PRECISE DEAD-RECKONING FOR MOBILE ROBOTS USING

MULTIPLE OPTICAL MOUSE SENSORS

Daisuke SEKIMORI

Akashi National College of Technology

Akashi, Hyogo 674-8501, Japan

Fumio MIYAZAKI

Graduate School of Engineering Science, Osaka University

Toyonaka, Osaka 560-8531, Japan

Keywords:

dead-reckoning, mobile robot, optical mouse sensor.

Abstract:

In this paper, in order to develop an accurate localization for mobile robots, we propose a dead-reckoning

system based on increments of the robot movements read directly from the ﬂoor using optical mouse sensors.

The movements of two axes are measurable with an optical mouse sensor. Therefore, in order to calculate a

robot’s deviation of position and orientation, it is necessary to attach two optical mouse sensors in the robot.

However, it is also assumed that a sensor cannot read the movements correctly due to the condition of the

ﬂoor, the shaking of the robot, etc. To solve this problem, we arrange multiple optical mouse sensors around

the robot and compare sensor values. By selecting reliable sensor values, accurate dead-reckoning is realized.

Finally, we verify the effectiveness of this algorithm through several experiments with an actual robot.

1 INTRODUCTION

For a mobile robot to move around autonomously, it

is necessary for it to possess the ability to estimate

its position and orientation. The localization of mo-

bile robots is roughly divided into those using internal

sensors and those using external sensors. The method

using internal sensors is known as dead-reckoning,

mainly, and estimates position by measuring and ac-

cumulating the rotation of the wheel with the rotary

encoder, etc. Dead-reckoning is a convenient estimat-

ing method using only internal sensors. However, the

accuracy of estimation decreases as the movement be-

comes longer since the errors of the transformations

and wheel slippage accumulate. On the other hand,

the method using external sensors estimates the posi-

tion by measuring positions of a landmark in the envi-

ronment with a vision sensor or a range sensor. Some

error is always caused by resolution or the noise of

the sensor; accumulated errors are not caused as such

by dead-reckoning. Therefore, because both meth-

ods have their respective merits and demerits, the two

methods are often used together (Cox, 1989) (Watan-

abe and Yuta, 1990) (Chenavier and Crowley, 1992).

In the case of the estimation method using both

dead-reckoning and an external sensor, it is advanta-

geous to improve the accuracy of dead-reckoning. As

for the reason, in general, many of the external sen-

sors are expensive, and processing is very complex.

Moreover, estimation methods using external sensors

need to have a previously installed landmark in the

environment. By improving the accuracy of dead-

reckoning and reducing the part that depends on the

method using the external sensor, the hardware and

software costs of the robot can be decreased, and the

time needed to install a landmark can be omitted.

In this paper, in order to develop an accurate

localizaion for mobile robots, we propose a dead-

reckoning system based on increments of the robot

movements read directly from the ﬂoor using optical

mouse sensors (Fujimoto et al., 2002). The move-

ments of two axes are measurable with an optical

mouse sensor. Therefore, in order to calculate a ro-

bot’s deviation of position and orientation, it is nec-

essary to attach two optical mouse sensors in the ro-

bot (Tobe et al., 2004) (Singh and Waldron, 2004)

(Cooney et al., 2004). However, it is also expected

that a sensor cannot read the movements correctly due

to the condition of the ﬂoor, the shaking of the ro-

bot, etc. To solve this problem, we arrange multiple

optical mouse sensors around the robot and compare

sensor values. By selecting reliable sensor values, ac-

curate dead-reckoning is achieved.

In section 2, we explain the optical mouse sen-

sor. In section 3, we describe the algorithm of dead-

reckoning based on optical mouse sensors. Finally, in

SEKIMORI D. and MIYAZAKI F. (2005).

PRECISE DEAD-RECKONING FOR MOBILE ROBOTS USING MULTIPLE OPTICAL MOUSE SENSORS.

In Proceedings of the Second Inter national Conference on Informatics in Control, Automation and Robotics - Robotics and Automation, pages 48-54

DOI: 10.5220/0001180300480054

 SciTePress

LEDlens/light pipeoptical mouse sensor

(inc. image sensor)

base plate

floor

Figure 1: Structure of optical mouse sensor

Table 1: Speciﬁcations of the optical mouse sensor (Agilent

Technologies, HDNS-2051)

resolution 800 counts/inch

max speed 14 inch/sec

scanning frequency 2300 Hz

power supply 5 volts

section 4, we verify the effectiveness of this algorithm

through several experiments with an actual robot.

2 OPTICAL MOUSE SENSOR

An optical mouse sensor is built into an optical mouse

for personal computers, and measures non-contact

movements. It is maintenance free and not inﬂuenced

by ﬂoor friction.

The principle of the optical mouse sensor is that

the installed small image sensor reads the change in

the image information on the ﬂoor and the optical

mouse sensor measures movement. The structure of

the optical mouse sensor is shown in Fig. 1. An op-

tical mouse sensor takes a ﬂoor picture irradiated by

a LED through a lens, with the image sensor located

on the sensor undersurface. Changes in the pictures

taken are processed within the sensor and transformed

into distance information. Finally the sensor outputs

a two phase pulse from the ports. The main speciﬁca-

tions of the optical mouse sensor(Agilent Technolo-

gies, HDNS-2051) used in our research are shown in

Table 1.

3 DEAD-RECKONING BASED ON

OPTICAL MOUSE SENSORS

This section describes the basic equation for dead-

reckoning based on optical mouse sensors and the

comparison method for increasing the reliability of

mouse sensor values. In this method, the mobility

range of the robot is limited to the ﬂoor whereby the

optical mouse sensor can initially measure the move-

ment.

η i

ξ j

η j

robot

optical mouse

sensor mi

optical mouse

sensor mj

φj

Figure 2: Conﬁguration of robot and optical mouse sensors

3.1 Basic Equation

Movement of the direction of two axes is measurable

by one optical mouse sensor. Therefore, movement

(translation and rotation) of the robot which moves

through a plane is calculable by using two optical

mouse sensors.

Firstly, a robot and two optical mouse sensors

, m

are arranged as shown in Fig. 2. The

world coordinate system (O

− XY ) is placed on

the ﬂoor, the robot coordinate system (O − xy)

is placed on the robot center, and coordinate sys-

tems (O

− ξ

), (O

− ξ

) are put on the cen-

ter of two optical mouse sensors m

, m

attached

to the robot. However, axes x

, x

of each sen-

sor are located in a radial direction from the ro-

bot center

. The positions of each sensor in terms

of the robot coordinate system are expressed by

cos φ

, d

sin φ

]

, [d

cos φ

, d

sin φ

]

. The re-

lation movement [∆ξ

, ∆η

]

, [∆ξ

, ∆η

]

measured

by each sensor and movement [∆x, ∆y, ∆θ]

of the

robot center is expressed as follows:



Cφ

−Sφ

Sφ

Cφ



∆ξ

∆η





∆x

∆y



+ ∆θ



−d

Sφ

Cφ



(1)



Cφ

−Sφ

Sφ

Cφ



∆ξ

∆η





∆x

∆y



+ ∆θ



−d

Sφ

Cφ



(2)

It is our goal to decrease the number of parameters used

for this method, and the basic equation can be derived re-

gardless of ξ

, ξ

axial direction of each sensor.

PRECISE DEAD-RECKONING FOR MOBILE ROBOTS USING MULTIPLE OPTICAL MOUSE SENSORS

Here, Sφ

∗

and Cφ

∗

mean sin φ

∗

and cos φ

∗

respec-

tively, and use this notation as follows. Moreover, up-

per formulas are arranged as follows:

Au = a (3)

u = [∆x, ∆y, ∆θ]

A =







1 0 −d

Sφ

0 1 d

Cφ

1 0 −d

Sφ

0 1 d

Cφ







a =







∆ξ

Cφ

− ∆η

Sφ

∆ξ

Sφ

+ ∆η

Cφ

∆ξ

Cφ

− ∆η

Sφ

∆ξ

Sφ

+ ∆η

Cφ







Here, elements of matrix A and vector a are replaced

with A

and a

(p = 1, 2, 3, 4; q = 1, 2, 3) respec-

tively. Furthermore, the squared error E

of move-

ments is deﬁned as follows:

p=1

∆x + A

∆y + A

∆θ − a

)

(4)

The movement u = [∆x, ∆y, ∆θ]

that has the min-

imum square error E

is determined by using the fol-

lowing equation.

u = A

−

a (5)

Here, matrix A

−

means a pseudo-inverse matrix of

After movement u of the robot can be deter-

mined, dead-reckoning is computed using the follow-

ing equation and robot position [X

, Y

, Θ

]

in terms

of the world coordinate system is determined. In ad-

dition, [X

t−1

, Y

t−1

, Θ

t−1

]

expresses the position at

a pre-measurement point.

t−1

+ ∆x CΘ

t−1

− ∆y SΘ

t−1

+ ∆x SΘ

t−1

+ ∆y CΘ

t−1

+ ∆θ

(6)

3.2 Comparison of Values of Optical

Mouse Sensors

Robot movements may be incorrectly measured by

the optical mouse sensor due to robot speed, robot

shaking, the condition of the ﬂoor, etc. When errors

arise in only one optical mouse sensor between two

optical mouse sensors (since the squared error E

(4) will be large), error is detectable by supervising

the value of E

. However, when an error arises in

both of two mouse sensors, there is no corroboration

to which the value of E

becomes large. That is, er-

ror is undetectable when only supervising the value

of E

. Thus, we proposed a method of computing

robot movements by comparison of the optical mouse

sensor values and by selecting reliable sensor values.

The number of optical mouse sensors is N , the

squared errors E

(i = 1 · · · N, j = 1 · · · N(i 6=

j)) of all optical mouse sensor values are calculated.

Then, threshold E

of E

is decided, and accuracy

of a measurement value is evaluated by the following

equation.

j=1

j6=i

, δ



1 (E

≤ E

)

0 (E

> E

)

(7)

Here, r

expresses the reliability of optical mouse sen-

sor m

. This reliability is computed to each optical

mouse sensor, and optical mouse sensors m

, m

, · · ·

with high reliability are elected using threshold r

And the following equation is derived using those val-

ues.

Bu = b (8)

B =







1 0 −d

Sφ

0 1 d

Cφ

1 0 −d

Sφ

0 1 d

Cφ

: : :







b =







∆ξ

Cφ

− ∆η

Sφ

∆ξ

Sφ

+ ∆η

Cφ

∆ξ

Cφ

− ∆η

Sφ

∆ξ

Sφ

+ ∆η

Cφ







A movement u of the robot is calculated by using the

following equation.

u = B

−

b (9)

In addition, when two or more sets of optical mouse

sensor values with high reliability do not exist, move-

ment of the robot is computed based on wheel rota-

tion.

4 EXPERIMENTS

In order to evaluate our methods, experiments were

executed using our robot. Firstly, we explain the sys-

tem conﬁguration of the robot. After that, we show

the results of self-localization using dead-reckoning

based on optical mouse sensors. Finally, we make one

evaluation of our method by reporting on the results of

the integration of the global camera information and

the dead-reckoning value using the Kalman Filter.

ICINCO 2005 - ROBOTICS AND AUTOMATION

Table 2: Speciﬁcations of the mobile robot

height 120 [mm]

width 262 [mm]

weight 2 [kg]

max speed 1000 [mm/s]

Table 3: Planned path cartesian coordinates

1 2 3 4 5

X [mm] 0 500 500 500 500

Y [mm] 0 0 0 500 500

Θ [rad] 0 0 π/2 π/2 0

6 7 8 9 10

X [mm] 1000 1000 1000 1000 1500

Y [mm] 500 500 1000 1000 1000

Θ [rad] 0 π/2 π/2 0 0

4.1 System Conﬁguration

The robot we have been developing is shown in Fig. 3,

and its control ﬂow is shown in Fig. 4. The ro-

bot has an omni-directional mobile mechanism driven

by three omni-directional wheels .Four optical mouse

sensors are attached around the robot. And in or-

der that an optical mouse sensor may stably scan

a ﬂoor, the sensor unit is forced onto the ﬂoor by

springs. Moreover, the CPU board and control board

are mounted onto the robot. And they control driving

motors and count the pulse from optical mouse sen-

sors. The main speciﬁcations of the robot are shown

in Table 2.

4.2 Dead-Reckoning Based on

Optical Mouse Sensors

We used two robot speeds: (a) v=300[mm/s],

ω=1.82[rad/s] and (b) v=500[mm/s], ω=3.03[rad/s] in

the experiments. Speed (a) is slower than the max-

imum measurement speed of the optical mouse sen-

sor(see Table 1), and speed (b) is faster. We deter-

mined speed (b) to be the general maximum speed of

an indoor mobile robot. The motion path of the robot

is shown in Table 3. The ﬂoor is covered with the felt

mat used in the RoboCup small size league competi-

tions . Moreover, in order to measure a robot’s real

trajectory, a camera is installed on the ceiling.

The comparison result of the real trajectory and

dead-reckoning values based on wheels, two optical

mouse sensors, and four optical mouse sensors are

shown in Fig. 5. As a result, when a robot speed is

(a), even if the dead-reckoning value based on the

wheels greatly differs from the real trajectory, two

dead-reckoning values based on the optical mouse

sensors are mostly in agreement with the real trajec-

CPU board

batteryoptical mouse sensor

control board

(a) Overall view of mobile robot

motor and encoder omni-wheel

chassis bevel gear

(b) Bottom view of mobile robot

LED spring

lens/light pipe optical mouse sensor

Figure 3: Robot equipped with omni-directional mecha-

nism and optical mouse sensors

PRECISE DEAD-RECKONING FOR MOBILE ROBOTS USING MULTIPLE OPTICAL MOUSE SENSORS

CPU

(Toshiba, TA8440H)

counter

(Nec, uPD4701)

DC motor

(Maxon, A-max)

encoder

(Maxon, 110520)

optical mouse

sensor

(Agilent Tech.,

HDNS-2051)

counter

(Nec, uPD4701)

counter

(Nec, uPD4701)

X 3

X 4

motor driver

motor unit

sensor unit

control board

(Hitachi,H8/3054F)

CPU board

Figure 4: Control ﬂows of the robot

Table 4: Errors in 10 dead-reckonings

(a) v = 300 [mm/s], ω = 1.82 [rad/s]

average of the maximum error

type

translation [mm] orientation [deg]

wheels 191.499 14.970

2 mice 44.516 4.918

4 mice 38.011 4.607

(b) v = 500 [mm/s], ω = 3.03 [rad/s]

average of the maximum error

type

translation [mm] orientation [deg]

wheels 239.397 19.264

2 mice 627.237 40.638

4 mice 61.593 8.588

tory. On the other hand, when robot speed is (b),

the dead-reckoning value based on the wheels dif-

fers greatly from the real trajectory as well as in the

case of speed (a). The method based on two op-

tical mouse sensors caused erroneous measurements

during movement, and a large error has arisen in the

dead-reckoning value. On the other hand, the method

based on four optical mouse sensors has carried out

position estimation with a small error, since a compar-

ison between optical mouse sensors was performed

correctly.

Moreover, we veriﬁed the dead-reckoning mea-

surements ten times under the same condition. The

average of the maximum error of the estimated value

and the measured value in the movement is shown in

Table 4. As a result, in the ten dead-reckoning mea-

surements, results similar to the above-mentioned are

obtained, and the stability of our method can be con-

ﬁrmed.

4.3 Integration of Global Camera

Information and

Dead-Reckoning Value

Using another evaluation method, we report on the

results of integration of the robot position via global

camera and dead-reckoning value using the Kalman

Filter. The handy-cam installed in the upper part of

the room is used as the global camera (A separate

camera is used for measuring). The global camera

measures only the robot position information (orien-

tation information is not included) for the sake of con-

venience. Though the extended Kalman Filter is used

for integrating the two values, its details are omitted.

We used v=500[mm/s] and ω=3.03[rad/s] as the robot

speed in the experiments.

Fig. 6 shows the results of (a) measurement value

using the handy-cam, (b) dead-reckoning value using

wheel rotation, (c) estimates based on (a) and (b), (d)

dead-reckoning value using optical mouse sensors,

and (e) estimates based on (a) and (c). As a result,

in the case of (c), even if estimates of the position are

mostly in agreement with the real trajectory, a large

error has arisen in the estimates of orientation. On

the other hand, in the case of (e), estimates of both

position and orientation are mostly in agreement with

the real trajectory. In this experiment, since the ori-

entation is not included in the information from the

global camera, the accuracy of the estimates of orien-

tation tends to worsen compared with the estimates of

position. However, by using optical mouse sensors,

accurate dead-reckoning can be realized, and conse-

quently, not only a position but also an orientation is

realizable with sufﬁcient accuracy.

5 CONCLUSION

In this paper, we proposed the method of accurate

dead-reckoning by measuring the movement of a ro-

bot directly from the ﬂoor with optical mouse sensors.

By comparing and selecting sensor values from the

multiple optical sensors, reliable dead-reckoning was

realized. Through several veriﬁcation checks with the

actual robot, we conﬁrmed that our dead-reckoning

can be realized accurately and with stability compared

with the method based on wheel rotation. In addi-

tion, we showed that the accuracy of estimation was

greatly improved by using only simple global camera

information.

This method of measuring the movement of the ro-

bot with optical mouse sensors is limited to the in-

door environment. Though the system becomes large

scale in an outdoor environment, it is also possible to

measure the movement of the robot by taking images

of the ground surface with multiple CCD cameras as

ICINCO 2005 - ROBOTICS AND AUTOMATION

-200

200

400

600

800

1000

1200

1400

0 500 1000 1500 2000

Y [mm]

X [mm]

real trajectory

wheels

2 mice

4 mice

-40

-20

100

120

140

0 5 10 15 20 25

Θ [deg]

t [sec]

real trajectory

wheels

2 mice

4 mice

(a) v=300[mm/s], ω=1.82[rad/s]

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140

0 5 10 15 20

Θ [deg]

t [sec]

real trajectory

wheels

2 mice

4 mice

(b) v=500[mm/s], ω=3.03[rad/s]

Figure 5: Self-localization based on dead-reckoning

well as optical mouse sensors. When CCD cameras

are used for the measurement, our method can be in-

troduced without the big alterations.

In future work, we will develop one sensor unit in-

cluding multiple optical sensors, and install this sen-

sor unit in various robots.

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Figure 6: Self-localization based on Integration of global camera information and dead-reckoning value( v=500[mm/s],

ω=3.03[rad/s] )

ICINCO 2005 - ROBOTICS AND AUTOMATION