International Journal of Robotics and Automation, 2019

MOTION CHARACTERISTIC

EVALUATION OF AN AMPHIBIOUS

SPHERICAL ROBOT

Yanlin He,∗,∗∗ Shuxiang Guo,∗,∗∗ Liwei Shi,∗,∗∗ Huiming Xing,∗,∗∗ Zhan Chen,∗,∗∗ and Shuxiang Su∗,∗∗

Abstract

This paper used three on-land locomotion gaits and underwater

swim for an amphibious spherical robot, which is controlled using

a closed-loop method. The aim of varying the on-land gaits and

underwater swim was to improve the motion performance and

stability of robot. To control the angle of joint, the displacement

and depth of robot, a PID method was used to control the robot.

Adams and MATLAB/SIMULINK were used to set the control

parameters; simulation results are presented for the three on-land

locomotion gaits and underwater swim, in terms of the motion

performance, stability, and velocity of the robot. Finally, the

effectiveness of the proposed methods was demonstrated by showing

that the on-land and underwater horizontal motion was stable.

Key Words

Amphibious spherical robot, PID control, co-simulation, locomotion

gaits, stability and autonomy

1. Introduction

Researchers around the world have been inspired by am-phibians to develop amphibious robots. Wheeled robotsperform well on even ground, whereas tracked and leggedrobots have good mobility on rough terrain. Comparedwith screw propellers, undulatory and oscillatory propul-sion mechanisms disturb the environment only slightly andare highly efficient and manoeuvrable. Some robots uti-lize two sets of propulsion mechanisms for their terrestrialand aquatic motions, which makes them heavy. To sim-plify the structure, robots like Whegs and AQUA2 usea composite propulsion mechanism to move in amphibi-ous environments [1], [2]. However, it is still difficultfor these amphibious robots to move in complex terrains;

∗ The Key Laboratory of Convergence Medical Engineering Sys-tem and Healthcare Technology, the Ministry of Industry andInformation Technology, School of Life Science, Beijing Insti-tute of Technology, Beijing 100081, China; e-mail: {heyanlin,guoshuxiang, shimiwei, xinghuiming, chenzhan, sushuxiang}@bit.edu.cn

∗∗ Faculty of Engineering, Kagawa University, 2217-20Hayashicho, Takamatsu, Kagawa 761-0396, JapanCorresponding authors: Shuxiang Guo and Liwei Shi

additionally, accurate control over the underwater posi-tion remains a challenge. To overcome the limitations ofthese amphibious robot, we developed a three-dimensional(3D) printing technology-based amphibious spherical robotwith transformable composite propulsion mechanisms [3]–[6]. The robot is capable of moving from the water tothe ground without manual intervention, and vice versa[4]–[9].

There is already extensive literature concerning on-land gaits of quadruped robots, including the crawling gait,trotting gait, etc.; these modes enable the robot to moveefficiently and remain stable in different environments.The literature covers a range of issues such as modellingand adaptive gait transition, and a number of mechanismsto control these robots have been investigated, and manystudies have been conducted on robot design, modelling,and control [10]. However, there are no accurately con-trollable robots capable of performing a range of land-based gaits and underwater movements with a water-jetpropeller, with a composite mechanism designed to switchbetween the water-jet propeller and legs.

To have better adaptability and performance of am-phibious motion in our robot, we used three locomo-tion gaits guided by a closed-loop controller to ensurethat the motion remained stable. A PID closed-loopmethod is used to control the robot. We confirmed thecorrectness of the proposed method using Adams andMATLAB/SIMULINK, which we used to demonstrate thestability of amphibious movements. This enabled us todetermine parameters for controlling the robot, as well asguided our selection of practical tests. We describe exper-iments in which we investigated three on-land gaits on acommon mat floor. The choice of these experiments wasguided by our simulation results. Underwater experimentswere conducted to examine the performance of the robotas it moved horizontally.

The paper is organized as follows. Section 2 describesthe design of robot. In Section 3, three on-land gaitsare described, and the PID controllers were designed tofacilitate co-simulation of on-land motion of robot. Section4 is dedicated to the cooperative simulation of underwatermotion. Some amphibious experimental is discussed inSection 5. Finally, Section 6 presents our conclusion.

1

Figure 1. Structure of the amphibious spherical robot.

2. General Design of Amphibious Spherical Robot

In our previous research, we developed an amphibiousspherical robot capable of motion on land and underwater.The design of the robot is shown in Fig. 1, which is ableto move from underwater to the ground without manualintervention, and vice versa. The robot is composed oftwo sealed transparent upper hemispheroids, two openabletransparent quarter spherical shells, and four actuatingunits, each of which consists of a water-jet propeller andtwo driving motors [3]–[13].

We used 3D printing technology, a minimal XilinxZynq-7000 SoC system, and an embedded computerequipped with an Intel Atom processor to fabricate therobot. We used an Avnet MicroZed core-board carryinga Xilinx all-programmable Zynq-7000 SoC, which is ahybrid processor combined with an advanced RISC ma-chine processor and field-programmable gate array. Themicrocontroller provides eight pulse-width modulation(PWM) signals to control the servomotors; four PWMsignals are used to actuate the water-jet propellers byregulating the signal duty ratio, and there are 12 generalpurpose input–output signals to control the optocouplerand relay [14].

3. On-Land Locomotion Gaits and Co-SimulationAnalysis

3.1 On-Land Gait Characterization

We have implemented three on-land gaits for our robot[15]. Figure 2 shows the event sequences of a one-gait cycle

Figure 2. Event sequence of one gait cycle for each of the gaits: (a) crawling; (b) trotting; and (c) pacing.

for each of the three gaits. The shadow indicates that thelegs are in contact with the ground. The legs are labelledas follows: left front (LF), right front (RF), left hind (LH),and right hind (RH). The duty factor of the crawling gaitis β=0.75; the duty factor of the trotting and pacing gaitsis β=0.5. There are times when the robot only has twolegs in contact with the ground.

The velocity of the robot is related to the step size andcycle of the gait as follows [6]:

v =0.1483 ∗ θT ∗ β

, (1)

where v is the velocity, T is the motion cycle, β is the dutyfactor, and θ is the rotation angle of hip joint.

3.2 On-Land Mathematical Modelling

As the movement mechanisms of four legs are essentiallythe same, we present the analysis of RF leg. As shownin Fig. 3, the inertial coordinate frame with respect tothe ground was denoted XYZ, the body fixed coordinatesystem {Xb, Yb, Zb} has its origin {Ob} located in the geo-metric centre of robot. Assuming that the position vectorof the rotational axes of the hip joint in the coordinate is{X0, Y0, Z0}, the position vector of the rotational axes ofthe knee joint in the coordinate is {X2, Y2, Z2}, and therelationship between rotational axes of the actuators withrespect to body fixed coordinate can be obtained accord-ing to the homogeneous transformation matrix. Each legis composed of a hip joint, a knee joint, and connecting

Figure 3. Force analysis and coordinate system of theamphibious spherical robot on land.

2

components. The dynamic Lagrange equation of robot isgiven below [16]:

L = Ek − Ep =

[1

2(m1 +m2)v

21 +

1

2(m3 +m4)v

22

]

+(m1+m2)gl2+(m3+m4)g(l2+ l3 cos θ2+ l4 sin θ2)

(2)

where Ek and Ep are the total kinetic and potential ener-gies; m1 and m2 are the corresponding qualities of l1 andl2; m3 and m4 are the corresponding qualities of l3 and l4;and θ1 and θ2 are generalized coordinate variables.

The torque of the joint can be expressed as follows:

Ti =d

dt

∂L

∂θi− dL

dθi(3)

The driving torques of the hip joint (T1) and knee joint(T2) are as follows:

T1 =d

dt

∂L

∂θ1− dL

dθ1= [(m1 +m2 +m3 +m4)l

21 + (m3 +m4)(l

23 sin

2 θ2 + l24 cos2 θ2 + 2l1l3 sin θ2 − l3l4 sin 2θ2

− 2l1l2 cos θ2)]θ + [(m3 +m4)(l23 sin 2θ2 − l24 sin 2θ2 + 2l1l3 cos θ2 − 2l3l4 cos 2θ2 + 2l1l4 sin θ2θ1θ2)]

(4)

T2 =d

dt

∂L

∂θ2− dL

dθ2=1

2(m3+m4)[(2l

23 sin

2 θ2+2l24 cos2 θ2 − 2l3l4 sin 2θ2)θ2−(l23 sin 2θ2− l24 sin 2θ2+2l1l3 cos θ2−2l3l4cos2θ2

+2l1l4cos2θ2+2l1l4 sin θ2)θ21+(l23 sin 2θ2− l24 sin 2θ2 − 2l3l4cos2θ2+2l3l4cos2θ2)θ

22 − 2g(l4 cos θ2 − l3 sin θ2)]

(5)

These general equations have been simplified and canbe represented in simple matrix forms:

⎡⎣ T1

T2

⎤⎦ =

⎡⎣D11(θ2) D12(θ2)

D21(θ2) D22(θ2)

⎤⎦⎡⎣ θ1

θ2

⎤⎦+

⎡⎣D111(θ2) D122(θ2)

D211(θ2) D222(θ2)

⎤⎦⎡⎣ θ21

θ22

⎤⎦+

⎡⎣D112 (θ2) D122 (θ2)

D212 (θ2) D221 (θ2)

⎤⎦⎡⎣ θ1θ2

θ1θ2

⎤⎦+

⎡⎣D1

D2

⎤⎦ (6)

where D11 and D22 are the effective inertia; D12 andD21 are the coupling inertia; D111, D122, D211, and D222

are the coefficients of the centripetal acceleration; D112,D121, D212, and D221 are the coefficients of the coriolisacceleration; and D1 and D2 are the gravity terms.

D11 =

[(4∑

i=1

mi4

)l21 + (m3 +m4)(l

23s

2θ2 + l24c2θ2

+2l1l3sθ2 − l3l4s2θ2 − 2l1l2cθ2)

](7)

D22 =1

2

(4∑

i−3

mi

)(2l23s

2θ2 + 2l24c2θ2 − 2l3l4s2θ2) (8)

D211 = −1

2(m3 +m4)(l

23s2θ2 − l24s2θ2 + 2l1l3cθ2

− 2l3l4c2θ2 + 2l1l4sθ2) (9)

D211 =1

2(m3 +m4)(2l

23s2θ2 − 2l24s2θ2 − 4l3l4cθ2

− l23s2θ2 + l24s2θ2 + 2l3l4s2θ2) (10)

D112 = D121 =1

2(m3 +m4)(l

23s2θ2 − l24s2θ2 + 2l1l3cθ2

− 2l3l4c2θ2 + 2l1l4sθ2 (11)

D2 = −2g(l4cθ2 − l3sθ2) (12)

3.3 On-Land Control System Design and theProcess of Co-Simulation

This section describes the modelling of robot in Adams.The 3D model of robot was simplified in SolidWorks andsaved as (*.xt) format, and then the model was importedinto Adams; some parameters were redefined and someconstraints were applied. The initial state of robot wasset as four-footed and assumed to be motioning on aground; the contact force between the foot end and groundwas set as friction force. Considering the experimentsenvironment, the dynamic/static coefficient of friction force

3

Figure 4. Virtual prototype of the robot developed usingthe Adams platform.

was set as 0.1/0.15, and the red portion in Fig. 4 representsthe ground.

Eight driving torques were set as input variables inthe co-simulation and can be expressed by the followingequation:

T = [TorqueLF1,TorqueLF2,TorqueLH1,TorqueLH2,

TorqueRF1,TorqueRF2,TorqueRH1,TorqueRH2]

(13)

where TLF1, TLF2, TLH1, TLH2, TRF1, TRF2, TRH1, and TRH2

are the single-component torques of hip/knee joint of the

Figure 5. Structure of the co-simulation.

LF/RF/hind leg. The eight output swing angle variablesof each joint can be expressed as follows:

A = [AngleLF1,AngleLF2,AngleLH1,AngleLH2,

AngleRF1,AngleRF2,AngleRH1,AngleRH2] (14)

where ALF1, ALF2, ALH1, ALH2, ARF1, ARF2, ARH1, andARH2 are defined as the swing angles of the hip/knee jointof the LF/RF/hind leg.

We used PID algorithm to control the velocity of joint,and its driving torque can be expressed as follows:

T = kpe+ kde+ ki

∫edt (15)

where T is the driving torque of joint; kp, ki, and kd are theproportionality, differential, and differential coefficients;and e is the difference between the intended angle andactual angle.

There are eight input and eight output in the sub-system. The angle of joint is used as feedback and mea-sured in Adams; through a mathematical operation, thedisplacement and velocity of joint can be determined, anda closed-loop control system was developed. Details of thecontrol system are shown in Fig. 5 [17]–[22]; we can set dif-ferent on-land locomotion gaits in MATLAB and measuretheir results.

4

Figure 6. Displacement of the centroid of the robot as it moves with crawling gait: (a) X-axis direction; (b) Y -axis direction;and (c) Z-axis direction.

Figure 7. Tracking error of joint as the robot moves with crawling gait: (a) hip joint and (b) knee joint.

Figure 8. Tracking error of joint as the robot moves with trotting gait: (a) hip joint and (b) knee joint.

3.4 Co-Simulation Results and Analysis of ThreeOn-Land Gaits

First, we studied the crawling gait and created a simula-tion of control system in MATLAB/SIMULINK, and thenadjusted the control parameters of robot; the trajectory ofthe centroid of robot in three directions are presented inFig. 6. In Fig. 6(a), we see that the change in X-directionis relatively stable, and the velocity of robot is around20 mm/s. Figure 6(b) shows the deviation displacementin Y -direction; the maximum deviation of robot was ap-proximately 6.2 mm, which is about 2.4% of the heightof robot. Figure 6(c) shows the vibration in Z-direction;the maximum translocations is 0.028 mm, which is about0.01% of the height of robot. Thus, the PID control isan effective method for controlling the crawling gait ofrobot.

The trajectory tracking error of hip and knee jointswhen guided by PID are shown in Fig. 7. In Fig. 7(a),except the maximum tracking error (0.08 mm) caused bythe instantaneous driving force when the hip joint swings,the tracking error is small and tends to zero in other timeperiods. In Fig. 7(b), the tracking error of knee joint isclosed to zero too. Consequently, the proposed controlmethods are able to track the intended trajectory of eachjoint when the robot moves with crawling gait.

From the trajectory results of the centroid of robotin the three directions with trotting gait, the velocity ofrobot is 43.3mm/s; the maximum deviation is 9.8mm.The maximum translocation is approximately 0.035mm.The trajectory tracking errors of hip and knee joints areshown in Fig. 8; as we can see, with the exception ofseveral individual large errors caused by the joints swing,the tracking error is minor.

5

Figure 9. Tracking error of joint as the robot moves with pacing gait: (a) hip joint and (b) knee joint.

The results showed that the pacing velocity of robotwas 50mm/s, the maximum deviation of robot was ap-proximately 88mm, and the translocation remained at ap-proximately 0.037mm. The maximum errors in the hipand knee joints were approximately 20◦ and 18◦, as shownin Fig. 9. Although the pacing gait were not stable as forthe crawling and trotting gaits, the final trajectory wasstill essentially as desired.

4. Underwater Movement and Co-SimulationAnalysis

When the robot in underwater environment, the four vec-tored propellers can change the directions and propulsiveforces of its. We carried out force analysis on an actuatorunit performing motions; and based on the leverage prin-ciple, we measured the thrust of a water-jet propeller forbetter control [3]–[6]. The results showed that the thrustincreases as the input voltage increases, and at the max-imum voltage of 16V, the maximum thrust in two spraydirections were 58.2mN and 38.8mN. At a voltage of 8V,the maximum thrust in two spray directions were 13.4mNand 6.4mN [23].

4.1 Underwater Control System Design and theProcess of Co-Simulation

When the robot moves in the horizontal direction, wemainly control its displacement and yaw angle [24]. Asshown in Fig. 10, αi and αo are the input and output anglesof robot, respectively. ri and ro are the displacement inputand output of robot, respectively. The driving force andtorque are given as follows:

MTi = kp1(αi − αo) + kd1d

dt(αi − αo) + ki1

∫(αi − αo)dt

(16)

FTi = kp2(ri−ro)+kd2d

dt(ri−ro)+ki2

∫(ri − ro)dt (17)

where ri=

√x2\i +y

2\i ;αi=arctan(yi/xi); ro=

√x2\o + y

2\o ;

αo = arctan(yo/xo)The motion of robot in the vertical plane is controlled

by the depth, pitch angle, and roll angle. The block

Figure 10. Block diagram of horizontal motion control.

Figure 11. Block diagram of vertical motion control.

diagram of the algorithm is shown in Fig. 11. θi and θoare the input and output angle of robot, respectively. Di

and Do are the displacement input and output of robot,respectively. The driving force and torque are given asfollows:

MTi = kp1(θi − θo) + kd1d

dt(θi − θo) + ki1

∫(θi − θo)dt

(18)

FTi = kp2(Di−Do)+kd2d

dt(Di−Do)+ki2

∫(Di −Do)dt

(19)

5. Motion Stability Experiments on Land andUnderwater

5.1 On-Land Gait Stability Experiments

We evaluated the motion of robot in terms of stabilityand velocity, and an NDI Polaris Vicra system was used

6

to evaluate the results, some of the control parameterswere not varied during the co-simulations. The robotwas programmed to move on a common mat floor; theexperimental setup is shown in Fig. 12.

Figure 12. Experiments to evaluate the stability of thecrawling gait.

Figure 13. Displacement of the robot as it moves withdifferent gaits.

Figure 14. Amplitudes of the vibrations that occur when the robot moves with crawling gait.

Figure 15. Attitude angle of the robot moves with trotting gait: (a) with PID control and (b) without PID control.

The displacement of three on-land locomotion gaitsof the PID-controlled robot are shown in Fig. 13. Thevelocity of the trotting gait increased quickly and becamestable. The crawling gait was the slowest. The pacinggait was larger than the trotting gait due to the large yawangle, the crawling gait was the most stable and the pacinggait was the least stable. Consequently, the crawling gaitand trotting gait were selected as two common on-landmovement gaits.

Figure 14 shows that the robot moved in a crawlinggait, which is controlled using the PID method and theopen-loop method. When the crawling gait was guided bythe PID controller, it pitched and rolled in a stable manner,and the trajectory converged to the desired trajectory. Therobot’s walk was also less bumpy than when it was guidedusing the open-loop controller. When the PID-controlledrobot moved with trotting gait, the pitch and roll angleswere relatively small, and the yaw angle was large becausethe robot has only two legs in contact with the ground, aspresented in Fig. 15, and the yaw angle gradually stabilizedalthough there exist some deviations. The pacing gait isinherently unstable, and the yaw angle was slightly largerthan it was with other gaits; but overall, the pacing motionwas relatively stable.

These experimental results show that when these threeon-land locomotion gaits are controlled using PID algo-rithm, the robot deviates far less from the desired trajec-tory, and its motion is smoother than when it is controlledby open-loop method. Overall, the motion on land meetsour requirements. Consequently, PID controller is suitablefor practical applications.

7

Figure 16. Underwater horizontal motion: (a) at 50 s and (b) at 3 s.

Figure 17. Trajectory comparison of the robot: (a) trajectory and (b) yawing angle.

5.2 Underwater Motion Stability Experiments

We evaluated the underwater performance of robot withboth PID control and open-loop control experimentally.Each experiment was repeated 10 times. Control signalsdirected the robot move forward for 200mm. The distanceand angle were measured by using a ruler and an IMUsensor, respectively [24]. Figure 16 shows a video sequenceof the horizontal motion; the red arrow indicates themoving direction.

The resulting trajectories and angles are shown inFig. 17. As shown in Fig. 17(a), when the robot wasguided by PID controller, the horizontal motion proceedsalong the desired trajectory, although there were somedeviations. However, when the robot was guided by open-loop controller, the errors were larger and the robot didnot arrive at the target position. Fig. 17(b) showsthe yaw angle of robot, the deviation at the start waslarge in both cases, and as the PID controller adjustsits control parameters, the deviation of the yaw anglegradually decreased and stabilized.

6. Conclusion

We aimed to improve the motion performance and sta-bility of our amphibious spherical robot. We devel-oped a PID closed-loop control method to guide therobot on land and underwater. To demonstrate the ef-ficacy of the proposed method, we developed on-landand underwater co-simulations in an Adams and MAT-LAB/SIMULINK. Informed by the simulation results, weperformed experiments on a common mat floor to evalu-ate the stability and velocity of three on-land gaits, andwe also conducted horizontal underwater experiments to

evaluate our control method. Finally, we compared theperformance of PID controller with the open-looped con-troller, and our proposed controller attained the bestmotion performance, with less deviation and vibration.In the future, we will improve on-land movement perfor-mance by developing new gaits and other adaptive controlalgorithm.

Appendix A Derivation of Robot Dynamic

According to Fig. 5, each leg consists of two links and twojoints. Link 1 consists of L1 and L2 and can be rotatedin the XbObYb plane; Link 2 consists of L3 and L4 andcan be rotated in the YbObZb plane; m1, m2, m3, and m4

are the corresponding qualities; li represents the lengthof the corresponding part; θ1 and θ2 represent generalizedcoordinates variables.

Kinetic energy and potential energy of Link 1 can beexpressed as follows:

K1 =1

2(m1 +m2) l

21θ

21

P1 = − (m1 +m2) gl2

The centroid of Link 2 in Cartesian coordinate systemcan be expressed as follows:

⎧⎪⎪⎪⎨⎪⎪⎪⎩x2 = (l1 + l3 sin θ2 − l4 cos θ2) cos θ1

y2 = (l1 + l3 sin θ2 − l4 cos θ2) sin θ1

z2 = −(l2 + l3 cos θ2 + l4 sin θ2)

8

It can be obtained from the upper equation derivative:⎧⎪⎪⎪⎪⎪⎪⎪⎪⎪⎨⎪⎪⎪⎪⎪⎪⎪⎪⎪⎩

x2 = −θ1 sin θ1(l1 + l3 sin θ2 − l4 cos θ2)

+ cos θ1(l3θ2 cos θ2 + l4θ2 sin θ2)

y2 = θ1 cos θ1(l1 + l3 sin θ2 − l4 cos θ2)

+ sin θ1(l3θ2 cos θ2 + l4θ2 sin θ2)

z2 = l3θ2 sin θ2 − l4θ2 cos θ2

v2 = x2 + y2 + z2 = θ21l21 + θ21l

23 sin

2 θ2 + θ21l24 cos

2 θ2

+2l1l3θ21 sin θ2 − 2l3l4θ

21 sin θ2 cos θ2

− 2l1l4θ21 cos θ2 + l23 θ

22 sin

2 θ2

+ l24 θ22 cos

2 θ1(l3θ2 cos θ2 + l4θ2 sin θ2)

So, the kinetic energy and potential energy of Link 2can be expressed as follows:

K2 =1

2mv2 =

1

2(m3 +m4) v

2

P2 = − (m3 +m4) g(l2 + l3 cos θ2 + l4 sin θ2)

The dynamic Lagrange equation of robot is givenbelow:

L = Ek − Ep = (K1 +K2)− (P1 + P2)

= [1

2(m1 +m2)v

21 +

1

2(m3 +m4)v

22 ] + (m1 +m2)gl2

+(m3 +m4)g(l2 + l3cθ2 + l4sθ2)

=1

2(m1 +m2)l

21 θ

21 +

1

2(m3 +m4)[θ

21l

21 + θ21l

23 sin

2 θ2

+ θ21l24 cos

2 θ2 + 2l1l3θ21 sin θ2

− 2l3l4θ21 sin θ2 cos θ2 − 2l1l4θ

21 cos θ2 + l23 θ

22 sin

2 θ2

+ l24 θ22 cos

2 θ2 − 2l3l4θ22 sin θ2 cos θ2]

+ (m1+m2)gl2+(m3+m4)g(l2+ l3 cos θ2+ l4 sin θ2)

Acknowledgement

This work was supported by National Natural ScienceFoundation of China (61503028 and 61773064). This re-search project was also partly supported by National Nat-ural Science Foundation of China (61375094) and NationalHigh Tech. Research and Development Program of China(no. 2015AA043202).

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Biographies

Yanlin He received the B.S.degree in communication engi-neering from Lanzhou JiaotongUniversity, China, in 2011. Cur-rently, she is a Ph.D. candidate inbiomedical engineering at BeijingInstitute of Technology, China.Her current research interests in-clude amphibious spherical robotand multi-robot system. She haspublished about 25 refereed jour-nal and conference papers in the

recent years.

Shuxiang Guo (IEEE SM’03)received the Ph.D. degree inmechanoinformatics and systemsfrom Nagoya University, Nagoya,Japan, in 1995. He is the chairprofessor in Key Laboratory ofConvergence Medical Engineer-ing System and Healthcare Tech-nology, Ministry of Industry andInformation Technology, BeijingInstitute of Technology, China.He had been a full professor at the

Department of Intelligent Mechanical System Engineering,Kagawa University, Japan, since 2005. He has publishedabout 500 refereed journal and conference papers. Hiscurrent research interests include biomimetic underwaterrobots and medical robot systems for minimal invasivesurgery, micro catheter system, etc.

Liwei Shi received the B.S. de-gree in mechanical engineeringfrom Harbin Engineering Univer-sity, China, in 2006, the M.S. andthe Ph.D. degrees in intelligentmachine system from KagawaUniversity, Japan, in 2009 and in2012, respectively. He was a post-doctoral researcher in KagawaUniversity, Japan. Currently, heis an associate professor at theBeijing Institute of Technology,

he researches on underwater micro-robot utilizing artificialmuscles, such as legged bio-inspired micro-robots, andspherical underwater robots, etc. He has published about55 refereed journal and conference papers in the recentyears.

Huiming Xing received the B.S.degree in automation from QiluUniversity of Technology, China,in 2013, and theM.S. degree in au-tomation from Harbin Engineer-ing University, China, in 2016,respectively. Currently, he is aPh.D. candidate in automation atBeijing Institute of Technology,China. His current research in-terests include the navigation andcontrol of amphibious spherical

robot andmulti-robot cooperation. He has published about10 refereed journal conference papers in the recent years.

Zhan Chen received the B.S.degree in automation engineer-ing from Beijing Information Sci-ence and Technology University,China, in 2016. Currently, he isan M.S. candidate in biomedicalengineering at Beijing Institute ofTechnology, China. He researcheson amphibiousmulti-robot forma-tion control and communication.

Shuxiang Su received the B.S. de-gree in automation from theNorthChina University of Technology,China, in 2016. Currently, heis a master from Beijing Insti-tute of Technology, China. Heresearches on amphibious spher-ical robot and autonomous mo-tion control of amphibious spheri-cal robot. He has published aboutnine refereed journal and confer-ence papers in the recent years.

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