Dynamics of a Four Wheeled Wall Climbing Robot

Anokhee Chokshi

and Jaina Mehta

School of Engineering and Applied Science, Ahmedabad University, Ahmedabad, Gujarat, India

Keywords:

Wall Climbing Robot, Dynamic Modeling, Wheel Slip, Wheel Dynamics, Vertical Contact Forces.

Abstract:

In this paper, a mathematical model of a four wheeled independently driven Wall Climbing Robot (WCR) is

developed. The consideration of only the kinematic model for a WCR may reduce its performance during sud-

den changes in acceleration and turning. To address this issue, a dynamic model that includes the wall/wheel

interactions i.e., lateral and longitudinal frictional forces, is proposed. The effect of wheel slip is considered

for a more realistic dynamic model. The models that are typically developed for the vertical contact forces, an

important parameter affecting the frictional forces, assume equal weight distribution on the wheels. However,

to accommodate the load shift due to the variation in acceleration along with the distribution of adhesion force,

lateral and longitudinal acceleration components are also taken into account. The major components of this

WCR model consist of the wheel dynamics, the wall/wheel interactions, the kinematics and the dynamics.

Simulations are performed to demonstrate and verify the model. The suggested model in the future can be

applied in the development of control algorithms for wheeled WCRs.

1 INTRODUCTION

Wall Climbing Robots (WCR)s have been extensively

studied in recent years for their potential applications

in regular maintenance and inspection of urban struc-

tures that may be arduous and dangerous to work on

due to their intricate construction. The use of these

robots ensures safety for humans to work in hostile

environments and ease in access to these structures.

Locomotion is the pivotal issue for the design of

any mobile robot. In the case of a WCR, there exist

different locomotion mechanisms: bio-inspired type

(Chen et al., 2015), (Aksak et al., 2008), legged type

(Palmer et al., 2009), (Zhan et al., 2017) and wheeled

type (Faisal and Chisty, 2018), (Jun Li et al., 2009). In

comparisonto vehicles that travelon the ground, these

robots require a potent adhesive mechanism to create

a ﬁrm grip on the wall. Generally, one of the three

types of adhesion mechanisms: suction cups (Shujah

et al., 2019), (Sano et al., 2017), magnetic adsorp-

tion (Gong et al., 2010), (Hu et al., 2017) or thrust

force(Inoue et al., 2018), (Alkalla et al., 2015) is used

to solve the purpose.

In this paper, a mathematical model for a WCR

which uses wheels for locomotion and thrust force for

adhesion is developed. The selection of these mecha-

https://orcid.org/0000-0003-3859-6543

https://orcid.org/0000-0003-1972-401X

nisms is based on the fact that the thrust force required

for adhesion, which is generated using a propeller or

impeller, allows the robot to travel over surfaces with

different gradients and the wheels enable the WCRs

to attain higher velocities.

Several models for the dynamics of ground ve-

hicles exist in the literature. The model developed

in (Sebsadji et al., 2008) is for the case of a vehi-

cle with two steering wheels traveling on a road with

a non-zero slope angle. (Liao et al., 2019) have de-

veloped a mathematical model for a four wheel inde-

pendently driven skid steer mobile robot. A model

for wheel dynamics has also been presented here.

(Kiencke and Nielsen, 2000) and (Wang, 2013) have

introduced models for normal forces in addition to the

vehicle lateral and longitudinal dynamic model for a

four wheeled vehicle traveling on the ground. The

theories of such models can be further extended to

formulate models that establish the case of a WCR.

A considerable amount of research has been car-

ried out for developing mathematical models for

WCRs using different approaches. Most researchers

ignore robot dynamics and only take kinematic

models into account for the purpose of simplicity

(Minzhao et al., 2015), (Gao and Kikuchi, 2004).

(Panchal et al., 2014) have considered the forces act-

ing on the WCR when it is traveling on a vertical wall.

But for the vertical contact forces, equal weight dis-

530

Chokshi, A. and Mehta, J.

Dynamics of a Four Wheeled Wall Climbing Robot.

DOI: 10.5220/0010615605300536

In Proceedings of the 18th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2021), pages 530-536

ISBN: 978-989-758-522-7

tribution of the robot on the four wheels is assumed.

(Xu and Liu, 2017) have presented a simpliﬁed model

for the dynamics of a four wheeled differential drive

WCR. However, the moment of inertia and the rolling

friction between the wheels and the wall are ignored

here. Certain other complex and complicated models,

which account for obstacle avoidance have also been

developed in (Xu et al., 2015) and (Ioi, 2012).

The main theme of the paper lies in the de-

velopment of a dynamic model that includes the

wall/wheel interactions i.e lateral and longitudinal

frictional forces acting on a WCR. The major pa-

rameters affecting these frictional forces are vertical

contact forces and wheel slip. In contrast to ground

robots where the vertical contact forces are depen-

dent on the weight distribution; in the case of a WCR,

they depend on the adhesion force. As discussed in

(Kiencke and Nielsen, 2000) and (Wang, 2013), in

this paper, vertical contact forces are derived based

on the load shift due to the variation in acceleration

and the distribution of adhesion force on each wheel.

The WCR dynamics proposed in this paper also ac-

count for the effect due to wheel slip, based on the

models of rolling friction between the wheels and the

ground for a mobile robot (Liao et al., 2019), (Cerkala

and Jadlovska, 2014). The main contribution of this

paper lies in the fact that it provides a realistic model

for four wheeled WCR. The proposed model can be

used for implementing control algorithms to enhance

the performance of the WCRs in the future.

The rest of the paper is organized as follows. Sec-

tion 2 presents the main contribution of the proposed

mathematical model. Section 3 validates the mathe-

matical model through simulations. Section 4 draws

the conclusion of the proposed mathematical model

and includes future direction.

2 SYSTEM MODELING

The design of a WCR consists of two parts: locomo-

tion and adhesion. In this paper, the WCR has four

wheels for locomotion, which can be driven indepen-

dently to maneuver the robot on a wall that is perpen-

dicular to the ground. For adhesion, it is considered

that the robot uses thrust force. This thrust force can

be generated by the blades of a propeller or impeller,

which are made to rotate such that air is thrown out

from the upper side of the robot. This creates a pres-

sure difference between the two sides of the robot and

increases the friction force between the wheels of the

robot and the wall. Figure 1 represents the forces act-

ing on a WCR when it is placed on the wall.

In this paper, it is assumed that all the wheels are

in contact with the wall at all times. This implies that

there is no roll or pitch motion of the robot. It is also

∗

1,2

∗

1 2

x, y)

(a) Front view of the WCR. (b) Isometric view of the WCR.

Figure 1: Representation of the forces acting on the WCR when it is at an arbitrary angle ψ.

Dynamics of a Four Wheeled Wall Climbing Robot

531

Wheel

Dynamics

Kinematics

Vertical

contact

forces

Angular velocity

of wheels

Lateral

frictional forces

Lateral and

Longitudinal

acceleration

Normal

forces

Adhesion

force

Input

torque

Lateral and

Longitudinal velocity

Angular

velocity

Position and

Orientation

Figure 2: Mathematical model of the WCR.

assumed that the centre of mass is the same as the

geometrical centre of the robot. A thrust force F

which creates enough adhesion for the robot to stick

to the wall, acts perpendicular to the wall.

As per Figure 1, let XYZ be the global co-ordinate

system and xyz be the co-ordinate system attached to

the robot. (X,Y) and ψ are the position and orientation

of the robot with respect to the global co-ordinate sys-

tem. l

and l

represent the distance between the cen-

tre of mass and the centres of the rear wheel and the

front wheel respectively, b is the distance between the

left and right wheels and H is the distance between

the centre of mass and the wall. m is the mass of the

robot. The gravitational acceleration acts in the −X

direction and has two components in x and y direc-

tion in the local co-ordinate frame that is attached to

the robot, denoted by g

= g cosψ and g

= g sinψ.

The mathematical model that is proposed in this

paper is illustrated by the block diagram in Figure 2.

It consists of four parts - the dynamics of the wheel,

which give a relation between the input torque and an-

gular velocity of each wheel while taking the damping

effect into account; the vertical contact forces on each

wheel; the WCR dynamics, which include the effect

of wheel slip; and the kinematics of the WCR, which

give the position and orientation of the robot w.r.t. the

global co-ordinates. The model of each sub-part is

discussed in detail in the subsequent sub-sections.

2.1 Vertical Contact Forces

When the mobile robot travels on the ground, the total

vertical force is caused by the force due to the earth’s

gravitational acceleration. Whereas, when the robot

is traveling on a wall, which is perpendicular to the

ground, the total vertical force is caused due to the

adhesion force. Apart from adhesion force, other fac-

tors like the longitudinal and lateral acceleration of

the robot chassis and the geometry of the robot are

considered in determining the normal force on each

wheel as discussed in (Kiencke and Nielsen, 2000),

(Wang, 2013). However, certain other factors like the

wall surface geometry and air resistance are not con-

sidered and some reasonable simpliﬁcations are made

for reducing the complexity.

The contact forces alter as the vehicle acceleration

changes. Due to inertia, the acceleration of the chas-

sis (a

, a

) is in the opposite direction of the longi-

tudinal and lateral accelerations (a

, a

) i.e. when the

robot accelerates in the forward direction, the chas-

sis accelerates in the backward direction because the

wheel load shifts to the rear axle. Hence, a

= −a

and a

= −a

Since it is assumed that there is no pitch, the force

due to acceleration in the +x-direction causes a torque

which reduces the load on the front axle and increases

the load on the rear axle. Here, axle is an imaginary

line that connects the centres of the front wheels or

rear wheels. As seen in Figure 1 (b), the normal force

acting on the front wheels (F

) is given by cal-

culating the total moment on the rear axle.

+ F

)(l

+ l

) = −ma

H − mg

H + F

(1)

The front and the rear axle are assumed to be

decoupled. As seen in Figure 1, m

∗

1,2

and m

∗

3,4

de-

note the virtual mass present at the front and rear

axle respectively. They can be expressed as m

∗

1,2

+ F

)/a

and m

∗

3,4

= (F

+ F

)/a

, where a

is the acceleration in the direction perpendicularto the

wall. Based on Equation (1), the virtual mass at the

front axle can be rewritten as:

∗

1,2

= −

+ l

)

−

gcosψH

+ l

)

m(l

)

+ l

)

(2)

Since it is also assumed that there is no roll, as

shown in Figure 1, considering the torque balance at

ICINCO 2021 - 18th International Conference on Informatics in Control, Automation and Robotics

532

the front right wheel, the normal force acting on the

front left wheel is calculated as:

(b) = m

∗

1,2

(b/2) + m

∗

1,2

H + m

∗

1,2

H (3)

When the longitudinal and lateral coupling is not

taken into account, the equations of the normal forces

acting on each wheel can be expressed as:

= −

m(a

+ gcosψ) H

2(l

+ l

)

2(l

+ l

)

m(l

)(a

+ gsinψ) H

(b)(l

+ l

)

= −

m(a

+ gcosψ) H

2(l

+ l

)

2(l

+ l

)

−

m(l

)(a

+ gsinψ) H

(b)(l

+ l

)

m(a

+ gcosψ) H

2(l

+ l

)

2(l

+ l

)

m(l

)(a

+ gsinψ) H

(b)(l

+ l

)

m(a

+ gcosψ) H

2(l

+ l

)

2(l

+ l

)

−

m(l

)(a

+ gsinψ) H

(b)(l

+ l

)

(4)

The above equations consider the effect of adhe-

sion force; and the longitudinal and lateral acceler-

ations on the vertical contact force acting on each

wheel.

2.2 Kinematic Model of the WCR

Based on the orientation of the co-ordinate systems as

shown in Figure 1, the kinematic model of the WCR

is expressed as:

X = v

cos(ψ) + v

sin(ψ)

Y = −v

sin(ψ) + v

cos(ψ)

ψ = ω (5)

, v

) denote the velocity of the robot in the x and

y directions respectively and ω is the angular velocity

of the robot.

2.3 Dynamic Model of the WCR

The dynamic model of the WCR considering slip

compensation is expressed as:

m ˙v

∑

i=1

+ mv

ω− mg

m ˙v

∑

i=1

− mv

ω− mg

ψ =

∑

i=1

(6)

and F

are the longitudinal and lateral fric-

tional forces. The moment around z-axis is given by

and the moment of inertia around z-axis is I

Generally, in the case of ground robots, the fric-

tion forces acting against the mobile robot are ig-

nored with the assumption of pure rolling. However,

it becomes necessary to include them in the dynamic

model of the WCR since there will be no adhesion in

their absence. A simpliﬁed model for friction forces

due to ground and wheel interactions based on (Liao

et al., 2019) is used.

= F

)

= F

)

∑

i=1

= l

+ F

) +

(−F

+ F

−F

+ F

) − l

+ F

) (7)

are the normal forces which are calculated in

Section 2.1. ; µ

and µ

are the rolling and sliding

co-efﬁcients of friction; s

and s

represent the lon-

gitudinal and lateral slip for each wheel and can be

calculated as:

= rω

− v

+ (b/2)ω, s

= v

+ l

= rω

− v

− (b/2)ω, s

= v

+ l

= rω

− v

+ (b/2)ω, s

= v

− l

= rω

− v

− (b/2)ω, s

= v

− l

ω (8)

is the angular velocity of each wheel. This

is obtained using the input torque on each wheel de-

scribed in the following sub-section. From Equa-

tion (8), s

+ s

and the dynamic feature of

the friction force can be approximated as: S

) =

atan(90s

2.4 Wheel Dynamics

The rotational dynamics of each wheel are derived

from Figure 3.

+ c

= u

− rF

(9)

Dynamics of a Four Wheeled Wall Climbing Robot

533

Figure 3: Wheel rotational motion.

represents the moment of inertia, c

is the

damping co-efﬁcient, ω

is the angular velocity, u

denotes the input torque and r is the radius of the

wheel.

3 SIMULATION RESULTS

The realistic dynamic model that includes wall and

wheel interactions and wheel slip for the WCR is sim-

ulated in the Simulink environment. The response of

the proposed model is generated with different robot

orientations and by providing different input torques

to the robot wheels. The solution of the model equa-

tions is obtained by ode45 solver, with the error tol-

erance set to 10

−4

and the simulation time set to 20s.

The lateral velocity and its derivatives are bounded

based on the robot geometry and physical constraints.

For the purpose of the simulation, it is consid-

ered that b = 610 × 10

−3

m, l

= 175.01 × 10

−3

= 175.01× 10

−3

m, H = 33.38× 10

−3

m, r = 35×

−3

m, c

= 0.1N/m, J

ωi

= 3.68× 10

−5

kgm

, µ

0.5, µ

= 0.9, m = 1.75kg, I

= 11.74 × 10

−2

kgm

and F

= 51.5N.

As illustrated in Figure 4, for Case 1, when the

WCR is initially at ψ = 0, a constant and identical in-

put torque is given to all the four wheels for the ﬁrst

time interval. This results in the upward movement

of the WCR i.e. movement in the +X direction. Due

to the consideration of lateral frictional forces, minor

changes in the orientation of the robot ψ and move-

ment in the Y-axis are observed. In the second time

interval, the input torque of the same magnitude but

opposite in direction is given to all four wheels. This

produces results similar to the ﬁrst interval. However,

the movement of the robot is in reverse direction i.e.

in the -X direction. It is important to note that the

same magnitude of torque in the reverse direction in

this case produces a greater amount of change in the

position of the robot. This is caused due to the grav-

itational acceleration acting in the -X direction. No

torque is given to the wheels in the third interval. As

−2 · 10

−2

×10

−3

−1

t = 0 s

7.5s

15s

20s

Y (m)

X (m)

2.01

×10

−3

t (s)

ψ (rad)

−1.5

1.5

t (s)

X (m)

−0.5

×10

−3

Y (m)

X Y

t (s)

(N)

−0.1

0.1

t (s)

(m/s)

−4

×10

−5

t (s)

(m/s)

Figure 4: (Case 1) : (X

) = (0,0); ψ

= 0; u

= 0.5 Nm

(0 ≤ t ≤ 7.5); u

= -0.5 Nm (7.5 < t ≤ 15) and u

= 0 Nm

(15 < t ≤ 20).

the robot is in motion, it takes a ﬁnite time for it to

preserve its ﬁnal position in X and Y directions.

It can be observed from the wheel slip graphs

in Figure 4 that when a constant and identical input

torque is given to all four wheels, the wheel slip is

close to zero. At t = 7.5s and t = 15s, i.e. at the

points when the torque value changes, there is a sud-

den change in wheel slip.

The longitudinal and lateral accelerations are zero

when the input torque is constant. It can be observed

from Figure 4 that the normal forces remain constant

for each time interval as the only other factors affect-

ing them are the gravitational acceleration and ad-

hesion force, which are constant. A sudden change

is seen only at the points when the input torque is

changed.

Figure 5 illustrates the results of Case 2, where the

input torque remains the same as Case 1, butthe initial

orientation of the robot is changed to ψ = π/2. This

means that the robot would replicate the movement of

the robot as in Case 1, but in the Y-axis instead. How-

ever, due to the absence of gravitational acceleration

in the direction of movement of the robot, when the

robot is at an angle ψ = π/2, the same magnitude of

torque in the reverse direction in the second time in-

terval would result in the same change in position as

seen in the ﬁrst time interval. In this case, the effect

of lateral frictional forces is seen in the X-direction.

ICINCO 2021 - 18th International Conference on Informatics in Control, Automation and Robotics

534

−1

−0.5

×10

−4

t = 0s

7.5s

15s

20s

Y (m)

X (m)

1.57

1.571

t (s)

ψ (rad)

×10

−4

t (s)

X (m)

−1.4

0.3

Y (m)

X Y

t (s)

(N)

−0.1

0.1

t (s)

(m/s)

−1.5

1.5

×10

−3

t (s)

(m/s)

Figure 5: (Case 2) : (X

) = (0,0); ψ

= π/2; u

= 0.5 Nm

(0 ≤ t ≤ 7.5); u

= -0.5 Nm (7.5 < t ≤ 15) and u

= 0 Nm

(15 < t ≤ 20).

Observations similar to Case 1 can be made for

the wheel slip and the normal forces acting on each

wheel in Case 2.

0.5

−1

t = 0s

3.7s

7.32s

11s

14.67s

18.2s

20s

Y (m)

X(m)

π/2

t = 0s

3.7s

7.32s

11s

14.67s

18.2s

t (s)

ψ (rad)

−2

t (s)

X (m)

−0.2

1.4

t = 3.7s

7.32s

11s

14.67s

18.2s

Y (m)

X Y

t (s)

(N)

−0.1

0.2

t = 0s

3.7s

7.32s

11s

14.67s

18.2s

t (s)

(m/s)

−0.3

0.3

t (s)

(m/s)

Figure 6: (Case 3) : (X

) = (0,0); ψ

= 0; u

r(1,3)

= 2 Nm

and u

r(2,4)

= 0.5 Nm (0 ≤ t ≤ 20).

As illustrated in Figure 6, in Case 3, wheels on

the left are given higher torque than the wheels on the

right. This type of differential input torque results in

a turn-like movement of the robot in the clockwise di-

rection. Therefore, change in both X and Y directions

is seen here.

In this case, a continuous change in the longitu-

dinal wheel slip is observed. The wheel slip takes

both positive and negative values. Based on Equa-

tion (8), the positive value of the s

indicates slipping

and the negative value indicates the skidding of the

wheel. The change in the longitudinal wheel slip in

Case 3 is due to differential input torque, which leads

to a continuous change in the orientation. When the

orientation of the robot is π/2 or 3π/2, the slip value

is near to zero.

The maximum skid is observed when ψ = π and

maximum slip is observed when ψ = 2π. It is im-

portant to note that if the difference between the input

torques of the left and right wheels is increased, it will

increase the magnitude of wheel slip.

Since the robot is turning, the longitudinal and lat-

eral acceleration of the robot changes constantly. This

leads to continuously changing normal forces on each

wheel.

4 CONCLUSION

This paper introduces a more realistic dynamic model

of a four wheeled WCR by considering wheel slip

and vertical contact forces on each wheel. The sim-

ulations are based on reasonable assumptions for the

physical constraints of the WCR when it is traveling

on the wall. The analysis of these simulations for

different conditions of input torque suggests that the

model is valid. The simulations also reveal that input

wheel torque and the orientation are factors that affect

the wheel slip and vertical contact forces of the WCR.

The current model only allows the yaw motion of

the robot with the consideration that all the wheels

are in contact with the wall at all times. Therefore, as

future work, adding the consideration of pitch and roll

will allow the model to be suitable even for the wall

surfaces that are irregular or not ﬂat. Moreover, the

implementation of control algorithms in the proposed

model will enable the derivation of optimal values for

the parameters like adhesion force and input torques

for the wheels. Subsequently, a physical model can

be constructed and the proposed mathematical model

can be veriﬁed experimentally.

Dynamics of a Four Wheeled Wall Climbing Robot

535

ACKNOWLEDGEMENTS

The authors would like to express their gratitude to

Dr. Harshal Oza (Associate Professor, Pandit Deen-

dayal Energy University) for his insights and exper-

tise which supported the research.

REFERENCES

Aksak, B., Murphy, M. P., and Sitti, M. (2008). Gecko

inspired micro-ﬁbrillar adhesives for wall climbing

robots on micro/nanoscale rough surfaces. In 2008

IEEE International Conference on Robotics and Au-

tomation, pages 3058–3063.

Alkalla, M. G., Fanni, M. A., and Mohamed, A.-F. (2015).

Versatile climbing robot for vessels inspection. In

2015 International Conference on Control, Automa-

tion and Robotics, pages 18–23.

Cerkala, J. and Jadlovska, A. (2014). Mobile robot dynam-

ics with friction in simulink. In 22th Annual Confer-

ence Proceedings of the International Scientiﬁc Con-

ference - Technical Computing Bratislava 2014.

Chen, J., Li, G., Zhang, J., and Yu, J. (2015). Caterpillar-

like climbing method incorporating a dual-mode op-

timal controller. IEEE Transactions on Automation

Science and Engineering, 12(4):1492–1503.

Faisal, R. H. and Chisty, N. A. (2018). Design and im-

plementation of a wall climbing robot. International

Journal of Computer Applications, 179(13):1–5.

Gao, X. and Kikuchi, K. (2004). Study on a kind of wall

cleaning robot. In 2004 IEEE International Confer-

ence on Robotics and Biomimetics, pages 391–394.

Gong, Y., Wang, Z., Wang, X., and Xu, J. (2010). Analysis

on turning stress states of magnetic sucking mecha-

nism unit of a large load wall climbing robot. In 2010

International Conference on Measuring Technology

and Mechatronics Automation, volume 1, pages 570–

573.

Hu, S., Peng, R., He, K., Li, J., Cai, J., and Zhou, W. (2017).

Structural design and magnetic force analysis of a new

crawler-type permanent magnetic adsorption wall —

climbing. In 2017 IEEE International Conference on

Information and Automation (ICIA), pages 598–603.

Inoue, F., Honjo, A., Makino, T., and Kwon, S. (2018). In-

spection robot system using duct fan and deterioration

estimation of building wall that can be applied even

in disaster. In 2018 18th International Conference

on Control, Automation and Systems (ICCAS), pages

331–334.

Ioi, K. (2012). Design of wall-climber with coaxial pro-

peller’s thruster. In The 43th International Symposium

on Robotics At: Taipei, pages 168–172.

Jun Li, Xueshan Gao, Ningjun Fan, Kejie Li, and Zhihong

Jiang (2009). Bit climber: A centrifugal impeller-

based wall climbing robot. In 2009 International

Conference on Mechatronics and Automation, pages

4605–4609.

Kiencke, U. and Nielsen, L. (2000). Automotive Control

Systems: For Engine, Driveline and Vehicle. Springer-

Verlag, Berlin, Heidelberg, 1st edition.

Liao, J., Chen, Z., and Yao, B. (2019). Model-based co-

ordinated control of four-wheel independently driven

skid steer mobile robot with wheel–ground interaction

and wheel dynamics. IEEE Transactions on Industrial

Informatics, 15(3):1742–1752.

Minzhao, X., Jichen, L., and Xiaoyi, L. (2015). The in-

novation design of the magnetic adsorption climbing-

wall ﬂaw detection robot. In The 27th Chinese Control

and Decision Conference (2015 CCDC), pages 4923–

4926.

Palmer, L. R., Diller, E. D., and Quinn, R. D. (2009). De-

sign of a wall-climbing hexapod for advanced maneu-

vers. In 2009 IEEE/RSJ International Conference on

Intelligent Robots and Systems, pages 625–630.

Panchal, K., Vyas, C., and Patel, D. (2014). Developing

the prototype of wall climbing robot. In International

Journal of Advance Engineering and Research Devel-

opment [IJAERD], Issue 3, volume 1.

Sano, S., Ohara, K., Ashizawa, S., Ichikawa, A., Suzuki, S.,

Omichi, T., and Fukuda, T. (2017). Development of

wall climbing robot using passive joint and vacuum

pad on rough surface. In 2017 International Sym-

posium on Micro-NanoMechatronics and Human Sci-

ence (MHS), pages 1–3.

Sebsadji, Y., Glaser, S., Mammar, S., and Dakhlallah, J.

(2008). Road slope and vehicle dynamics estimation.

In 2008 American Control Conference, pages 4603–

4608.

Shujah, A., Habib, H., Shaikh, S., Ishfaq, A. R., Tahir, H.,

and Iqbal, J. (2019). Design and implementation of

semi-autonomous wall climbing robot using vacuum

suction adhesion. In 2019 IEEE 17th World Sympo-

sium on Applied Machine Intelligence and Informatics

(SAMI), pages 275–280.

Wang, B. (2013). State observer for diagnosis of dynamic

behavior of vehicle in its environment. Theses, Uni-

versit´e de Technologie de Compi`egne.

Xu, F., Shen, J., and Jiang, G. (2015). Kinematic and dy-

namic analysis of a cable-climbing robot. Interna-

tional Journal of Advanced Robotic Systems, 12:1.

Xu, Y. and Liu, R. (2017). Concise method to the dynamic

modeling of climbing robot. Advances in Mechanical

Engineering, 9:168781401769167.

Zhan, Q., Yang, L., Zhang, Y., Ma, Y., and Rahmani, A.

(2017). Research on torque optimization of biped

wall climbing robot based on genetic algorithm. In

2017 International Conference on Computer Tech-

nology, Electronics and Communication (ICCTEC),

pages 1030–1035.

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