2011 11th International Conference on Control, Automation and Systems

Oct. 26-29, 2011 in KINTEX, Gyeonggi-do, Korea

1. INTRODUCTION

Recently, two-wheeled balancing robot platforms are

being actively developed for the purpose of practical

applications in diverse areas. The two-wheeled mobile balancing robot is a kind of under-actuation system

where the posture control and speed control are

performed together with only two actuators of driving

wheels. Since the development of Segway [1] as a

typical commercial product, a lot of versions of the

balancing robot were announced through the research

activities in academy and industry. For examples, JOE

[2] enhanced control performance based on the detailed dynamic modeling. EN-V [3] is a two-seater vehicle to

cover 40 km on a single charge. EMEIW2 has a kind of

wheeled-leg architecture to cope with floor level

differences in the office environment.

On the other hand, as the advanced control

performance is required for the two wheeled mobile

robot, the exact dynamic modeling is becoming more

important. Basically, the dynamic motion of the two-wheeled balancing robot can be modeled as a 3

DOF equations of motion when considering forward

translational motion and pitching/yawing rotational

motions [4-6]. Also, some nonlinear control techniques

were tried [7, 8] in order to get over the performance

limit of linear control methods [9].

However, the two-wheeled robots are still greatly

limited in the quick rotation movement because the

conventional designs lack in the capability of the

centrifugal force compensation in the roll direction with

respect to the forward movement. As the driving speed

increases, the roll instability gets more serious. For

these reasons, the turning speed is inevitably confined to

a certain limit and the conventional two-wheeled robot

has difficulty in following paths on uneven or

high-slope terrains such as hills. Specifically, as the

position of the center of gravity is high and the distance

between the two wheels is narrow, the rollover

phenomena could happen more frequently and the

passengers may experience uncomfortable feelings in

fast driving.

In order to overcome these problems which are

caused by the intrinsic characteristic of a two wheeled

robot, this paper investigates a mobile robot with active

tilting motions to compensate the centrifugal forces in

high speed turns. In this way, the balancing robot can be

equipped with high speed turning performance without

unnecessary slowdowns before turning and also the

passenger will have more comfortable rides. A

representative example which applied the tilting motion

to a vehicle design is the tilting trains, which are

commercially running in many countries.

This paper is organized as follows. Section 2

discusses the effect of the tilting motion in balancing

robots. Section 3 describes a hardware configuration

suitable for the tilting mechanism. Section 4 derives the

equations of motion of the suggested MTB robot.

Finally, Section 5 draws concluding remarks.

2. Effect of the Tilting Motion

Two-wheeled mobile balancing robot has been

studied by many companies and research institutes because of its wide applicability, structural simplicity

and the needs of compact short-range personal

transportation. The main purpose of this study is a

development of a 2-wheeled mobile balancing robot as a

next generation vehicle. Actually, two essential factors

that must be considered in the balancing robot design

are stability and high mobility. To meet these two

factors, the study of 2-wheeled mobile balancing robot has been focused on the exact modeling of the equation

of motion [2, 4~6] and the control methods [7~9]. More

accurate dynamic model can contribute to the stability

analysis and also the nonlinear control method is

desirable to improve the mobility of the robot.

However, these studies cant remove the trade-offs of high mobility and stability yet. To satisfy one condition,

the other must be lost, because of structural limitation of 2-wheeled balancing robot.

This paper suggests the structural changes using

tilting mechanism to eliminate the trade-off relation of

Development of a Two-Wheeled Mobile Tilting & Balancing (MTB) Robot

Sangtae Kim , Jungmin Seo, and SangJoo Kwon

School of Aerospace & Mechanical Engineering,

Korea Aerospace University, Goyang, 412-791, Korea

(Tel : +82-2-300-0366; E-mail: {kimonkey, jmseo, sjkwon}@kau.ac.kr)

Abstract: Two wheeled mobile balancing robot is a kind of under-actuation system that can maintain its posture and

drive the robot with only two wheels. In order to overcome the limitation in turning velocity due to the centrifugal force

effect, this paper proposes a tilting balancing mechanism which is to offset the centrifugal force by active tilting

motions. The newly suggested two-wheeled mobile tilting and balancing robot (MTB) can prevent unnecessary

slowdowns in turning motions and increase passengers riding feelings. To validate the tilting effect, the equation of motion of the MTB robot is derived and analyzed and the hardware design is followed.

Keywords: Two-wheeled mobile robot, balancing robot, inverted pendulum robot.

1978-89-93215-03-8 98560/11/$15 ICROS

2-wheeled mobile balancing robot. The tilting method is

tilting the center of gravity to the inward of rotation to

compensate the centrifugal force. Fig. 1 shows the

canceling of the centrifugal force by tilting method.

Centrifugal force

Centripetal force

Normal force

Gravity

Tilting

Fig. 1 Forces acting on the tilting mobile robot.

By using the tilting mechanism, as shown in Fig. 2,

the robot can prevent falling down or unnecessary reduction of speed when it rotates.

Fig. 2 Conventional 2-wheeled mobile balancing

robot(left) and 2-wheeled MTB robot(right).

The control of the MTB is more complicate than the

tilting train which is the typical example of tilting

mobile robot. Because, as shown in Fig. 3, tilting the

train has just 2-DOF(longitudinal, roll direction

components), but 2-wheeled MTB robot has

4-DOF(coupled longitudinal, pitch, yaw, roll direction

components).

Fig. 3 The DOF of tilting train(left) and 2-wheeled

MTB robot(right).

If this difficulty is solved, the utilization of tilting

method will be able to be increased because of free

mobility of the MTB robot. The MTB robot will

overcome the problems of conventional 2-wheeled

mobile balancing robot which are the speed limit and

absence of stability. Also, it will open a new chapter of

studies of high mobility 2-wheeled mobile balancing

robot.

3. HARDWARE DESIGN

Fig. 4 shows the drawings and a picture of MTB

robot. It is composed of DC servo motors, drivers,

encoders, wheels, a gyro sensor and a SBC(Single Board Computer) which are not significantly different

from the existing balancing robot. The overall platform of the robot is made with general aluminum profiles and

polycarbonate plates to reduce weight.

Fig. 4 The design of MTB.

Motor selection [10] which is the most important

thing in the hardware selection of the MTB robot was

determined by Eqs. (1) ~ (2).

4

Weight DiameterTorque Safety factor

(1)

TorqueGear rate

Rated torque

(2)

To reserve enough clearance between the ground and

the bottom of the robot, 16-inch wheels were used.

Considering the weight of the robot and dummy or

passenger, a total weight was assumed to be 120kg.

Table 1 is the hardware specification of the MTB robot.

Table 1 The hardware specifications of the MTB robot.

Specifications

Size 450460550mm

Weight 45kg

Wheel

diameter 406mm

Travel speed 10km/h

Battery 24V 10Ah Ni-MH(2ea)

Maximum

tilting angle 20

2

3.1 Effective platform design for tilting

The MTB robot has tilting motion in a different way

from the tilting train. The case of tilting trains, as shown

in Fig. 5(top), does tilting by using difference between

the displacements of two actuators mounted on both

side. This way requires two actuators and it should

support all the weight of the body. However, The MTB

robot in Fig. 5(bottom) has a tilting actuator between

two divided platforms.

By through this way, the robot can be reduced the

number of used actuators. Also, it is able to tilt by the

lower-output actuator.

Fig. 5 Tilting methods of tilting train(top) and

2-wheeled MTB robot(bottom).

The Fig. 6 shows the tilting motion of the MTB robot

by difference in vertical displacement between two parts.

Each part is equipped with a DC servo motor, worm

gear, battery, and other equipments symmetrically.

Fig. 6 The tilting appearance of the MTB robot.

3.2 Tilting actuator

For optimal platform size, MTB robots tilting

system consists of rack-pinion gear and stepping motor

which can make a long stroke in spite of a small volume.

In the middle of the two parts, rack-pinion gear is

mounted, and stepping motor connected with it to apply

force for tilting. Fig. 7 is the used rack-pinion gear and

stepping motor.

Fig. 7 Rack-pinion gear and stepping motor.

And, a bi-directional slide is attached between two

parts of body to prevent a misalignment and gab. The

slide is chosen by considering strength to bear the load

of body and moment caused by repeated tilting motion.

3.3 Main motor

Fig. 8 explains the relationship of required tilting

stroke and distance between two wheels. Although the

same angle is tilted, different strokes are required

depending on the distance between two wheels.

Fig. 8 required strokes difference depending on the

distance between two wheels.

To reduce the distance between the wheels, motor

were mounted vertically. The worm gear helped motors

to be stand uprightly. In addition, the platform size can

be more reduced through this way. Fig. 9 is the picture

of a DC servo motor equipped with worm gear.

Fig. 9 DC motor with worm gear.

3

4. EQUATIONS OF MOTION

A two wheeled MTB robot has 4 degrees of freedom

of movement having straight direction ( x ), pitch

direction ( ), yaw direction ( ), and tilt direction (phi,

). The equation of motion in this paper is derived

from Kanes method [11]. This method uses the relationship that the sum of the generalized active force

and the generalized inertia force is equal to zero. By assuming no slip condition between the wheels

and ground, we have the dynamic equation of motion,

where the parameters are detailed in table 2. Through

Fig. 10, {N} is Newtonian reference frame, {F} is fixed reference coordinate system to find the direction of the

robot for the yaw direction, {T} tilting direction of the

coordinate system, and {P} pendulum coordinate

system located in the center of gravity. The generalized

active force and the generalized inertia force is written

as iF ,*

iF , i=1 is the tilting direction, i=2 is direction of

the pitch, i=3 is direction of yaw, and i=4 represents a

straight direction. Induced Eq. (3) appears a differential equation of 4 degrees of freedom in each direction.

To appear the tilting effect better, the dynamics of

MTB robot is compared with the dynamics of balancing

robot ( 0 ). In the existing dynamics of balancing

robot[6], the turning direction state( ) is coupled less

about the other states and the variables on turning

direction almost doesnt contribute the other motion. But turning direction is coupled complicatedly in Eq.

(3) and a fast turn driving makes the strong connection

with the other motion.

*

1 1

*

2 2

*

3 3

*

4 4

0

0

0

0

F F

F F

F F

F F

, (3)

1

2

3 4

cos sin

sin cos ( )cos

1( ), ( )

P T

P L R

R L L R

F l M g T

F l M g T T

dF T T F T T

R R

*

1 1 1 2 3 2 3

3 3 1 2 1 2

2

2

cos { ( ) }

sin { ( ) }

cos { cos (2 cos )sin

( 2 cos cos sin )cos }

P P P

P P P

P

F I I I

I I I

xM l

l

*

2 2 2 3 1 1 3

2

{ ( ) }

{ cos sin sin sin

(2 sin 2 cos 2 )sin cos

cos (cos 2 1)}

P P P

P

F I I I

M l x x l l

l

l

*

3

2 2

2 2 2

2

1 1 2 3 2 3

2 2

{ sin cos sin

sin 2 sin cos (1 cos cos )

( 2 sin ) sin sin cos

sin cos (cos 2 1)

cos sin cos 2 cos sin }

cos sin { ( ) }

sin {

P

P P P

P

F M l x x

l l l

l

l

l l

I I I

I

3 1 1 3

3 3 1 2 1 2

2 2

( ) }

cos cos { ( ) }

2( ( ) )

P P

P P P

I I

I I I

dMd K J

R

*

4 2

2 2 2

2( ) { cos sin cos

cos sin 2 cos cos sin }

P

JF M x M x l l

R

l l l

1

2

3

cos cos sin

sin

sin cos cos

P

P

P

1

2

3

cos cos cos cos sin

sin sin sin

sin cos

sin cos sin cos cos

cos sin cos

P

P

P

P

R

L

I

N

x

P

R

L

I

1N

3N

2N

2F 1F

1P

3P2P

T

3F

3T

1T

2T

N

x

Fig. 10 4 DOF two-wheeled MTB robot.

4

To understand the degree of this relationship, the

overshoot value of pitch angle is investigated while the

reference value of each state is changed. If there is a

small overshoot of pitch ( ) due to the turning ( )

reference change, the state of turn direction affects less to dynamics. All values except the reference value are

fixed, and the tilting directions reference of MTB robot is included. In this simulation, the tilting angle reference

is inward of the curve.

Fig. 11(top) shows the relationship of pitch overshoot

and reference of yaw, x velocity in 2-wheeled mobile

balancing robot. The change of yaw velocity does not

affect the pitch overshoot and the longitudinal velocity is only effective. In Fig. 11(bottom), the pitch overshoot

of the 2-wheeled MTB robot is affected by both yaw

and longitudinal velocity. And the velocity is faster, this

tendency is more obvious. This result is that the fast turn

driving effects pitch state strongly and the MTB robot

with the tilting movement as well as the actual

two-wheeled balancing robot has this physical

characteristic. However, the existing balancing robots study does not consider the centrifugal force. Through

this result, it can be seen that the MTB robot is more

appropriate type for high-speed & personal riding than

2-wheeled balancing robot.

0.81

1.21.4

1.61.8

00.5

11.5

22.5

0.2

0.25

0.3

0.35

0.4

Reference of x Velocity(m/s)Reference of Yaw Velocity(rad/s)

Overs

hoot

of

Pitch P

ositio

n(r

ad)

0.81

1.21.4

1.61.8

00.5

11.5

22.5

0.1

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

Reference of x Velocity(m/s)Reference of Yaw Velocity(rad/s)

Overs

hoot

of

Pitch P

ositio

n(r

ad)

Fig. 11 Overshoot of the pitch angle of

2-wheeled balancing robot(top) & MTB robot(bottom)

Table 2 Parameters of two-wheeled MTB robot.

Frame {N} Newtonian Reference Frame

Point P The center of mass

Body L, R Wheels of pendulum

Point I Point at the center of axle to connect L

and R

x Distance from origin of frame N to point I

Roll Angle

Pitch Angle

Yaw Angle

TT Tilting Torque

,L RT T Torque of left and right wheel

d Distance from point I to wheel

l Distance from point I to mass center of

P

PM Mass of body P

M Mass of wheel

1 2 3, ,I I I MOI of Pendulum

,K J MOI of Wheel

5. CONCLUSION

In this paper, it is revealed that conventional

two-wheeled balancing robot has limitations, and a new

mechanism to solve the problem of the robot is

proposed. This mechanism is that tilting method is a way to offset the centrifugal force on the inside of the

curve when driving by paying load. The robot hardware

conditions for the effective movement are presented.

Especially the robot divided into two rectangular

modules to reduce the number of actuators, the amount

of body weight was distributed to the wheels. As a

result, a moving platform for a small tilting torque is

developed. In addition, the analysis of the movement through the

4 degrees of freedom of mobile balancing robot has

become a possibility by the extended equations of

motion of the two-wheeled MTB robot. And the effect

of the turning motion on the other states is analyzed.

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