Wireless Sensor Network, 2010, 2, 347-357
doi:10.4236/wsn.2010.24046 Published Online May 2010 (http://www.SciRP.org/journal/wsn)
Cooperative Distributed Sensors for Mobile Robot
Localization
Zhiwei Liang, Songhao Zhu
College of Automation, Nanjing University of Post s an d T e l ecom mu nic ations, Nanjing, China
Received December 24, 2009; revised February 22, 2010; accepted March 17, 2010
Abstract
This paper presents a probabilistic algorithm to collaborate distributed sensors for mobile robot localization.
It uses a sample-based version of Markov localization—Monte Carlo Localization (MCL), capable of local-
izing mobile robots in an any-time fashion. During robot localization given a known environment model,
MCL method is employed to update robot’s belief whichever information (positive or negative) attained
from environmental sensors. Meanwhile, an implementation is presented that uses color environmental cam-
eras for robot detection. All the parameters of each environmental camera are unknown in advance and need
be calibrated independently by robot. Once calibrated, the positive and negative detection models can be
built up according to the parameters of environmental cameras. A further experiment, obtained with the real
robot in an indoor office environment, illustrates it has drastic improvement in global localization speed and
accuracy using our algorithm.
Keywords: Monte Carlo Localization, Environmental Camera, Positive Information, Negative Information
1. Introduction
Mobile robot localization is the problem of estimating a
robot’s pose (location, orientation) relative to its envi-
ronment. The localization problem is a key problem in
mobile robotics. There are two classes of localization
problem, position tracking and global localization. In
position tracking, a robot knows its initial position [1]
and only needs to reduce uncertainty in the odometer
reading. If the initial position is no t known or the robo t is
kidnapped to somewhere, the problem is one of global
localization, i.e., the mobile robot has to estimate its
global position th rough a sequence of sensing actions [2].
In recent years, a flurry of publications on localization
document the importance of the problem. Occasionally,
it has been referred to as “the most fundamental problem
to providing a mobile robot with autonomous capabili-
ties” [3].
So far, virtually all existing work addresses localiza-
tion only using sensors onboard mobile robot. However,
in robot navigation, the robot cannot always determine
its unique situation only by local sensing information
since the sensors are prone to errors and a slight change
of the robot’s situation deteriorates the sensing results.
Along with the rapid development of computer networks
and multimedia technology, research on how to make an
‘intelligent’ environment for the robot to fulfill the same
functions makes sense, especially in home environment.
In this case, various sensors are embedded into the envi-
ronment (environmental sensors), and communication
between the robot and environmental sensors is utilized.
Sogo et al. [4] proposed a distributed vision system for
navigating mobile robots in a real world setting. To ob-
tain robustness and flexibility, the system consisted of
redundant vision agents connected to a computer net-
work. These agents provided information for robots by
organizing the communication between vision agents.
Morioka et al. [5] defined the space in which many vi-
sion sensors and intelligent devices are distributed as an
intelligent space. Mobile robots exist in this space as
physical agents that provide humans with services. A
concept called a distributed modular robot system was
also proposed in [6]. In that robot system, a modular ro-
bot was defined as a mono-functional robot (either a
sensor or an actuator) with a radio communication unit
and a processing unit. Such robots were usually small
and could be easily attached to operational objects or
dispersed into the environment. A modular robot system
for object transportation was developed by using several
distributed-placed camera modules and wheel modules.
All studies mentioned above mostly focus on the struc-

Z. W. LIANG ET AL. 348


ture of system, while don’t put forward an effective me-
thod to incorporate the information of environmental
sensors. On the other hand, they only apply the positive
information (it represents a sensor detects the robot) to
localize robot, while don’t take into account how to
make use of the negative information which represents
that a sensor doesn’t detect the robot.
The aim of this paper is to show how positive and
negative information of environmental sensors can be
incorporated in robo t localization. Therefore, an efficient
probabilistic approach based on Markov Localization
[7-9] is proposed. In contrast to previous research, which
relied on grid-based or coarse-grained topological repre-
sentations of the robot’s state space, our approach adopts
a sampling-based representation [10]—Monte Carlo Lo-
calization (MCL), which is capable of approximating a
wide range of belief functions in real-time. Using the
positive and negative detection model of environmental
sensors, the MCL algorithm can improve localization
accuracy and shorten the localization time. In terms of
practical applications, while our approach is applicable
to any sensor capable of detecting robot, we present an
implementation that uses color environmental cameras
for robot localization . The location and parameters of all
environmental cameras are unknown and need to be ca-
librated by robot. Once getting the cameras’ parameters,
the positive and negative detection models can be at-
tained. Experimental results, carried out with two envi-
ronmental cameras fixed in an indoor enviro nment, illus-
trate the appropriateness of the approach in robot global
localization.
This paper is organized as follows. In Section 2, the
MCL only depending on the robot’s own sensor is intro-
duced. Section 3 extends the algorithm to integrate the
positive and negative information coming from envi-
ronmental sensors. Experimental results are shown in
Section 4. Finally, in Section 5, our conclusions are de-
rived.
2. Monte Carlo Localization
In this section we will introduce our sampling-based lo-
calization approach only depending on robot itself. It is
based on Markov localization [7-9], which provides a
general framework for estimating the position of a mo-
bile robot. Markov localization maintains a belief
over the complete three-dimensional state
space of the robot. Here, denotes a random variable
and denotes the robot’s belief of being at
location , representing its


r
Bel L
BelL
l

r
L


rl
-
x
y coordinates (in some
Cartesian coordinate system) and its heading direction

. The belief over the state space is updated whenever
the robot moves and senses.
Monte Carlo localization relies on sample-based rep-
resentations for the robot’s belief and sampling/importance
resampling algorithm for belief propagation [11,12]. The
sampling/importance resampling algorithm has been in-
troduced for Bayesian filtering of nonlinear, non-Gaussian
dynamic models. It is known alternatively as the boot-
strap filter [13], the Monte-Carlo filter [10], the Conden-
sation algorithm [14], or the survival of the fittest algo-
rithm [15]. All these methods are generically known as
particle filters, and a discussion of their properties can be
found in [16].
More specifically, MCL represents the posterior be-
liefs


BelL over the robot’s state space by a set of
weighted random samples denoted .
A sample set constitutes a discrete distribution. However,
under appropriate assumptions (which happen to be ful-
filled in MCL), such distributions smoothly approximate
the correct on at a rate of
N

|1...
i
Ssi N
1N as goes to infinity.
Samples in MCL are of the type
N
,lp, where de-
notes a robot position in
l
--
x
y

space, and is a
numerical weighting factor, analogous to a discrete
probability. For cons istency, we assume
0
1
p
1i
p
N
i

.
In analogy with the general Markov localization ap-
proach, MCL propagates the belief as follows:
1) Robot motion. When a robot moves, MCL gener-
ates new samples that approximate the robot’s posi-
tion after a motion measurement . Each sample is
generated by randomly drawing a sample from the pre-
viously computed sample set, with lik elihood determined
by their . Let
Na
-valuepl

denote the ,,
x
y

position
of this sample. The new sample’s is then determined
by generating a single, random sample from the distribu-
tion
l


|,laPl

, usingthe observed motion . The
of the new sample is . Here
a
-vaplue 1 N


Pl a|,l

is
called the motion model of the robot. It models the un-
certainty in robot motion.
2) Environment measurements are incorporated by
re-weighting the sample set, which is analogous to the
application of Bayes rule to the belief state using impor-
tance sampling. More specifically, let ,lp be a sam-
ple. Then

|pPo  

l
(1)
where is a sensor measurement, and o

is normali-
zation constant that enforces 1. 1
N
i
ip 



|Pol, also
called the environment perceiving given that the ro-
bot is at position . The incorporation of sensor read-
ings is typically performed in two phases, one in which
o
l

Z. W. LIANG ET AL.349


p
Po
-ax
is multiplied by , and one in which the vari-
ous are normalized.

|Pol
o
l
o
xis
l
o
-valuep

|l
xis
For proximity sensors such as laser range-finders
which is adopted in my approach, the probability
can be approximated by , which is the
probability of observing conditioned on the expected
measurement at location . The expected meas-
urement, a distance in this case, is easily computed from
the map of the environment using ray tracing. Figure 1
shows a perception model for laser sensor. Here the
is the distance expected given the world
model, and the is distance o measured by the
sensor. The function is mixture of a Gaussian (centered
on the correct distance ), a Geometric distribution
(modeling overly short readings) and a Dirac distribution
(modeling max-range readings). It integrates the accu-
racy of the sensor with the likelihood of receiving a “r an-
dom” measurement (e.g., due to obstacles not modeled in
the map [9]).

|l Poo
l
o
y
l
-a
3. Cooperative Distributed Sensor
Localization
In this section, we will first describe the basic statistical
mechanism for cooperative distributed sensor localiza-
tion and then its implementation using MCL. The key
idea of cooperative distributed sensor localization is to
integrate measurements taken at different platforms, so
that robot can benefit from information gathered by en-
vironmental sensors, which are embedded in the envi-
ronment, other than itself. The information coming from
environmental sensors includes “positive” detections, i.e.,
cases where an environmental sensor does detect the
robot, and “negative” detection events, i.e., cases where
an environmental sensor does not see the robot.
Figure 1. Perception model for laser range finders.
3.1. Positive Detections
When one environmental sensor detects the robot, sam-
ple set is updated using the detection model, according to
the update equation




  




,
r rr mmm
l
B
el lBel lPLlLlrBell





(2)
Notice that this equation requires the multiplication of
two densities. The crucial component is the probabilistic
detection mode
  


,
rm
PL lLlr



m
which describes
the conditional probability that robot is at location ,
given that sensor is at possible location ll m

and
perceives robot with po sitive measurement . From a
mathematical point of view, our approach is sufficiently
general to accommodate a wide range of sensors for ro-
bot detection, assuming that the conditional density

m
r
  


,
rmm
PL Lr
 is adjusted accordingly. However, for
environmental camera it is not necessary to build the
probabilistic detection m ode
  


m
,
m
lr


Bel
rm
PL lL and
the environmental camera localization model

l

respectively. As a substitute, joint detection model
 


  




|,
rr mmm
l
PL lrPL lLlrBell


 

m
(3)
is constructed directly according to the environmental
cameras’ parameters. Before integrating positive infor-
mation of environmental cameras into robot’s belief, the
cameras’ parameters need to be calibrated by robot.
3.1.1. Camera Self-Calibration
In our method, all parameters of the environmental cam-
eras are unknown in advance and their visual fields are
not overlaid each other. So, in order to apply them to
localize the robot, each camera’s parameters need to be
calibrated at first. Assuming that the system is always
ready for using in different environments, calibration
instruments (such as patterns and measuring devices)
may more or less hinder portability. Our objective is to
introduce a self-calibration concept [17] into the system
and take the mobile robot as a calibration instrument.
Because the visual fields of all cameras are not overlaid,
each camera’s calibration is independent.
During the calibration, the robot location is known.
When the robot moves depending on laser and odometry
in visual field of any environmental camera, the camera
does detect the robot and gathers the relative data be-
tween the robot global location and detected image pix-

Z. W. LIANG ET AL. 350
els. The sample space of relative data is designed to sat-
isfy a condition that the distance between two neighbor
global locations of relative data is more than 0.2 m. Once
the number of relative data sums up to a threshold which
is set as 200 in this paper, camera calibration can be
conducted. Because the mobile robot always moves in a
plane, the coplanar camera calibration method of Tsai is
adopted here [18].
In addition, unlike ordinary calibration devices, the
mobile robot is much less accurate when moving. As the
most distinct point of the robot’s error, it is cumulative
and increase over time or repeated measurements.
Moreover, the random motion input of the robot, which
may take too much time, is not suitable for our method.
For all these reasons, robot’s motion during calibration
process should be designed to avoid serious calibration
error and to meet the accuracy demands of calibration. In
our method, the robot in the cameras’ visual field moves
as a zig, which is shown in Figure 2.
3.1.2. Detection
To determine the location of the robot, our approach
combines visual information obtained from environ-
mental cameras. Camera images are used to detect mo-
bile robot and determine the position of the detected ro-
bot. The two rows in Figure 2 shows examples of cam-
era images recorded in a room. Each image shows a ro-
bot, marked by a unique, colored marker to facilitate its
recognition. Even though the robot is only shown with a
fixed orientation in this figure, the marker can be de-
tected regardless of the robot’s orientation.
To find the robot in a camera image, our approach first
(a) (b)
(c) (d)
Figure 2. Image sequences of successful detecting the robot which moves as a zig.

Z. W. LIANG ET AL. 351

m
filters the image by employing local color histograms
and decision trees tuned to the colors of the marker.
Threshold is then employed to search for the marker’s
characteristic color transition. If found, this implies that
the robot is present in the image. The small black points,
superimposed on each marker in the images in Figure 2,
illustrate the center of the marker as identified by this
distributed environmental camera.
Once a robot has been detected, the current environ-
mental camera is analyzed for the location of the robot in
image coordinates. Then transform the detection pixels
in image coordinates to positions in world coordinates
according to the calibrated parameters of the camera.
Here, tight synchronization of photometric data is very
important, especially because the mobile robot might
shift and rotate simultaneously when it is sensed. In our
framework, sensor synchronization is fully controllable
because all data is tagged with timestamps.
3.1.3. J oint Detecti on Model
Next, we have to devise a joint detection model of the
type . To recap, denotes a posi-
tive detection event by the m-th environmental camera,
which comprises planar location of the detected robot in
world coordinates. The variable describes the loca-
tion of the detected robot. As described above, we will
restrict our considerations to “positive” detections, i.e.,
cases where an environmental camera did detect a robot.


|
r
PL lr


 m
r

r
L
The joint detection model is trained using data. More
specifically, during training we assume that the exact
location of robot is known. Whenever an environmental
camera takes an image which is analyzed as to whether
robot is in its visual field, it is to exploit the fact that the
locations of robot are known during training. Then, the
image is analyzed, and for detected robot global location
is computed according to the calibrated parameters of the
environmental camera above. This data is sufficient to
train the joint detection model
 






1 1
2 2
1
|2
1
exp 2
rm
m
PL lr
lr lr

 



 

 




AA

m




(4)
where ,
100
01 0



A2
2
0
0
x
y








,
Figure 3. Gaussian model representing camera’s detection
error.
coordinates, and the y-axis the y direction error. The pa-
rameters of this Gaussian model has been obtained
through maximum likelihood estimation [19] based on
the training data. As is easy to be seen, the Gaussian
model is zero-centered along both dimensions, and it
assigns low likelihood to large errors. Assuming inde-
pendence between the two errors, we found both errors
of the estimation to be 15 cm.
To obtain the training data, the “true” location was not
determined manually; instead, MCL was applied for po-
sition estimation (with a known starting position and
very large sample sets). Empirical results in [20] suggest
that MCL is sufficiently accurate for tracking a robot
with only a few centimeters error. The robot’s positions,
while moving at speeds like 30 cm/sec through our envi-
ronment, were synchronized and then further analyzed
geometrically to determine whether (and where) the ro-
bot is in the visual fields of environmental cameras. As a
result, data collection is extremely easy as it does not
require any manual labeling; however, the error in MCL
leads to a slightly less confined joint detection model
than one would obtain with manually labeled data (as-
suming that the accuracy of manual position estimation
exceeds that of MCL).
3.2. Negative Detections
Most of the techniques of state estimation use a sensor
model that update the state belief when the sensor reports
a measurement. However it is possible to get useful in-
formation of the state from the absence of environmental
sensor measurements. There are two main reasons for
environmental camera not to measure the robot marker.
The first one is that the robot marker is not in the field of
view of the environmental camera and the second one is
that the environmental camera is unable to detect the
robot mark, due to occlusions.
2
x

and 2
y

represent mean square error in
x
direction and
direction respectively. Let as coordinate origin,
and the Gaussian model showed in Figure 3 models the
error in the estimation of robot’s location. Here the
y

m
r
x
-axis represents the error of
x
direction in the world

Z. W. LIANG ET AL. 352
This situation of no detecting a robot mark can be
modeled by considering the environmental camera field
of view and by using an obstacle detection to identify
occlusions as shown:




 


|,,obs
rrmrm
BelL lBelL lTrL l

 vm
m
m
(5)
where
,
represents the negative information of envi-
ronmental sensor, describes the visibility area of
the sensor and represents the occlusion area.
 

 
 
0 and ob s
|,,obs1 or obs
m
mrm m
m
ll
Tr Llll







v
vv

m
r-thm

m
v

obs m
The negative information has been applied to target
tracking using the event of not detecting a target as evi-
dence to update the probability density function [21]. In
that work negative information means that the target is
not located in the visual area of the sensor and since the
target is known to exist it is certainly outside the area.
In robot localization domain, the work of Hoffmann
et al. [22] on negative information in ML considers
negative information the absence of landmark sensor
measurements. Occlusions are identified using a visual
sensor that scans colors of the ground to determine if
there is free area or obstacle. The environment is soccer
field in green with white lines. So, if a different color is
identified, it means that an obstacle could be occluding
the visibility of a landmark.
In the cooperative distributed sensor localization
problem for mobile robot, negative information can also
mean the absence of detections (in the case that an envi-
ronmental sensor does not detect the robot), which con-
figures a lack of group information. In this case, the neg-
ative detection measurement can provide the useful in-
formation that the robot is not located in the visibility
area of an environmental sensor. In some cases, it can be
essential information as it could improve the pose belief
of the robot in short time.
Our contribution in this paper is the proposal of a neg-
ative detection model and its incorporation into MCL
approach based on distributed sensors. Consider an en-
vironmental camera, within a known environmental and
its field of view as shown in Figure 4(a). If the envi-
ronmental camera does not detect the robot, negative
information is reported, which states that the robot is not
in the visibility area of the camera, as depicted in Figure
4(a).
The information gathered from Figure 4(a) is true if
we consider that there are no occlusions. In order to ac-
count for occlusions it is necessary to sense the environ-
ment to identify free areas or occupied areas. For envi-
ronmental cameras, we apply background subtraction
approach described in [23] to detect the occupied areas.
If it is identified as an occupied area it means that the
robot could b e occluded by an obstacle. In this case, it is
possible to use geometric inference to determine which
part of the visual area can be used as negative detection
information, as shown in Figure 4(b).
3.3. Cooperative Distributed Sensor Localization
According to above positive and negative information,
the cooperative distributed sensor localization algorithm
for robot is summarized in Table 1.
(a) (b)
Figure 4. (a) Negative information; (b) Occlusion in the field of view.

Z. W. LIANG ET AL.353
Table 1. MCL algorithm to cooperate distributed sensors.
for each location do /*initialize the belief*/ l




0
rr
B
ellP Ll
end for
forever do
if the robot receives new laser inputs do /*apply the laser perception model*/ o
for each location do l






rr
B
el lPolBel l  
end for
end if
if the robot receives new odometry readings do /*apply the motion model*/ a
for each location do l





,
rr
l
B
el lPlalBel l



end for
end if
if the robot receives positive information from the-th environmental sensor do /*apply the positive detection model*/ m
for each location do l




 




,
rr rmmm
l
B
el lBel lPLlLlrBell


 

end for
end if
if the robot receives negative information from the -th environmental sensor do /*apply the negative detection mode l* / m
for each location do l




 

|,,obs
rrmrm
BelLl BelLlTrLl

 v
m
end for
end if
end forever
4. Experimental Results
In this section we present experiments conducted with
real robot. The mobile robot used is Pioneer3 DX, which
is equipped with a laser sensor. In whole experiments,
the number of samples is fixed to 400. Figure 5(a)
shows our experimental setup along with a part of the
occupancy grid map used for position estimation, and
that two cameras are fixed on the wall applied to detect
and localize the robot. Figure 5(a) also shows the visual
fields of the two environmental cameras (the purple rec-
tangle regions) and the path from A to C taken by Pio-
neer 3 DX with laser sensor, which was in the process of
global localization. Figure 5(b) represents the uncertain
belief of the robot on point A f rom scratch.
N
In order to evaluate the benefits of collaborative dis-
tributed sensor localization for robot, three different
types of experiment are performed using the above de-
ployment. The first one is that the robot performs global
localization by using the positive information of envi-
ronmental cameras, and the field of each camera is not
occupied. The second one is to use positiv e and negative
information of environmental cameras whose fields of
view are not occupied for robot localization. Compared
with the second on e, the only difference of the last one is
that visual area of camera one is partly occupied.
4.1. No Occlusions and Only Using Positive
Information
Before robot passes point B (shown in Figure 6(a)), the
robot is still highly uncertain about its exact location
only depending on its onboard laser sensor. The key
event, illustrating the utility of cooperation in localiza-
tion, is a detection event. More specifically, the envi-
ronmental camera 1 detects the robot as it mo ves through
its visual field (see Figure 7). Using the joint detection
model described in Section 3, the robot integrates the
positive information into its current belief. The effect of
this integration on rob ot’s belief is sh own in Figure 6(b).
As this figure illustrates, this single incident almost
completely resolves the uncertainty in robot’s belief and
shortens the time of robot global localization effectively.
4.2. No Occlusions and Using All Information
It can be seen from Figure 8(a) that the particles existing
in the visibility area of two cameras are disappeared due
to using the negative information. After five seconds, the
effect of this integration on robot’s belief is shown in

Z. W. LIANG ET AL. 354
A
B
C
v
(1)
v
(2)
Camera 1
Camera 2
(a) (b)
Figure 5. (a) Experimental setup; (b) The sample cloud represents the robot’s belief on point A from scratch.
(a) (b)
Figure 6. (a) Sample set before passing point B; (b) Achieved localization by integrating the positive information of camera 1.
Figure 7 . D ete cti on ev ent of cam era 1 on robot pa ssin g po int B.
Figure 8(b). Compared with experiment one, Localiza-
tion results obtained with negative detection information
into robot global localization are more accurate and pro-
vide the ability to localize robot more quickly.
4.3. Occlusions and Using All Information
In this experiment, we take into account the camera one
being occupied by a people. The camera one applies
background subtraction approach described in [23] to
detect the occupied areas. The detection result is shown
in Figure 4(b). Due to the occlusion, the particles exist-
ing in the occupied areas are still reserved (see Figure
9(a)). After ten seconds, the effect of robot’s belief is
described in Figure 9(b). From the experiment, it can be
seen that though the camera one is partly occupied, the
accuracy of the localization is still greatly improved us-
ing the negative detection information compared with
experiment one.
4.4. Localization Error Analysis
In the case of no occlusions, we conducted ten times for
the first two experiments and compared the performance
to conventional MCL for robot which ignores environ-
mental cameras’ detections. To measure the performance
o localization we determined the true locations of the t

Z. W. LIANG ET AL.355
(a) (b)
Figure 8. (a) The particles represent the robot’s belief by integrating the negative information of two cameras; (b) Archived
localization after five seconds.
(a) (b)
Figure 9. (a) Particles set after integrating negative information of two cameras among which the camera 1 is occupied by a
people; (b) Archived localization after 10 seconds.
robot by performing position tracking and measuring the
position of each second. For each second, we then com-
puted the estimation erro r at the reference positions. Th e
estimation error is measured by the average distance of
all samples from the reference position. The results are
summarized in Figure 10. The graph plots the estimation
error (y-axis) as a function of time (x-axis), averaged
over the ten experiments, along with their 95% confi-
dence intervals (bars). Firstly, as can be seen in the fig-
ure, the quality of position estimation increases faster
when using environmental camera detection (positive
information) than one without environmental cameras.
Please note that the detection event typically took place
14-16 seconds after the start of each experiment. Sec-
ondly, as can be also seen in the figure, the quality of
position estimation increases much faster when using all
information of environmental cameras. Obviously, this
experiment is specifically well-suited to demonstrate the
advantage of positive and negative information of envi-
ronmental cameras in robot global localization. Of
course, the performance of our approach in more com-
plex situations, especially highly symmetrical and dy-
namic environments, is more attractable to solve robot’s
global localization.
Figure 10. Comparison of localization error using three
localization algorithms.

Z. W. LIANG ET AL. 356
5. Conclusions
In this paper we presented an approach to collaborate
distributed sensors for mobile robo t localization that uses
a sample-based representation of the state space of a ro-
bot, resulting in an extremely efficient and robust tech-
nique for global position estimation. Here we use envi-
ronmental cameras whose parameters is unknown in ad-
vance to determine robot’s position. In order to apply
environmental cameras to localize the robot, all parame-
ters of each environmental camera are calibrated inde-
pendently by robot. During calibration, the robot local-
ization is known and can navigate by its onboard laser
sensor. Once calibrated, the positive and negative detec-
tions of the environmental cameras can be applied to
localize robot. Experimental results demonstrate that, to
combine all information of environmental cameras, the
robot’s belief can reduce its uncertainty significantly.
6. Acknowledgements
This work was supported by the Program of Nanjing
University of Posts and Telecommunications (Grant No.
NY209020).
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