Radio Source Search Using Force Field Vectors Weighted

By Received Signal Strength Gradients

Xiaochen Zhang, Yi Sun, and Jizhong Xiao*Department of Electrical Engineering

The City College of New YorkNew York, NY 10031, US

{xzhang15, ysun, jxiao}@ccny.cuny.edu

Abstract—The indoor radio source search using receivedsignal strength (RSS) is difficult due to the multipath propaga-tion effects. Robots driven by the ordinary gradient searchingmethods are always stuck in local maxima. Chemotaxis searchand theseus gradient search can overcome local extreme traps,however they are inefficient in terms of travel distance. Inthis study, we propose a force field searching algorithm whichis efficient in travel distance and invulnerable to RSS localmaxima. A virtual attraction force weighted by RSS gradientfrom each possible location of the radio source is modeled,by gradually discard the impossible radio source locationseventually the robot can reach the true location of the radiosource. Force field search is robust and fast even when the RSSreadings are highly influenced by multipath effects. Simulationresults driven by real data show the high efficiency of thismethod.

Index Terms—mobile robot, radio source search, receivedsignal strength, force field vector.

I. INTRODUCTION

Search of radio sources using received signal strength

remains an important focus of research in both robotics and

wireless sensor networks communities due to vast potential

applications across sensor network management [1], main-

tenance [2] and sweeping. Moreover, the research is closely

connected with the develop of hazardous media probe used

in urban search and rescue. Inspired by a wide variety

of seeking and tracking instinctive behaviors in biosphere,

various methods based on gradient ascent [3]–[7] arises. In

gradient based search, how to overcome the local maxima

is crucial. Fig. 1 shows a contour map of actual RSS

distribution in a hallway, a robot is likely to be trapped in

local maxima other than the true global peak if the only

guide line is RSS gradients.

A bacterium inspired method named chemotaxis [3]

search is one candidate solution. Motions in chemotaxis are

classified as the smooth move and tumble [8]. Chemotaxis

approach is fundamentally a biased random walk method,

a mathematical model can be found in [9] and another

simplified model is in [10]. A study on olfaction-based

search [4] describes the pheromone search which is able

to achieve better performance than the ordinary chemotaxis

This work is partially supported by the U.S. Army Research Office undergrant No. W911NF-08-1-0531, W911NF-09-1-0565, and U.S. NationalScience Foundation under grants No.CNS-0619577 and No. IIS-0644127

Fig. 1. The contour map of actual RSS distribution in a hallway. Theupper-right part shows the layout of the environment: the radio transmitter,the hallway boundary and RSS local maxima.

search in noisy environments. Inspired by the study of

optimization on random walks [11], [12], a method [5],

[10], [13] using levy walks achieves better performance

compared with chemotaxis especially when the gradients

are not always perceivable. Compared with chemotaxis [14],

levy walk is preferable to a search with sparse and fixed

small targets. By actively switching the behavior between

levy walk [12] and biased random walk, the levy walk guided

random walk is more efficient than chemotaxis in source

finding. These works use varieties of biased random walks in

escaping local maximum traps. However, they are suffering

from the high cost in terms of travel distance or searching

time. The reason of high cost is obvious: random walks are

inefficient.

We previously proposed a period gradient method which

fits the need of outdoor source search [6]. For indoor cases,

we proposed another method named theseus gradient guide

[7]. Borrowing the idea of self-avoid-walk [15], the robot

tries to avoid the visited sites in search. Since random walk

is no longer involved, the searching cost is less.

In this paper, we further improve the efficiency of the

radio source search by generating force field vectors weight-

ed by RSS gradients. Specifically, the locations where the

robot cannot be located is estimated at each step. At the

same time, each possible radio source location generates an

attraction force weighted by RSS gradient to the robot. By

this way, the robot will be pulled to the target. By gradually

531978-1-4244-8115-6/11/$26.00 ©2011 IEEE

Proceedings of the 2011 IEEEInternational Conference on Mechatronics and Automation

August 7 - 10, Beijing, China

building up the map using laser range finder, the search can

be planed in a global view other than ordinary local view.

Moreover, since the robot learn its own location from laser

reading instead of dead reckoning, the effect of motion error

is minimized.

This approach has some advantages in indoor search

compared with other RSS gradient guided approaches: first,

the search is robust in indoor environment since attraction

forces are generated by possible locations of a radio source

instead of noisy RSS gradients. Second, the travel distance is

shorter: when RSS gradients are heading to the radio source

robot guided by force field vector is most likely to follow

RSS gradients; when RSS gradients are not heading to the

radio source the robot will not be trapped and is still able

to move towards the radio source since RSS gradient cannot

dominate its motions.

This paper is organized as follows. The force field search-

ing algorithm is presented in Section II. Simulation results

are stated in Section III. Section IV conclude the paper.

II. RADIO SOURCE SEARCH ALGORITHM

A. Scenario of radio source search

Consider a scenario that a mobile robot is sent to an indoor

environment to find a radio source or a few radio sources.

A receiver is used to get real time RSS readings and A laser

range finder is mounted to get geometry layouts.

Fig. 2. Scenario of radio source search.

B. System outline

As stated in [16], [17], it is promising to localize the

radio source if the real propagation is well fitted by the

open space decay model. However, the indoor model is more

difficult to obtain compared with the open space one [18]–

[20]. Dozens of works localize the target directly while less

attention is paid to the indirect localization. Actually, it is

better to narrow the range of the possible locations first when

the true location cannot be estimated immediately. In indoor

radio source search, it is always possible to estimate part

of ”impossible locations”. The ”impossible locations” will

be termed discarded area and denoted by D, and ”possible

locations” is termed candidate area and denoted by C. Dand C usually are complementary sets, the union of D and

C equals the detected area S which is initially null.

Borrowing ideas of potential field, all locations in Cgenerate attraction forces weighted by RSS gradient to the

robot. After summing up all forces together a guiding vector

can be found.

The system architecture is shown in Figure 3.

Line mappingLaser

reading

Discarded area

estimation

RSS

reading

RSS Gradient

estimation

Force Field

estimation

Motion

planning

Fig. 3. System architecture.

C. Line mapping

The line mapping is indispensable for this algorithm since

it gives the location of robot and geometry layout which

is used in estimating discarded area and motion planning.

Typical procedure of line mapping in step k is shown in

Fig. 4: by fusing the line map Lk−1 (blue lines) built in

step k−1 with latest point map (dark dots) the line map Lk

is obtained; a compensation line set Bk (red lines) is then

generated to completely enclose the detect area Sk together

with Lk. For more details of line map construction, please

refer to [21]–[23].

Fig. 4. A typical procedure of line mapping.

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D. Discarded area estimation

In free spaces, the signal propagation follows the inverse

square law stating that the power density is proportional to

the inverse of square of the distance from the source

P (d) = P0/d2 (1)

where P0 and d0 are power and distance scaling factors, re-

spectively, d is the distance between the radio source and the

receiver. In indoor cases, the signal power can be regarded

as the vectorial sum of powers reaching the receiver through

multi-propagation channels. In other words, signal power is

effected by wave reflection, scattering and diffraction. Either

Multipath add-up or cancelation may occur with respect to

particular geometry layouts. Thus, the received power in a

particular location can be written as

P ∗ = P × (1 + ε) (2)

where P is received power on direct transmission as P (d)in propagation model (1), ε stands for the multipath effect

factor with respect to P , P ∗ and ε are determined by the

locations of radio source and receiver as well as the geometry

layout.

If ε at each step can be found, the radio source localization

can be done under bayes framework. Unfortunately, ε is

highly non-Gaussian and differs everywhere thus very diffi-

cult to estimate in real time. However, we can conservatively

assume a lower bound of ε to estimate an lower bound of

d. If we have ε < ε, an lower bound of d can be found as

d =√(1 + ε)× P0/P ∗ < d (3)

where ε and d stands for the lower bound of ε and drespectively. Note these lower bound are not rigorous lower

bound, ε is empirically decided according to particular

applications, for eg. ε as −65% in this work. By using

statistical methods, d will not exceed d if ε < ε is true in

latest several steps. To be specific, we use the mean power

value z∗x in a small area centered at current location x with

radius η1 to produce a neutralized power measurement in

(3), that is

z∗x =1

k

∑

||x−x+||<η1

z(x+) (4)

where z(x+) is the RSS measurement at location x+, k ≥1 is the number of z(x+) involved, x+ are chosen from

visited locations. Substitute P ∗ by z∗x in (3) the robot is

able to estimate d. Recall d stands for a lower bound of

the distance between robot and radio source, thus the radio

source is not within a distance d. The robot is going to

continuously estimate these impossible locations and record

them as discarded area D. To be specific, at step n,

Dn= Dn∪Dnew (5)

Dnew = {xnew| ‖xnew − xk‖ < d,xnewxk∩Lk = φ}.

(6)

where xk is the location of the robot in step k, Lk is the

line sets of line map, xnew is the locations to be included

in the discarded area.

We would like to mention two important properties of

discarded area estimation: first, the growing speed of dis-

carded area is fast when the robot is far away from the radio

source, and becomes slower when the robot is closer to the

radio source. Second, the construction of discarded area is

safe since geometry layout is considered. For example, in

Fig. 5, due to the line of sight transmission is blocked, the

RSS measured by the robot is weak. Although the Euclidean

distance between the robot and the radio source might be

smaller than the estimated discarded area radius the radio

source is not going to be included in the discarded area

according to (6).

Fig. 5. The estimation on discarded area considering geometry layout.

E. RSS gradient and force field estimation

At time n, the robot is located at xn. The RSS gradient

considering RSS in adjacent area within distance η2 is

gn =∑

‖xn−xi‖<η2

(zn − zi)xn − xi

‖xn − xi‖2. (7)

where zn is the RSS measurement at time n, zi is the RSS

measurement of visited locations xi. The gradient gn is then

unitized as gn and used as a weighting vector of force field.

According to the assumption that the radio source exists in

areas other than D. A force field is generated. We use the

term cell to indicate the small area elements in candidate

area C. For the ith cell Ci, its location is xCi which is the

center of Ci. Similarly, we use the same term to indicate

the small line segment in compensation line set B. For the

ith cell Bi, its location is xBi which is the middle of cell

Bi. These cells have the following properties: Ci∩Cj = φ,∑Ci = C,Bi ∩ Bj = φ,

∑Bi = B. The total number of

cells depends on an arbitrary resolution.

The reason we consider cells in B and C is straightfor-

ward, cells in C are possible locations of the radio source

and cells in B potentially hide more cells of C. Thus both

types of cells have attractions to the robot.

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An attraction force from cell Ci ∈ C is modeled as

f(Ci) =wCi × ζC

‖xn − xCi‖2(8)

wCi = τ(1−gT

n ·U(xCi))/2

C (9)

where ζC is the attraction constant for cells in C, wCi is

produced by the transfer function which maps gTn × (xCi

−xn) to the range τC˜1, U(xCi) is the unit vector of (xCi −xn).

The overall attraction force caused by C is:

F (C) =∑

f(Ci)× U(xCi). (10)

Similarly, an attraction force from cell Bi ∈ B is modeled

as

f(Bi) =wBi × ζB

‖xn − xBi‖2(11)

wBi = τ(1−gT

n ·U(xBi))/2

B (12)

where ζB is the attraction constant for cells in B, wBi is

produced by the transfer function which maps gTn × (xBi −

xn) to the range τB˜1, U(xBi) stands for the unit vector of

(xBi − xn).

The overall attraction force caused by B is:

F (B) =∑

f(Bi)× U(xBi). (13)

The overall attraction force vector is defined as

G =F (B) + F (C)

||F (B) + F (C)|| (14)

Upon this, the input of motion planning xm chosen from

set C can be found as:

xm = max{τ(1−GT

n ·U(xCi))/2

G

‖xCi − xn‖ } (15)

where τG is the transition parameter similar to τB and τC .

F. Motion planning

After getting the xm which is the output of force field

estimation at step k, the motion planning starts. Unlike the

free space cases, the indoor search has to guarantee collision

avoidance. The bug algorithm [24] [25] is selected as the

basis of motion planner due to its two merits: (1) The bug

algorithm provides a robust solution as long as a path exists.

(2) It is simple however efficient in collision avoidance. Note

the robot is not going to reach xm, instead the robot just

follows the direction towards xm and moves for a given

step length.

III. SIMULATION AND RESULTS

In this section, simulation results driven by real data

are illustrated. The scenario is the hallway of 6th floor of

Steinmen Hall in CCNY, three radio sources are placed in

different locations as shown in Fig. 6. For collecting the

RSS data, the hallway is partitioned into 343 uniformly

distributed grids, on each grid 10 readings from each radio

source are collected. The simulated laser range finder has a

detection range of 10 meters with angular resolution 1◦. In

simulation, we use step length 0.488 m, ε = −65%, η1 = 1m, η2 = 1 m, ζC = 10, ζB = 100, τC = 0.5, τB = 0.5,

τG = 0.1. A search for a radio source will be regarded as

succeed if the distance between robot and source is smaller

than 0.6096 meters.

Fig. 6. Hallway and radio source locations.

A. A sample of searching trajectory

Here a typical searching trajectory (Fig. 7) is shown to

illustrate two properties of force field search. First, the robot

is neither loop nor trapped in small areas although the robot

movements are not always towards the radio source. The

reason is that the force field is generated by candidate area

C. The local maxima of RSS cannot dominate the motions.

Secondly, the search is flexible that is the robot is able to

turn back fast when it is moving towards a wrong direction.

This property is very important for a searching algorithm.

B. Comparison with chemotaxis and theseus gradient meth-ods

We use simulation to compare force field search with two

other methods: the chemotaxis using simplified model [10]

the theseus gradient searching method [7]. Some terms have

to be defined before illustrating the simulation results. The

cost of travel distance is not directly used in comparison

since the trajectory and travel distance varies given different

starting positions. Instead a term cost indicator which equals

the actual travel distance divided by the Euclidean distance

from the starting position to the source. For example, a robot

starts from a position 3 meters away from the radio source

and travels 5 meters to reach the radio source, then the cost

indicator is 5/3. In simulation, 50 trials for each radio source

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Fig. 7. A Typical searching trajectory.

are launched. The starting positions are random selected

from all vacant positions at least 2 meters away from the

corresponding radio source.

Fig. 8. Histogram of cost indicator.

Figure 8 shows the histogram of cost indicator in simula-

tion. The vertical axis indicates the frequency of occurrence

of corresponding cost indicator. For instance, the frequency

on cost indicator interval 5˜5.4 equals to 1 in force field

search means in all 50× 3 trials using force field search the

cost indicator fall into interval 5˜5.4 once. 55% of trials

using force field are falling into intervals 1˜5, compare

with 42% using theseus gradient search and 19% using

chemotaxis falling into the same interval. This result is

not surprising since theseus gradient search is using self-

avoiding walk and chemotaxis is using biased random walk

in escaping the RSS local maxima while force field search is

invulnerable to RSS local maxima. However, the force field

search has a probability to fail: in our simulation, three trials

are failed. The reason is that although robot driven by force

field search will not be trapped in RSS local maxima, it has

a chance to be trapped in force field local extremes. That is,

by very particular chance the robot may loop its movements

between two locations forever. The force field search will

also fail if the true radio source location is included in

discarded area. Two trails of theseus gradient search and 16trails of chemotaxis are out of the histogram interval range

in Fig. 8 since cost indicators larger than 40 are not shown.

IV. CONCLUSION

We proposed an efficient indoor radio source searching al-

gorithm using RSS. A force field generated by possible radio

source locations are used as the motion guider. Since RSS

gradients are not directly controlling the motions, a robot

guided by force field search is invulnerable to local RSS

maxima. The searching cost in terms of travel distance is

less than ordinary chemotaxis and theseus gradient methods

under conditions in this work.

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