Study on Cooperative Positioning System(Basic Principle and Measurement Experiment)
Ryo Kurazume and Shigeo Hirose

Shigemi Nagata and Naoki Sashida

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

FUJITSU LABORATORIES LTD.
1015, Kamikodanaka Nakahara-ku,
Kawasaki 211, Japan

Abstract
Several position identification methods have been used
for mobile robots. Dead reckoning is a popular method,
but is not reliable for long distances or uneven surfaces
because of variations in wheel diameter and slippage. The
landmark method, which estimates current position relative to landmarks, cannot be used in an uncharted environment. We have proposed a new method called ”Cooperative Positioning System (CPS).” For CPS, we divide
the robots into two groups, A and B. One group, A, remains stationary and acts as a landmark while group B
moves. Group B then stops and acts as a landmark forgroup A. This ”dance” is repeated until the target position
is reached. By using the concept of ”portable landmarks”,
CPS has a far lower accumulation of positioning error
than dead reckoning, and can work in three-dimensions
which is not possible with dead reckoning. CPS, therefore, can work in uncharted environments. In this paper,
we outline a second prototype CPS machine model (CPSII) and report the results of position identification experiments. Experimental results using this model give a positioning accuracy of 0.4% for position and 1.0 degree for
attitude.

1

Introduction

Control of mobile robots traveling in an uncharted environment necessarily requires a method of identifying thepositions of the robots. A number of position identification techniques for mobile robots have been proposed. The
methods can be roughly classified into two types: deadreckoning and landmark. The dead reckoning method [14] identifies robot positions by calculating the amount oftravel from the starting point. It does this by integrating rotations of the right and left wheels, such as on wheel-driven
vehicles. This method is simple and is easily implemented.
It can also identify robot positions in an uncharted environment because it only employs internal sensors.
The dead reckoning method, however, has a serious
problem. Wheel slippage causes measurement errors,
which accumulate as the vehicles travel. Dead reckoning

does not work in three-dimensions involving differences of
elevation.
The landmark method [5-7] identifies the position of amobile robot by measuring the current position relative tolandmarks at identified positions. There are many typesof landmark methods depending on the type of landmark
and how it is placed. The use of the shape of the horizon
line [8-9] and stationary satellites (GPS) are classified under the landmark method. This method features high measurement accuracy with no accumulation of measurement
error. It also provides three-dimensional information including elevation. However, it has a great drawback in thatthe environment around the mobile robot must be known
and the specified landmarks must be placed in the environment in advance.
As a solution to the problems presented by both methods, we have proposed a new method called ”Cooperative Positioning System (CPS)[10].” This method covers
the weaknesses of the previous two methods and enables
position identification even in uncharted environments anduneven surfaces. CPS uses multiple robots each equippedwith sensors to measure their positions relative to one another. The entire group of robots moves while at least one
robot remains stationary, acting as a landmark for the others. This operation is repeated while relative positions aremeasured until the target robot position is reached.
In this paper, we first discuss the basic principles of the
proposed CPS. We then outline a new second prototype
CPS machine model (CPS-II) and report the results of position identification experiments using the model. CPS-II
consists of a master robot equipped with a high-precisionlaser range finder and two slave robots equipped with corner cubes.

2

Cooperative Positioning System (CPS)

2.1 Standard CPS Configuration
The proposed cooperative positioning system (CPS)with multiple robots may be referred to as a mobile landmark method. In this section, we define the basic principlesof CPS clearly and show examples of standard CPS con-

figuration. Robots were divided into two groups, groups A
and B.
1. While robot group A with its initial position identified remains stationary, robot group B travels a certain
distance. The position of traveling group B is roughly
determined by measuring its position relative to group
A and using internal sensors as well.

P2

zZ

y

r φ

2. After group B travels an arbitrary distance, its positionis accurately measured in reference to the position ofgroup A.

P1

θ

3. Group B then remains stationary while group A travels an arbitrary distance.
4. Steps 1 to 3 are repeated until the position of the target
robot group is reached.
Figure 1 and 2 show how positioning is actually performed with CPS. Figure 1 shows an example using two
robots. When position P 1 x1 ; y1; z1 of stationary robot 1
is known, CPS is implemented as follows: First, the threedimensional position P 2 x2; y2 ; z2 of robot 2 that moved
and stopped is determined, as indicated by the solid line.
This is done by measuring distance r between the robots,
azimuth angle  of a turn against the vertical axis in the
direction of gravity, and elevation angle  from the levelsurface and assigning these measurements in the following
equations:

(

(

)

= x1 + r cos  cos 
y2 = y1 + r cos  sin 
z2 = z1 + r sin 

(1)
(2)
(3)

Next, robot 1 moves as indicated by the dotted line. The
position where robot 1 stops is determined in reference tothe position of robot 2. These operations are repeated.
Figure 2 shows an example using three robots. When
positions P 1 x1; y1 ; z1 of robot 1 and P 2 x2; y2 ; z2 ofrobot 2 are known, CPS is implemented as follows: First,
position P 3 x3 ; y3; z3 of robot 3 that moved and stopped
is determined, as indicated by the solid line. This is doneby measuring azimuth angles 1 and 2 and elevation angles 1 and 2 of robot 3 as seen from robots 1 and 2 andassigning these measurements in the following equations:

(

)

)

x3

= x1t1

y3

=
z3

(x2

(

)

x2 t2
t1

+ (y2

y1 t1 t2

t2

)

+

y2 t2

x1 t1 t2 y1 t1
t1 t2

)

(4)

(5)

= z1 + c1(t1t2 t2) l tan 1= z2 + c (t t1 t ) l tan 2
2 1

Figure 1: Type 1 positioning principle

)

x2

(

x

2

(6)

where
tn

= tan n;
l

=

p(x

cn

2

= cos n (n = 1; 2)(7)) + (y2

(8)

x1 2

)

y1 2

Next, robot 1, for instance, moves as indicated by thedotted-line arrow. The position where robot 1 stops is determined in reference to the positions of robot 2 and 3.
These operations are repeated.
CPS is not limited to these examples; many other configurations are possible. For instance, the position of one
robot relative to two stationary robots in Figure 2 may be
determined differently. That is, instead of being identified
by a combination of azimuth angle  and elevation angle
, the determination may be based on a combination of
distance r between robots and elevation angle . Another
CPS, unlike the one that classifies robots into two groups,
may cyclically select stationary robots from a group ofrobots to allow the entire group to move continuously. Another CPS may determine more accurate positions basedon redundant measurements from a number of stationary
robots.
In [10], we have already discussed its positioning accuracy using the error variances, and the suitable moving
strategies with several triangle chains.
2.2 CPS Characteristics
CPS position identification has the following characteristics:
1. CPS determines position by repeated measurement
and therefore accumulates positioning errors as withthe dead reckoning method. However, CPS has far
fewer positioning errors because it can accurately determine position and attitude by measuring stationary

y

P3

zZ

φ1
P1

φ

θ1 θ

2

2

P2

x
Figure 2: Type 2 positioning principle

markets. This cleaning robot could clean a wide area basedon a map. Dead reckoning based on wheel rotation has
some problems for this application. One of these problems is errors in movement measurement caused by slippery floors. Another problem is the substantial azimuth
measurement errors likely to occur when the cleaning robot
runs against a wall or pillar. In addition, a cleaning robot
would probably need to go up and down stairs and clean
floors that have uneven surfaces. As stated in item 3 above,
dead reckoning, which cannot work for three-dimensional
measurement, is inappropriate for this application. The
landmark method is not effective, either, because landmarks will not necessarily be placed in advance in manyenvironments. GPS, which is remarkably effective outdoors, cannot be used for cleaning indoors.
CPS is an effective method for cleaning indoors thathave uneven surfaces and many obstacles. Furthermore,in this application, it is effective to use multiple cleaning
robots and all that is required is to equip each robot with ameasuring device as shown in Figure 3.

points in the same way as the surveying. CPS provides a good basis for extraordinarily higher positioning accuracy than does the dead reckoning method
based on wheel rotation.
2. Unlike the landmark method, CPS does not requireprior placing of landmarks. It allows movement in
an uncharted environment or even underground where
Global Positioning System (GPS) cannot be used.
3. By measuring elevation angles, CPS can determine
three-dimensional positions, which is not possible
with dead reckoning.
In contrast, CPS has the following problems:
1. At least two robots are required.
2. At any one time, at least one robot must be stationary,
which slows down overall speed.
3. An accurate measuring device (including a device thatmeasures a robot’s attitude relative to gravity) must be
built into each robot.
Items 1 and 2 are not problems if an application essentially uses multiple robots and does not require high-speed
movement. Item 3 depends on technological innovation in
the field of measuring instruments, which has been rapidly
progressing. The authors believe this problem will soon
be solved. The performance of the prototype measuring
instrument we assembled will be discussed later.
2.3 Fields of CPS Applications
We believe that CPS that has the foregoing characteristics can be used effectively if proper applications are selected. Two possible applications are discussed below.
One application is the automatic control system of arobot that cleans the inside of train stations or undergroundFigure 3: CPS application for cleaning robots
The point to be specifically noted for CPS is that any
disturbance of the cleaning robots while working, such asa collision with a obstacle, has no effect on positioning accuracy.
A system configuration consisting of cleaning robots
and a dedicated measurement robot is also a possibility.
Each cleaning robot is equipped with only a marker lightsource. The dedicated measurement robot is equipped withsensors that measure the distance to and the angle of themarker light source in each cleaning robot. This configuration provides an inexpensive implementation of CPS.
Another possible application is the use of robots to explore unknown environments, such as planets. For this typeof investigation, use of many small robots is most effective to take advantage of the high reliability of a redundant
system. Some researchers have previously advocated theeffectiveness of this multiple robots approach. The authors
also have proposed a new concept of multiple planetaryrovers “Gunryu” and developed a prototype [11] as shownin Figure 4. The “Gunryu” consists of multiple mobile
robot with manipulators. These robots usually operate individually. As they move over an uneven surface, they areconnected to one another using the manipulators. Suppose
the multiple robots such as the “Gunryu” move aroundover an uncharted planet to perform a geological survey
or make a detail topographical map. For position identification, both the dead reckoning and landmark methods
are inappropriate from the standpoint of required precisionand environmental conditions. In contrast, CPS has almost
no problems with this application and is essentially effective. Furthermore, each robot of the “Gunryu” must comeclose to one another for connection or break away from one
another for separation. Therefore, it is assumed that eachrobot is equipped with a relative position measuring sensor. CPS can thus be used for the “Gunryu” as is without
adding new measuring devices.

2. To calculate the position of robot 1, robot 0 measuresthe distance l1 , azimuth angle 1 , and elevation angle
1 relative to robot 1.
3. Similarly, to calculate the position of robot 2, robot 0
measures the distance l2 , azimuth angle 2 , and elevation angle  2 relative to robot 2.
4. Robot 0 moves and then stands still.
5. To calculate the position and attitude of robot 0, robot
0 measures the distances l1 and l2 , azimuth angles
1 and 2 , and elevation angles 1 and 2 relative torobots 1 and 2.
6. Return to 1.

Figure 4: Cooperative multiple robots “Gunryu” in planet
exploration

3

Move and Measurement ExperimentThis section outlines a new prototype CPS machinemodel (CPS-II), and reports the results of position identification experiments using the model. CPS-II consists ofa master robot equipped with a high-precision laser range
finder and slave robots each equipped with corner cubes.
This prototype system is capable to :

 Search for other robots.
 Measure the distance to and azimuth angle of otherrobots.

 Automatically move each robot based on the measurement results.

3.1 Principles of Measurement in CPS-IICPS-II consists of one master robot, 0, equipped witha laser range finder and two slave robots, 1 and 2, eachequipped with corner cubes. The master and slave robots
move while alternately performing position identificationaccording to the following procedure: First, the initial position and attitude of robot 0 are measured, then
1. Robots 1 and 2 move and then stand still.

The above operation cycle is repeated until the entire
robot group reaches the target position.
3.2 Outline of CPS-II
Figure 6 shows our experimental system. The masterrobot is equipped with a laser range finder of TOPCON
Ltd. (Table 1) that is capable to search and trace a cornercube in arbitrary position automatically and a 2-axis inclinometer. By detecting laser reflected from the slave robots,
the master robot automatically and accurately measures the
distances from the slave robots and the azimuth angles. On
top of each slave robot are six corner cubes arranged at intervals of 60 degrees around the vertical axis. This mechanism can accurately reflect a laser beam that project form
any direction. Each robot has a built-in microcomputer (8086-8MHz, Japan System Design Co., Ltd. ), driving circuit, battery ( Yuni-Z, YUASA BATTERY Co., Ltd. ) , andcommunication system ( HRF-600 (RS-232C), HERUTU
Co,. Ltd. ), and is controlled centrally from the host computer ( S-4/Liea, Fujitsu Ltd. ).

Table 1: Range finder specifications
AP-L1 (TOPCON Ltd.)Range
4  400 [m]Distance resolution
0.2 [mm]Angle resolution
5 [”]Distance precision
3+2ppm [mm]Angle precision
5 [”]

3.3 Move and Measurement Experiment
An experiment for measuring positioning accuracy was
performed using our prototype mobile robot system (CPSII) in an indoor environment. In this experiment, threerobots traveled on an even surface along the wall in a roommeasuring 6 m x 12 m. The robots traveled around theroom clockwise while repeatedly determining their position using CPS. When they returned to almost same area

1
1

0

0

l1

θ1
φ1
2

2

(1) Robot 1 and 2 move.

Parent robot(2) Robot 0 measuresrobot 1.

Child robot 1
1

0

0

θ2

φ2

l1

φ1
θ1
θ2

Figure 6: Appearance of the robot system

φ2l2(3) Robot 0 measuresrobot 2.

Child robot 2

1

2

l2

2

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

Figure 5: Experimental CPS system

This experiment was performed on a even surface withno roughness. The positioning accuracy of CPS, however,is not affected by an environment where CPS is used. It
is expected that the positioning accuracy obtained by thisexperiment could also be obtained easily in an uneven outdoor terrain, and obtained accuracy of CPS can be far better
than that of dead reckoning.

1mof the initial positions, the position of the master robot wascompared with it’s initial position determined by fixedpoint measurement.
Figure 7 shows how the robots moved in this experiment. In this figure, the master robots are each represented
by a square and the slave robot is represented by a circle.
The three robots started from their original positions (indicated by an up-side-down triangle at the lower left) along
the y axis. They repeated the operation cycle shown in
Figure 5 ten times to return to their initial positions. The
route traveled by the master robot is indicated with a solidline in the figure. Table 2 lists the average positioning errors of position and attitude of the master robot. The total
travel distance of the master robot was 21.6 m. The average positioning error was 82.3 mm (0.38% of the total
travel distance); the average attitude error was 1.0 degree.
For comparison, a robot with an encoder of 47,520
pulses per rotation attached to its driving wheel was simply moved in a straight-line with the distance of 5 m andmeasured positioning accuracy of dead reckoning. The positioning accuracy was 1.4% of the total travel distance.
Next, the robot traveled in the same environment of Figure 7 with dead reckoning only. The route traveled by the
robot is indicated with a dotted line in Figure 7. Whena change of direction was involved, azimuth errors greatly
affected the positioning accuracy, pushing the error rate up
to as much as 10%. This proves that CPS can determine
position with a much higher precision than dead reckoning
can.

CPS

Dead Reckoning

Final position

Initial positionyx

Figure 7: Experimental results

4

Conclusion

We have proposed the cooperative positioning system(CPS) that can accurately determine the positions of multiple robots through cooperative control of individual robots

Table 2: Position and attitude accuracy of CPS-II after
robot 0 moves a distance of 21.6 m

x y z

79.5

17.8

11.5

Average
82.3



1.0

[9] K. T. Sutherland and W. B. Thompson, Localizing in
Unstructured Environments: Dealing with the Errors,
IEEE Trans. on Robotics and Automation, Vol. 10,
No. 6, pp.740-754, 1994.
[10] R. Kurazume, S. Nagata, and S. Hirose, Cooperative Positioning with Multiple Robots, Proc. IEEE
Int. Conf. on Robotics and Automation, Vol. 2, pp.
1250-1257, 1994.
[11] S. Hirose, N. Ootsukasa, T. Shirai, H. Kuwahara, andK. Yoneda, Fundamental Considerations for the Design of a Planetary Rover, Proc. IEEE Int. Conf. on
Robotics and Automation, pp. 1939-1944, 1995.

in the group. We then discussed that CPS enables highly
accurate positioning of mobile robots in an uncharted or
uneven environment, which was difficult previously, andthat CPS can be used in several fields. Next, we reported the results of an experiment using a prototype system equipped with a laser range finder. This experimentshow that CPS could perform far more accurate measurements than the dead reckoning method even in uneven environments.

References[1] R. Chatila and J. laumond, Position Referencing andConsistent World Modeling for Mobile Robots, Proc.
of IEEE Int. Conf on Robotics and Automation,
pp.138-145, 1985
[2] J. L. Crowley, Dynamic World Modeling for anIntelligent Mobile Robot Using a Rotating UltraSonic Ranging Device, Proc. of IEEE Int. Conf. on
Robotics and Automation, pp.128-135, 1985
[3] Y. Watanabe and S. Yuta, Estimation of Position andits Uncertainty in the Dead Reckoning System of the
Wheeled Mobile Robot, Proc. of 20th ISIR, pp.205212, 1990.
[4] T. Tsubouchi and S. Yuta, Map Assisted Vision System of Mobile Robots for Reckoning in a Building
Environment, Proc. of IEEE Int. Conf. on Robotics
and Automation, pp.1978-1984, 1987
[5] L. Matthies and S. A. Shafer, Error Modeling in
Stereo Navigation, IEEE J. of Robotics and Automation, Vol. RA-3, No. 3, pp.239-248, 1987.
[6] H. Nasr and B. Bhanu, Landmark Recognition forAutonomous Mobile Robots, Proc. of IEEE Int. Conf.
on Robotics and Automation, pp.1218-1223, 1988
[7] E. Krotkov, Mobile Robot Localization Using A Single Image, Proc. of IEEE Int. Conf. on Robotics andAutomation, pp.978-983, 1989
[8] R. Talluri and J. K. Aggarwal, Position Estimation for
an Autonomous Mobile Robot in an Outdoor Environment, IEEE Trans. on Robotics and Automation,
Vol. 8, No. 5, pp.573-584, 1992.