A New Design Concept of a Fully-Actuated UnmannedSurface Vehicle

Kantapon Tanakitkorna,∗, Philip A. Wilsonb

aFaculty of International Maritime Studies, Kasetsart University, ThailandbFluid Structure Interactions Research Group, University of Southampton, UK

Abstract

To be effective in their roles, unmanned surface vehicles (USVs) need to be capa-

ble of performing a variety of distinct manoeuvres, including trajectory tracking

and station-keeping. The conventional X-type thruster configuration permits

an accurate station-keeping ability at the expense of the propulsion efficiency,

which may be a critical factor for long-range, high-speed operation. This pa-

per presents a new USV thruster configuration that can transform between the

under-actuated mode which suits high-speed operation and the fully-actuated

mode which is effective for station-keeping. Besides, the trimaran design offers

wide deck space and great roll stability which is beneficial for a wide range of

potential applications. The possible control system is also suggested for util-

ising multiple actuators that are equipped on the vehicle in the most energy-

efficient way. Regarding the simulation studies, although the proposed design

is equipped with fewer thrusters, it has shown to achieve comparable station-

keeping performance with the conventional X-type configuration even when the

USV is subjected to a sway disturbance.

Keywords: fully-actuated, unmanned surface vehicle (USV), station-keeping,

control, allocation

∗Corresponding authorEmail addresses: kantapon.ta@ku.th (Kantapon Tanakitkorn),

philip.wilson@soton.ac.uk (Philip A. Wilson)

Preprint submitted to Ocean Engineering July 3, 2019

1. Introduction

Unmanned surface vehicles (USVs) are marine crafts that are capable of

unmanned operation. They have varying degrees of autonomy ranging from

remote-controlled vehicles to ones that govern their decisions during the mis-

sion with minimum human intervention. The latter may be referred to as au-5

tonomous surface vehicles (ASVs). Since the vehicles are unmanned, they may

be designed to have just sufficient room to accommodate different sets of sen-

sors and actuators (Naeem et al., 2008; Ferri et al., 2015; Liu et al., 2016; Vasilj

et al., 2017). This compact design contributes to lower maintenance and opera-

tion costs as well as access to shallow water areas. USVs also have the potential10

to perform monotonous work such as an environmental survey for an extended

period of time at precision and robustness that manned vehicles cannot compare

with (Bibuli et al., 2012; Sharma et al., 2014; Matos et al., 2017; Park et al.,

2017).

The USVs are presented in various designs, but the typical ones are mono-15

hull or catamaran designs with differential thrust drives (Demetriou et al., 2016;

Gan & Xiang, 2017; Jin et al., 2018). A bow thruster may be added to enhance

manoeuvrability (Park et al., 2017). The differential thrust design is preferable

to the conventional rudder-based vehicle because it offers great manoeuvrability

even at zero-speed. Motion control of USV involves three degrees of freedom20

(3 DOFs) on the horizontal plane: surge, sway and yaw. Since USVs with

differential thrust drives cannot exert pure sway force, they may be categorised

as under-actuated vehicles.

The majority of the USV’s roles involve path following for navigation within

different location (Ferri et al., 2015; Bibuli et al., 2012; Pastore & Djapic, 2010;25

Naeem et al., 2008). Underactuated USVs can effectively achieve this path

following ability via simultaneous control of speed and heading, as presented by

Jin et al. (2018); Park et al. (2017); Xiang et al. (2016); Fossen et al. (2003).

However, there is a case where a USV needs to perform station-keeping which is

to maintain constant pose (position and orientation) over a period of time. For30

2

instance, a USV may need to inspect an underwater structure from a specific

view angle. Additionally, a USV may be employed as a support vessel for an

autonomous underwater vehicle (AUV) (Pearson et al., 2014; Sarda & Dhanak,

2017; Phillips et al., 2018). Fixing USV’s pose will be highly beneficial in this

scenario because a complicated task such as autonomous launch and recovery35

can be simplified into a static docking of the AUV (Jantapremjit & Wilson,

2007; Vidal et al., 2018).

Panagou & Kyriakopoulos (2014) presented a station-keeping technique for

an underactuated vehicle. The strategy was to initially drive the vehicle into a

neighbour of the desired location then the control objective switched between40

position and heading stabilisation. While the vehicle’s pose was bounded closed

to the desired values, the results highlighted a conflict between regulating the

position and the orientation. Sarda et al. (2015) developed three distinct station-

keeping controllers for a USV with twin azimuth propellers. The work was then

extended to feedforward control theory for suppressing the effect of wind dis-45

turbances (Sarda et al., 2016). Although the twin azimuth drives could permit

motion in all 3 DOFs on the horizontal plane, it did not allow pure sway mo-

tion. Due to this reason, the vehicle was still considered under-actuated, which

implies that improvement in heading control could increase position error and

vice versa. Nevertheless, the experiment results (Sarda et al., 2015, 2016) have50

shown that the vehicle was able to maintain its position and heading errors

within 3 m and ±20 degrees, respectively.

Nađ et al. (2015) presented the experimental study of a USV that was capa-

ble of moving on the horizontal plane in any orientation. The vehicle employed

the X-type thruster configuration that is typically used for fully-actuated re-55

motely operated underwater vehicles (ROVs) (Omerdic & Roberts, 2004; Liu

et al., 2012). Although the fully-actuated design permits precise motion control

in all DOFs, the larger frontal projected area contributes to less hydrodynami-

cal efficiency which significantly impacts propulsion power and endurance of the

vehicle. Furthermore, because of the diagonal thruster placement, the vehicle60

loses some amount of thrust on sway DOF in generating forward motion. These

3

factors could be critical concerns for USVs that need to travel a long distance,

particularly at high forward speeds. This paper proposed a new thruster con-

figuration of a USV that can be transformed to suit both long-range operation

at high speeds and precise manoeuvre at low speeds.65

2. Vehicle design

Differential drives are advantageous for simultaneous heading and speed con-

trol at a wide range of speeds; therefore, this drive concept is typically used

on USVs to effectively transit within different locations (Park et al., 2017; Ferri

et al., 2015; Pearson et al., 2014; Caccia et al., 2008; Naeem et al., 2008). Adding70

more thrusters can make the vehicle fully-actuated, extending their capability

toward station-keeping. However, the typical X-type configurations (Nađ et al.,

2015; Liu et al., 2012; Omerdic & Roberts, 2004), as shown in Figure 1a, is not

energy efficient in producing forward motion because some amount of thrust is

wasted on sway DOF. Hence, this configuration should be avoided when the75

vehicle’s speed and endurance are critical concerns.

(a) typical configuration (b) proposed configuration

Figure 1: Fully actuated thruster configurations.

This paper presents a USV thruster configuration that is optimised for both

4

high-speed style and station-keeping style (see Figure 1b). A trimaran hull

design is adopted because of its great stability concerning roll motion. It also

has wide deck space to accommodate mission-related equipment. The thruster80

configuration can be adjusted to suit different operating styles. The first is the

under-actuated mode that has all the three thrusters align with the longitudinal

axis. The mid thruster can effectively exert force in the surge direction while

the two side thrusters are also used for controlling surge as well as yaw DOF.

The second is the fully-actuated mode that has the mid thruster rotated by 9085

degrees. This means the mid thrusters can now exert sway force, but it also

induces yaw motion. To this end, the two side thrusters can be controlled to

counter excessive moment as well as inducing surge motion. With this thruster

configuration, the USV is capable of independent motion control in 3 DOFs,

which is significantly important for precise manoeuvre and station-keeping.90

2.1. Dynamic model

The horizontal-plane (3 DOFs) dynamic model of a USV, with centre of

gravity at the origin, may be described in a matrix form according to Fossen

(2011); Liu et al. (2016):

M · ν +C(ν) · ν +D(ν) · ν = τ, (1)

where ν = [u, v, r]ᵀ is the velocity vector, η = [x, y, ψ]ᵀ is a pose vector, and

τ = [X,Y,N ]ᵀ is a generalised force vector due to actuators. Respectively, the

inertia matrix, Coriolis-centripetal matrix and damping matrix for decoupled

surge dynamics are:

M =

m−Xu 0 0

0 m− Yv 0

0 0 Izz −Nr

, (2)

C(ν) =

0 0 −(m− Yv)v

0 0 (m−Xu)u

(m− Yv)v −(m−Xu)u 0

, (3)

5

D(ν)=−

Xu+X|u|u|u| 0 0

0 Yv+Y|v|v|v| Yr+Y|r|r|r|

0 Nv+N|v|v|v| Nr+N|r|r|r|

. (4)

The following expression transforms the velocity on the body-fixed frame, ν,

to the equivalent vector in the Earth-fixed frame:

η = J(η) · ν, (5)

J(η) =

cos(ψ) −sin(ψ) 0

sin(ψ) cos(ψ) 0

0 0 1

. (6)

For a USV that has n actuators, the generalised force vector, τ , due to the

actuators may be characterised by the following form (Fossen, 2011):

τ = T f. (7)

A column vector, f = [f1, f2, ..., fn]ᵀ, represents the total force of individual

actuators expressed in their local frame. The force configuration matrix, T =

[t1, t2, ..., tn], transforms f into equivalent generalised force vector, τ , acting on

origin of the USV. Deducing from Figure 1b, the components of the thruster

configuration matrix for the proposed USV design are expressed below:

t1 =

cos(α)

sin(α)

−L2sin(α)

, t2 =

1

0

L1

, and t3 =

1

0

−L1

. (8)

3. Station-keeping control

Motion control of USVs involves surge, sway and yaw (heave, roll and pitch

DOFs are typically neglected because these are passively stable). The control

system is typically designed to consist of control law and control allocation95

(Stephan & Fichter, 2019; Tanakitkorn et al., 2018; Johansen & Fossen, 2013),

as shown in Figure 2.

6

controllaw

controlallocation

USVmodel

ν

ηfτd

νd

ηd+

+-

- η~

ν~

Figure 2: A station-keeping control block diagram.

3.1. Control law

The control law determines a generalised force demand, τd = [Xd, Yd, Nd]ᵀ,

that is necessary for driving the USV to the desired state. To this end, the USV

mathematical model from (1) and (5) may be represented in a state-space form

as shown: νη

︸︷︷︸

x

=

−M−1(C(ν) +D

)03×3

I3×3 03×3

︸ ︷︷ ︸

A

νηb

︸ ︷︷ ︸

x

+

M−1

03×3

︸ ︷︷ ︸

B

τd, (9)

where the error vectors are ν = ν − νd and η = η − ηd; the pose error vector in

the body-fixed frame is ηb = Jᵀη. A linear quadratic regulator (LQR) control

technique is used to compute the optimal feedback gain matrix K that satisfies

the following objective (Fossen, 2011; Sharma et al., 2012):

minτd

{∫ [xᵀQx + τᵀdRτd

]dt

}. (10)

Respectively, the diagonal matrices Q and R are penalties on the state

tracking errors and the control actions. Then, the desired control force vector

is computed as follows:

τd = −Kx. (11)

3.2. Control allocation

The control allocation seeks for the most energy efficient set of actuator

forces, f , that meets the generalised force vector, τd, demanded by the control

7

law. This may be presented as an optimisation problem in the following form

(Fossen & Johansen, 2009):

minf,s

{fᵀW f + sᵀP s} (12)

subject to

τd − T f − s = 0 (13)

The slack variable, s, is introduced to relax the allocation constraint based on100

the fact that the available thrusters may not always satisfy all the components

of τd. The diagonal matrices W and P are relative weights for the control

power and the force allocation error, respectively. When all the actuators are

identical, W may be set to be the identity matrix. The diagonal elements of

P , on the other hand, should be significantly large to emphasise the penalty on105

the force allocation error.

This optimisation problem may be solved with the Lagrange multiplier method.

However, for ease of derivation, the above optimisation problem is rewritten into

the following form:

minσ

{σᵀGσ}, (14)

subject to

τd −Hσ = 0, (15)

where

σ =

fs

,G =

W 03×3

03×3 P

, and H =[T I3×3

], (16)

The solution of (14) via the Lagrange multiplier method is given below (Liu

et al., 2012; Johansen & Fossen, 2013; Sarda et al., 2015):

σ = [G−1Hᵀ(HG−1Hᵀ)−1︸ ︷︷ ︸H+

]τd (17)

The matrix H+ is regarded as a weighted pseudoinverse in which it dis-

tributes the demanded generalised force vector, τd, onto available thrusters, f ,

such that the objective function (12) is minimised.

8

4. Results and discussion110

Simulation studies were implemented in MATLAB with three different thruster

configurations being considered: 1) the proposed design with all the thruster

aligned longitudinally (under-actuated mode), 2) the proposed design with the

mid thruster rotated by 90 degrees (fully-actuated mode), and 3) the typical

X-type thruster configuration as a benchmark. Their principle dimensions are115

described in Table 1. The hydrodynamic derivatives used in the simulation were

adopted from a catamaran style USV with similar size (Sarda et al., 2015).

Table 1: Principle particulars of each thruster configuration

thruster configuration L1 [m] L2 [m] α [deg]

under-actuated 1.5 1 0

fully-actuated 1.5 1 90

X-type 1.5 - 45

9

Figure 3: Pose tracking performance of each configuration when the vehicle was demanded to

align their heading against the 20 N disturbance (scenario 1).

There are two simulation scenarios presented. In scenario 1, the vehicle

was demanded to keep its position while maintaining its heading against a 20

N disturbance. Gaussian noises with standard deviations of 2 N and 5 degrees120

were added to vary both magnitude and direction of the disturbance. Simulation

results in Figure 3 has shown that all the three configurations were able to

maintain their position and align their heading against the disturbance. The

position errors in steady state were nearly identical and were kept to below

1 m from the desired position. This result has proven that even the under-125

actuated USV can perform station-keeping if the heading demand is set to

align against the disturbance field, like a wind vane. However, since the under-

actuated configuration does not have a sway motion control, the vehicle needs

to perform a zigzag motion to reach the desired location, and this results in a

slower convergence when compared to the other two configurations.130

10

Figure 4: Pose tracking performance of each configuration when the vehicle was demanded to

align theirs heading perpendicular to the 20 N disturbance (scenario 2).

A more challenging station-keeping condition is when the heading demand

is perpendicular to the 20 N disturbance. This was simulated in scenario 2.

Since the under-actuated configuration lacked a direct sway motion control, the

vehicle needed to move back and forth while repeatedly adjust its heading to

maintain the desired pose. This resulted in a steady oscillation of both heading135

and position errors, as shown in Figure 4; the fluctuations agreed well with

the experimental studies presented by Sarda et al. (2016, 2015); Panagou &

Kyriakopoulos (2014). On the other hand, the fully-actuated configuration had

the mid thruster rotated. Although the vehicle was now able to exert sway

force, the force that the side thrusters generated for sway DOF also caused140

the excessive moment. Anyway, this moment was cancelled out by the two

side thrusters. In this configuration, the vehicle became fully-actuated, and

even the pure sway motion was now possible, which was highly beneficial for

11

station-keeping. As a result, the vehicle could smoothly maintain its pose and

directly counteracted the sway drift that was caused by the disturbance. Despite145

equipping with fewer thrusters, the under-actuated configuration was able to

achieve similar pose tracking performance to the X-type configuration.

Energy consumption of the three configurations was analysed in terms of the

sum of the absolute thruster forces. According to Figure 5, in the steady state of

scenario 1, both configurations of the proposed design consumed less energy than150

the X-type. This was because, unlike the X-type configuration, they did not

waste energy on the sway DOF in generating surge control force. Hence, they

are more energy efficient in moving forward at speeds, especially for the under-

actuated design that has all the thrusters focussing on surge DOF. However,

as shown in the steady state of Figure 6, the X-type configuration was slightly155

more efficient in holding pose against the sway disturbance because it did not

need to constantly correct vehicle’s pose like the under-actuated configuration,

or to counter the excessive moment like fully-actuated configuration.

Figure 5: The sum of absolute thruster forces for each configuration when the vehicle was

demanded to align their heading against the 20 N disturbance (scenario 1).

12

Figure 6: The sum of absolute thruster forces for each configuration when the vehicle was

demanded to align their heading perpendicular to the 20 N disturbance (scenario 2).

5. Conclusion

USVs have been developed for various applications over the past two decades.160

The typical designs are under-actuated differential drives that can effectively

perform path following over a wide range of speeds. However, the vehicles ex-

hibit consistent oscillation in both heading and position errors when demanded

to hold their pose against any sway disturbance. The heading constraint may

be dropped off to alleviate the oscillation and let the USVs align naturally to165

the disturbance field, but this may not be an option in some scenarios.

This paper presented a new USV thruster configuration that consists of

trimaran hulls with one thruster attached to the rear of each hull. In the

under-actuated thruster configuration, all the three thrusters align longitudi-

nally, making it efficient in producing surge force and suitable for high-speed170

operation. In addition, the USV was able to transform to the fully-actuated

mode by reconfiguring the mid thruster to produce sway force with some exces-

sive moment that is then cancelled out by the two side thrusters. The simula-

tion results have proven that, although the presented fully-actuated USV was

13

equipped with fewer thrusters, it was able to achieve comparable station-keeping175

performance with the X-type configuration.

References

Bibuli, M., Caccia, M., Lapierre, L., & Bruzzone, G. (2012). Guidance of

Unmanned Surface Vehicles. IEEE Robotics & Automation Magazine, (pp.

92–102).180

Caccia, M., Bibuli, M., Bono, R., & Bruzzone, G. (2008). Basic navigation,

guidance and control of an Unmanned Surface Vehicle. Autonomous Robots,

25 , 349–365. doi:10.1007/s10514-008-9100-0.

Demetriou, G. A., Hadjipieri, A., Panayidou, I. E., Papasavva, A., & Ioannou,

S. (2016). ERON: A PID controlled autonomous surface vessel. In 2016185

18th Mediterranean Electrotechnical Conference (MELECON) April (pp. 1–

5). IEEE. doi:10.1109/MELCON.2016.7495463.

Ferri, G., Manzi, A., Fornai, F., Ciuchi, F., & Laschi, C. (2015). The HydroNet

ASV, a Small-Sized Autonomous Catamaran for Real-Time Monitoring of

Water Quality: From Design to Missions at Sea. IEEE Journal of Oceanic190

Engineering, 40 , 710–726. doi:10.1109/JOE.2014.2359361.

Fossen, T. I. (2011). Handbook of Marine Craft Hydrodynamics and Motion Con-

trol. Chichester, UK: John Wiley & Sons, Ltd. doi:10.1002/9781119994138.

Fossen, T. I., Breivik, M., & Skjetne, R. (2003). Line-of-sight path following of

underactuated marine craft. IFAC Proceedings Volumes, 36 , 211–216. doi:10.195

1016/S1474-6670(17)37809-6.

Fossen, T. I., & Johansen, T. A. (2009). A Survey of Control Allocation Methods

for Underwater Vehicles. In Underwater Vehicles. InTech. doi:10.5772/6699.

Gan, S., & Xiang, X. (2017). Control system design of an autonomous surface

vehicle. In 2017 29th Chinese Control And Decision Conference (CCDC) (pp.200

495–499). IEEE. doi:10.1109/CCDC.2017.7978145.

14

Jantapremjit, P., & Wilson, P. A. (2007). Optimal Control and Guidance for

Homing and Docking Tasks using an Autonomous Underwater Vehicle. In

2007 International Conference on Mechatronics and Automation (pp. 243–

248). IEEE. doi:10.1109/ICMA.2007.4303548.205

Jin, J., Zhang, J., & Liu, D. (2018). Design and Verification of Heading and Ve-

locity Coupled Nonlinear Controller for Unmanned Surface Vehicle. Sensors,

18 , 3427. doi:10.3390/s18103427.

Johansen, T. A., & Fossen, T. I. (2013). Control allocation—A survey. Auto-

matica, 49 , 1087–1103. doi:10.1016/j.automatica.2013.01.035.210

Liu, Q., Zhu, D., & Yang, S. X. (2012). Unmanned Underwater Vehicles Fault

Identification and Fault-Tolerant Control Method Based on FCA-CMAC Neu-

ral Networks, Applied on an Actuated Vehicle. Journal of Intelligent &

Robotic Systems, 66 , 463–475. doi:10.1007/s10846-011-9602-4.

Liu, Z., Zhang, Y., Yu, X., & Yuan, C. (2016). Unmanned surface vehicles: An215

overview of developments and challenges. Annual Reviews in Control, 41 ,

71–93. doi:10.1016/j.arcontrol.2016.04.018.

Matos, A., Silva, E., Almeida, J., Martins, A., Ferreira, H., Ferreira, B., Alves,

J., Dias, A., Fioravanti, S., Bertin, D., & Lobo, V. (2017). Unmanned Mar-

itime Systems for Search and Rescue. In Search and Rescue Robotics - From220

Theory to Practice. InTech. doi:10.5772/intechopen.69492.

Nađ, Ð., Mišković, N., & Mandić, F. (2015). Navigation, guidance and control

of an overactuated marine surface vehicle. Annual Reviews in Control, 40 ,

172–181. doi:10.1016/j.arcontrol.2015.08.005.

Naeem, W., Xu, T., Sutton, R., & Tiano, A. (2008). The design of a nav-225

igation, guidance, and control system for an unmanned surface vehicle for

environmental monitoring. Proceedings of the Institution of Mechanical En-

gineers, Part M: Journal of Engineering for the Maritime Environment, 222 ,

67–79. doi:10.1243/14750902JEME80.

15

Omerdic, E., & Roberts, G. (2004). Thruster fault diagnosis and accommodation230

for open-frame underwater vehicles. Control Engineering Practice, 12 , 1575–

1598. doi:10.1016/j.conengprac.2003.12.014.

Panagou, D., & Kyriakopoulos, K. J. (2014). Dynamic positioning for an un-

deractuated marine vehicle using hybrid control. International Journal of

Control, 87 , 264–280. doi:10.1080/00207179.2013.828853.235

Park, J., Kang, M., Kim, T., Kwon, S., Han, J., Wang, J., Yoon, S., Yoo, B.,

Hong, S., Shim, Y., Park, J., & Kim, J. (2017). Development of an Unmanned

Surface Vehicle System for the 2014 Maritime RobotX Challenge. Journal of

Field Robotics, 34 , 644–665. doi:10.1002/rob.21659.

Pastore, T., & Djapic, V. (2010). Improving autonomy and control of au-240

tonomous surface vehicles in port protection and mine countermeasure sce-

narios. Journal of Field Robotics, 27 , 903–914. doi:10.1002/rob.20353.

arXiv:10.1.1.91.5767.

Pearson, D., An, E., Dhanak, M., von Ellenrieder, K., & Beaujean, P. (2014).

High-level fuzzy logic guidance system for an unmanned surface vehicle (USV)245

tasked to perform autonomous launch and recovery (ALR) of an autonomous

underwater vehicle (AUV). In 2014 IEEE/OES Autonomous Underwater

Vehicles (AUV) (pp. 1–15). IEEE. doi:10.1109/AUV.2014.7054403.

Phillips, A. B., Kingsland, M., Pebody, M., Roper, D., Templeton, R., Mcphail,

S., Prampart, T., & Wood, T. (2018). Autonomous Surface / Subsurface250

Survey System Field Trials. In 2018 IEEE OES Autonomous Underwater

Vehicle Symposium November. Porto.

Sarda, E. I., Bertaska, I. R., Qu, A., & von Ellenrieder, K. D. (2015). Develop-

ment of a USV station-keeping controller. In OCEANS 2015 - Genova (pp.

1–10). IEEE. doi:10.1109/OCEANS-Genova.2015.7271425.255

Sarda, E. I., & Dhanak, M. R. (2017). A USV-Based Automated Launch and

16

Recovery System for AUVs. IEEE Journal of Oceanic Engineering, 42 , 37–55.

doi:10.1109/JOE.2016.2554679.

Sarda, E. I., Qu, H., Bertaska, I. R., & von Ellenrieder, K. D. (2016). Station-

keeping control of an unmanned surface vehicle exposed to current and wind260

disturbances. Ocean Engineering, 127 , 305–324. doi:10.1016/j.oceaneng.

2016.09.037. arXiv:1702.04941.

Sharma, S. K., Naeem, W., & Sutton, R. (2012). An autopilot based on a

local control network design for an unmanned surface vehicle. Journal of

Navigation, 65 , 281–301. doi:10.1017/S0373463311000701.265

Sharma, S. K., Sutton, R., Motwani, A., & Annamalai, A. (2014). Non-linear

control algorithms for an unmanned surface vehicle. Proceedings of the In-

stitution of Mechanical Engineers, Part M: Journal of Engineering for the

Maritime Environment, 228 , 146–155. doi:10.1177/1475090213503630.

Stephan, J., & Fichter, W. (2019). Fast Exact Redistributed Pseudoinverse270

Method for Linear Actuation Systems. IEEE Transactions on Control Sys-

tems Technology, 27 , 451–458. doi:10.1109/TCST.2017.2765622.

Tanakitkorn, K., Wilson, P. A., Turnock, S. R., & Phillips, A. B. (2018). Sliding

mode heading control of an overactuated, hover-capable autonomous under-

water vehicle with experimental verification. Journal of Field Robotics, 35 ,275

396–415. doi:10.1002/rob.21766.

Vasilj, J., Stančić, I., Grujić, T., & Musić, J. (2017). Design , Development

and Testing of the Modular Unmanned Surface Vehicle Platform for Marine

Waste Detection. Journal of Multimedia Information System, 4 , 195–204.

doi:10.9717/JMIS.2017.4.4.195.280

Vidal, E., Vallicrosa, G., Palomeras, N., Hurtos, N., Mallios, A., Bosch, J.,

Carreras, M., & Ridao, P. (2018). AUV homing and docking for remote op-

erations. Ocean Engineering, 154 , 106–120. doi:10.1016/j.oceaneng.2018.

01.114.

17

Xiang, X., Yu, C., Zhang, Q., & Xu, G. (2016). Path-Following Control of an285

AUV: Fully Actuated Versus Under-actuated Configuration. Marine Technol-

ogy Society Journal, 50 , 34–47. doi:10.4031/MTSJ.50.1.4.

18