a new design concept of a fully-actuated unmanned surface
TRANSCRIPT
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: [email protected] (Kantapon Tanakitkorn),
[email protected] (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.
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