Study on Cooperative Positioning System- Optimum Moving Strategies for CPS-III Ryo Kurazume

Shigeo Hirose

Tokyo Institute of Technology
2-12-1, Oo-okayama Meguro-ku, Tokyo 152-8552, Japan

Abstract

Several position identi cation methods are being
used for mobile robots. Dead reckoning is a popularmethod but due to the accumulation error from wheelslippage, reliability is low for the measurement of long
distances especially on uneven surfaces. Another popular method is the landmark method, which estimatescurrent position relative to known landmarks, but thelandmark method's limitation is that it cannot be usedin an uncharted environment. Thus, this paper proposes a new method called "Cooperative Positioning
System (CPS)" that is able to overcome these shortcomings. The main concept of CPS is to divide therobots into two groups, A and B respectively, group
A remains stationary and acts as a landmark whilegroup B moves and then group B stops and acts asa landmark for group A. This process is repeated until the target position is reached. Compared with deadreckoning, CPS has a far lower accumulation of positioning error, and can also work in three-dimensions.
Furthermore, CPS employs inherent landmarks andtherefore can be used in uncharted environments unlike the landmark method. In this paper, focus will beon the discussion of the relationship between moving
con gurations of CPS and its positioning accuracy forthe latest prototype CPS model, CPS-III, using simulation and analytical techniques. Optimum moving
strategies in order to minimize positioning error arethen discussed and veri ed through experiments.

1 Introduction
An accurate position identi cation method for amobile robot that can be used in various environments is an important consideration in the design ofautonomous mobile robots. Although in recent years
accurate positioning on the surface of earth has been
made possible by the development of GPS, it cannot

be used underground nor inside buildings. Therefore, to realize an accurate positioning system thatis able to perform based on local information about
the robot and its surroundings is still an importantresearch theme.
A number of simple techniques have been proposed
based on local information such as dead reckoning,whereby mobile robots with wheels identify their current position from the number of rotations of thewheels [1],[2]. The dead reckoning method is simple
and therefore easy to implement, using only internalsensors which allows the use in uncharted environments. However the dead reckoning method's drawback is that the position recorded is directly a ectedby the wheel contact with the ground, the type ofwheel xture, and by external disturbances such astire slip, thus resulting in serious positioning accuracy
problems over long distances and with unpaved roads
or other outdoor environments. In addition, deadreckoning also cannot be used for three-dimensional
positioning involving level di erences.
Other, more accurate positioning techniques formobile robots have been proposed. These techniques
use optical or other sensors on the robots to detectwalls, pillars, and other landmarks in the work environment [3],[4],[5]. The robots then are able to determine their positions from their positional relationshipwith such landmarks. The landmark method can givehighly accurate positioning information over long distances and in rugged environments, but requires theprevious placing of landmarks. Thus, it cannot, for example, be used for planetary exploration robots thatwould be in uncharted environments. With these considerations in mind, we have proposed a new method
named "Cooperative Positioning System (CPS)[6]"and discussed its viability through measurement experiments using specially constructed robots [6],[7].
CPS overcomes the shortcomings of the previous two
methods and thus enables position identi cation inunfamiliar environments and uneven surfaces utilizing
only local information stored by multiple robots.
Fig. 1 shows an example of CPS that consists of
one parent robot equipped with sensors and two childrobots equipped with targets for measurement.
1. While the parent robot whose initial position ismeasured previously remains stationary, child robots
1 and 2 travel certain distances and stops. 2. Parent robot measures distances, azimuth angles, and elevation angles from the child robot 1 with the sensors equipped, and calculates the positions of the childrobot 1 3. Same thing is done for the child robot 2
5. Steps 1 to 4 are repeated until the robot group hasreached the target position.
1. While the parent robot whose initial position
is measured previously remains stationary, childrobots 1 and 2 travel certain distances and stops.
2. Parent robot measures distances, azimuth angles,
and elevation angles from the child robot 1 withthe sensors equipped, and calculates the positionsof the child robot 1.
3. Parent robot measures the child robot 2 in thesame way as step 2
4. Parent robot travels a certain distance and stops.
Then, parent robot measures distances, azimuth
angles, and elevation angles from the child robots,and calculates own position.
5. Steps 1 to 4 are repeated until the robot grouphas reached the target position.
CPS has the following characteristics:
1. Utilizing high accuracy sensors developed for surveying to measure stationary points, CPS provides a good basis for higher positioning accuracy
compared with the dead reckoning method thatuses wheel rotation.
2. Unlike the landmark method, CPS does not require apriori knowledge of landmark locations.
It allows measurement of position not only inforeign environments but even underground orwithin building where GPS cannot be used.
3. By measuring elevation angles, CPS can determine three-dimensional positions, which is notpossible with dead reckoning.
From these characteristics, CPS can be used e ectively as the automatic control system for robots that

Slave robot
Master robot
1
1

0

0

r1

ψ1
φ1

z
x

2

2

y

(1) Robot 1 and 2 move.

(2) Robot 0 measuresrobot 1.
1

0

1

0

φ2

ψ2

r2

(3) Robot 0 measuresrobot 2.

2

r1

ψ1
φ1
φ2

ψ2 r2
2

(4) Robot 0 moves andmeasures robots 1 and 2.

Figure 1: Example of CPS

cleans the inside of train stations or underground markets, and for exploration robots such as a planetaryrover [6].
Two prototype models have been introduced named
CPS-I that is equipped with laser and photo detector,
and CPS-II that equipped with laser range nder andcorner cubes respectively. Through measurement experiments by using these models the viability of CPS
have been considered [7].
Since CPS determines position by successive measurements of relative distances and angles from stationary robots, positioning errors are accumulativeand position accuracy decreases. The degree of theseaccumulated errors is in uenced not only by the accuracy of the sensors but also by the moving strategies
and movement histories of the multiple robots. With
these considerations, discussions have been made of
the possibility to estimate positioning accuracy of CPS
for various moving strategies by assuming the measurement errors have Gaussian distributions and evaluating accumulated errors as a propagation of error
variance matrixes [6].
In this paper, discussion will be made on the basic
properties of accumulated errors for the latest model of
CPS named CPS-III, and the optimum moving strategies to minimize the accumulated errors over long distances will be proposed. In Section 2, the basic equations will be introduced for the propagation of accumulated errors by utilizing weighted least square
method. By using these equations it is possible torealize the information fusion of various sensor data
and to estimate positioning accuracy more eÆciently
than the previously proposed method [6]. In Section 3,
the CPS third model, CPS-III will be introduced. In
Section 4, moving strategies to minimize the accumulation of positioning error for CPS-III is discussed, andthree moving strategies to optimize positioning accuracy are proposed. In Section 5, experimental results
are shown.

2 The basic equations for the propagation of accumulated errors
This section introduces the error analytical technique utilizing weighted least square method. Thismethod enables the information fusion of various sensor data and allows the accumulated error calculation
to be treated in a systematic way.
2.1

Estimation of positioning accuracy byweighted least square method

As shown in Fig. 1(4), there are three robots
and if the positions of two robots are already known
and if the third robot is able to measure its distance, azimuth and elevation angles relative to theother two then the third robot's position can be determined as follows. We de ne the positions of robots
0, 1, and 2 as P0(x0; y0 ; z0; 0 ), P1 (x1; y1 ; z1; 1 ), andP2(x2; y2; z2; 2) and relative distances , azimuth andelevation angles from robot 0 to robots 1 and 2 as
r1; r2; 1; 2; 1, and 2 . Equations that are established (observation equations) are(x0xi )2 + (y0yi )2 = ri2 cos2 iz0 = zi
0 =ri sin iyi y0
i + tan 1
xi x0

(1)
(2)
(3)

for i = 1 and 2. If the absolute position of robot i is
P~ i(~xi; y~i; z~i; ~i) but is measured as Pi = (~xi + dxi; y~i +dyi ; z~i + dzi ; ~i + di ) then from the Taylor expansionof above equations
ai dx + bi dy = (ri cos idi )+ai dxi + bidyi + cos i dri ri sin i d i (4)dz = z~i ri sin i z~0 +dzi sin i dr ri cos i d i (5)biaiy~i y~0dx + dy d0 = (~i + ~0 tan 1)
didix~i x~0biai
dxi + dyi + di
di
di

(6)

can be obtained by assuming the errors are small andthe second andphigher order terms may be disregarded,
where di = (x~i x~0 )2 + (y~i y~0 )2 , ai = x~idix~0
and bi = y~idiy~0 .
Next, we de ne

0 a
1
B
a2
B
B 0
A=B
B
0
B
@ db11

0
0

a1
d1
a2
d2

b2
d2

1

0
0
1
1
0
0

b1
b2

0
0 C
C
0 C
C
0 C
C
1 A
1

(7)

0 (r cos  d ) 1
1
1
1
C
B
(
r2 cos 2 d2)CBCB
z~1 r1 sin 1 z~0
B
L = B z~2 r2 sin 2 z~0 C
CBA@ 1 + ~0 tan 1 xy~~11 xy~~00 C(8)

2 + ~0

tan 1 xy~~22 yx~~00
and substitute dxi; dyi and dzi as 0 by assuming previous measurements are correct, then Eqs.(4), (5), (6)are
AX = L(9)
T
where X = (dx0; dy0; dz0; d0) . Resulting in the error equation
V = L AX(10)
Furthermore the error variance of the observed
value L can be derived from the averages of the squareof Eqs.(4), (5), and (6) asL = K1KT1 + K2pKT2
where K1 and K2 are
0 a
1
B
0
B
B 0
K1 = BB
0
B@ db11
0

b1

0
0
0

a1
d1

0

0
0
1
0
0
0

0
0
0
0
0
0

0
cos 1 0B
cos 2 0B
B
sin 1 0K2 = BB
sin 2 0
B
@ 0
1

0

0

(11)

a2

b2

b2
d2

a2
d2

0
0
0
1
0
0

r1 sinr2 sinr1 cosr2 cos

1
2
1
2

0
0
0

0
0
0

1

0
0 C
C
0 C
C (12)
0 C
C
0 A
0

1
C
C
C
C
C
C
A

(13)

0
0
1
0
And  is the error variance matrix for the positionsof robot 1 and 2 and p is the error variance matrix forthe measurement of distances, azimuth and elevation
angles.
 = 1121 1222(14)

p = diag(r2; 2 ; 2 )(15)

From Eqs.(10) and (11) the change in position ofrobot 0 (X) that minimizes the sum of the squared
remain error under the weight of L 1 can be derived
by solving the following equation
min VT L 1 V(16)

be accurately re ect. Each robot has a built-in microcomputer (8086-8MHz, Japan System Design Co.,
Ltd.), driving circuit, battery (Yuni-Z, YUASA BATTERY Co., Ltd.), and communication system (HRF600 (RS-232C), HERUTU Co,. Ltd.), and is controlled centrally from the host computer (Pentium Pro
200).

as

X = (AT L 1A) 1AT L 1L= BL

Table 1: Speci cations of a range nder.
(17)

Finally, following the next steps to calculate theoptimum position of robot 0, i) assume arbitrary
position of robot 0 as P~0. ii) calculate X =(dx0; dy0; dz0; d0)T form Eq.(17). iii) repeat P~0
P~0 + X until X ! 0. And thus the error variance ofthe position of robot 0 can be calculated form Eq.(17)as00 = BLBT = (AT L 1A) 1(18)

AP-L1 (TOPCON Ltd.)Range
4  400 [m]Resolution (distance)
0.2 [mm]
Resolution (angle)
5 ["]3+2ppm [mm]Precision (distance)
Precision (angle)
5 ["]

Child robot 2

and the covariance matrixes between robots 0 and 1,
and robots 0 and 2 are(01; 02) = BK

(19)

By repeating the above steps, the positioning accuracy of the robot after performing several measurements successively can be estimated by calculating theerror variance matrix and covariance matrixes from
Eqs.(18) and (19).

Parent robot
Child robot 1

Figure 2: Total view of the mechanical model CPS-III.

3 CPS-III
This section introduces the latest prototype modelof CPS (CPS-III shown in Fig. 2). CPS-III consistsof one parent robot that is equipped with a high accuracy laser range nder and two child robots thatare equipped corner cubes. The basic method of position identi cation is identical to that of the method
presented in Fig. 1.
The master robot is equipped with a laser rangender supplied by TOPCON Ltd. (Table 1) that has
the ability to automatically search and trace a cornercube in any arbitrary position and a 2-axis inclinometer. By detecting the laser re ected from the childrobots, the master robot then automatically and accurately measures the distances and the azimuth angles from the child robots. On top of each child robot
is six corner cubes arranged at intervals of 60 degrees
around the vertical axis and with this mechanism alaser beam that is projected from any direction can

4 Optimum moving con gurations of
CPS-III
This section discusses the relationship between themoving con guration of CPS-III and its positioning accuracy by computer simulation and analyticalmethod, and proposes three moving strategies to optimize positioning accuracy.
First assume the following conditions.
1. CPS consists of one parent robot equipped withlaser range nders and two child robots equippedwith corner cubes.
2. Each robot has accurate sensors to measure its
orientation around roll and pitch axis to gravity.
3. Robots move in a 2-D plane.

4. Angle and distance errors have Gaussian distributions and therefore have mean averages of zero.

yTarget positions

5. The error variances of distance and angle measurements are constant with any measured distances and angles.
Assumption 5 is a inherent characteristic of the distance measurement sensor that utilizes a laser or electromagnetic waves. For this sensor, measurement error is not in uenced by the measured distance when
the distance between measurement points is close andthe refractive index is not a ected by temperatureand humidity di erences in the air. The validity ofassumptions 4 and 5 have already been con rmed by
iteration of error measurement experiments with CPSIII.
In addition, several other conditions need to be assumed for the computer simulations.

10m

3. The positioning accuracy at the target positionis given as a trace of parent robot error variancematrix. Error variance matrix and error covariance matrixes are calculated by Eqs.(18) and (19)at each step.
4. As shown in Fig. 3, robots move along the yaxis and the distances between parent and childrobots are r1; r2 and the azimuth angles to thechild robots from the parent robot are 1; 2.

4.1

Simulation analysis

First, consider the case that the robots repeat only
one type of movement by using a set of parameters r1 ,r2, 1, and 2 to reach the target points. The moving strategy that minimizes positioning error when the
robot arrives at the target position is then calculated
by using Newton method. Where 32,400 initial conditions are generated by dividing the distance between
robots r1 and r2 from 0 m to 1000 m into 10 parts,
and angle 1 and 2 from 0 [deg.] to 360 [deg.] into
18 parts. From the results of these simulations, three
local minimums were discovered that corresponded tothe optimum moving strategies as shown in (Table
2).

1
φ2

Child robot 2

3
r1

r2

φ 1 Child robot 1xParent robot

Figure 3: Simulation model.

1. The standard deviation of the distance measurement sensors is 3 [mm] and the angle measurement sensor is 5 [sec].
2. Each robot moves along a straight line towards
each target point that is placed 1 [km] ahead andthe movement distance of each step is 10 [m]. Resulting in a total of 100 movements.

1km

2Table 2: Optimum robots con gurations.
ABC

r1 [m]

80.3
528.2
72.7

r2[m]

80.3
518.0
106.2

1[deg:]

3.0
53.1
89.6

2[deg:]

176.1
126.3
-90.5

x2 + y2

0.02030.02180.0207For two local minimums A and B, both cases indicate the child robots are symmetrical towards thetarget direction. Local minimum for A shows all therobots are on a line perpendicular to the target direction while for B the azimuth angles to the child robots
from the parent robot are 45  55[deg:]. From here
onward each is de ned as optimum moving strategies
A and B respectively as shown in Fig. 4. In addition,
local minimum C is a moving strategy in which all
the robots are along a line toward the target direction
and from here onward is de ned as optimum moving
strategy C as shown in Fig. 4.
Next, consider the case that the robots repeat two
moving strategies alternatively. In the same manneras the rst case, the consecutive moving strategies
that minimize positioning error at target position is
calculated by using Newton method from various initial conditions. From these simulations, the moving
strategies that minimize the positioning error at target positions are given as a combination of three optimum moving strategies A, B, and C found in the rst
case which consequently increases the likelihood that
A, B, and C are part of the optimum moving strategy.

45˜ 55[deg.]
Optimum moving configuration A

Optimum moving configuration B

From the analytical examination of these equations,the optimum conditions for each optimum moving
strategy in order to minimize error variance of parent robot at target position, x2 + y2 , is derived asshown in Table 3.
Table 3: Optimum con gurations of moving strategies
A, B, and C.
A
B

Optimum moving configuration C

Figure 4: Optimum moving con gurations.
C
4.2

Derivation of analytical error equation for each optimum moving strategy

As previously explained in Section 2, positioning
accuracy after robot movements of a certain distancecan be written as a recursive equation of the error
variance matrix and error covariance matrixes from
Eqs.(18) and (19). And in order to derive the answers
for these recursive equations is very diÆcult because of
the complexity of the equations. But since the robots
orientation of the optimum moving strategies are symmetrical, it is possible to simplify each term of observation equations Eq.(9) so the accumulated errors of
the solutions of each strategy can be easily analyzed.
This section discusses these characteristics of positioning errors for the optimum moving strategies A, B, and
C and considers the mechanisms that the errors occur.
4.3

Analytical solution for each optimum
moving strategy

The analytical solution of positioning accuracy for
optimum moving strategies A and B are shown in Appendix A. This solution shows the error variance matrix after the parent robot moves n times where theposition of the parent robot is (x; y), the positions of
the child robots are (x + d; y + h) and (x d; y + h),
and the distance that each robot travels in y-directionis l.
Likewise, the analytical solution of positioning accuracy for optimum moving strategy C is shown inAppendix B where the child robots are along the line
towards the target direction with a distance of r1 andr2, and the distance that each robot travels in the ydirection is l.

r[m]

x2

y2

70.6 0.0202 0.0003
434.2 0.0201 0.0016

r1[m]

63.2

r2 [m]

90.7

x2

y2

x2 +y2

0.02050.02170.0198 0.0009

x2 +y2

0.0207

Also, the following characteristics are revealed fromthe analytical solutions of each optimum moving conguration.
1. In optimum moving con gurations A and C, themeasured distance and angle are used for positioning, independently. On the other hand, in
optimum moving con guration B, measured distance and angle for the positioning are coupled.
Thus, optimum moving con guration B is moreadvantageous in the case that the distance between robots is large because the angle measurement error, which increases with the distance between robots, is limited. By using analytical solutions, variation of positioning error of optimum
moving strategies as a function of the distance
between robots are shown in Fig. 5.
2. Optimum moving strategies are given as shown in
Table 3 in any distance and angle measurement
errors.

5 Experiments
Experiments to verify the validity of proposed optimum moving strategies were performed using CPS-III
in a at outdoor environment. CPS-III moved by optimum moving strategies A and C, and unoptimum
moving strategy D ((1 = 80[deg:]; 2 = 110[deg:]) for
a comparison as shown in Fig. 6. Positioning accuracy after the robots moved forward and backward 5
times was measured by the observation of xed-points.
Experiments for each moving strategy were performed 10 times and the average positioning error

6 Conclusion

0.05
B

Error variance [mm 2]

0.04

0.03

0.02
C

A

0.01

00

50
100
150 200 250 300
Distance between parent-child robots [m]Figure 5: Variation of positioning error of optimum
moving strategies A,B, and C.

This paper discusses the basic property of accumulated errors for the latest CPS model (CPS-III) using
computer simulation and analytical methods. Three
optimum moving strategies are then proposed for a criterion of positioning accuracy and are veri ed throughexperiments with CPS-III.
To apply CPS in actual work environments, choiceof the moving strategies will became an important
problem. This paper presents basic characteristics ofthis problem. For example, the analysis of three optimum moving strategies of CPS that may be used indi erent environments. Optimum moving strategy B
is suitable for large open area because long distancemeasurement is possible without lossing accuracy. On
the other hand, optimum moving strategies A and C
can be better adapted in environments with obstacles
where the robot's eld of view is hindered.
Future work will focus on CPS for speci c applications, such as a planet exploration robot system or
janitorial robots, and the optimizing number of robots
and control methodology for positioning accuracy andadaptability in any environment.

Figure 6: Moving strategy D for experiments.

A Analytical error solution for optimum moving strategies A and B

is compared with the corresponding analytical value(evaluated in A and B) using distance measurement
error is 3 [mm] and angle measurement error is 5 [sec.](shown in Table 4).

This section shows the derivation of the analyticalerror solution after each robot movement for optimum
moving strategies A and B.
First, de ne the position of parent robot as (x; y),
the positions of child robots as (x + d; y + h) and (xd; y + h), and the distance that each robot travels in
the y-direction as l. Each term of the parent robot
error variance matrix after the robot moves n steps
can be derived by Eq.(18) as follows.

Table 4: Positioning accuracy for optimum moving
strategies. Theoretical values are shown in ().

q

A
C
D

x2 + y2 [mm]100.3 (22.9)
38.2 (9.8)
175.1 (100.6)

0 2 
xy;nx;n2
n = @ xy;n y;n [deg.]

0.387 (0.054)
0.085 (0.005)
1.162 (0.260)

Examining the results of these experiments, the positioning accuracy of optimum moving strategy C is as
expected the most accurate with an error of only 28.8[mm] (0.07% of travel distance) after 42 [m] of movement by the parent robot. In addition, the positioning
accuracies of both optimum moving strategies A and C
are higher than that of the unoptimum moving strategy D, which proves the e ectiveness of the proposed
optimum moving strategies.

x;n

y;n

x;n
y;n
2
;n

1
A

(20)

If we assume the initial positioning error equals 0,
then each term of the parent robot error variance matrix after 1 robot movement step is
2 =
x;
1
2 =
y;
1

l2 d2(r2

2d2fL21 (r2

2L21 L22 d2l2 2 l2 2
r + 
2d2L2222 )(2
L21
r

(21)

L22 2 ) + Kr2 2
2)
L21 

g + K2

h2 L22 + (h + l)2 L21 2
22
;r + 
1=
2d2L21 L22(23)

L222 ) + L22 (r2(22)x;1 =where,L21

2hL22 + ld2 2
r
2d2L22

l 2


(24)

2

= d2 + h2= d2 + (h + l)2= 2(L21 + L22 )L21 L22

L22
K

(25)
(26)
(27)

And each term of the parent robot error variance matrix after n robot movement steps is
2

x;n

2

=

2

2 2

n(2n

1)(n
6

x;1 + x;n 1 + l ;n 12=

nx;1 +n(n1)lx;1

;1

(28)

2

2

2
y;n

=

2
2
2
y;
1 + y;n 1 = nr

(38)

2
;n

=

2 + 22
;1
;n 1 = n;1

(39)

=

x;1 + x;n 1=nx;1

x;n

n(n

2
y;n = xy;n = 0

2
l;n
1

1)l 2

;1

(40)

y;n

=

y;1 + y;n 1 = ny;1

(29)

2
;n

=

2
2
2
;
1 + ;n 1 = n;1(30)References(31)[1] Y. Fuke and E. Krotkov: Dead Reckoning for a
Lunar Rover on Uneven Terrain, Proc. of IEEE
Int. Conf. on Robotics and Automation, , ,pp.411-416, 1996=

x;1 + x;n 1

2
l;n
1

=

x;1

;1

n(n

2

1)l 2

y;n = xy;n = 0(32)

B Analytical error solution for optimum moving strategy C
This section shows the derivation of the analyticalerror solution after each robot movement for optimum
moving strategy C.
First, de ne the position of the parent robot as(x; y) and the child robots are along on the line towards the target direction with a distance of r1 andr2, and the distance that each robot travels in the ydirection as l. Each term of the parent robot error
variance matrix after n robot movement steps can bederived by Eq.(18) as follows. If we assume the initial positioning error equals 0, then each term of theparent robot error variance matrix after 1 robot movement step is
2 =
x;
1

r22 )

2

x;n

2

2lx;n 11)l2 2l2 (r122r1r2(r1 r2 ) 4lr1 r2 2
 (36)(r1 + r2)2
And each term of the parent robot error variance matrix after the n robot movement steps is2
2 + 2
2 2
x;n
= x;
2lx;n 11x;n 1 + l ;n 1
21)l 2
2 + n(2n 1)(n= nx;
;11
6n(n 1)lx;1(37)
x;1 =

l2 (r12 + r22)

2lr1 r2(r1(r1 + r2)22 = 2
y;
1
r

2
;
1=

r2 ) + 4r12 r22 2


2fl2 + l(r1 r2) + r12 + r22 g 2(r1 + r2 )2

(33)
(34)
(35)

(41)

[2] J. Borenstein and L. Feng: Gyrodometry: A
New Method for Combining Data from Gyros andOdometry in Mobile Robots, Proc. of IEEE Int.
Conf. on Robotics and Automation, , , pp.423428, 1996
[3] K. Sugihara: Some Location Problems for robot
navigation Using a Single Camera, "Computer
Vision, Graphics, and Image Processing", 42, 1,
pp.112-129, 1988
[4] E. Krotkov: Mobile Robot Localization Using
A Single Image, Proc. of IEEE Int. Conf. on
Robotics and Automation, , , pp.978-983, 1989
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