347

Sensors and Materials, Vol. 35, No. 2 (2023) 347–363
MYU Tokyo
S & M 3172

Design of Self-balancing Model-size Electrical Motorbike Robot
Using Control Moment Gyroscope
Rodi Hartono,1 Seung Bin Kim,1 Patrick Tshibang A Kalend,1
Nam Kyun Baik,2* and Kyoo Jae Shin1
1Department of Artificial Intelligence Convergence, Busan University of Foreign Studies,

65, Geumsaem-ro 485 Beon-gil, Geumjeong-gu, Busan, 46234, Republic of Korea

2Department of Smart Convergence Security, Busan University of Foreign Studies,

65, Geumsaem-ro 485 Beon-gil, Geumjeong-gu, Busan, 46234, Republic of Korea(Received October 18, 2022; accepted November 28, 2022; online published November 30, 2022)

Keywords: electrical motorbike robot, control moment gyroscope, pole placement controller, linearquadratic regulator controller

In recent years, a significant amount of study has been conducted on how to control theequilibrium of an electrical motorbike robot (EMBot). This is essential because a stable EMBot
must be controlled by a reliable system. In this study, we explored a number of approaches forstabilizing an EMBot by using a control moment gyroscope (CMG). The momentum from a
flywheel’s rotation at a set speed is employed to counteract gravity and keep the EMBot
balanced. To measure the roll angle of the EMBot, an inertial sensor is used. From generalized
coordinate systems, a nonlinear mathematical model of the EMBot is derived using Lagrange’s
equation. Pole placement (PP) and linear-quadratic regulator (LQR) controllers are utilized totest and observe the system’s stability. By determining the appropriate locations of the closedloop poles in the PP controller and finding the optimal K-matrix value by selecting closed-loop
characteristics in the LQR method, the performance of the system in maintaining stability canbe identified.

1.

Introduction

Single-track vehicles, such as an electrical motorbike robot (EMBot), offer a number ofbenefits, one of which is that they are more convenient to use than multi-track vehicles. On theother hand, due to the nonlinear and unstable nature of the system, controlling an EMBot can bechallenging.(1–3) One of the difficulties is in maintaining vertical stability or balance control
when an EMBot is both in a static state and moving through the environment.(1–4) Therefore, asignificant amount of research has been conducted in an attempt to discover a method that willstabilize an EMBot.
The method chosen to control the vertical stability of an EMBot is highly dependent on the
EMBot’s movement conditions. When an EMBot is not moving, the external torque affects the
direction of the wheels and makes it more difficult for the EMBot to remain balanced. This is*Corresponding author: e-mail: white-knight@hanmail.net

https://doi.org/10.18494/SAM4168

ISSN 0914-4935 © MYU K.K.
https://myukk.org/

348

Sensors and Materials, Vol. 35, No. 2 (2023)

because when the wheels are not rotating, there is no angular momentum. In general, there arethree different approaches for controlling the vertical stability of an EMBot, each with benefits
and drawbacks. The approach of steering control has excellent performance when an EMBot istraveling at medium and high speeds but not when it is traveling at low speeds or stationary. Thisapproach also has disadvantages, including ground friction and a lack of resistance when the
EMBot is tilted at a steep angle. To balance the EMBot, the approach of shifting the center ofmass can also be used.(5,6) However, a disadvantage of this approach is that the torque output
cannot be very high. The final approach is the use of a control moment gyroscope (CMG).(7–16)
The large torque that can be generated by a CMG allows it to overcome the need to stabilize the
EMBot both at rest and at medium and high speeds. The CMG functions by rotating a flywheelthat serves as a rotor and is mechanically connected to a motorized gimbal. The shift in the
angular momentum in gaining the torque that results from the tilting of the spinning flywheel by
the gimbal motor generates a gyroscopic torque effect, which can help the EMBot maintain its
equilibrium.
As described in the literature on the application of gyroscopic effects to actively stabilize asingle-track vehicle, we conducted research on a model-size EMBot by employing the gyroscopic
torque of a spinning flywheel to maintain the stability of the EMBot when stationary. Two DC
motors were utilized to rotate the flywheel and the actuator used for twisting the gimbal that
controlled the roll angle of the EMBot. As a sensor input, an inertial sensor is employed tomonitor the roll angle of the EMBot. The roll angle data is then fed into a control system togenerate the motor torque output as a drive actuator for tilting a spinning flywheel. Poleplacement (PP) and linear-quadratic regulator (LQR) controllers are utilized to test and observe
the system’s stability. In this paper, we focus on system modeling, simulation, and observing the
response of the EMBot system by implementing PP and LQR controllers based on real hardware
parameters employed in maintaining stability. By determining the appropriate locations of theclosed-loop poles in the PP control system and finding the optimal K-matrix value by selecting
closed-loop characteristics in the LQR method, we can determine the performance of the system.

2.

Dynamic Model of EMBot

2.1

Coordinates, parameters, and assumptions

Figure 1(a) is an illustration of an EMBot with a gyroscope attached to control its balance,and Fig. 1(b) shows a front view of the EMBot coordinate system. The coordinate reference orroll angle of the EMBot is denoted by Oh [xh, yh, zh]; the centers of mass of the EMBot, gimbal,
and flywheel are Oem, Ogim, and Ofly with heights above the ground of hem, hgim, and hfly,
respectively; and the roll angle of the EMBot is denoted by γ. The coordinate system for the
gimbal is denoted by Ogc [xgim, ygim, zgim], the coordinate system for the moving EMBot is Xem[xem, yem, zem], and the coordinate reference for the gimbal angle is denoted by β.
When a flywheel spins at a speed of σ, it has angular momentum denoted by l. The directionof the angular momentum is based on the rotation direction of the flywheel α. As shown in Fig.
2(a), the direction of the angular momentum is along the zfly -axis when the flywheel rotates inSensors and Materials, Vol. 35, No. 2 (2023)

(a)

349

(b)

Fig. 1. (Color online) EMBot with a gyroscope. (a) Definition of coordinate system. (b) Front view of EMBot
coordinate system.

(a)

(b)

Fig. 2. (Color online) Gyroscopic effect of spinning flywheel. (a) Flywheel coordinate system. (b) Gimbal
precession on its axis.

a clockwise direction. The angular momentum of the flywheel will change when a force or atorque is applied to it. We use τ to denote the torque. Then if we apply an external torque along
the ygim-axis, the direction of the torque τ will be along the yfly -axis perpendicular to both theforce and the radius. Because the CMG can produce torque in the direction of the xfly -axis,
the precession torque that is generated by the angular momentum rate of the gimbal β makes
it possible for the EMBot to self-stabilize on its own. Tables 1 and 2 respectively show thedefinitions for the EMBot rotation system and the notation for the parameters of the system.

350

Sensors and Materials, Vol. 35, No. 2 (2023)

Table 1
Definitions for EMBot rotation system.
Parameter
Flywheel spin direction
Gimbal angle
Roll angle

Table 2
Notation for the parameters.
Parameter
Flywheel mass moment of inertia
Gimbal mass moment of inertia
EMBot mass moment of inertia
Flywheel mass & height
Gimbal mass & height
EMBot mass & height
Flywheel spin velocity
Angular velocity of EMBot
Angular velocity of gimbal
Angular velocity of flywheel
Gravitational acceleration

Symbol
α
β
γ

Unit
rad
rad
rad

Symbol
Ifly
Igim
Iem
mfly and hfly
mgim and hgim
mem and hem
σ
ωem
ωgim
ωfly
g

Unit
kgm 2
kgm 2
kgm 2
kg & mkg & mkg & m
rad/s
rad/s
rad/s
rad/s
m/s2

The following assumptions are taken into consideration in Lagrange’s method to obtain aclose approximation of a mathematical representation: 1. The EMBot has no longitudinalvelocity caused by the gyroscope torque on the vertical axis. 2. The EMBot has no lateral slip at
the contact base. 3. The EMBot, gimbal, and flywheel are all point masses at their centers ofgravity.
2.2

Modeling of EMBot motion with CMG

The gyroscopic effect is a result of the principle of angular momentum conservation. Whenthe flywheel spins, it generates an angular momentum. The angular momentum l is the productof the moment of inertia I and the spin velocity σ. In particular, the curve, the axis of rotation,and the mass of the flywheel influence the moment of inertia. Thus, the angular momentum l is
l = Iσ .

(1)Another important factor is the torque. The angular momentum dl only changes when atorque is applied to it. The torque will cause a change in the angular momentum with respect totime. The torque τ is the cross product of the distance vector and the force vector applied
perpendicular to the radius. Thus, the magnitude of the torque τ on the horizontal axis isτ = β l cos β .

(2)Sensors and Materials, Vol. 35, No. 2 (2023)

351

Figure 1 shows the definition of the coordinate system of the EMBot used to describe thesystem’s motion. The coordinate Xem rotates about the xh-axis of Oh through angle γ. The
transformation between coordinate Xem and Oh is01
Rem =  0 cos γ
 0 − sin γ

0 
sin γ  .
cos γ (3)

The gimbal consists of a frame that holds the flywheel and the gimbal motor, and the frame ismolded with the main body of the EMBot. Ogc is the center of rotation of the gimbal and Fgim
rotates about its ygim-axis through angle β, where the transformation is cos βR fgim =  0 sin β

0 − sin β 
10  .
0 cos β 

(4)The position of the center of mass of the EMBot Oem in the coordinate system Xem is
rem = [ xemyemzem ] .

T

(5)

y gc

z gc  .

T(6)

In Xem, the position of the gimbal joint Ogc is
rgc =  xgc

The positions of the gimbal frame’s center of mass of Ogim and Ofly in the Fgim coordinate
system are, respectively,Trgim =  xgim

y gim

z gim  ,r fly =  x fly

y fly

z fly  .

T

(7)

Therefore, the positions of the EMBot, gimbal, and flywheel centers of mass in Oh are,respectively,Trhem = Rem
rem ,

(
=
r
R (r + R

)
r ).

T
=
rhgim Rem
rgc + R fgimT rgim ,
hfly

T
em

gc

T
fgim fly

(8)

352

Sensors and Materials, Vol. 35, No. 2 (2023)

The angular velocities of the EMBot, gimbal, and flywheel are calculated as=
ωem 0 0]T γ,[γ=Tγ cos βω gim =
R fgimωem + 0 β 0  =Tγ cos βω fly =
ω gim + [ 0 0 σ ] =β γ sin β  ,(9)β σ + γ sin β  .

The velocities of the EMBot, gimbal, and flywheel are computed as
vem = ωem rem ,()(ωgim rfly ).

vgim ωem rgc + R fgimT ω gim rgim ,
=
=
v fly

ωem rgc + R fgimT(10)

From Eqs. (9) and (10), we can derive the kinetic energy of the system as

(

)

gimz

gimy

1
1
1
KEem =mem vemT vem + ωemT I emωem = mem vem 2 + I em γ 2 ,
2
2
2
1
1
=
KE gimmgim vgimT vgim + ω gimT I gimω gim
2
2
2 2
= m v
γ + I γ 2 cos 2 β + I γ 2 sin 2 β + I
β 2 ,
gim gim

gimx

(11)

1
1
m fly v flyT v fly + ω flyT I flyω fly
2
2
1= m fly v fly 2γ 2 + I flyxγ 2 cos 2 β + I flyz σ + γ 2 sin 2 β + I flyy β 2 .
2KE fly =

(

(

)

)

The total kinetic energy of the system is
KE = KEem + KE gim + KE fly ,(12)where Iem is the moment of inertia of the body mass of the EMBot about its tire contact line (xhaxis), Igim [Igimx, Igimy, Igimz] is the moment of inertia of the body mass of the gimbal about its
xgim, ygim, and zgim axes, and Ifly [Iflyx, Iflyy, Iflyz] is the moment of inertia of the body mass of the
flywheel about its xfly, yfly, and zfly axes.
Potential energy exists in nonmoving objects and is converted to kinetic energy when a force
such as gravity is applied and the object is set in motion by interacting with another object. The
potential energies of the EMBot, the gimbal, and the flywheel are described as follows:
PEem = mem rhem g cos γ ,PE gim = mgim rhgim g cos γ ,PE fly = m fly rhfly g cos γ .

(13)Sensors and Materials, Vol. 35, No. 2 (2023)

353

The total potential energy of the system is
PE =PEem + PE gim + PE fly .

(14)

To take the entire system as a single entity, we applied the Lagrangian equation to Eqs. (12)and (14). The mathematical model of the system is obtained asd  ∂L  ∂L
=
Qi,

−
dt  ∂qi  ∂qi(15)

where L is the Lagrangian function and L = KE − PE, qi is the generalized coordinate of theobject, and Qi is the generalized force applied at each rotating joint. Then we obtain the equationsof motion by solving the Lagrangian equation for qi = γ. The roll angle dynamic of the EMBot isthus obtained as



 
sin β cos β − I flyz σ cos ββ mem rhem + mgim rhgim + m fly rhfly  g sin γ + 2  I gimx + I flyx − I gimz − I flyz  γβ,Iem +  mem rhem2 + mgim rhgim2 + m fly rhfly 2  +  I gimx + I flyx  cos2 β +  I gimz + I flyz  sin 2 β

 




γ = (16)

and for qi = β, the gimbal angle dynamic of the CMG isβ =( I gimz + I flyz ) γ 2 sin β cos β − ( I gimx + I flyx ) γ 2 sin β cos β + I flyzγσ cos β .
( I gimy + I flyy )(17)Equation (16) shows that the movement of the flywheel strongly affects the stability of thevertical position of the EMBot. Also, it can be deduced that as the EMBot’s tilt increases, theflywheel is likely to change direction, enabling it to generate more reactive torque. This meansthat stabilization can occur at a greater tilt angle or if there are larger disturbances. Moreover,from the viewpoint of control, the system dynamics can be explained by the following nonlinear
state model:=γ f ( γ , γ, β ) + g ( u , γ ) ,y = [γ , β ] ,

(18)

where
f =

g=

( mem rhem + mgim rhgim + m fly rhfly ) g sin γ,
I em + ( mem rhem 2 + mgim rhgim 2 + m fly rhfly 2 ) + ( I gimx + I flyx ) cos 2 β + ( I gimz + I flyz ) sin 2 β

(

(

)

  sin β cos β - I flyzσ cos ββ
2 I gimx + I flyx - I gimz - I flyz γβ

) (

)

(

)

I em + mem rhem 2 + mgim rhgim 2 + m fly rhfly 2 + I gimx + I flyx cos 2 β + I gimz + I flyz sin 2 β(19)

u . (20)

354

Sensors and Materials, Vol. 35, No. 2 (2023)

3.

Description of Model-size EMBot and Linearization

3.1

Description of model-size EMBot robot

We built a model-size EMBot, as illustrated in Fig. 3, which is currently being utilized toevaluate various control strategies. The model is 22.5 cm long, 18 cm wide, and 20 cm high tothe top of the flywheel motor. Its total weight is 0.319 kg, including the gimbal and the flywheel.
The body and the gimbal frame are made of acrylic, whereas the flywheel is made of 3D-printed
plastic with a bolt included as ballast. The flywheel is a cylinder with a radius of 4.5 cm and aheight of 1.1 cm. Table 3 shows the specifications of the model-size EMBot system.
The base of the acrylic material used to structure the model-size EMBot is shaped like abicycle tire, and it is coated with rubber to prevent it from sliding. The diameter of the wheels of

(a)

(b)

Fig. 3. (Color online) Model-size EMBot and the experimental setup. (a) Experimental setup. (b) Dimensions of
EMBot.
Table 3Specifications of model-size EMBot system.
Parameter
Value
0.00004472, 0.00004472, 0.000089375
Iflyx, Iflyy, Iflyz
Igimx, Igimy, Igimz
0.0001701, 0.0003402, 0.0001701
Iem
0.00638
hfly
0.135
0.148
hgim
0.11849
hem
0.055
mfly
0.134
mgim
0.13
mem
σ
314.159
g
9.806

Unit
kgm 2
kgm 2
kgm 2
m
m
m
kg
kg
kg
rad/s
m/s2

Sensors and Materials, Vol. 35, No. 2 (2023)

355

the EMBot is 5 cm and the distance between the axles is 16.5 cm. To prevent the EMBot fromtilting by more than 30°, a limiter is placed on each side of the EMBot. To rotate both the
flywheel and the gimbal frame, two DC motors with fused gear boxes and integrated encoders
are installed. The inclination of the EMBot is read by an inertial sensor connected to a
microprocessor for processing. The flywheel, the gimbal motor, and the data processing system
including the sensor system are powered by their own independent power sources. Other
electronic components, including the processor and power supply, are located outside the EMBot
and connected to it with a cable.
3.2

Model linearization

Linearization is a technique for calculating linear approximations of a nonlinear system
function that are valid within a restricted range of values around the operational point. Using the
Taylor series expansion of the first order, the linear approximation is evaluated to ensure local
stability and the steady-state condition at the equilibrium point. This aids in the analysis of thestability and disturbance rejection properties of a system. After linearizing the movement
equation around the equilibrium point, the following equation of motion is obtained:γ =( mem rhem + mgim rhgim + m fly rhf ly ) gγ − I flyzσβ .
I em + ( mem rhem 2 + mgim rhgim 2 + m fly rhfly 2 ) + ( I gimx + I flyx )(21)

By expanding Eq. (21), the numerical results for a linear model in state-space form are
obtained as
0
1 0



 mem ⋅ rhem + mgim ⋅ rhgim 



g




+ m fly ⋅ rhfly

0 0 ,A=
I + m ⋅r 2 + m ⋅r 2 + m ⋅r 2 + Iem hemgim hgim
fly hflygimx + I flyx
 em


0
0 0






0




I flyz ⋅ σ
B=
 u,
2
2
2
 I em + mem .rhem + mgim .rhgim + m fly .rhfly + I gimx + I flyx 


1


C = [1 0 0 ],D = [ 0 ].

(

(

) (

) (

)

(22)

)

The specifications of the EMBot listed in Table 3 are determined from the model-size EMBot
hardware system shown in Fig. 3(b). By substituting these values into Eq. (22), a MATLAB

356

Sensors and Materials, Vol. 35, No. 2 (2023)

simulation of the behavior of the system is performed. An examination of poles and zeros foundthat the uncompensated system has two poles but no zeros. One of the poles is a positive number,which means that the pole on the right side of the imaginary axis causes the system to become
unstable.

4.

Control System Implementation and Analysis

Since we are attempting to control the position of the EMBot, which should return to thevertical position after the inclination, the reference signal we are tracking should be zero.
Various full-state feedback control methods, mainly the PP and LQR control methods, were
implemented and analyzed for the control system. The scheme of the PP and LQR control system
is shown in Fig. 4(b).
For a classical feedback controller such as a PID controller, when the input u and output y
are known, the objective is to build a feedback control system that changes the output
to adesired value. Then, in the process block section, we compare the actual value of the output
signal with the reference signal to obtain a new control signal. Then, this new control signal is
fed as the input signal to control the plant block section with the aim of reducing the error to
zero. Instead of feeding back the output y for the PP control, we feed back every state variable inthe state vectors. In this case, we were convinced of the importance of each state value. The statevalues are then multiplied by a matrix comprised a variety of gain values, also known as the gain
matrix. Then the result is subtracted from the scale of the reference signal. This signal is thendirectly supplied as an input to the system. The controller comprises the entire block of the
feedback system.

(a)

(b)
Fig. 4.

(Color online) PID vs full-state feedback control scheme. (a) PID controller. (b) PP and LQR controllers.

Sensors and Materials, Vol. 35, No. 2 (2023)

357

As previously mentioned, using the PP control method, we can compute the appropriate gain
matrix to ensure system stability. A reference scaling term is also utilized to guarantee sufficient
steady-state performance. In addition, rather than randomly selecting poles in the PP controller
method, the LQR method provides a more systematic approach through finding the optimal
K-matrix value by selecting the closed-loop characteristics. This makes LQR control one of themost powerful algorithms for controlling a dynamic system at the lowest possible cost, and it isextensively applied in many fields of industry control.
4.1

PP controller

The state-space equation of the system represents the multiple n th-order input linear timeinvariant systems as described by=x Ax + Bu,(23)

where Ax describes the dynamics of the system and Bu describes how the system responds to an
input. In addition, the Ax term describes how energy is stored and transferred in the system.
Therefore, it is reasonable to assume that the matrix Ax is unique for each controller design. Thisis particularly relevant in terms of system stability, because each feedback controller must
update matrix A to adapt to the system’s dynamics. The eigenvalues of matrix A are equal to thesystem’s poles, and the location of the poles determines the stability of the linear system. This is
the crucial aspect of the PP controller. The poles or the eigenvalues of the closed-loop matrix A
are modified to ensure the stability of the closed-loop system. The closed-loop system is createdby submitting state variables back through a real constant matrix K:=x( A − BK ) x .

(24)

As discussed previously, after running the system, one of the eigenvalues appears on thepositive side of the imaginary axis in the open-loop system, causing the system to become
unstable. Using the PP controller by moving the unstable pole to the left half-plane will stabilize
the system.
From our closed-loop matrix A, which is (A − BK)x, and our gain matrix K, which is a 1 × 3
matrix, the following expression can be derived:
1 0
 0
T

BK ) x 69.98 0 0  − [ 0 4.697 1] ⋅ [ K1
( A −=
 0
0 0 

K2

K3 ].

(25)

T

In this case, we choose the eigenvalues λ = [ −24 −6 −12] . Using these eigenvectors, we
can solve the eigenvalues of the closed-loop system by finding the characteristic equation of thethree gain values358

Sensors and Materials, Vol. 35, No. 2 (2023)

det ( ( A − BK ) x − λ I ) =
0,

(26)

and we find appropriate values of K1, K2, and K3 as follows:=
K [122.1954 14.1979 −24.6913].

(27)

Using these three gain values in the path of the system will stabilize the system as shown in
Fig. 5. Using the root locus method, it is only possible to move the poles along the locus lines byadjusting the gain. However, using the PP control system, we have a gain matrix with which thepoles can be moved anywhere in the complex plane, as shown in Fig. 5. We first choose thedesired pole location of [−24 −6 −12], for which we obtain the response system at Tr = 0.120 s and

(a)

(b)
Fig. 5. (Color online) Response system with PP control. (a) Roll angle response at desired pole position [−24 −6−12]. (b) Roll angle response at desired pole position [−24 −6 −12] × 4.

Sensors and Materials, Vol. 35, No. 2 (2023)

359

Ts = 0.899 s, and if we attempt to move a large number of eigenvalues extremely far to the left,
we achieve a rapid reaction, as shown in Fig. 5(b).
There are some deficiencies in choosing the poles in the PP method, especially for a highorder system. We wish to retain the poles closest to the imaginary axis, but this causes thesystem to behave as a conventional second-order system, because the poles move more slowly
and typically govern the system’s response. Attempting to move a large number of eigenvalues
extremely far to the left of the imaginary axis to achieve a rapid reaction revealed that ouractuators lack the necessary speed or power to produce the desired response. This is because it
requires greater actuator torque to move the eigenvalues from their initial position. Lastly, in ourmathematical model, we communicate back every state, but we are unable to do this in practice.
To solve this problem, sensors will be added to the system to measure the missing states. In
contrast, rather than randomly selecting poles in the PP control method, the LQR control method
is expected to be a more systematic process.
4.2

LQR controller

The PP and LQR methods have exactly the same physical structure. Also, the key to theirimplementation is the same, but how the K value is chosen is different. Using the PP controller,
we determined the K value by deciding where we wanted to place the closed-loop poles.
However, with this method, it is necessary to find the optimal location for the closed-loop poles,
which is essential for high-order systems or systems with multiple actuators. Thus, with the LQR
method, we do not choose the locations of the poles. Instead, we find the best K-matrix value bychoosing the closed-loop characteristics that we consider important.
As discussed previously, the linear time-invariant system was expressed in the state-space
form [Eq. (23)], and the state variable of the feedback control can be found from Eq. (24). Next,
the quadratic cost function for the system is defined as=J∫ ( x Qx + u Ru ) dt ,
T

T

(28)

where Q is a positive definite or positive semi-definite symmetric matrix when used inconjunction with R, a symmetric positive definite matrix. Both matrices are weight matrices,and each of them should be diagonal. Each element of the weight matrix has an associated valuethat reflects its effect on the performance index J. Here, we adjust Q to penalize the performanceand adjust R to penalize the amplitude of the actuator.
From the state-space model system described in Eq. (22), we design a full-state feedback
control using LQR with the identity matrix as the starting matrix for Q. The first diagonal entry
corresponds to the EMBot angular error, and the second is related to the angular rate of the
EMBot. There is also an actuation input for the input rotation torque system. These components
work together to create the torque command. Therefore, R is a single value. Then the optimal
feedback is obtained using the LQR command and from the state-space object that represents theclosed-loop dynamics. Finally, using the designed controller, we can observe the response timeof the system with an initial tilt position of 0.087 rad or 5°. Figure 6 shows the performance ofthe control system in keeping the EMBot balanced in the vertical position.

360

Sensors and Materials, Vol. 35, No. 2 (2023)

(a)

(b)

(c)

(d)

Fig. 6. (Color online) Response system with LQR control showing roll angle responses for (a) Q = [1 0 0; 0 1 0; 0 01] and R = 1, (b) Q = [1 0 0; 0 1 0; 0 0 1] and R = 4, (c) Q = [10 0 0; 0 0.1 0; 0 0 1] and R = 0.01, and (d) Q = [40 0 0; 0
0.025 0; 0 0 40] and R = 0.01.

As shown in Figs. 6(a)–6(d), the system with different Q and R values has different response
times of Tr = 0.302 s and Ts = 3.602 s, Tr = 0.383 s and Ts = 5.504 s, Tr = 0.161 s and Ts = 1.284 s,
and Tr = 0.102 s and Ts = 0.844 s, respectively, with zero steady-state error in each case. Whenthe control signals are active, they generate a torque that accelerates the EMBot over time;
therefore, the torque is proportional to the error’s integral. The longer the acceleratation, thegreater the torque employed. Utilizing less torque and increasing the penalty on R by a factor offour results in a slower response. Moreover, by penalizing the angular rate portion of the Q
matrix and the R value in more aggressive tuning, as respectively shown in Figs. 6(c) and 6(d),we obtain a much faster reaction of the EMBot roll response that can meet the requirements ofour response system. As shown in Fig. 7, for different initial inclinations, we obtain different
EMBot roll responses. Finally, these optimal values of the LQR controller then can be supplied
to the embedded processor of the EMBot to maintain the stability.

Sensors and Materials, Vol. 35, No. 2 (2023)

361

(a)

(b)

Fig. 7.

5.

(Color online) Response system with LQR control for different initial inclination angles.

Conclusions

In this study, we designed the posture control stabilization system of the EMBot using a
CMG. A reduced mechanical model of the EMBot was designed, which included an inertial
sensor to provide the input data of the EMBot’s roll angle with the necessary components of thesystem. The EMBot system was also modeled, where Lagrange’s equation was used to derive thenonlinear mathematical model of the EMBot in a generalized coordinate system. As a control
system, the PP and LQR control methods were designed to simulate and evaluate theperformance of the EMBot system. The experimental results showed that both control methods
have a good response and the ability to return the EMBot to the equilibrium position after it has
been tilted. However, the proposed LQR controller ensures that the EMBot has less vibration, afaster response, and greater robustness than the PP method. This is because the optimal gain
value was determined by determining the closed-loop characteristic rather than by choosing thepole position. The LQR controller designed in this study is expected to be applied to the actual
EMBot.

Acknowledgments
This research was supported by the Ministry of Science and ICT (MSIT), Korea, under the
ICT Challenge and Advanced Network of HRD (ICAN) program (IITP-2022-2020-0-01825)
supervised by the Institute of Information & Communications Technology Planning &Evaluation (IITP). This research was partly supported by the Institute for Information &Communications Technology Promotion (IITP) grant funded by the Korea Government (MSIT)
and the Korea Institute for Advancement of Technology (KIAT) grant funded by the Korea

362

Sensors and Materials, Vol. 35, No. 2 (2023)

Government (MOTIE) (P0008703, The Competency Development Program for Industry
Specialist).

References
1 K. J. Astrom, R. E. Klein, and A. Lennartsson: IEEE Control Syst. Mag. 25 (2005) 26. https://doi.org/10.1109/
MCS.2005.1499389
2 H. Fu: Bull. Jpn. Soc. Mech. Eng. 9 (1966) 284. https://doi.org/10.1299/jsme1958.9.284
3 L. Guo, Q. Liao, S. Wei, and Y. Huang: The 2010 IEEE Int. Conf. Information and Automation (IEEE, 2010)
1613–1617. https://doi.org/10.1109/ICINFA.2010.5512251
4 C. Xiong, Z. Huang, W. Gu, Q. Pan, Y. Liu, X. Li, and E. X. Wang: 2018 3rd Int. Conf. Robotics and Automation
Engineering (IEEE, 2018) 24–28. https://doi.org/10.1109/ICRAE.2018.8586765
5 C. H. Chiu and C. Y. Wu: IEEE Access 8 (2020) 84837. https://doi.org/10.1109/ACCESS.2020.2992792
6 H. Jin, Y. Zhang, H. Zhang, Z. Liu, Y. Liu, Y. Zhu, and J. Zhao: Math. Problems Eng. (2018). https://doi.
org/10.1155/2018/5240594
7 N. K. Vu and H. Q. Nguyen: Math. Problems in Eng. 2020 (2020). https://doi.org/10.1155/2020/6724382
8 D. A. Bravo M., C. F. Rengifo R., and J. F. Díaz O.: IEEE 4th Colombian Conf. Automatic Control (IEEE, 2019)
1–6. https://doi.org/10.1109/CCAC.2019.8920870
9 S. C. Spry and A. R. Girard: Vehicle Syst. Dynamics 46 (2008) 247. https://doi.org/10.1080/00423110801935863
10 M. H. Shafiei and M. Emami: Syst. Sci. Control Eng. 7 (2019) 12. https://doi.org/10.1080/21642583.2018.155506
211 S. H. Park and S. Y. Yi: Int. J. Control Autom. Syst. 18 (2020) 217. https://doi.org/10.1007/s12555-018-0749-7
12 D. Karnopp: Vehicle Syst. Dynamics. 37 (2002) 145. https://doi.org/10.1076/vesd.37.2.145.3535
13 R. Lot and J. Fleming: Vehicle Syst. Dynamics. 57 (2018) 1. https://doi.org/10.1080/00423114.2018.1506588
14 P. Gogoi, M. Nath, B. T. Doley, A. Boruah, and H. J. Barman: Int. J. Eng. Tech. 9 (2017) 2051. https://doi.
org/10.21817/ijet/2017/v9i3/1709030206
15 D. Horla and A. Owczarkowski: 2015 Int. Conf. Industrial Eng. and Syst. Management (IEEE, 2015) 998–1003.
https://doi.org/10.1109/IESM.2015.7380276
16 P. Y. Lam: 2011 IEEE 5th Int. Conf. Cybernetics and Intelligent Syst. (IEEE, 2011) 247–252. https://doi.
org/10.1109/ICCIS.2011.6070336

About the Authors
Rodi Hartono is an electrical engineer with a strong interest and ability in AI
convergence, control systems, robotics, image recognition, deep learning, andautomation systems. He has worked extensively in the field of robotics andintelligent systems and has more than 12 years of experience working as
lecturer and a full-time researcher. He is also responsible for managing andsupervising the Indonesian Computer University robotics team to performresearch and build computing robots that have been entered in regional,
national, and international robot competitions. He also designs, researches,and builds robotics products required by the industrial community. He
received his bachelor’s degree from Indonesian Computer University,
Indonesia, in 2010 and his master’s degree from the School of Electrical andInformatics Engineering, Bandung Institute of Technology, Indonesia, in 2014.
Since 2021, he has been pursuing a doctor’s degree at the Department of
Artificial Intelligence Convergence, Busan University of Foreign Studies,
Republic of Korea. (rodihartonoo@gmail.com)

Sensors and Materials, Vol. 35, No. 2 (2023)

		

363

Seung Bin Kim received his bachelor’s degree from Busan University ofForeign Studies, Republic of Korea, in 2021. Since 2021, he has been pursuing
his master’s program at the Department of Artificial Intelligence Convergence,
Busan University of Foreign Studies. He has a strong interest in AI
convergence, image recognition, deep learning, and IoT.
(skbbq123@naver.com)
Patrick Tshibang A Kalend received his bachelor’s degree in computerscience engineering, focusing on the field of information system engineering,from Université Protestante de Lubumbashi, Democratic Republic of Congo,
in 2016. After his graduation, he presented lectures and led students in theirprojects for graduation. Since 2022, he has been pursuing his master’s degree
at the Department of Artificial Intelligence Convergence, Busan University ofForeign Studies. He has a strong interest in AI, computer vision, robotics, and
IoT. (patricktshibang7@gmail.com)
Nam Kyun Baik is a professor in the Department of Smart Convergence
Security, Busan University of Foreign Studies. He received his B.S., M.S., andPh.D. degrees from the School of Electronic Engineering, Soongsil University.
From 2000 to 2017, he was a senior researcher at Korea Internet & Security
Agency. He has a strong interest in convergence security, security consulting,information security management systems, AI security, and IoT security.
(namkyun@bufs.ac.kr)
Kyoo Jae Shin is a professor of intelligent robot science at Busan Universityof Foreign Studies, South Korea. He is the director of Future Creative Science
Research Institute at BUFS. He received his B.S. degree in electronics
engineering in 1985, his M.S. degree in electrical engineering from Cheonbuk
National University in 1988, and his Ph.D. degree in electrical science from
Pusan National University in 2009. Dr. Shin has been a professor at Navy
Technical Education School and a main director and research associate ofdynamic stabilization systems at Busan Defense Weapon Research Institute.
He has also researched and developed a fish robot, a submarine robot, an
automatic dog spaying robot operating in a glass room, an automatic milking
robot using a manipulator, a personal electrical vehicle, a smart accumulated
aquarium using a heat pump, a solar tracking system, a 3D hologram system,
and a gun/turret stabilization system. He is interested in intelligent robots,
image signal processing application systems, smart farms, and aquariums
using new energy and IoT technology. (kyoojae@bufs.ac.kr)