Modeling and Experimental Verification of

a New Spherical Underwater Robot

Ruochen An*1 Shuxiang Guo*2*3, Liang Zheng*1, Tendeng Awa*1,

Wenbo Sui*1 *1Graduate School of Engineering, Kagawa University

Takamatsu, Kagawa 761-0396, Japan

*2Key Laboratory of Convergence Medical Engineering

System and Healthcare Technology, The Ministry of Industry

and Information Technology, School of Life Science and

Technology, Beijing Institute of Technology,

Haidian District, Beijing 100081, China *3Department of Intelligent Mechanical Systems Engineering,

Kagawa University, Takamatsu, Kagawa 761-0396, Japan

s19d501@stu.kagawa-u.ac.jp guo@eng.kagawa-u.ac.jp

Abstract - Underwater robots provide great possibilities for

people to detect the marine environment. Robots need to keep

moving stability, need to ensure the safety of the robot during the

movement. A novel spherical underwater robot (SUR V) with

hybrid propulsion devices that divided into two parts- vectored

water-jet and propeller thrusters. A camera is added at robot to

monitor the environments. To analyze the motion characteristics

of the SUR V, the computational simulation is calculated in

ADAMS and ANSYS CFX respectively. The simulation results

verify the performance of the improved spherical underwater

robot. Finally, the thrust experiments were conducted that

evaluate the performance of the hybrid thruster. The thrust

experiment proves that in the improved hybrid thruster proposed

in this paper, the maximum thrust of the propeller thruster has

increased by 4 times than before.

Index Terms - Spherical underwater robot, Motion state

simulation, Computational fluid dynamics simulation.

I. INTRODUCTION

Due to the increasing demand for ocean exploration and

ocean research, people's research on the ocean is still

challenging [1]. Human knowledge of the ocean is very

shallow, and human cognitive methods are extremely limited.

In the past development, underwater robots can realize more

applications and can provide more detailed and complex data

during underwater detection. These data make people's

understanding of the ocean more profound, and have a profound

impact on ocean research. Underwater environment is a

dangerous danger, and people have limited diving depth, so

underwater robots have become an important tool for

developing the ocean. At present, underwater robots have

various of applications such as dam detection, underwater

fishing, underwater tracing, underwater breeding, pipeline

testing, and underwater scientific research. The IFREMER

L’Eqaulard AUV was probably the first AUV which applied in

scientific research [2,3]. Different tasks require different shapes

and sizes of AUVs [4,5]. For example, Mini-Autonomous

Underwater Explorer was a swarm of autonomous miniature

underwater robot [6]. Daniele Costa et al. design and fabrication

of an ostraciiform swimming robot, the architecture has easier

to waterproof and capable to withstand greater pressures to

achieve long-term detection under water [7]. UX-1 robot that a

spherical underwater vehicle, can be carried out exploration

missions in submerged mine tunnels [8]. A key feature of the

underwater robot is its specially shaped hull, which is designed

to more flexibility at the design speed. In these shapes of robots,

the spherical underwater has more flexibility and can achieve

multi-degree of freedom of motion. Spherical underwater

robots with multiple functions and high maneuverability to

generated significant interest due to their wide range of

potential applications in various surroundings.

A spherical underwater robot (SUR) with vectored water-

jet thrusters was designed firstly in our previous study [9,10].

Then a Father-son Underwater Intervention Robotic System

(FUIRS) that the SUR II as the father robot and an IPMC micro-

robot plays the role of the son robot was proposed [11,12]. SUR

II with three vectored water-jet thrusters distributed in

equilateral triangular, so it can work with high stability. After

SUR II, the SUR Ⅲ which has four vectored water-jet thrusters

for the propulsion system was proposed [13-15]. Our lab also

developed an amphibious spherical robot, it has a

communication module devoted to allowing the robot to both

move on land and underwater, relative close-range localization

and real-time tracking [16-19]. And then evaluation of

amphibious spherical robot characteristics, such as motion

characteristics, communications characteristics, location

characteristics [20,21]. In order to carry more sensors to

increase the robot's modular function and improve the robot's

motion performance, the new spherical underwater robot has

been redesigned. This paper proposed a novel SUR with hybrid

thruster system and an OPENMV camera. The reminder of this

paper is organized as follows: section 2 introduces the multi-

vectored propulsion system, the mechanism of camera and the

advanced control circuit of the spherical underwater robot. In

section 3 is described to the motion simulation in ADAMS and

ANSYS-FLUENT. Experiments of thrust experiments and

results of the hybrid thruster are described in section 5. It also

dedicated the performance of thruster system. Finally, section 6

concludes this paper.

II. THE NOVEL SPHERICAL UNDERWATER ROBOT

A. Inspiration for design of SUR V

The design of the SUR propulsion system is inspirited

from the propulsive mechanism of the jellyfish. As shown in

Fig. 1, jellyfishes shrink the shell to squeeze the inner cavity,

change the volume of the inner cavity, spray the water in the

cavity, and move by the way of water spray propel-ling. The

muscle fibers in the jellyfish epidermis that extend from the

apex to the end of the umbrella control the contraction and

expansion of the lumen. The inner cavity expands, and the

water flow is slowly sucked in, filling the inner cavity; the inner

cavity quickly contracts, pushing the water flow out of the

cavity, and the thrust generated by the water flow ejects the

jellyfish in the axial direction of the body. So, the movement

mode of jellyfish is the most efficient underwater swimmers.

SUR is designed to mimic jellyfish's efficient movement and its

advantages in symmetry, stability and performance.

B. The Design of SUR V

In order to realize the detection of underwater targets, to

ensure the safety of underwater motion, we designed SUR V

which mainly consists of two hemisphere hull, propeller of

composite propulsion mechanism, a waterproof bin with

4000mAh batter cabin and sensors, such as the pressure sensor,

IMU, camera. The overview structure diagram of the robot is

shown as Fig. 2. A diameter of 460 mm of the robot. As shown

in Fig.2, Four thrusters were annular symmetrical located on a

support in the propulsion system of the SURII. The propeller

system is composed of water-jet thruster and propeller thruster

and the two thrusters are placed symmetrically. The maximum

distance between the two opposite thrusters is 54 cm, and its

thickness is 1.5 cm that improved the hardness of the thrusters.

This layout is limited to achieve multi-angle rotation of the

servo motor in a compact layout, which improves the robot's

motion performance. In the previous study [22], we proved the

advantages of the symmetrical thruster system in the spherical

underwater robot, so the symmetric structure of the push

machine was retained in this study. This study mainly changed

the structure of the motor and servo motor, to ensure that the

stability of the robot is not affected, and improve the robot's

movement efficiency.

C. The Multi-Vectored Propulsion System

It has 6 Degrees of Freedom (DoF) of the underwater robot.

In the study of the different motion states of underwater robots,

based on the relevant research proofs [23] and the previous

research experience of the laboratory [24], as long as there are

four degrees of freedom, they are surge, sway, undulation and

yaw. In the previous research, the robot can achieve these four

degrees of freedom, and realize high-speed free movement in

the water. The new propulsion system guarantees the realization

of four degrees of freedom, and further improves the thrust of

the propeller and the control of the stability of the propeller. The

propeller system that it consists of a propeller and a water jet

propeller, and is connected to a servo system through a bracket

in the previous study. This has also proved that the stability of

the robot can be achieved [25]. The propeller thruster has strong

thrust, and the water jet thruster can achieve more stable low-

speed rotation. For the purpose of improved the efficiency of

the thruster in a limited space and structure, according to the

needs of different motion states, while increasing the service

life of the thruster system, a new type of hybrid thruster is

shown in Fig. 3. The structure of the robot consist of the

motors, two propellers, two water jet propellers, a bracket and

a servo arm as shown in Fig. 4. From the side view of the

thruster system in Figure 4b, the hybrid thruster will rotate from

0 ° to 360 °. By combining these movement changes, the basic

movement of the robot can be achieved. In fact, details of the

hybrid propeller, which includes four servos the four DOFs of

surge, sway, heave, and yaw will be considered SUR V’s main

movements. Two opposite thrusters, namely water-jet thruster

and a propeller, are used, is realized by switching the working

conditions of the propeller and water-jet thrusters to realize the

more difficult motion modes.

Fig 3. 3D model of SUR V.

Fig 2. Structure of proposed spherical robot.

Fig. 1 Propulsion mechanism of the Jellyfish and SUR motion.

D.The Mechanism of camera

In order to achieve underwater target recognition and

safety when the robot moves, the robot uses a camera. As shown

in Fig. 2, an OPEN MV camera which can capture color images

with 320×240 resolution at 16-bit and grayscale map images

with 640×480 resolution at 8-bit. The OpenMV camera is a

small, low-power, low-cost circuit board, which helps you

easily complete machine vision applications and can be scripted

by high-level language Python. This camera is adopted to the

robot to perceive the underwater environment. OpenMV uses

STM32F765VI ARM Cortex M7 processor (216 MHz, 512KB

RAM, 2 MB flash). This processor has an SPI bus speed up to

54Mbs, allowing simple image stream data to be transferred to

LCD expansion board, Wi-Fi expansion board, or another

controller. It also has an I2C bus, a CAN bus, and an

asynchronous serial bus (TX / RX), which can be used to link

other controllers or sensors. All IO ports can be used for

interrupts and PWM (there are 10 I / O pins on the board). A

customized waterproof hull is made using 3D printing

technology to suitable the underwater working environment

and mounted middle the robot by the extended connector. Two

pieces of optical glasses are fixed in the front of the camera

sensor and the mechanism of camera.

E. Control circuit

Due to realize to switch modes based on the motion mode,

the control circuit as shown in Fig. 5. The ATMega2560 is

employed as the control center. The battery uses a modular

design to improve battery efficiency. Sensors consist of IMU

and depth sensor to provide feedbacks of posture and depth

information of the SUR V are also employed and to send the

information to the control center. OpenMV communicates with

the main control board and feeds back image information to the

main control board. 6-axis sensor and pressure sensor to correct

position information. Finally, the control center to adjust the

robot’s attitude in time by thruster system based on feedbacks.

(a) The structure of the hybrid thruster.

(b) The detail of one thruster.

Fig 4. The improved hybrid thruster.

Fig 5. The control circuit of SUR V.

Fig 6. Zero error correction of 9-DoFs IMU.

Fig 7. Result of velocity correction. Green boxes mean

the range of constant velocity.

By processing the data acquired from IMU, it’s possible to track

the position and orientation of the device, thus in this way,

localization and navigation of the robot can be realized in a

given environment. JY901 integrates high-precision

gyroscope, accelerometer, magnetic field that is a nine DoFs

sensor as for obtain the tilt angles of the x-, y-, and z-axis of the

object (four axis, stability cart, angle roll, yaw angle) ,

accelerometer of the x-, y-, and z-axis of the object and

magnetic field orientation. Digital Motion Processor (DMP)

hardware accelerator engine with an auxiliary I2C port and the

other serial communication USART. It can acquire the current

three acceleration components and three rotational angular

velocities. The error of JY901 comes mainly from three parts,

including noise (deviation and noise), scale errors and axis

misalignments. Tracking the position and orientation of SUR V

needs to obtain by the accelerometer, the error processing of the

accelerometer is necessary. In the case of static placement,

regardless of the position of the accelerometer, the measured

modulus of acceleration should always be the local gravity

acceleration g. Help of six-sided calibration method that via

obtained data of up, down, left, right, reverse, horizontally

placed for calibration should to remove the zero offset. These

three axes are supposed to be orthogonal, thus:

2 2 2 ,x y zAcc Acc Acc g (1)

[3*3]

0 0

0 0 ,

0 0

x x mx x

t y y my y

z z mz z

A Scale A offset

A A R Scale A offset

A Scale A offset

(2)

In this equation, tA and *mA are true value and

measurements respectively. *Scale is scale coefficient and

*offset is zero offset of 3 axes.

Transform it into the form of homogeneous coordinate,

and transpose the matrix:

1 2 3

4 5 6

7 8 9

,

1

x

y

Z

mxoffx

my

y off

mz

zoff

AC C C CA

AA C C C C

AA C C C C

(3)

where 1 2X XmAcc A Acc A ,

3 4Y YmAcc A Acc A and 5 6Z ZmAcc A Acc A .

Least Square Method is applied to fit these equations. The

simulation results of zero offset as show in Fig. 5. The

minimum value of zero drift is -0.067 mm/s and 0.067mm/s is

the highest value. The error of the accelerometer at rest is

greatly improved after the correction. After the six-sided

calibrations, the modulus of three components of accelerations

maintains stability within an acceptable range at value g.

Accelerometers can cause large cumulative errors over time,

leading to a decrease in sensor accuracy. Therefore, it is

necessary to periodically correct the cumulative error.

Therefore, the cumulative error correction needs to be

performed at regular time intervals. Since the speed of the robot

during the movement is a fixed value, the correction is

performed by the difference between the speed value at this

time and the speed value obtained through the accelerometer.

The correction formula is

0

( ) ( ) ,t

IMU

vV t a dt

T (4)

In the formula, a is the acceleration value obtained by the

accelerometer, v is the difference between the speed of the robot

and the speed obtained by the accelerometer at time t and T is

the time spent swimming at a speed other than constant speed.

The Z-axis angle of the 9-axis does not have an accumulated

error according to the magnetic field solution, the rotation angle

of the z-axis is obtained by the IMU. The result as shown in

Fig.6.

III. SPHERICAL UNDERWATER ROBOT SIMULATION

AND VERIFICATION

A. Motion state simulation

To establish the virtual model of the prototype in ADAMS

software mainly has two types. The first is to model the

prototype in ADAMS directly. Another one is to model the

protype in SolidWorks, Creo or another software firstly, and

then to import the model into ADAMS. However, the ADAMS

has the better ability of simulation but has not the specialize

design of the model. For the above reasons, the 3D model of

SUR V was designed by SolidWorks 2018 firstly. Then to save

a parasolid (*.stp file) imported into ADAMS software and set

the location to origin, as shown in Fig. 8. Since the external files

imported by ADAMS have no material parameters, such as

weight and the material of the component, by default, the

materials or quality settings of each part need to be set after

merging parts without relative motion. Finally, we did some

simulations of robot motion. Through the post-processing

function of ADAMS/View, and the motion curve in x, y and z

axis of the robot was obtained as shown in Fig.9. These

movement curve also demonstrate the stability of the robot.

B. Motion performance simulation on Ansys CFD

To obtained the hydrodynamic characteristics of the robot,

we establish the 3D model of SUR V as shown in Fig.9 is also

established in SolidWorks 2018. A key parameter of the

efficiency and accuracy of the control system for a robot

operating in an underwater environment is hydrodynamic

characteristics. For this reason, the hydrodynamic analysis is

carried out by the ANSYS-FLUENT. To estimate the

parameters of dynamic model of robot, we set that the thrust of

robot thrusters and the environment of flow field was 20°C

without external disturbances. The two thrusters were set to 400

rev/min and 4200 rev/min respectively. The results of the

vector and pressure shown in the CFX post-processing in Fig.

11. From simulation results of vector,we can see the motion of

robot is smmothly,and the pressure of robot can be ignored.

IV. THRUST EXPERIMENTS AND RESULTS

The thrust experimental setup consists of a 6-DoF load

cell, a water-jet thruster, a propeller thruster and support

frames. The experiment of thrust is divided into 2 cases that

include the positive and negative rotation of the water-jet and

propeller respectively. The two cases of thrust experiments are

measured in different voltage and the rated voltages of the two

types of DC motors are is 7.2 V and 12 V respectively.

Therefore, for water jet thrusters, the voltage is set to 0-7 V, and

for propeller thrusters, the voltage for this experiment is set to

0-24 V. As shown in Fig. 12, we summarized the experimental

results of two types thruster at different voltage. The maximum

thrust of the waterjet-thruster at 7 V is 1.84 N and it is the same

of the previous waterjet-thruster. For the propeller thrust, the

thrust in positive and negative is 9.8 N and 8.43N in rated

voltages respectively. At the maximum voltage (24 V), the

thrust of the propeller is 19.6N.

Fig 8. 3D model of robot based on ADAMS platform.

(a) Displacement curve of the centroid in the Y direction.

(b) Displacement curve of the centroid in the Z direction.

(c)Angular velocity of the Z direction.

Fig 9. The simulation results of SUR V.

Fig 9. Simplified 3D model.

(b)Velocity vectors.

Fig 11. Results of FLUENT simulation of forward motion.

(a) Contours of static pressure.

Fig 10. Simplified 3D model.

IV. CONCLUSION

This paper presented a fifth-generation spherical

underwater robot (SUR V) with the hybrid propulsion device

and three cameras. First of all, the novel mechanism of SUR V

was proposed, divided into the thruster device including both

two propellers and two water-jet thrusters, and the camera. The

thruster device can realize switching motion mode fast. The

structure of the new propeller system can effectively avoid the

involvement of underwater plants and gravel, causing damage

to the propeller. And then, the simulation of SUR motion by

using ADAMS. The simulation results show that the robot can

moving stability in forward motion, rotation motion and

heaving motion. And the CFD simulation for the robot was

carried out. The simulation results show that the novel robot can

move stability and provide a premise for subsequent program

design. Finally, the thrust experiments at different cases were

conducted. The experimental results shown the maximum

thrust of propeller mode is 22.5% higher than before. While

ensuring the stability of the robot, the thrust of the thruster is

increased, and it is verified that adding a camera will not affect

the movement of the robot.

ACKNOWLEDGMENT

This research is partly supported by National High Tech.

Research and Development Program of China

(No.2015AA043202), and SPS KAKENHI Grant Number

15K2120.

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Fig. 12 Experimental results for the different thrusters.