time i and forward the packet according to the Whisper algorithm variation in use. These variations of the Whisper algorithm are explained in the next sections. A. Whisper The Whisper is the most intuitive variation of the proposed algorithm. Basically, at each hop, the intermediate Algorithm 1 - Whisper algorithm Variables: 1: Fwd i ; {Table of forwarded queries and replies avoid loops} : Neig i ; {Neighbor table stores id, position, etc} 3: id i ; {Last query sent by the sink node} Input: : Sink node enters the sensor field to send a qry packet with id id. Action: 5: id id + 1; {Query id} 6: cmd SELECT from RSSF where temperature >= ; 7: src v ; R ; {Source and routing time} 8: T traj(); S speed(); {Sink s trajectory and speed} 9: Lp (Xc i,yc i); {Last position} 1: Broadcast qry(src,id,cmd,t,s,r,lp i); {Sends the query} Input: 11: msg i = qry(src k,id k,cmd k,t k,s k,r k,lp k ); d i = delay(msg i). Action: 1: R i R k + d i; {Update routing time} 13: if k then -{IF: the packet is not directly from the sink node...}- 1: Neig i Neig i (k,lp k ); {Update the neighbor table} 15: end if 16: if (src k,id k ) / Fwd i then -{IF: the node never forwarded the query...}- 17: Fwd i Fwd i (src k,id k ); {Update the forward table} 18: Lp i (Xc i,yc i); {Position of the current node} 19: Broadcast qry(src k,id k,cmd k,t k,s k,r i,lp i); {Fwd. the query} : end if 1: if data i evaluate(cmd k ) then-{if: node has data to reply the sink...}- : src i i; {Reply source} 3: Fwd i Fwd i (orig k,id k ); : P i = dist((xc i,yc i),t k )/R i; {Query s propagation speed} 5: hop i nexthop(); {Computes the next hop} 6: time i nexttime(); {Computes the next time} 7: Send reply(src i,id k,data i,t k,s k,r i,p i) to hop i in time i sec.; 8: end if Input: 9: msg i = reply(src k,id k,data k,t k,s k,r k,p k ); d i = delay(msg i). Action: 3: if k = then -{IF: it is the sink node...}- 31: store(data k ); {Sink receives and stores the reply data} 3: else 33: if (src k,id k ) / Fwd i then -{IF: node never forwarded the reply...}- 3: Fwd i Fwd i (src k,id k ); 35: R i R k + d i; 36: hop i nexthop(); 37: time i nexttime(); 38: Send reply(src k,id k,data k,t k,s k,r i,p k ) to hop i in time i s.; 39: end if : end if Figure : (a) Routing time of a packet; (b) Delay measurement of a hop.

Figure 3: Variations of the Whisper Algorithm. (a) Whisper ; (b) Whisper ; e (c) Whisper. node will compute the current position of the sink node (sinkp os). Then, this intermediate node immediately forwards the reply packet toward its neighbor that is closer to the current position of the sink node. Thus, sinkpos.x = T k.x + S k cos(t k.θ) R i; (1) sinkpos.y = T k.y + S k sin(t k.θ) R i; sinkpos.z = T k.z; nexthop() = closestneigh(sinkp os.x, sinkp os.y, sinkp os.z); nexttime() =.; As depicted in Figure 3(a), the trajectory of the reply packet in the Whisper algorithm tends to be a parabolic curve since, for each hop, the sink node will be in a different location. B. Whisper The Whisper, instead of computing the current position of the sink, calculates the first point of interception between the trajectories of the sink node and the reply packet, which is forwarded immediately. This point of interception is computed based on the speeds of both sink and query propagation (Definition 7). Definition 7 (Query s Propagation Speed P k ): a sensor node, when receiving a query packet can compute the average speed of this packet, which is basically the distance between the sink and the current node divided by the query s routing time, i.e., P k = distance((xc i,yc i ),T k )/R i This point of interception can be obtained by first computing the time of interception: (T k.y Yc i) time = Pk (S () k sin(t k.θ)) sinkpos.x = T k.x + S k cos(t k.θ) (R i + time); sinkpos.y = T k.y + S k sin(t k.θ) (R i + time); sinkpos.z = T k.z; nexthop() = closestneigh(sinkp os.x, sinkp os.y, sinkp os.z); nexttime() =.; In the Whisper, the reply tends to follow a straight line, since all intermediate nodes will compute approximately the same point of interception (Figure 3(b)). However, some factors such as a higher delay in an intermediate node can make this point of interception change in some cases since it is recomputed at each hop. This behavior makes the proposed algorithm robust to changes in the speed of the reply packet (i.e., higher or slower delays). C. Whisper The Whisper, instead of computing the first point of intercept, calculates the shortest point of intercept. Also, the reply packet is not forwarded immediately, since the sink might be far from this shortest point. Thus, the node waits for the sink to be closer before sending the reply packet. In this case, the reply packet will have a higher delay but, on the other side, lower communication paths. dx = S k cos(t k.θ) R i; (3) dy = S k sin(t k.θ) R i; tan = (Xci T k.x) dx + (Yc i T k.y) dy dx + dy ; sinkpos.x = T k.x + tan dx; sinkpos.y = T k.y + tam dy; sinkpos.z = T k.z; nexthop() = closestneigh(sinkp os.x, sinkp os.y, sinkp os.z); timesink = distance(sinkpos,t k )/S k ; timepkt = distance((xc i,yc i),sinkpos)/p k ; nexttime() = timesink timepkt; As depicted in Figure 3(c), the trajectory of the reply packet tends to be a line perpendicular to the sinks trajectory. If the computed timesink is negative, than the sink node already crossed the closest interception point. In this case, the reply packet is sent immediately by using the Whisper variation. V. PERFORMANCE EVALUATION The performance evaluation is performed through simulations using the NS- simulator. The simulation parameters are based on the MicaZ platform, and the default values are shown in Table I. In all results, curves Parameter Value represent average Sensor field 758m 758m 576 nodes values, while error bars represent confidence intervals for 95% of confidence from 33 independent instances (seeds). Regarding the network topology, we assume that the node deployment obeys Nodes density.1nodes/m Communication range 5 m Number of neighbors 7.6 nodes One Hop Delay.1s Non-determin. errors 3 µs Localization error m Sink s height 3 m Sink s speed 6 km/h Sink s trajectory line Table I a disturbed grid, in which the location of each node is disturbed by a random zero-mean Gaussian error. Therefore,

Query speed (km/h) 3 5 15 1 5 Estimated Actual Error 6 1 1 18 1 9 8 7 6 5 3 6 1 1 18 Number of hops 1 1 1 8 6 6 1 1 18 Packet delay (s) 5 3 1 6 1 1 18 (a) (b) (c) (d) Query speed (km/h) 3 5 15 1 5 Estimated Actual Error 5 6 7 8 9 1 Comunication range (m) 1 9 8 7 6 5 3 5 6 7 8 9 1 Communication range (m) Number of hops 1 1 1 8 6 5 6 7 8 9 1 Communication range (m) Packet delay (s) 5 3 1 5 6 7 8 9 1 Communication range (m) (e) (f) (g) (h) Figure : Scalability and communication range. nodes will tend to uniformly occupy the sensor field without forming a regular grid. To simulate position computation inaccuracies, we disturbed the position of the nodes by m [15] using a Gaussian distribution. To simulate delay measurement inaccuracies we disturbed the mean delay by 3µs [13]. At last, the trajectory of the sink node is a line passing through the middle of the sensor field. A. The Impact of Network Scale Scalability is evaluated by increasing the network size from 1 to 8 while keeping the same density. Thus, the sensor field is resized according to the number of sensor nodes. A key factor of the Whisper algorithm, especially the and variations, is the computation of the Query Speed. Thus, Figure (a) compares the perfect and computed average speed of the query packet while increasing the number of nodes. In this evaluation, as well as in similar speed results, the error curve is multiplied by 1 to facilitate visualization. Thus, in the worst case, the error in the query speed computation was only 13km/h. This error decreases to 3 km/h when increasing the number of nodes, since the average number of hops also increases. Figure (b) shows that all techniques were able to deliver almost 1% of the packets, except when increasing the numberofnodestonear8,inwhichcasethereplypacket of the most distant nodes does not have time to reach the sink before it leaves the sensor field. Slowing down the sink node solves this problem, as we show in Section V-D. In Figure (c), we can see that the Whisper leads to a smaller number of hops for the reply packet to reach the sink node. Also, we can see that there is no statistical difference between the Whisper and the Whisper, since the curvature of the reply packet of parabolic trajectory in the Whisper is not high enough to increase the number of hops. At last, Figure (d) shows a small disadvantage of the Whisper algorithm: an increase in the packet delay, i.e., the time interval between sending the query and receiving the reply. This behavior was expected, since the Whisper algorithm waits for the sink node to be closer before sending the reply. On the other hand, this result clearly shows the need for new algorithms in these scenarios, since a delay of almost s means that the sink node would be at least 67m far from the location it sent the query packet. B. The Impact of the Communication Range To evaluate the impact of the communication range, we increase this parameter from 37m to 1m. When increasing the communication range, the packet speed also increases, as depicted in Figure (e). After a communication range of 5m, almost 1% of the packets are delivered, as shown in Figure (f). In 37m of communication range (and the sink node at a height of 3m), we can notice a decrease in the packet delivered. However, the Whisper was still able to deliver more than 9% of the packets, which indicates that this variation of the Whisper algorithm is more reliable. The number of hops decreases in all variations of the Whisper algorithm, when increasing the communication range, as depicted in Figure (g). An interesting result can be seen in Figure (h): the packet delay decreases in both and variations of the Whisper algorithm. However, in the Whisper, the packet delay remains

Query speed (km/h) 3 5 15 1 5 Estimated Actual Error.8.1 1 9 8 7 6 5 3.6.8.1.1.1.16 Number of hops 1 1 1 8 6.6.8.1.1.1.16 Packet delay (s) 5 3 1.6.8.1.1.1.16 (a) (b) (c) (d) 1 9 8 7 6 5 3 3 6 8 1 1 Sink speed (km/s) (e) 1 9 8 7 6 5 3 3 3 3 36 38 6 8 Sink height (m) (f) 1 9 8 7 6 5 3 6 8 1 Localization error (m) (g) 1 9 8 7 6 5 3.5 1 1.5 Non deterministic error (ms) (h) Figure 5: Hop delay, sink speed, sink height, localization error, and delay measurement error. almost the same, since the nodes still have to wait for the sink node to get closer. C. The Impact of the Hop Delay The hop delay refers to the processing time of the sensor node before forwarding a packet (i.e., context change, to compute the location of the sink, the next hop). To evaluate the impact of this delay, we vary this parameter from.5s to.s. As depicted in Figure 5(a), this delay also affects the packet speed. As depicted in Figure 5(b) when the delay is higher than.1s, reply packets from distant nodes do not reach the sink node before it leaves the sensor field, so the packet is dropped. In Figure 5(c), we can see differences in the number of hops for both Whisper and, as the delay causes the packet to reach the sink node while it is in the middle of the network (decreasing the average number of hops). We can also notice that the number of hops in the Whisper is not highly affected by the packet delay, which can also be seen in Figure 5(d) regarding the total packet delay. D. The Impact of Speed and Height of the Sink Node To evaluate the impact of the sink s speed, we increase thisparameterfrom3km/h(speedofauav)to1km/h (more than the speed of a Boeing-77). As depicted in Figure 5(e), in 1km/h, less than 8% are delivered mostly because the sink leaves the sensor field before receiving all replies. This fact reinforces the need for new algorithms in these high speed sink scenarios, since even when sending packets toward an updated position of the sink node, some of these packets are still lost. We also increased the height of the sink node from 3m to 8m. As depicted in Figure 5(f), more than 9% of the packets are delivered when the sink s height is m, which is only 6m less then the communication range of the nodes. We can also notice a better performance of the Whisper algorithm in this case. E. The Impact of Localization and Delay Measurement Errors As depicted in Figure 5(g) the Whisper algorithm can be affected by localization errors, specially for higher localization errors, such as greater than [1]m (which is % of the communication range). On the other hand, as depicted in Figure 5(h), the Whisper algorithm is not affected by nondeterministic errors on the delay measurement technique, since we increased these errors up to ms, which is far greater than the 3µs obtained by Maroti et al. [13]. The main reason for this behavior is the use of a Gaussian distribution to disturb the delay, which tends to zero as the number of hops increases. VI. APPLICABILITY OF THE PROPOSED SOLUTION In this work, we consider a delay of.1s at each hop, which can be considered a high delay even for WSNs. Preliminary real world experiments indicate that Sun SPOT sensor nodes have a delay of only.15s. However, these sensors are known to have relative high-speed processors and, also, these experiments do not include data processing and environmental monitoring. On the other side, experiments with MicaZ nodes, from Crossbow, demonstrate that some floating-point operations can take more than one second to finish executing. Thus, we believe that a delay of

.1s per hop can easily be reached in WSNs, especially if we are dealing with information fusion. A high speed communication is also another point to be discussed. In this work, we consider that it is possible to send data to a node moving at, for instance, the speed of 6 km/h without having influence on the data delivery rate. Recent research [7], [8] also indicates this possibility at lower speeds. Furthermore, this problem needs to be addressed by media access algorithms, and not by routing algorithms the case of our work. Finally, it is important to note that the proposed Whisper algorithms are basically Greedy Forward algorithms and, such as, they still need a perimeter/face routing algorithm in order to bypass holes or voids in the WSN. However, current perimeter/face routing algorithms do not work at high speed scenarios, which shows the need for new algorithms for these scenarios. This issue will be addressed in the future work. VII. CONCLUSION In this paper, we proposed three new propagation techniques for routing data towards a high speed sink node, which we referred to as the Whisper (Wireless High Speed Routing) algorithms. In scenarios where the sink node moves at a high speed, propagated queries cannot be replied toward the location of the sink node when the queries were sent. Thus, the main idea of the Whisper algorithms is to forward the reply toward the current location or even toward a future location of the sink node. We have proposed three variants of the Whisper algorithm. In the Whisper, at each hop, the reply is forwarded toward the current location of the sink node. In the Whisper, the reply is forwarded toward the point of intercept in the sink s trajectory. Finally, in the Whisper, the reply is forwarded toward the point in the sink s trajectory that is closer to the forwarding node. We presented an extensive set of simulation experiments that show the need for new algorithms in these high speed scenarios, and also clearly indicate the good performance of the proposed algorithms. The Whisper algorithm was the one that obtained the best results in most simulation scenarios. Although delay is higher, when replying the queries to the sink node, this is delay is still small, since it does not affect the scenarios in which the sink node flies over the sensor field, gather data, and comes back to the base to delivery the data to the monitoring facility. The results are very promising, but some advantages and limitations still need to be further exploited as future work: the combination of our solution with a perimeter/face routing algorithm, and also track trajectories described by non-linear models and subjected to non-gaussian noises. REFERENCES [1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. 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