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Development of a novel quadruped hybrid wheeled-legged mobile robot with telescopic legs

Shuaiby Mohamed 1 , 2 1 , 2 ^(1,2){ }^{1,2}. , YoungWoo Im 2 2 ^(2)^{2}, HyeonSang Shin 2 2 ^(2){ }^{2}, Youngshik Kim 2 2 ^(2){ }^{2} and Buhyun Shin 2 2 ^(2){ }^{2}

Abstract

This paper presents a novel design of a quadruped hybrid leg-wheel mobile robot comprising two DOFs (a prismatic joint and a revolute joint) for the legs and one rotational joint for the wheel. The study begins by detailing the design of the structure and mechanism of the proposed system. We created the dynamic model of the proposed robot using MATLAB Simscape Multibody. The legged mode gait is developed using three supporting legs and one transferring leg. We developed a walking algorithm for the quadruped robot that comprises six motion steps. The simulation and experimental results demonstrate that our proposed robot has the ability to successfully traverse both flat surfaces and rough terrain. The robot’s design also enables it to perform various modes of movement, including normal vertical and horizontal driving, rotation around the robot’s centre of gravity, rotation in a large arc, and walking on flat terrain.

Keywords

Mobile robotics, quadruped robot, hybrid locomotion, telescopic legs
Date received: 2I March 2024; accepted: II June 2024

Introduction

In recent years, mobile robots have attracted significant research attention due to their potential applications in fields such as search and rescue, transportation, agriculture operations, reconnaissance, surveillance, medical care, petrochemical applications, and maintenance. 1 − 7 1 − 7 ^(1-7){ }^{1-7} However, one of the main challenges faced in research involving these robots is the navigation of complex terrain that includes obstacles, uneven surfaces, and stairs. To address this challenge, researchers have proposed different locomotion mechanisms, such as wheeled, legged, and hybrid systems. 8 − 13 8 − 13 ^(8-13){ }^{8-13} The development of mobile robots has also seen significant advancements over the years, as various designs and structures has been used in attempts to achieve efficient locomotion. One such design is the hybrid wheel-leg mobile robot, which combines the best of both worlds: that is, the stability and speed of wheeled robots on the one hand and the adaptability and versatility of legged robots on the other hand. 14 − 17 14 − 17 ^(14-17){ }^{14-17}
Ground locomotion platforms commonly utilise two methods of movement: legs and wheels. Most ground animals have evolved agile and robust legs that allow them to move swiftly and smoothly on uneven natural terrain. 18 , 19 18 , 19 ^(18,19){ }^{18,19} By contrast, wheels are a
human invention and designed specifically to roll on flat ground, thereby providing excellent power efficiency and travel speed that are difficult to match when using legs. Therefore, researchers have designed a hybrid platform that combines both legs and wheels, to operate on rough terrain by walking or driving rapidly on flat ground using its wheels, as appropriate for immediate conditions. 20 − 23 20 − 23 ^(20-23){ }^{20-23} This design allows for the versatile use of a robot in different environments. By using a walking gait on rough terrain, the robot can navigate through obstacles and uneven surfaces with ease. On flat ground, the robot can utilise its wheels to achieve rapid movement. This approach is commonly used in mobile robots that must adapt to different types of terrain, such as those used in search and rescue missions or the inspection of outdoor areas.
Table I. Main characteristics of a quadruped hybrid wheeled-legged mobile robots.
Platform Size ( L × W × H ) ( m ) ( L × W × H ) ( m ) (LxxWxxH)(m)(\mathrm{L} \times \mathrm{W} \times \mathrm{H})(\mathrm{m}) DOF per leg Mass (kg) Telescopic legs
Wheeleg robot 26 26 ^(26){ }^{26} 0.66 × 1.11 × 0.4 0.66 × 1.11 × 0.4 0.66 xx1.11 xx0.40.66 \times 1.11 \times 0.4 4 25 2
TITAN-XIII 27 27 ^(27){ }^{27} 0.213 × 0.5584 × 0.34 0.213 × 0.5584 × 0.34 0.213 xx0.5584 xx0.340.213 \times 0.5584 \times 0.34 5 5.65 No
JINPOOG 28 28 ^(28){ }^{28} 1.1 × 0.4 × 1.2 1.1 × 0.4 × 1.2 1.1 xx0.4 xx1.21.1 \times 0.4 \times 1.2 - 120 No
Xiaotian-Hybrid 29 29 ^(29){ }^{29} 0.7 × 0.4 × 0.5 0.7 × 0.4 × 0.5 0.7 xx0.4 xx0.50.7 \times 0.4 \times 0.5 4 30 No
HuboDog 36 36 ^(36){ }^{36} 0.8 × 0.34 × 0.86 0.8 × 0.34 × 0.86 0.8 xx0.34 xx0.860.8 \times 0.34 \times 0.86 3 42 No
HyTRo- 31 31 ^(31){ }^{31} 0.52 × 0.398 × 0.42 0.52 × 0.398 × 0.42 0.52 xx0.398 xx0.420.52 \times 0.398 \times 0.42 3 7 No
FUHAR 32 32 ^(32){ }^{32} 0.453 × 0.245 × 0.265 0.453 × 0.245 × 0.265 0.453 xx0.245 xx0.2650.453 \times 0.245 \times 0.265 - 9.8 No
Scout II 33 33 ^(33){ }^{33} 0.323 (leg length) 2 20.865 4
Kirin 34 34 ^(34){ }^{34} 0.7 × 0.24 × 0.6 0.7 × 0.24 × 0.6 0.7 xx0.24 xx0.60.7 \times 0.24 \times 0.6 3 50 4
Proposed system 0.37 × 0.22 × 0.21 I 0.37 × 0.22 × 0.21 I 0.37 xx0.22 xx0.21 I0.37 \times 0.22 \times 0.21 I 2 1.47 4
Platform Size (LxxWxxH)(m) DOF per leg Mass (kg) Telescopic legs Wheeleg robot ^(26) 0.66 xx1.11 xx0.4 4 25 2 TITAN-XIII ^(27) 0.213 xx0.5584 xx0.34 5 5.65 No JINPOOG ^(28) 1.1 xx0.4 xx1.2 - 120 No Xiaotian-Hybrid ^(29) 0.7 xx0.4 xx0.5 4 30 No HuboDog ^(36) 0.8 xx0.34 xx0.86 3 42 No HyTRo- ^(31) 0.52 xx0.398 xx0.42 3 7 No FUHAR ^(32) 0.453 xx0.245 xx0.265 - 9.8 No Scout II ^(33) 0.323 (leg length) 2 20.865 4 Kirin ^(34) 0.7 xx0.24 xx0.6 3 50 4 Proposed system 0.37 xx0.22 xx0.21 I 2 1.47 4| Platform | Size $(\mathrm{L} \times \mathrm{W} \times \mathrm{H})(\mathrm{m})$ | DOF per leg | Mass (kg) | Telescopic legs | | :---: | :---: | :---: | :---: | :---: | | Wheeleg robot ${ }^{26}$ | $0.66 \times 1.11 \times 0.4$ | 4 | 25 | 2 | | TITAN-XIII ${ }^{27}$ | $0.213 \times 0.5584 \times 0.34$ | 5 | 5.65 | No | | JINPOOG ${ }^{28}$ | $1.1 \times 0.4 \times 1.2$ | - | 120 | No | | Xiaotian-Hybrid ${ }^{29}$ | $0.7 \times 0.4 \times 0.5$ | 4 | 30 | No | | HuboDog ${ }^{36}$ | $0.8 \times 0.34 \times 0.86$ | 3 | 42 | No | | HyTRo- ${ }^{31}$ | $0.52 \times 0.398 \times 0.42$ | 3 | 7 | No | | FUHAR ${ }^{32}$ | $0.453 \times 0.245 \times 0.265$ | - | 9.8 | No | | Scout II ${ }^{33}$ | 0.323 (leg length) | 2 | 20.865 | 4 | | Kirin ${ }^{34}$ | $0.7 \times 0.24 \times 0.6$ | 3 | 50 | 4 | | Proposed system | $0.37 \times 0.22 \times 0.21 I$ | 2 | 1.47 | 4 |
Hybrid wheeled-leg mobile robots are versatile machines that combine the advantages of wheeled and legged locomotion. However, the design and control of such robots pose unique challenges due to their integration of these two locomotion modes. Mechanical legs are a crucial element of quadruped robots, and they play a significant role in achieving diverse locomotion gaits. In analysing their mechanical performance, the legs of standard quadruped robots can be categorised into three types: articulated, prismatic, and redundant articulated legs. 24 24 ^(24){ }^{24} Over the past few decades, several researchers have conducted significant research into the mechanical legs used by quadruped robots. For example, Nakajima et al. 25 25 ^(25){ }^{25} proposed a leg-wheel robot with two big wheels and four degrees of freedom. In another study, Lacagnina et al. 26 26 ^(26){ }^{26} proposed the Wheeleg robot, which was equipped with two front legs, each powered by pneumatic actuators and featuring three degrees of freedom. The robot also has two rear wheels that can be actuated independently, where each is powered by its own DC motor. Meanwhile, Kitano et al. 27 27 ^(27){ }^{27} proposed the design of a quadruped walking robot, named TITAN-XIII. Cho et al. 28 28 ^(28){ }^{28} proposed the JINPOOG quadruped robot, which is powered by hydraulic actuators and features 16 degrees of freedom (DOFs). Ren et al. 29 29 ^(29){ }^{29} proposed the Xiaotian-Hybrid robot, which has four legs and two wheels. However, for this robot to walk on foot, it is necessary to immobilise the wheels by locking them. Chung et al. 30 30 ^(30){ }^{30} proposed and developed HuboDog, a quadruped robot with a weight of 42 kg and dimensions of 0.8 m ( L ) × 0.34 m 0.8 m ( L ) × 0.34 m 0.8m(L)xx0.34m0.8 \mathrm{~m}(\mathrm{~L}) \times 0.34 \mathrm{~m} ( W ) × 0.86 m ( H ) ( W ) × 0.86 m ( H ) (W)xx0.86m(H)(\mathrm{W}) \times 0.86 \mathrm{~m}(\mathrm{H}). This robot has three active degrees of freedom (DOF) per leg and uses harmonic drive reduction gear with brushless DC electric motors to drive all its joints. As another example, HyTRo-I 31 31 ^(31){ }^{31} is a leg wheel hybrid robot that is equipped with four legs and four wheels, thus providing it with the ability to walk and roll. Mertyuz 32 32 ^(32){ }^{32} proposed the FUHAR wheeled legged robot, which has four convertible wheels and a size of 0.435 m in length and 0.1844 m in width when excluding the wheels. Poulakakis et al. 33 33 ^(33){ }^{33} proposed Scout II, a quadruped robot with a main body weight of 20.865 kg and four compliant
prismatic legs, each of which has a mass of 0.97 kg . In another study, Luo et al. 34 34 ^(34){ }^{34} proposed a new quadruped robot named Kirin, which features four prismatic legs that use a belt driven linear mechanism to achieve leg movement. However, each leg of this robot weighs approximately 1.9 kg .
With this background, the present study aims to design a novel quadruped hybrid wheeled-legged mobile robot using telescopic legs. We presented the legged mode gait with three supporting legs and one transferring leg. We constructed the prototype using 3D printing technology, which resulted in reductions in both production time and the overall weight of the robot. Experiments conducted on a quadruped hybrid wheeled-legged platform, with supporting video, revealed that the proposed robot displayed reliable navigation and control capabilities, while successfully maintaining the desired yaw angle even when having to move on challenging terrain. The robot’s design also enables it to perform various modes of movement, including normal vertical and horizontal driving, rotation around the robot’s centre of gravity, rotation in a large arc, and walking on flat terrain.
The rest of this paper is organised as follows. A detailed description of the design of the quadruped hybrid wheeled legged mobile robot is included in Section 2. Motion analysis and gait control are presented is Section 3. Section 4 introduces the simulation results. Experiments with the proposed robot are discussed in Section 5. Lastly, conclusions and future work are drawn in Section 6.

Design of a quadruped hybrid wheeledlegged mobile robot

After reviewing existing quadruped wheeled legged robots, we compiled their main characteristics in Table 1, including platform size, degrees of freedom (DOF) per leg, platform mass, and use of telescopic legs. The proposed quadruped wheeled robot with telescopic legs stands out among existing platforms due to its compact design, which is made possible by the use of the telescoping legs; it is one of the smallest
Figure I. (a) 3D model of the proposed robot and (b) leg mechanism.
platforms in the comparison. The robot is also lightweight, which can be attributed to the use of 3Dprinted mechanical parts. Overall, our proposed robot has a smaller size, fewer DOF per each leg, and a lighter weight than the other compared platforms. The next Subsection 2.1 provides details about the system structure, while the following Subsection 2.2 focuses on the design of the control system.

System structure

This study proposes a quadruped hybrid wheeled legged mobile robot with telescopic legs. Figure 1(a) presents a 3D model of the proposed robot. The system has a rectangular main body that is designed to support the control hardware and actuators, including four DC motors, four rotary RC servo motors (as a revolute joint) and four linear RC servo motors (as prismatic joints). Figure 1(b) shows the leg mechanism, which consists of one rotary RC servo motor, one linear RC servo motor and one DC motor. The linear RC servo motor controls the up and down movement of the legs, while the DC motor is locked during walking and only powered when using the wheels for movement. Table 2 list the parameters of the linear RC servo motor.

Control system design

The proposed mobile robot’s control equipment scheme is shown in Figure 2. The control equipment scheme consists of several components. These include a joystick module, an Arduino Mega 2560 microcontroller, a sensor shield, four rotary RC servo motors, four linear RC servo motors, four DC motors, four
Table 2. Parameters of LI 2-R linear servo.
Parameters Value (unit)
Max speed (no load) 12 ( mm / s ) 12 ( mm / s ) 12(mm//s)12(\mathrm{~mm} / \mathrm{s})
Backdrive force 80 ( N ) 80 ( N ) 80(N)80(\mathrm{~N})
Input voltage 6 ( V ) 6 ( V ) 6(V)6(\mathrm{~V})
Gear ratio 1 : 100 1 : 100 1:1001: 100
Stroke 100 ( mm ) 100 ( mm ) 100(mm)100(\mathrm{~mm})
Weight 56 ( g ) 56 ( g ) 56(g)56(\mathrm{~g})
Max side force (fully extended) 15 ( N ) 15 ( N ) 15(N)15(\mathrm{~N})
Stall current 450 ( mA ) 450 ( mA ) 450(mA)450(\mathrm{~mA})
Parameters Value (unit) Max speed (no load) 12(mm//s) Backdrive force 80(N) Input voltage 6(V) Gear ratio 1:100 Stroke 100(mm) Weight 56(g) Max side force (fully extended) 15(N) Stall current 450(mA)| Parameters | Value (unit) | | :--- | :--- | | Max speed (no load) | $12(\mathrm{~mm} / \mathrm{s})$ | | Backdrive force | $80(\mathrm{~N})$ | | Input voltage | $6(\mathrm{~V})$ | | Gear ratio | $1: 100$ | | Stroke | $100(\mathrm{~mm})$ | | Weight | $56(\mathrm{~g})$ | | Max side force (fully extended) | $15(\mathrm{~N})$ | | Stall current | $450(\mathrm{~mA})$ |
DC motor drivers and a Lipo power battery. The joystick module is used to send commands to the Arduino Mega 2560 microcontroller, which then controls the rotary RC servo motors, linear RC servo motors and DC motors through the DC motor drivers. The Lipo power battery provides the necessary power to the system via a 6 V regulator to lower the voltage of the battery. This control equipment scheme allows for precise control over the robot’s movement, walking and direction. The joystick module is used to transmit direct commands to the robot, including forward, backward, left and right movements; turning in place; and rotation at a certain point.
The DC motor drivers are connected to the digital input-output sections on the Arduino Mega microcontroller. The PWM signals are used to simultaneously control the speed and direction of the DC motors, and these signals are transmitted by the motor drivers. The software running on the Arduino Mega 2560 microcontroller controls the PWM signals that are sent to the DC motors based on the information received from the control module.
Figure 2. Control hardware system of the proposed quadruped hybrid wheeled mobile robot.
Figure 3. Creep gait pattern.
The modularised design and control software of the control panel allows the Arduino Mega microcontroller to control each motor function independently. This means that each motor can be controlled separately, thus enabling precise and flexible movement of the robot. The modular design also allows for easy maintenance and upgrades, as individual components can be replaced or modified without affecting the rest of the system.

Motion analysis and gait control

The robot proposed in this work moves in a creeping walking mode. The creeping gait is a movement pattern for quadruped mobile robots that requires at least three legs to be in contact with the ground at all times, while the fourth leg moves forwards using either quadrilateral or triangular support patterns. 35 35 ^(35){ }^{35} In this study, we have used the creeping gait as a walking gait method for locomotion using the triangular support pattern, as shown in Figure 3. During the locomotion process, it is important to maintain the stability of the quadruped mobile robot. The robot keeps its centre of gravity (COG) inside the red triangle formed by the three supporting legs. If the COG moves outside this triangle for an extended period, the robot may lose its balance and fall down.
Figure 4 illustrates the creep gait sequence utilised by the robot during the movement that is followed in the simulation and experimental work. Overall, the COG is a critical consideration in the design and programming of walking robots, and it plays a significant role in ensuring the robot’s stability and balance during movement. Let us take a closer look at how to maintain the COG when a robot is walking. If all the legs of the robot are positioned at 45 ∘ 45 ∘ 45^(@)45^{\circ} angles, the COG will be maintained perfectly in the centre ( x , y ) = ( 0 , 0 ) ( x , y ) = ( 0 , 0 ) (x,y)=(0,0)(x, y)=(0,0), as shown in Figure 5. However, if any of the legs are moved, the COG will shift towards that side, which can cause the robot to become unbalanced and fall over in that direction. A red triangle (as shown in the relevant figures) is created based on the three legs (leg 1 , leg 2 and leg 3 ), and this triangle contains the COG, as shown in Figure 5.
The coordinates of the vertices of the red triangle can be expressed as follows:
( x 1 , y 1 ) = ( W 2 + L cos ⁡ θ 1 , H 2 + L sin ⁡ θ 1 ) ( x 2 , y 2 ) = ( − W 2 − L cos ⁡ θ 2 , H 2 + L sin ⁡ θ 2 ) ( x 3 , y 3 ) = ( − W 2 − L cos ⁡ θ 3 , − H 2 − L sin ⁡ θ 3 ) x 1 , y 1 = W 2 + L cos ⁡ θ 1 , H 2 + L sin ⁡ θ 1 x 2 , y 2 = − W 2 − L cos ⁡ θ 2 , H 2 + L sin ⁡ θ 2 x 3 , y 3 = − W 2 − L cos ⁡ θ 3 , − H 2 − L sin ⁡ θ 3 {:[(x_(1),y_(1))=((W)/(2)+L cos theta_(1),(H)/(2)+L sin theta_(1))],[(x_(2),y_(2))=((-W)/(2)-L cos theta_(2),(H)/(2)+L sin theta_(2))],[(x_(3),y_(3))=((-W)/(2)-L cos theta_(3),(-H)/(2)-L sin theta_(3))]:}\begin{aligned} & \left(x_{1}, y_{1}\right)=\left(\frac{W}{2}+L \cos \theta_{1}, \frac{H}{2}+L \sin \theta_{1}\right) \\ & \left(x_{2}, y_{2}\right)=\left(\frac{-W}{2}-L \cos \theta_{2}, \frac{H}{2}+L \sin \theta_{2}\right) \\ & \left(x_{3}, y_{3}\right)=\left(\frac{-W}{2}-L \cos \theta_{3}, \frac{-H}{2}-L \sin \theta_{3}\right) \end{aligned}
Where ( x 1 , y 1 ) x 1 , y 1 (x_(1),y_(1))\left(x_{1}, y_{1}\right) is the coordinate of wheel 1 , ( x 2 , y 2 ) 1 , x 2 , y 2 1,(x_(2),y_(2))1,\left(x_{2}, y_{2}\right) is the coordinate of wheel 2 , and ( x 3 , y 3 ) x 3 , y 3 (x_(3),y_(3))\left(x_{3}, y_{3}\right) is the coordinate of wheel 3 . W 3 . W 3.W3 . W is the width of the body, H H HH is the length of the body and L L LL is the distance between the rotation axis of the servo motor to the wheel. θ 1 θ 1 theta_(1)\theta_{1} is the rotation angle of servo motor 1 , θ 2 1 , θ 2 1,theta_(2)1, \theta_{2} is the rotation angle of servo motor 2 , θ 3 2 , θ 3 2,theta_(3)2, \theta_{3} is the rotation angle of the servo motor 3 and θ 4 θ 4 theta_(4)\theta_{4} is the rotation angle of servo motor 4.
Figure 4. Walking steps.
Figure 5. Proposed quadruped robot (top-view).
The linear function between the two points ( x 1 , y 1 ) x 1 , y 1 (x_(1),y_(1))\left(x_{1}, y_{1}\right), and ( x 3 , y 3 ) x 3 , y 3 (x_(3),y_(3))\left(x_{3}, y_{3}\right) can be obtained as follows:
y − ( H 2 + L sin ⁡ θ 1 ) = ( H + L ( sin ⁡ θ 1 + sin ⁡ θ 3 ) W + L ( cos ⁡ θ 1 + cos ⁡ θ 3 ) ) × ( x − ( W 2 + L cos ⁡ θ 1 ) ) y − H 2 + L sin ⁡ θ 1 = H + L sin ⁡ θ 1 + sin ⁡ θ 3 W + L cos ⁡ θ 1 + cos ⁡ θ 3 × x − W 2 + L cos ⁡ θ 1 {:[y-((H)/(2)+L sin theta_(1))=((H+L(sin theta_(1)+sin theta_(3)))/(W+L(cos theta_(1)+cos theta_(3))))],[ xx(x-((W)/(2)+L cos theta_(1)))]:}\begin{aligned} y-\left(\frac{H}{2}+L \sin \theta_{1}\right)= & \left(\frac{H+L\left(\sin \theta_{1}+\sin \theta_{3}\right)}{W+L\left(\cos \theta_{1}+\cos \theta_{3}\right)}\right) \\ & \times\left(x-\left(\frac{W}{2}+L \cos \theta_{1}\right)\right) \end{aligned}
The COG will be maintained perfectly in the centre at the coordinates of ( x , y ) = ( 0 , 0 ) ( x , y ) = ( 0 , 0 ) (x,y)=(0,0)(x, y)=(0,0), which will allow the robot to rotate around its vertical axis while keeping its legs fixed at diagonal angles. Therefore, when it moves any of its legs, the COG will shift towards that side, which can cause the robot to become unbalanced.
Substituting x = 0 x = 0 x=0x=0 and rearranging equation (1), we obtain
y = ( H 2 + L sin ⁡ θ 1 ) − ( H + L ( sin ⁡ θ 1 + sin ⁡ θ 3 ) W + L ( cos ⁡ θ 1 + cos ⁡ θ 3 ) ) ( W 2 + L cos ⁡ θ 1 ) y = H 2 + L sin ⁡ θ 1 − H + L sin ⁡ θ 1 + sin ⁡ θ 3 W + L cos ⁡ θ 1 + cos ⁡ θ 3 W 2 + L cos ⁡ θ 1 {:[y=((H)/(2)+L sin theta_(1))],[-((H+L(sin theta_(1)+sin theta_(3)))/(W+L(cos theta_(1)+cos theta_(3))))((W)/(2)+L cos theta_(1))]:}\begin{aligned} y & =\left(\frac{H}{2}+L \sin \theta_{1}\right) \\ & -\left(\frac{H+L\left(\sin \theta_{1}+\sin \theta_{3}\right)}{W+L\left(\cos \theta_{1}+\cos \theta_{3}\right)}\right)\left(\frac{W}{2}+L \cos \theta_{1}\right) \end{aligned}
Substituting y = 0 y = 0 y=0y=0 and rearranging equation (1), we obtain
x = ( W 2 + L cos ⁡ θ 1 ) − ( W + L ( cos ⁡ θ 1 + cos ⁡ θ 3 ) H + L ( sin ⁡ θ 1 + sin ⁡ θ 3 ) ) ( H 2 + L sin ⁡ θ 1 ) x = W 2 + L cos ⁡ θ 1 − W + L cos ⁡ θ 1 + cos ⁡ θ 3 H + L sin ⁡ θ 1 + sin ⁡ θ 3 H 2 + L sin ⁡ θ 1 {:[x=((W)/(2)+L cos theta_(1))],[-((W+L(cos theta_(1)+cos theta_(3)))/(H+L(sin theta_(1)+sin theta_(3))))((H)/(2)+L sin theta_(1))]:}\begin{aligned} x & =\left(\frac{W}{2}+L \cos \theta_{1}\right) \\ & -\left(\frac{W+L\left(\cos \theta_{1}+\cos \theta_{3}\right)}{H+L\left(\sin \theta_{1}+\sin \theta_{3}\right)}\right)\left(\frac{H}{2}+L \sin \theta_{1}\right) \end{aligned}
We used equations (2) and (3) during the movement of the robot to maintain balance and keep the COG inside the red triangle. When the robot is rotating around the instantaneous centre of rotation (ICR), as shown in Figure 6, the rotation angles θ 1 θ 1 theta_(1)\theta_{1}, θ 2 , θ 3 θ 2 , θ 3 theta_(2),theta_(3)\theta_{2}, \theta_{3} and θ 4 θ 4 theta_(4)\theta_{4} of servo motors 1 , 2 , 3 1 , 2 , 3 1,2,31,2,3 and 4 can be respectively expressed, as follows:
θ 1 = arctan ⁡ y − H 2 x − W 2 θ 2 = arctan ⁡ y − H 2 x + W 2 θ 3 = arctan ⁡ y + H 2 x + W 2 θ 4 = arctan ⁡ y + H 2 x − W 2 θ 1 = arctan ⁡ y − H 2 x − W 2 θ 2 = arctan ⁡ y − H 2 x + W 2 θ 3 = arctan ⁡ y + H 2 x + W 2 θ 4 = arctan ⁡ y + H 2 x − W 2 {:[theta_(1)=arctan((y-(H)/(2))/(x-(W)/(2)))],[theta_(2)=arctan((y-(H)/(2))/(x+(W)/(2)))],[theta_(3)=arctan((y+(H)/(2))/(x+(W)/(2)))],[theta_(4)=arctan((y+(H)/(2))/(x-(W)/(2)))]:}\begin{aligned} & \theta_{1}=\arctan \frac{y-\frac{H}{2}}{x-\frac{W}{2}} \\ & \theta_{2}=\arctan \frac{y-\frac{H}{2}}{x+\frac{W}{2}} \\ & \theta_{3}=\arctan \frac{y+\frac{H}{2}}{x+\frac{W}{2}} \\ & \theta_{4}=\arctan \frac{y+\frac{H}{2}}{x-\frac{W}{2}} \end{aligned}
Figure 6. Rotation a round instantaneous centre of rotation (ICR).

Simulation results

A motion simulation was created for the proposed robot under two different condition scenarios:
  1. Wheeled mode.
  2. Legged mode.
The dynamic model of the proposed robot has been created using MATLAB Simscape Multibody as shown in Figure 7.

Wheeled mode

While the proposed robot can achieve smooth, highspeed, and flexible locomotion on flat terrain using only the DC motors, the robot can also achieve normal vertical driving, horizontal driving, rotating around its COG, and rotating in a large arc, as shown in Figure 8.
(a) Normal vertical driving: The robot can achieve normal vertical driving (straight driving), including straight movement, by horizontally fixing the angle of the legs using the servo motors. This method enables precise control over the robot’s movement, specifically allowing it to move forwards and backwards without adjusting its body or wheels. By adjusting the angle of its legs in this way, the robot can move smoothly and efficiently over either flat ground or rough terrain.
(b) Normal horizontal driving: The robot can achieve horizontal driving with the angle of its legs fixed vertically via the servo motors. This method allows the robot to move horizontally in a controlled manner while the leg angle remains fixed. By adjusting the angle of the legs vertically, the robot can move sideways, which is useful for navigating confined spaces or avoiding obstacles. The servo motor provides precise control over the leg angle, thus enabling the robot to move accurately and efficiently. This
capability makes the robot versatile and adaptable to different environments and tasks.
© Turn in place: The robot can achieve rotation in place by fixing all of its leg angles diagonally using the rotary RC servo motors. This method allows the robot to rotate around its vertical axis while keeping its legs fixed at diagonal angles. By adjusting the leg angles in this manner, the robot can maintain stability and balance while rotating, which is useful for tasks that require precise positioning or manoeuvring in tight spaces.
(d) Steering at a certain point: The robot can rotate in a large arc by reducing the angle of both legs. This method allows the robot to pivot around a central point while maintaining its stability and balance. By reducing the angle of both legs, the robot can achieve a wider turning radius, which is useful for navigating around obstacles or turning in confined spaces.

Legged mode

The robot proposed in this study was designed to move according to a creep walking mode, which was modelled and assumed. The proposed robot can achieve walking on flat terrain using the rotary RC servo motors and the linear RC servo motors, and it is also able to walk in six steps as shown in Figure 9.
(a) Step A1: The starting position in which two legs (A2 and B2) are extended out ards on one side, while the other two legs (A1, B1) are pulled inwards towards the body.
(b) Step B1: Leg B1 is lifted and extended forwards, while the three remaining legs (A1, A2 and B2) remain on the ground to guarantee the robot’s stability.
© Step forward: All legs (A1, A2, B1 and B2) move backwards and the body moves forwards.
(d) Step A2: Leg A2 moves forward, and to ensure the stability of the robot, the three legs that remained (A1, B1, and B2) maintained contact with the ground.
(e) Step B2: Leg B2 is lifted and extended forward, and to ensure the stability of the robot, the three legs that remained (A1, B1 and A2) maintained contact with ground.
(f) Step forward: All legs (A1, A2, B1 and B2) move backwards and the body moves forwards.
The proposed robot can also achieve walking with turning, as shown in Figure 10. This procedure is similar to the walking steps listed above.
  • The rotary RC servo motor B 2 is rotated counterclockwise by an angle of 15 ∘ 15 ∘ 15^(@)15^{\circ}.
  • The rotary RC servo motor A2 is rotated clockwise by an angle of 15 ∘ 15 ∘ 15^(@)15^{\circ}.
Figure 7. System modelling by MATLAB Simscape Multibody: (a) wheeled mode and (b) legged mode.
Figure 8. Simulation result of the proposed robot under wheeled mode.
Figure 9. Simulation result: walking steps of the proposed robot.
  • The four rotary RC servo motors of the quadruped robot are rotated clockwise by an angle of 15 ∘ 15 ∘ 15^(@)15^{\circ} after supporting all legs on the ground.
  • The rotary RC servo motor A1 is rotated clockwise by an angle of 15 ∘ 15 ∘ 15^(@)15^{\circ}.
  • The rotary RC servo motor B1 is rotated clockwise by an angle of 15 ∘ 15 ∘ 15^(@)15^{\circ}.

Experiments with quadruped hybrid wheeled legged mobile robot

The proposed quadruped hybrid leg-wheel mobile robot with a telescopic leg was created based on the
Figure 10. Simulation result of the proposed robot under legged mode.
above analysis, and simulations, are shown in Figure 11. The accompanying video supplement features laboratory tests showcasing the operation of the quadruped hybrid leg-wheel mobile robot with telescopic legs. It can perform multiple motion modes to adapt to different surfaces.

Controlling the robot's body in the presence of external disturbances

We conducted an experiment to evaluate the suggested robot body control system by positioning the robot on the top of a plate and manually inducing disturbances through changes in the plate’s angle. Two Inertial Measurement Units (IMUs) were affixed to measure the roll and pitch angles, with one on the robot body and the other on the plate. As shown in Figure 12, the proposed robot was able to automatically adjust its posture to adapt to sudden variations in terrain configuration. Figure 13 displays the response of the roll and pitch angle adjustments under the orientation disturbances, thus highlighting the proposed robot’s ability to compensate for these disturbances and reduce pitch and roll angle deviations to zero.

Experimental results under wheeled mode

We conducted several experiments to evaluate the performance of the proposed robot, where the velocity of the robot was 0.3 m / s 0.3 m / s 0.3m//s0.3 \mathrm{~m} / \mathrm{s}. Figure 14 displays a video capture of an experiment conducted to evaluate the robot’s performance in normal vertical driving under the wheeled mode. The video highlights the capabilities of our robot and showcases its proficiency in this specific mode. Figure 15 depicts a video
Figure II. Physical system.
Figure 12. Video capture of experimental results: disturbances caused by changes in the plate’s angle.
Figure 13. Experimental results obtained while controlling the roll and pitch angles under disturbances, as depicted in Figure 12.
capture from an experiment aimed at assessing the robot’s performance in normal horizontal driving within the wheeled mode. The experimental results showcased the robot’s capability to achieve controlled horizontal movement by adjusting its leg angle vertically with the assistance of servo motors. Figure 16 showcases a video capture from an experiment conducted to examine the robot’s ability to rotate around its COG. This was achieved by fixing all leg angles diagonally using RC servo motors. As a result, the robot successfully accomplished rotational movement around its COG. Figure 17 displays a video capture from an experiment conducted to assess the robot’s performance in executing a large arc rotation within the wheeled mode; this particular movement was accomplished by reducing the angle of both legs, thus enabling the robot to rotate around a central point while maintaining its stability and balance.

Experimental results under legged mode

In this experiment, we have used the creeping gait as a walking gait method for locomotion, which relies upon the triangular support pattern. Our proposed robot demonstrates the ability to walk on flat terrain using a combination of rotary RC servo motors and linear RC servo motors. It is also founded to be capable of walking with turns. Figure 18 displays a video capture of the experiments conducted under the legged mode, thus showcasing the robot’s walking and turning capabilities, which are achieved by using rotary RC servo motors and linear RC servo motors.

Conclusions and future work

In this paper, we introduce a new design for a quadruped hybrid leg-wheel mobile robot that incorporates telescopic legs. The proposed robot design merges the benefits of wheeled and legged mobility mechanisms, ultimately offering a promising solution for search and rescue robots. A physical prototype of the proposed quadruped hybrid leg-wheel mobile robot has been designed and produced based on the analysis and simulation results. We constructed this prototype using 3 D printing technology, which resulted in reductions in both the production time and overall weight of the robot. The results of experiments that were conducted on a quadruped hybrid wheeled-legged platform, with supporting video, revealed that the proposed robot displayed reliable navigation and control capabilities, while successfully maintaining the desired yaw angle even when moving on challenging terrain. We implemented the creeping gait method for locomotion, which involved moving one leg while the other three legs remained on the ground to guarantee the robot’s balance. The design indicates that the robot can perform multiple motion modes to adapt to different surfaces. We are currently in the process of refining the design of a quadruped hybrid wheeled-legged mobile robot with telescopic legs. In future work, we aim to focus on control approaches that can enhance the robot’s autonomy
Figure 14. Video capture of the experiment assessing the proposed system in wheeled mode: normal vertical driving.
Figure I5. Video capture of the experiment assessing the proposed system in wheeled mode: horizontal driving.
Figure I6. Video capture of the experiment assessing the proposed system in wheeled mode: rotating around COG.
Figure 17. Video capture of the experiment assessing the proposed system in wheeled mode: rotating in a large arc.
Figure 18. Video capture of the experiment assessing the proposed legged system in walking mode.
and detection capabilities. This will involve incorporating various sensors such as GPS, LIDAR, and camera to improve its perception ability and enable it to navigate and operate autonomously in different environments.

Declaration of conflicting interests

The author(s) declare no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclose the receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by Basic Science Research Programme through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (No. NRF-2020R1I1A3070333).

ORCID iD

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  1. 'Department of Mechatronics Engineering, Faculty of Engineering, Assiut University, Assiut, Egypt
    2 2 ^(2){ }^{2} Department of Mechanical Engineering, Hanbat National University, Deajeon, South Korea