Ad Hoc Networks 11 (2013) 1963–1974

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Ad Hoc Networks

journal homepage: www.elsevier .com/locate /adhoc

An autonomous Wireless Networked Robotics System forbackbone deployment in highly-obstructed environments

1570-8705/$ - see front matter � 2012 Elsevier B.V. All rights reserved.http://dx.doi.org/10.1016/j.adhoc.2012.07.012

⇑ Corresponding author.E-mail addresses: mvieira@dcc.ufmg.br (M.A.M. Vieira), ramesh@usc.

edu (R. Govindan), gaurav@usc.edu (G.S. Sukhatme).

Marcos A.M. Vieira a,⇑, Ramesh Govindan b, Gaurav S. Sukhatme b

a Universidade Federal de Minas Gerais, Belo Horizonte, Brazilb Department of Computer Science, University of Southern California, Los Angeles, CA, United States

a r t i c l e i n f o a b s t r a c t

Article history:Received 11 November 2011Received in revised form 9 July 2012Accepted 31 July 2012Available online 24 August 2012

Keywords:Wireless Networked Robotics SystemSearch and rescueComplex environmentsMobile ad hoc networksExperimental and prototype resultsWireless Backbone Deployment

A Wireless Networked Robotics System can assist in settings that lack infrastructure e.g.,urban search and rescue. A team of networked mobile robots can provide a communicationsubstrate in those settings by acting as routers in a wireless mesh network. We study theproblem of deploying a few mobile robots, and how to position them, so that all clientsusing the resulting robotic network are connected and all network links satisfy minimumrate requirements. The key challenge we address is that in an environment with obstaclesthe strength of a wireless link is a non-monotonic function of the distance between the linkend-points. The problem is thus fundamentally one of making router placement decisionsin a non-metric space. Our approach to the problem is based on virtual potential fields. Cli-ents and environmental obstacles are modeled as virtual charged particles exerting virtualforces on the robots. We validate our algorithm with physical robots in an indoor environ-ment and demonstrate that we are able to get feasible solutions.

� 2012 Elsevier B.V. All rights reserved.

1. Introduction

With advances in processor, memory, sensing, actua-tion, and radio technology, it is possible to put togetherinteresting systems using off-the-shelf components. Agood example is a robot with navigation capabilities, andan on-board processor with wireless communication capa-bilities. Among its many uses, such robots can be used as arouters in a mobile wireless mesh network. In such a net-work, a team of robotic routers can provide a communica-tion substrate for a collection of clients. We envision ateam of robot router-based providing communication asa Wireless Networked Robotics System.

Such a Wireless Networked Robotics System might findapplication in various settings which are either withoutinfrastructure or infrastructure-impoverished e.g., militaryoperations, urban search and rescue, disaster response andfire-fighting [1].

In this paper, we consider a specific problem that arisesnaturally in such settings: how and where to deploying awireless (robot router-based) backbone to ensure pairwiseconnectivity between a given set of clients. The clients canbe, for instance, firefighters or computational devices. Weaddress this problem in the face of a realistic performanceconstraint: each backbone link is required to operate at orabove a pre-specified data rate.

Our work focuses on highly-obstructed environments.In such environments, prior approaches to deploying awireless backbone [2,3] that have used convex optimiza-tion fail: in obstructed environments, wireless propagationdoes not observe the triangle inequality, (for example, thestrongest radio signal is not necessarily from the closestradio), resulting in a non-metric space and violating a fun-damental assumption upon which prior work is based.

1.1. Contributions

To overcome this challenge, we develop an algorithmcalled Potential Field-based Wireless Backbone Deployment(or, PFWD, for short). In PFWD, a team of mother ship

1964 M.A.M. Vieira et al. / Ad Hoc Networks 11 (2013) 1963–1974

robots, each starting from one of the clients, deploys into agiven environment, guided by attractive and repulsiveforces in a potential field, thus forming a wireless meshnetwork. We define an attractive force between each clientand each robot, where the force is derived from an indoorradio propagation model. The attractive forces are de-signed to ensure that the mother ship robots converge tothe point where the maximum wireless signal attenuationfrom each client to the mother ship robots is minimized.Repulsive forces are used for obstacle avoidance and toavoid local minima. As each mother ship moves, it deploysrobots along the way in order to maintain the followinginvariant: there must exist a connected multi-hop pathfrom each mother ship to the client where it started from.Robot deployment uses a feature of the 802.11a/b/g/nstandard, which specifies the minimum radio signal re-quired to establish a link of a given rate. Eventually, themother ships converge at the point of lowest potential,ensuring that each client is connected to every other clientat the specified link rate.

We validate and evaluate PFWD using simulation andexperimentation. Using simulations, we illustrate variousdeployment instances and give an intuition of how PFWDworks. We then present an experimental validation ofPFWD in realistic scenario and measure an important net-work metric: minimum TCP flow between clients. We alsoperformance comparison against other candidate deploy-ment strategies.

This paper is structured as follows. In the next section,we discuss the problem formulation (Section 2). In Sec-tion 3.2, we describe the key challenge: the wireless radiois not a metric space. We provide describe a radio propaga-tion model for and indoor environment and how to handlethe data rate link constraint in Section 3.1. Next thealgorithm based on the virtual potential fields (Section 4)is described. We describe our experimental methodology,simulation results and validate our algorithms by measur-ing TCP and UDP throughput at realistic environment inSection 5. Finally, related work is described in Section 6.

2. Problem formulation

We wish to deploy a team of N mobile robots to connectC clients in a given environment. We define the problem asfollows:

2.1. Input

Given C clients, their positions, a map E of the environ-ment, and a performance specification in the form of aminimum data link rate constraint of D Mbps.

The environment map E includes a complete floorplan,with forbidden zones and walls. The forbidden zones spec-ify an area where it is not possible to deploy robots, such asholes. Walls might affect radio propagation since radio sig-nals are attenuated when traversing walls. In Section 3.1,we present a radio model that takes walls into account.Modern wireless standards operate at different transferrates or speeds. For example, the popular 802.11a standardcan operate at 8 different rates, ranging from 6 Mbps to

54 Mbps. The highest rate at which a wireless link betweentwo nodes can operate depends upon their distance(among other factors): intuitively, the closer the nodesare, the higher their achievable operating rate.

Although an approach without a map might seem moregeneric, the approach with a stretch of a map presentssome advantages. Instead of spreading out robots to cover-age a huge area, it is possible to use fewer robots to deploythe network backbone. Another advantage is that is notnecessarily to execute a brute-force search on the environ-ment to find the clients. The deployment with a stretch ofthe map has lower latency because we do not need to findthe clients. Finality, the maps as input does not represent ahuge overhead. In Robotics, there is a vast body of work inmapping an environment.

2.2. Objective

Deploy a few mobile robots to form a (possibly) multi-hop wireless backbone that ensures connectivity betweeneach pair of clients, while ensuring that each wireless linkcan operate at least D Mbps, and without violating restric-tions imposed by the environment (e.g., robots cannot beplaced in occupied areas).

Our problem specification requires that, in the resultingnetwork backbone, the minimum rate at which each link inthe network must operate is D Mbps. This represents atradeoff between performance and the number of robotsneeded to cover the set of clients C: with a higher D, morerobots are necessary, but can ensure better performance(as perceived by the clients).

2.3. Output

The position prifor each robot ri in the environment E.

Fig. 1 shows an instance of the problem, and a viable solu-tion. The map E contains obstacles and walls. Clients arerepresented by laptops, and robots by an image of the iRo-bot Create. The position of the robots is the output of thealgorithm. The black lines show the links in the networkbackbone. Each client can connect to at least one robot; be-tween each pair of clients, there exists a multi-hop net-work path. There are two constraints for robotplacement. The first constraint, which is illustrated by for-bidden zones, indicates zones where no robots can be de-ployed. The second constraint, illustrated by walls,indicates where radio signals might be attenuated. Observethat some inter-robot links might still traverse walls andforbidden zones. Indeed, this last point indicates why thisproblem is very challenging. Previous approaches to ro-botic deployment [3] have generally assume unobstructedenvironments. In such environments, it is reasonable to as-sume that signal strength of radio propagation decaysmonotonically with distance thus the problem is one ofdeployment in a metric space. Techniques like convex opti-mization or linear programming apply in such a setting. Inthe presence of obstacles, this assumption is violated, andnew techniques must be found. In the next section, we de-scribe our approach to robotic deployment in obstructedenvironments.

Fig. 1. A sketch of the problem and a solution over a floorplan.

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3. Solution overview

In this section, we present an overview of our approach.As discussed in Section 2, radio propagation in obstructedenvironments forms a non-metric space (e.g., the triangleequality does not hold for radio signal strength in an envi-ronment with obstacles). To understand this better, wefirst describe models of radio propagation both in free-space and in the presence of obstacles, and then explainhow radio propagation in the presence of obstacles formsa non-metric space.

Since traditional solutions no longer apply, we have de-signed an algorithm called Potential Field-based WirelessBackbone Deployment (or, PFWD, for short). This algorithmuses virtual potential fields. Potential Fields provide virtualforces similar to an electric field. They provide attractiveand repulsive virtual forces to cause robots to move froma high potential state to a low potential state similar tothe way in which a charged particle would move in anelectrostatic field.

We use potential fields in two ways. First, an attractiveforce determined by the radio propagation model guidesrobot placement to ensure connectivity. This is a departurefrom previous work, which has used physical distance toset the attractive force. Our use of a potential field-basediterative approach results in an algorithm guaranteed toconverge, for a given fixed environment E, (but possiblyto a local optimum) even in a non-metric space [4]. Second,we use repulsive forces in the potential field for obstacleavoidance, a more traditional use of potential fields.

Finally, to guarantee the data rate constraint, we use afeature of the 802.11a wireless standard specification. Thisstandard specifies the minimum signal-to-noise ratio(SNR) required to decode transmissions, at each allowabledata rate. PFWD leverages this in a novel manner as fol-lows: It uses an indoor radio propagation model to predictSNR between robots or between a robot and a client, andguides the deployment of robots such that the SNR

between backbone links is sufficient to ensure the data-rate constraint.

PFWD is designed as an offline deployment tool: giventhe inputs described in Section 2, it is executed offline toproduce the robot positions. We have left an online ver-sion, which incrementally deploys robots, for future work.

While PFWD is discussed in greater detail in the nextsection, we now preview radio propagation and its impli-cations for robot deployment in obstructed environments.

3.1. Radio model

While wireless propagation is known to be hard to char-acterize in general, there has been a significant line of re-search attempting to fit models to radio propagationcharacteristics observed in different environments [5–8].An indoor radio propagation model predicts the path lossfrom a transmitter to a receiver inside a building delimitedby walls. The attenuation factor (AF) model [5] is a com-monly-used radio propagation model for indoor environ-ments. It is an in-building site-specific propagationmodel that includes the effect of building materials andbuilding structures.

This model decomposed the path loss into three factors:attenuations from propagation through an office or hall-way, propagation through a wall, and propagation througha floor. Specifically, the model is described by an equationthat calculates the multiplicative factor PL(d) by which sig-nal power is attenuated (hence the attenuation factor or AFmodel) between a transmitter and a receiver whose phys-ical distance is d. The model is approximate, since it mod-els only the direct (or primary) path between transmitterand receiver, and not any reflected paths. As such, it doesnot incorporate multi-path fading: in prior work, we havediscussed techniques to improve network throughputusing robotic motion to mitigate multi-path fading [9].The AF model is reported [5] to provide loss within 4 dBof the actual path loss.

Fig. 3. Each region is colored according to the strongest radio transmitter.Realize that the colored regions might be disjointed. Thus, the spacepartition of wireless signals might result in disjointed cells.

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According to the AF model, PL(d) is given by:

PLðdÞ ¼ PLðd0Þ þ 10nlogdd0

� �þWL �wþ FAFðf Þ ð1Þ

where n is the path loss exponent and indicates the rate atwhich the attenuation increases with distance. d0 is a ref-erence distance. The variable WL represents attenuationthrough a single wall, and the term WL � w representsthe attenuation factor for communication traversing wwalls. (This is a simplified model: in practice, because ofmaterial and construction differences, different walls havedifferent attenuation factors, which we discuss later). FAFis a function that represents a floor attenuation factor fora specified number f of floors; generally, FAF is monotoni-cally increasing. Since we assumed a 2D environment, weincluded the term FAF just for completeness of the model.

An important component of this model is the increasingattenuation as a function of distance: in general, the wire-less signal attenuates logarithmically with distance. More-over, note that the model has several parameters, whichneed to be empirically measured for a given environmentE: the path loss exponent n, and, the attenuation factorW (or more generally, an attenuation factor Wl for each dis-tinct wall type l). In lieu of measurement, one can obtainnominal values for these parameters from standard texts[5].

Observe that the radio model presented in Eq. (1) canalso be applied to outdoor scenarios. In this case, the num-ber of walls would be zero, and the main attenuation factorwould be the path loss exponent (n).

3.2. Attenuation in the presence of walls

In unobstructed environments (i.e., in the absences ofwalls/floors), the attenuation factor satisfies the triangleinequality (or, equivalently, defines a metric space). Tosee why this is so, consider two points x and z and tworays: one directly from x to z and another reflected froma point y (Fig. 2). In the absence of walls, the attenuationof the reflected ray will always be higher than that of thedirect ray. However, if there is a wall between x and z,the direct ray may be attenuated more than the reflectedray, depending on the value of W, resulting in a non-metricspace.

Why is this important? Previous work on roboticdeployment has assumed that wireless attenuation is a

Fig. 2. Triangle inequality does not hold for path loss.

metric space (i.e., they have ignored walls and obstacles).In such a regime, it is possible to use common well-knownmathematical optimization tools such as linear program-ming, or to use geometric techniques based on VoronoiDiagrams for deployment of robotic networks [3]. How-ever, these algorithms cannot be easily extended to non-metric spaces.

To understand this, consider Fig. 3 which depicts twowireless transmitters and the result of applying a Voronoispace partition based on the attenuation factor. Withineach region, all points experience lower attenuation factorfrom the corresponding transmitter than from any othertransmitter. In the presence of the wall, the Voronoi cellsmight not be convex and might result in disjoint cells, asshown in the figure. Prior work has deployed robots atthe centroid of each Voronoi cell, but, in our example, thiscentroid may not even fall within the cell! For this reason,PFWD uses a qualitatively different approach, based oniterative potential fields.

4. The PFWD algorithm

In this section, we describe the PFWD algorithm. Thealgorithm takes as input pcj

, the position of client j for1 6 j 6m, an environment map E, and a data rate con-straint D. The outputs are the N robot positions pri

.As discussed below, PFWD is an iterative potential field-

based approach. In PFWD, a robotic mother ship is initiallyco-located with each client. m clients imply that our algo-rithm uses m mother ships. Each mother ship is thenguided by the potential field towards the minimum energyposition (we describe the choice of the forces, and the min-imum energy position below). As each mother ship moves,it continuously evaluates whether it needs to deploy arobot1 ri (a node in the wireless backbone): if so, it marksthe current position as one of the outputs pri

. Thus, PFWDhas two components: the attractive and repulsive forces thatdefine the potential fields, and the deployment algorithm

1 For the purposes of this paper, the deployed object need not be a robot,but can be a wireless router. However, we envision [9] that the deployedwireless backbone will need to be iteratively repositioned, using localmotions in order to mitigate fading due to multi-path effects.

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that determines when robots are deployed by mother ships.We discuss each component in turn.

4.1. Potential fields in PFWD

Potential Fields are used to represent goals and con-straints. In PFWD, they provide virtual forces to guide themother ships to move from a high potential state (neareach client) to a low potential state similar to the way inwhich a charged particle would move in an electrostaticfield. The design of these forces in order to achieve thedeployment objective is a novel contribution of this paper.

In PFWD, there are two kinds of forces. The first, Fclient,is an attractive force defined between each mother shipand every client, and causes the mother ships to convergeto a low potential state. The second, Fobstacle causes mothership robots to be repelled by obstacles (forbidden zones).By using a combination of these forces each robot mini-mizes its energy by moving to a ‘‘rendezvous’’ point, tryingto minimize the traveled distance while avoiding obstacles.Mathematically, the forces are expressed as follows. Con-sider a network of M mother ships hs1, s2, . . . , smi and M cli-ents hc1, c2, . . . , cmi. Let the position of the j-th client bedenoted by pcj

and that of the i-th mother ship, at any in-stant, by psi

. For position pi, we use (xi, yi) to denote itscoordinates on a 2-D plane.

A force has two components: an orientation and a mag-nitude. For a mother ship robots i and a client j, the orien-tation of the force is given by Eq. (2).

h ¼ atan2ðyj � yi; xj � xiÞ ð2Þ

The function atan2 is a variant of the trigonometric arctan-gent function, but accounts for the quadrant in which hlies.

For a mother ship si and a client cj, the magnitude of theforce is given by:

Fig. 4. Perpendicular potential field applied to the forbidden zone.

Fclient ¼ Kclient

� PLðd0Þ þ 10nlogdi;j

d0

� �þWL �wþ FAFðf Þ

� �ð3Þ

where di,j is the distance between si and cj, w is the numberof walls and f the number of floors between si and cj, andKclient is a force constant, and other terms are as definedin Eq. (1). Thus, the attractive force is proportional to the sig-nal attenuation (even in the presence of obstacles): collec-tively, these attractive forces ensure that each mother shipmoves to a point where the maximum path loss between amother ship and every other client is minimized.

PFWD also defines repulsive forces between mothership and forbidden zones. Forbidden zones represent 2dimensional objects within which no robots can be de-ployed. The repulsive forces ensure entering forbiddenzones. However, a repulsive force alone may result in a lo-cal minimum for concave objects [10], so we also include atangential force that moves the mother ship along the sideof the object. We discuss more about local minimum in theend of this subsection.

Thus, between each mother ship i and a forbidden zoneo, we define a force F(i, o) that consists of two components:a repulsive force that is perpendicular to the forbiddenzone and a tangential force to avoid local minima. Eq. (4)shows the magnitude of the tangential and perpendicularobstacle force, which is a constant (Kobstacle). This constantKobstacle is the same for all forbidden zones. The value isconfigured to be higher than the attractive force to avoida robot entering a forbidden zone. Figs. 4 and 5 illustratethe perpendicular and tangential potential fields, respec-tively. The force between each mother ship and a forbiddenzone o only exists if their distances are shorter than athreshold. The tangential force needs to be defined in thesame orientation for all surfaces. This force will cause therobot to circumvent any corner element, avoiding the ro-bot being trapped in a corner element.

Fobstacle ¼ Kobstacle ð4Þ

We make one subtle distinction between forbidden zonesand walls. In our model, walls are 1D objects which merelyattenuate wireless signals, but can be navigated around bya robot. Since initially PFWD was designed as an offlinetool to determine positions of robot deployment, in thesimulator, we let mother ships pass through walls follow-ing radio propagation. When using PFWD online for

Fig. 5. Tangential potential fields applied to the forbidden zone.

Table 1Necessary SNR (dB) for required data rate (Mbps).

Rates 6 9 12 18 24 36 48 54

SNR 6.02 7.78 9.03 10.79 17.04 18.80 24.05 24.56

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deployment, we fix this with a navigation algorithm thatcauses the robot to navigate around the wall to reach thedesired position on the other side of the wall. Forbiddenzone is an area where it is not possible to deploy robots,such as holes in a floorplan. Observe that forbidden zonesimpose restrictions on where a robot might be deployedbut walls do not.

Finally, we note that there is no force between themother ship robots. The second component of PFWD en-sures inter-robot placement distance, as described below.

Thus, mother ship robot i will experience a net force of

Fi ¼X

8 clients j

Fði; jÞ þX

8 obstacles o

Fði;oÞ ð5Þ

Following basic physics, the equation of motion for node iis:

€xiðtÞ ¼Fi � m _xi

m

� �ð6Þ

where €x denotes the acceleration of the robot, m is the vir-tual mass of the robot which is assumed to be 1, and _xi isthe robot velocity. The second term on the right hand sideof this equation has a viscous friction term in which m is theviscosity coefficient. The viscous friction is a damping fac-tor that has the effect of removing energy from the system:the total energy decreases monotonically over time, andsince the potential energy of the system is bounded, thisensures that the system will ultimately reach a state of sta-tic equilibrium (i.e., a state in which all mother ship robotshave stopped moving).

Eq. (6) can be used to map the virtual force onto a veloc-ity control vector. We can calculate the next position by,for every time step Mt, calculating:

1. Total force Fi.2. Velocity as _xtþ1 ¼ _xt þ ðFi�m _xtÞ

m Mt.3. Position to xtþ1 ¼ xt þ _xtþ1Mt.

Using these equations, each mother ship determineswhere to move, iteratively, until it converges to the mini-mum potential energy point.

In summary, these forces ensure that each mother shipmoves to a point where the maximum path loss between amother ship and every other client is minimized, whileavoiding obstacles. However, the correctness and perfor-mance of PFWD depends upon the choices of its parame-ters. The algorithm is not guaranteed to converge for allchoices of parameters, for a given environment E. Forexample, a choice of a high m can cause the system to runout of energy prematurely. Similarly, if the obstacle tan-gential force is not strong enough, a mother ship may notbe able to exit a local optimum. Currently, PFWD userscan overcome this by using conservative parameters (lowm values or high tangential forces) at the expense of con-vergence time. But if the local optimum problem persistsfor a challenging environment E, one approach is to applycomplimentary techniques. One such technique is the Har-monic Potential Fields [10], which uses harmonic functionsto build an artificial Potential Field free of local minima.

Understanding optimal parameter settings for a givenenvironment E is left to future work.

4.2. The deployment decision in PFWD

The second component of PFWD determines where themother ship will deploy robots. To do this, it uses an algo-rithm that tests the following invariant for each mothership si: si always has a multi-hop path from itself throughalready-deployed robots (possibly deployed by othermother ships) to its ‘‘own’’ client ci, and that each hop inthe path can sustain a link rate of D. When si is at a positionwhere this invariant is violated, it backtracks to a previousposition where the invariant holds, and deploys the robotthere. The movement of each mother ship is guided bythe forces described above.

The pseudo-code for the algorithm is in Algorithm 1.

Algorithm 1. Deployment algorithm

1: while has energy to move do2: if Is D Mbps connected with last deployed robot?

then3: Move using Potential Fields4: else5: Move one step back6: Deploy Robot7: add new entry to adjacency matrix of deployed

robots8: end if9: if all clients connected? then10: break11: end if12: end while

To check whether the mother ship is connected to itsclient, it needs to know the positions of all robots that havebeen deployed until now, and each deployed robot’s neigh-bors. For this, the algorithm maintains an adjacency ma-trix. It uses a graph connectivity algorithm to determineif connectivity exists between itself and the client. (In apractical system, the mother ship can use a decentralizedrouting protocol [11] to determine the existence of connec-tivity). When all the clients converge to the minimum po-tential point, by construction there will exist a multi-hoppath between every pair of clients.

How does PFWD determine that a mother ship is ‘‘dis-connected’’ from its client, and also ensure the link datarate constraint D? To do this, it relies on a feature of mod-ern standard radios, which can operate on different datarates. Moreover, the standard defines the minimum SNRneeded to decode a transmission at a given rate. Table 1[12,13] presents these SNR values. Given a mother ship’s

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location, PFWD uses (1) to determine the SNR between it-self and its neighboring deployed robots. When the SNR toevery neighbor is below the minimum SNR required tomaintain the target rate D, the mother ship considers itselfto be disconnected, backtracks and deploys a robot. Thus,at each step of PFWD , each robot is guaranteed to haveat least one link capable of operating at D Mbps.

This guarantee is true in PFWD assuming that the pathloss model holds; as we shall see in our evaluations, thisworks quite well. In a practical deployment system, amother ship can directly measure the SNR and maintainthe above guarantee. We want a practical solution. Weadopted SNR since this is the metric provided by theMadwifi driver for the Atheros wireless card. Thus, forpractical and realistic purpose, we included SNR whichwas provided by the Madwifi driver. To guarantee theminimal interference among robots, Algorithm 1 deploysthe robots far away as possible while guaranteeingconnectivity.

Finally, our description of PFWD has implicitly assumedthat each mother ship initially has an infinite number ofrobots. Thus, PFWD may deploy more robots than the usermay have at her disposal. To obtain a deployment requir-ing no more than the number of available robots, the usercan try lower D values: a lower value of D generally resultsin ‘‘longer’’ wireless links, and therefore fewer robots.

5. Evaluation

In this section, we validate and evaluate PFWD usingsimulation, and experimentation. We begin by illustratingvarious wireless backbone topologies using simulations ofPFWD. We then present an experimental validation ofPFWD, followed by a performance comparison againstother candidate deployment strategies.

5.1. Validating the PFWD tool

We have implemented the PFWD algorithm in an offlinetool, which takes the inputs discussed in Section 2, andoutputs robot positions pri

. We illustrate the outputs ofPFWD for some canonical topologies (Fig. 6a–e), with twogoals: to validate that PFWD produces reasonable results,and give the reader some intuition for its operation. Inthe figures, the black dots represent the clients, the green2

dots (lighter) the deployed robots and the red dots (gray) themother ships. The blue lines represent the trajectory of themother ships, and the green circles represent the communi-cation range in free space.

Fig. 6a shows the result for three clients. Notice how themother ships converge on the centroid of the triangle, andthe robots are deployed at regular intervals along themedians, as expected. This deployment is optimal, in thesense that it deploys fewest robots. Fig. 6c shows the resultfor three clients in an asymmetric configuration. Fig. 6bshows the output when the configuration is the same asFig. 6a but with the addition of a wall. Since a wall attenu-

2 For interpretation of color in Fig. 6, the reader is referred to the webversion of this article.

ates radio signals, robots are deployed more frequently onthe segment crossing the wall.

Fig. 6d depicts the simulation output for four clients,where the mother ships again converge at the centroid ofthe figure. In this case, too, we can show the deploymentto be optimal. Finally, Fig. 6e depicts the case where thereis an obstacle in the environment. We can see impact of theforce Fobstacles: the mother ships move counter-clockwisearound the periphery of the obstacle until the viscousdamping causes the system to lose energy and the algo-rithm converges.

5.2. Validating the PFWD algorithm

PFWD is an offline tool for suggesting a Wireless Back-bone Deployment in an environment E. A natural questionto ask is: does PFWD produce a feasible wireless backbone,namely one in which all clients are connected and everybackbone link can operate at D Mbps. It is not immediatelyobvious that the answer should be affirmative, since PFWDmakes several simplifying assumptions: the vagaries ofwireless propagation are well known, the AF model forpath loss and wall attenuation is known to be an approxi-mation, and the SNR to data rate table is an idealized map-ping which may not be fully met because of wireless cardmanufacturing variations.

To validate PFWD experimentally, we employ the fol-lowing methodology:

� We take an indoor office environment E and measurethe parameters for the AF model.� We then feed E and several client configurations to the

PFWD tool.� For each output from PFWD, we deploy robots at posi-

tions corresponding to the clients, and at the backbonerobot positions suggested by PFWD.� We then measure TCP and UDP data throughput

between each pair of clients. The network configurationis said to be feasible if each data connection achieves anon-negligible throughput. Each flow (network trafficcorresponding to a conversation between end hosts) isthe average of at least five measurements. Flows werecreated with the iperf [14] tool and SNR values weremeasured (per link) using the iwspy Linux command.

We use a commoditized robotics platform and mademinimal modifications to it using off-the-shelf compo-nents. Our platform consists of an iRobot Create and asmall embedded computer (Ebox 3854) mounted on topof it (Fig. 7). For sensing and control, we developed a Createdriver for Player [15]. The embedded computer, the Ebox3854, is an 800 MHz embedded PC with 256 MB sharedDDR memory and runs Ubuntu (Linux Kernel 2.6.22) asthe operating system. It has Atheros wireless card withMadwifi driver.

Fig. 8a shows the PFWD tool output for an environmentwith three clients, with a data rate constraint of 54 Mbps.PFWD suggests a backbone consisting of three robots(Fig. 8b) and we measure the traffic throughput betweenthe clients shown. Fig. 8c shows the TCP and UDP through-puts obtained for the suggested configuration. In each case,

Fig. 6. Simulation results.

Fig. 7. Robot platform.

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notice that each flow receives non-zero throughput: this isencouraging, indicating that our radio model, togetherwith the data rate model and the potential fields approachwork well together to deliver a feasible network.

The same is true for a more complex setting. Fig. 8eshows the PFWD output for the same environment butwith four clients. In this case, interestingly, PFWD suggestsusing only two robots, as shown in Fig. 8f. It also depictsthe configured flows we measure. Fig. 8g shows the TCPand UDP throughput for four flows traversing the networklinks: here, too, the configuration suggested by PFWD re-sults in a feasible network.

We have conducted a more rigorous evaluation ofPFWD. For each of 3 and 4 clients, we computed the outputof PFWD for 3 different client locations and two differentdata rate requirements (54 Mbps and 36 Mbps). In all, thisresulted in 12 different instances. For each instance, we de-ployed the requisite number of robots at the suggestedlocations, then measured all possible end-to-end TCPthroughput between clients. For a given instance, we cal-culated the minimum TCP throughput among all pairwiseTCP measurements. TCP is a fairly complex network proto-col that is quite sensitive to wireless link quality: as such, anon-zero value of this metric is a good adversarial indica-tion of the quality of a network connection and indicatesthat the suggested network configuration is feasible.Fig. 9 shows the minimum pairwise TCP throughput be-tween the 4 sets, sorted by instance. We can see that theminimum pairwise throughput is greater than zero inevery instance. Even with paths of 5 hops, we were ableto get a connected network (the 4 clients-54 set): this issignificant because TCP throughput is known to degradedramatically and often fail in multi-hop network paths.

Thus, we conclude that there is strong evidence to sug-gest that PFWD can yield feasible network configurationsin indoor settings. Much work remains, however: experi-ments in other realistic settings; the design of a through-put optimal configuration (not merely a ‘‘good’’ one, aswe have done). We have left these to future work.

5.3. Comparing against alternative approaches

Finally, we compare PFWD along two other dimensions,against other candidates. First, PFWD is designed to deploy

(a) Simulation

4th fl.

1

2

31 Flow 1

Flow 2Flow 3

3

2

(b) Deployment

Configuration Throughput

02468

1012

Flow 1 Flow 2 Flow 3

Flows

Thro

ughp

ut (M

bps)

UDPTCP

(c) Throughput (d) Random

(e) Simulation

1

2

Flow 1

Flow 2

Flow 3

Flow 41

3 4

2

(f) Deployment

Configuration Throughput

0.002.004.006.008.00

10.0012.00

Flow 1 Flow 2 Flow 3 Flow 4

Flows

Thro

ughp

ut (M

bps)

UDPTCP

(g) Throughput (h) Random

4th fl.

Fig. 8. PFWD experiments with 3 and 4 clients. The first column shows the robot traversals in simulation. The second column shows the experiment set up,including robots positions and flows. The third column illustrates the network experiment throughput. PFWD comes up with feasible flows. The fourthcolumn depicts the maximum link data rate configuration for one hundred random configurations. This illustrates that, with random configurations, it isunlikely to obtain configurations with 54 Mbps links. However, PFWD is able to derive such configurations by carefully searching the space.

Minimum TCP Flow

00.5

11.5

22.5

33.5

44.5

3Clients54Mbps

3Clients36Mbps

4Clients54Mbps

4Clients36Mbps

Configurations

Thro

ughp

ut (M

bps)

Min MinMedian MinMax Min

Fig. 9. Minimum throughput flow for different configurations.

Table 2Comparison of necessary number of robots.

Algorithm

PFWD 7 9 11 13MST 10 12 14 14

M.A.M. Vieira et al. / Ad Hoc Networks 11 (2013) 1963–1974 1971

as few robots as possible. Although we do not yet have aproof of optimality, we can compare the number of robotsdeployed by PFWD with those suggested by other plausiblestrategies. Second, we consider if a simpler, randomdeployment strategy could have produced comparableresults.

To compare the number of deployed robots using analternative plausible strategy, we calculate the MinimumSpanning Tree using the set of clients as nodes. Then, weuse the same deployment algorithm as for PFWD (Sec-tion 4.2). Table 2 compares the necessary number of robotsto provide a connected topology for clients placed at thenodes on different regular polygons. In each case, note thatPFWD deploys fewer robots.

We also compare the quality of PFWD’s solution againsta random placement strategy. We ask: could a randomdeployment strategy have resulted in a feasible network?To answer this, given the set of clients, we calculate theconvex hull. Then, we deploy the same number of robotsas PFWD suggested, but randomly within the convex hull.Fig. 8d shows the minimum data rate link obtained from100 random deployments for the client configurationshown in Fig. 8b. None of the 100 random deploymentsis able to satisfy the minimum link rate requirement of54 Mbps, while PFWD is able to find a feasible configura-tion. With 4 clients, the results are similar, as shown inFig. 8h: no random deployment was able to satisfy theminimum link rate requirement. Fig. 8d and h illustratethat by comparing with the random deployment strategywith a 54 Mbps deployment requirement, PFWD calculatessolutions that are not so trivial to find.

6. Related work

The Group of Unmanned Assistant Robots Deployed inAggregative Navigation by Scent (GUARDIANS) [16]

1972 M.A.M. Vieira et al. / Ad Hoc Networks 11 (2013) 1963–1974

presents a Cyber-Physical System application similar toour work. A multi-robot team is to be deployed in a largewarehouse in smoke. The team is to assist firefighterssearch the warehouse in the event or danger of a fire. Theirwork focus on a robot formation, instead of connectivityguarantee.

In [17], a similar problem is presented. Given a set ofclients, robots move following a bio-inspired algorithm toincrease communication coverage. Their work is designedfor an unknown environment so, unfortunately, the pro-posed algorithm has no guarantees that the network willbe connected. We, on the other hand, take advantage of aknown global map to guarantee connectivity. We also donot focus on coverage but forming a backbone, which re-quires less number of robots. Their work consider nodefailures, which we left as future work. Finally, we evalu-ated on a more significative network metric (end to endTCP throughput) instead of RSSI signals.

Our work is inspired by three prior pieces of work on areacoverage, where two of them make uses of Potential Fields.Howard et al. [4] present a distributed and scalable ap-proach to deploy robots such that the area covered by thenetwork is maximized. Each node is repelled by both obsta-cles and by other nodes, thereby forcing the network tospread itself throughout the environment. Poduri and Suk-hatme [18] extended the previous work to maximize thearea coverage with the additional constraint that each nodehas at least K neighbors. Another important work on deploy-ment to increase coverage is [19], which uses a more sim-plistic radio model, considering only if radios have line-of-sight or not. In contrast to area coverage, PFWD focuses onguaranteeing connectivity between clients.

A body of work has examined the problem of guaran-teeing connectivity between a single mobile user and abase station, using a team of robots. Tekdas and Isler [20]presents a game theoretic approach: the problem is mod-eled as a pursuit-evasion game, with the goal of findingthe shortest escape trajectory. Stump et al. [2] show thatthe quality of connectedness can be represented by the Fie-dler value (second-smallest eigenvalue of a weightedLaplacian) from algebraic graph theory; by increasing theFiedler value, the connectedness is indirectly improved.Our problem setting is qualitatively different, that ofdeploying a team of robots to form a backbone for a collec-tion of static clients.

A related problem that has received some attention isthat of maintaining connectivity among a team of mobile ro-bots. Esposito and Dunbar [21] study the problem of main-taining connectivity for a team of robots in the presence ofobstacles. The achieve this goal by adding potential fieldscorresponding to line-of-sight and distance range, guidingrobot navigation. Their approach is different from PFWDin two ways: they are not constrained by fixed client posi-tions; moreover, by constraining wireless propagation toline-of-sight they cannot leverage wireless propagationthrough walls, as we do. Hsieh et al. [22] study a comple-mentary problem to ours, that of driving a team of robotsto specific locations along a parameterized curve whilemaintaining point-to-point communication links. Two dif-ferent metrics, point-to-point signal strength and datathroughput, were used to monitor the network connectivity

of the system. Their approach receives as input specific goalpositions for each robot in the team; in PFWD, the goal posi-tions are the output of the system.

In indoor scenarios with many walls, fading also mightimpact on the wireless channel. Vieira et. al. [23] provide asystem where robots coordinate small movements to mit-igate multi-path fading. This work is complementary to oursince we focus on macro-motion movements while theirapproach was towards micro-movements. For future work,we intend to couple their approach to our system.

Other approaches used SNR and potential fields to placerobots in their environment. Work by Guan et al. [24] andDixon and Frew [25] utilizes the SNR measurements tomaintain RF connectivity between a pair of robot whilemoving. Guan’s work [24] focuses on coverage, so, the ro-bots spread out while maintaining connectivity. In Dixon’swork [25], although robots position themselves in 2D, thegoal is to maintain a simple one dimensional chain shape.Our approach is different. We utilize the SNR measure-ments to determine the layout of the network. It is impor-tant to notice that our network layout is not a simple 1-dchain but involves many clients. Besides that, our radiomodel is more complete. Dixon’s work considers obstaclesto communication in the form of noise sources, while ourradio model is designed for complex environments, includ-ing walls. Finally, we validated with an important networkmetric: TCP throughput.

Several other tangentially-relevant pieces of work exist.Zeiger et al. [26] explore the performance of ad hoc routingprotocols by moving a single robot in a field of static wire-less nodes. Hseih et al. [27] address the problem of con-structing radio signal strength maps with multiple robots.More precisely, they determine what sequence of moves ateam of robots must perform to sample all edges in a givengraph. The goal is to minimize the total number of robots’moves such that all edges in a given graph are sampled. Falland others [28,29] discuss a delay-tolerant network archi-tecture which uses mobile elements that may be intermit-tently connected, a goal different from that of PFWD.

As discussed previously, it is possible to use geometrictechniques based on Voronoi Diagrams for deployment ofrobotic networks [3] but this techniques are not designedfor non-metric spaces.

A related problem in optimization is the Steiner TreeProblem. Given a weighted graph G = (V, E) and a subsetR # V, the goal is to find the smallest tree connecting allthe vertices in R. This problem differs from the MinimumSpanning Tree in the sense that it allows to select interme-diate connection points to reduce the cost of the tree. TheSteiner Tree Problem is useful for wire networks but is notdesigned for wireless networks, where the radio signalpropagates in all directions.

Finally, our problem bears superficial resemblance to thefacility location problem in operations research. The objec-tive is to open a facilities so that each client can be con-nected to a facility while minimizing the total connectivitycost (there is a cost for connecting each client to a facility).In a non-metric space, Hochbaum [30] developed a O(logn)approximation. Unfortunately, this formulation does notapply to our multi-hop network, since we also need to con-sider the connectivity between facilities (robots in our case).

M.A.M. Vieira et al. / Ad Hoc Networks 11 (2013) 1963–1974 1973

7. Conclusion

We showed that a mobile wireless network can takeadvantage of mobility from networked robots. A mobilewireless network can quickly and autonomously be de-ployed in urban search and rescue efforts, forming a com-munication substrate. We investigated the problem ofdeploying a few mobile robots and how to position themso all clients are connected and there is some data rate linkconstraint. We described an algorithm based on virtual po-tential fields to deploy a wireless backbone in a non-metricspace. We verified that the radio propagation model followsthe log-distance path model in our testbed. We evaluatedour system with physical robots in an indoor environmentand demonstrated that we are able to get feasible solutions.

We did not provided an approximation bound due tothe hard nature of the problem: the problem is very hardto treat since it is a non-linear optimization problem wherethe triangle inequality does not hold. But, we were able toguarantee that the deployed network will be connectedand also compared against existing scheme (MST andrandom).

For future research, it is still interesting to explore theproblem where we need to provide a wireless communica-tion backbone for dynamics clients.

Acknowledgments

This material is based in part upon work supported inpart by the National Science Foundation under GrantsNos. CCF-0820230, CNS-0540420, CNS- 0325875 andCCR-0120778 and a gift from the Okawa Foundation. Anyopinions, findings, and conclusions or recommendationsexpressed in this material are those of the author(s) anddo not necessarily reflect the views of the National ScienceFoundation. The work was also supported in part by DAR-PA contract N00014-08-1-0693/489. Marcos A. M. Vieirawas supported in part by Grant 16557 FAPEMIG, Brazil.

References

[1] H. Liu, J. Li, Z. Xie, S. Lin, K. Whitehouse, J.A. Stankovic, D. Siu,Automatic and robust breadcrumb system deployment for indoorfirefighter applications, in: MobiSys ’10: Proceedings of the 8thInternational Conference on Mobile Systems, Applications, andServices, ACM, New York, NY, USA, 2010, pp. 21–34.

[2] E. Stump, A. Jadbabaie, V. Kumar, Connectivity management in robotnetworks, in: IEEE International Conference on Robotics andAutomation (ICRA), Pasedena, 2008.

[3] F. Bullo, J. Cortés, S. Martínez, Distributed Control of RoboticNetworks, Applied Mathematics Series, Princeton University Press,2009.

[4] A. Howard, M.J. Mataric, G.S. Sukhatme, Mobile sensor networkdeployment using potential fields: a distributed, scalable solution tothe area coverage problem, in: Proceedings of the InternationalSymposium on Distributed Autonomous Robotic Systems, 2002, pp.299–308.

[5] T. Rappaport, Wireless Communications: Principles and Practice,Prentice Hall PTR, Upper Saddle River, NJ, USA, 2001.

[6] J. Robinson, R. Swaminathan, E.W. Knightly, Assessment of urban-scale wireless networks, with a small number of measurements, in:In Proceedings of ACM Mobicom, 2008.

[7] Propagation data and prediction models for the planning of indoorcommunication systems and local area networks in the frequency

range 900 MHz to 100 GHz, in: International TelecommunicationUnion, ITU-R Recommendation, 1997.

[8] O. Chipara, G. Hackmann, C. Lu, W.D. Smart, G.-C. Roman, Practicalmodeling and prediction of radio coverage of indoor sensornetworks, in: IPSN ’10: Proceedings of the 9th ACM/IEEEInternational Conference on Information Processing in SensorNetworks, ACM, New York, NY, USA, 2010, pp. 339–349.

[9] M.A.M. Vieira, The Interplay Between Networks and Robotics:Networked Robots and Robotic Routers, Ph.D. Thesis, University ofSouthern California, US, 2010.

[10] J.-O. Kim, P. Khosla, Real-time obstacle avoidance using harmonicpotential functions, IEEE Transactions on Robotics and Automation 8(3) (2002) 338–349.

[11] T. Clausen, P. Jacquet, RFC3626: Optimized Link State RoutingProtocol (OLSR), 2003.

[12] IEEE Std. 802.11a-1999, Part 11: Wireless LAN Medium AccessControl (MAC) and Physical Layer (PHY) Specifications, IEEE, 1999.

[13] J. Yee, H. Pezeshki-Esfahani, Understanding Wireless LANPerformance trade-offs, CommsDesign.com.

[14] A. Tirumala, F. Qin, J. Dugan, J. Ferguson, K. Gibbs, Iperf. <http://dast.nlanr.net/Projects/Iperf/>.

[15] B.P. Gerkey, R.T. Vaughan, K. Støy, A. Howard, G.S. Sukhatme, M.J.Mataric, Most valuable player: a robot device server for distributedcontrol, in: Intl. Conf. On Intelligent Robots and Systems, vol. 3,Maui, HI, USA, 2001, pp. 1226–1231.

[16] J. Saez-Pons, L. Alboul, J. Penders, L. Nomdedeu, Multi-robot teamformation control in the GUARDIANS project, Industrial Robot: AnInternational Journal 37 (4) (2010) 372–383.

[17] H.C.H. Chiu, B. Ryu, H. Zhu, P. Szekely, R. Maheswaran, C. Rogers, A.Galstyan, B. Salemi, M. Rubenstein, W.-M. Shen, Tentacles: self-configuring robotic radio networks in unknown environments, in:IROS’09: Proceedings of the 2009 IEEE/RSJ International Conferenceon Intelligent Robots and Systems, IEEE Press, Piscataway, NJ, USA,2009, pp. 1383–1388.

[18] S. Poduri, G.S. Sukhatme, Constrained coverage for mobile sensornetworks, in: IEEE International Conference on Robotics andAutomation, 2004, pp. 165–172.

[19] A. Howard, M.J. Mataric, G.S. Sukhatme, An incremental self-deployment algorithm for mobile sensor networks, AutonomousRobots Special Issue on Intelligent Embedded Systems 13 (2) (2002)113–126.

[20] O. Tekdas, V. Isler, Robotic routers, in: Proc. IEEE Int. Conf. onRobotics and Automation, 2008.

[21] J.M. Esposito, T.W. Dunbar, Maintaining wireless connectivityconstraints for swarms in the presence of obstacles, in: ICRA, 2006,pp. 946–951.

[22] M.A. Hsieh, A. Cowley, V. Kumar, C.J. Taylor, Towards thedeployment of a mobile robot network with end-to-endperformance guarantees, in: Proceedings of the 2006 IEEEInternational Conference on Robotics and Automation, 2006, pp.2085–2091.

[23] M.A.M. Vieira, M.E. Taylor, P. Tandon, M. Jain, R. Govindan, G.S.Sukhatme, M. Tambe, Mitigating multi-path fading in a mobile meshnetwork, Ad Hoc Networks 11(4) (2013), pp. 1510–1512.

[24] K. Guan, D. Imbrenda, R. Ghanadan, J. Hsu, Distributed sensing andcommunications in tactical robotic networks, in: MilitaryCommunications Conference, 2008. MILCOM 2008, IEEE, 2008, pp.1–7.

[25] C. Dixon, E.W. Frew, Maintaining optimal communication chains inrobotic sensor networks using mobility control, Mobile Networksand Applications Journal 14 (3) (2009) 281–291.

[26] F. Zeiger, N. Kraemer, K. Schilling, Commanding mobile robots viawireless ad-hoc networks – a comparison of four ad-hoc routingprotocol implementations, in: ICRA, 2008, pp. 590–595.

[27] M. Ying A. Hsieh, V. Kumar, C.J. Taylor, Constructing radio signalstrength maps with multiple robots, in: ICRA, 2004, pp. 4184–4189.

[28] K. Fall, A delay-tolerant network architecture for challengedinternets, in: SIGCOMM ’03: Proceedings of the 2003 Conferenceon Applications, Technologies, Architectures, and Protocols forComputer Communications, ACM, New York, NY, USA, 2003, pp.27–34.

[29] S. Jain, K. Fall, R. Patra, Routing in a delay tolerant network, in:SIGCOMM ’04: Proceedings of the 2004 Conference on Applications,Technologies, Architectures, and Protocols for ComputerCommunications, ACM, New York, NY, USA, 2004, pp. 145–158.

[30] D.S. Hochbaum, Heuristics for the fixed cost median problem,Mathematical Programming 22 (1) (1982) 148–162.

1974 M.A.M. Vieira et al. / Ad Hoc Networks 11 (2013) 1963–1974

Marcos Augusto Menezes Vieira is an Assis-tant Professor of Computer Science at theFederal University of Minas Gerais (UFMG).He received his undergraduate and M.S. at theFederal University of Minas Gerais in BeloHorizonte, and M.S. and Ph.D. degrees inComputer Science from the University ofSouthern California (USC). His research inter-ests are in Wireless Sensor Networks andMulti-Robot Systems.

Ramesh Govindan received his B.Tech.degree from the Indian Institute of Technol-ogy at Madras, and his M.S. and Ph.D. degreesfrom the University of California at Berkeley.He is a Professor in the Computer ScienceDepartment at the University of SouthernCalifornia. His research interests includescalable routing in internetworks, and wire-less sensor networks.

Gaurav S. Sukhatme is a Professor of Com-puter Science (joint appointment in ElectricalEngineering) at the University of SouthernCalifornia (USC). He received his undergrad-uate education at IIT Bombay in ComputerScience and Engineering, and M.S. and Ph.D.degrees in Computer Science from USC. He isthe co-director of the USC Robotics ResearchLaboratory and the director of the USC RoboticEmbedded Systems Laboratory which hefounded in 2000. His research interests are inmulti-robot systems and sensor/actuator

networks. He has published extensively in these and related areas. Suk-hatme has served as PI on numerous NSF, DARPA and NASA grants. He is aCo-PI on the Center for Embedded Networked Sensing (CENS), an NSF

Science and Technology Center. He is a fellow of the IEEE and a recipientof the NSF CAREER award and the Okawa foundation research award. Heis one of the founders of the Robotics: Science and Systems conference. Hewas program chair of the 2008 IEEE International Conference on Roboticsand Automation and is program chair of the 2011 IEEE/RSJ InternationalConference on Robots and Systems. He is the Editor-in-Chief of Autono-mous Robots and has served as Associate Editor of the IEEE Transactionson Robotics and Automation, the IEEE Transactions on Mobile Computing,and on the editorial board of IEEE Pervasive Computing.