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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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