Ocean Engineering 197 (2020) 106868

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Ocean Engineering
journal homepage: www.elsevier.com/locate/oceaneng

Development of an Autonomous Surface Vehicle capable of tracking

Autonomous Underwater Vehicles
Boris Braginsky ∗, Alon Baruch, Hugo Guterman
Department of Electrical and Computer Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel

ARTICLE INFO ABSTRACT

Keywords: This work presents an Autonomous Surface Vehicle (ASV) with tracking capability. The ASV is able to follow
ASV after an Autonomous Underwater Vehicle (AUV) without prior knowledge of the AUV’s actual position.
AUV Tracking an AUV can significantly increase the communication range and bandwidth of the transferred data,
Tracking
which means that the AUV can operate without nearby operators. Mathematical models to represent ASV’s
kinematics and kinetics were developed as well as a controller that takes into account sea wave effects.
Simulations of the ASV with a ranger interrogator system was developed to test the tracking algorithm.
The proposed method allows computing the possible location of the AUV, which can be used to reduce the
navigation error of the AUV. This method was tested both in a simulation environment and at sea trials in the
Red Sea. In both cases, the algorithm performed well and precise tracking was achieved.

1. Introduction (i) point stabilization, where the goal is to stabilize a vehicle at a

given target point with the desired orientation;
There is a growing interest worldwide in the use of Autonomous (ii) trajectory tracking, where the vehicle is required to track a
Surface Vehicles (ASVs) to execute missions of increasing complexity time-parameterized reference; and
without direct supervision by human operators. The increasing needs (iii) path following, where the objective is for the vehicle to con-
of the oceanographic community for better environmental monitoring verge to and follow a desired geometric path, without an explicit timing
and surveillance systems have stimulated much research within the law assigned to it (Aguiar et al., 2009).
academic and commercial robotics communities. Thus, considerable In this study, a tracking algorithm based on a ranger interrogator
progress has been observed in the development and use of ASVs. These system (Benthos, 2017) will be presented. The ranger system provides
platforms provide various capabilities for payload, communication, distance and discrete bearing between the AUV and the ASV. Typically,
mobility, and autonomy (Curcio et al., 2005a; Dunbabin et al., 2009). a USBL have an accuracy of 0.25◦ (Link-Quest, 2019). The proposed
In recent years, many ASVs have been developed for bathymetric approach provides the same accuracy of a USBL based tracking systems
data recording in shallow waters and for monitoring various marine at lower cost (half the typical cost of a USBL systems).
environmental data (Gupta and Sakhare, 2015). Their dimensions are The proposed algorithm allows the ASV to follow an AUV without
usually above three meters long by one meter wide, depending on their the need to know the AUV’s actual position. Sample points derived from
form (monohull, catamaran, trimaran) (Manley, 2008). More detailed the ranger are updated dynamically to predict the position of the AUV
information about the target platforms that are used in this research is
for stable tracking. The goal is to overcome the difficulties attributable
presented in Section 4.
to discrete bearing measurements. An ASV with tracking capabilities,
Autonomous Underwater Vehicles (AUVs) have played a significant
such as ASV equipped with acoustic and RF modems, can extend the
role in underwater mapping, ocean sampling (Fiorelli et al., 2006),
capability of an AUV by improving position estimation and can also
and plankton sampling (Zhang et al., 2010). Tracking algorithms for
serve as a relay station (Curcio et al., 2005b). Additionally, it can be
the ASV-AUV has become an important research topic in recent years
critical for an ASV to be able to follow an AUV as closely as possible.
(Majid and Arshad, 2016; Miskovic et al., 2015; Eiler et al., 2013). An
For example, during optical communication with an AUV, the ASV must
example of a tracking scenario is presented in Fig. 1.
“hover” above the AUV (Farr et al., 2005; Carder et al., 2001).
A key enabling element for the execution of such missions is the
To achieve the necessary accuracy required for AUV tracking, the
availability of advanced systems for the ASV’s motion control. There
control approach is presented (see Section 6). The controller allows the
are three main issues to solve:

∗ Corresponding author.
E-mail address: borisbr@post.bgu.ac.il (B. Braginsky).

https://doi.org/10.1016/j.oceaneng.2019.106868
Received 28 March 2019; Received in revised form 23 October 2019; Accepted 14 December 2019
Available online 20 December 2019
0029-8018/© 2019 Elsevier Ltd. All rights reserved.
B. Braginsky et al. Ocean Engineering 197 (2020) 106868

Table 1
Comparison between the different techniques of acoustic positioning.
Range Accuracy Remarks
LBL ∼5 km ∼0.1 m Requires complex infrastructure
SBL ∼3 km ∼0.5 m Effective when deployed from a large ship
USBL ∼1–4 km ∼1 m Provides additional attitude information
SBN ∼0.5–1 km ∼1 m This method is very versatile

as the Time of Flight (TOF) of an electromagnetic signal between the

satellite and the navigating vehicle (Groves, 2013). In the case of an
acoustic positioning system, the reference could be one of the following:

• an acoustic transponder in a fixed position on the sea floor;

• a GNSS Intelligent Buoy (GIB), which is a floating buoy with both
an acoustic transponder and GNSS for positioning; or
• an acoustic transceiver that is located on a supporting vessel with
some absolute or relative positioning capabilities.

Fig. 1. Tracking scenario. The navigating vessels could be a ship, an ASV, or another AUV. The
distance between two transponders can be extracted from the time
measurement of the acoustic waves, and their speed in the following
vehicle to perform the tracking despite the effect of the sea waves (Bra- different ways:
ginsky and Guterman, 2015). Ordinarily, coupling between heading • Time of Arrival (TOA) - the average time it takes the acoustic
and position makes tracking particularly difficult. In order to solve the signal to travel back and forth between the two transducers;
tracking control problem under the effect of sea waves, two controllers • One Way Time of Arrival (OWTA) - the TOF of the signal, which
are offered that use an acoustic system as reference. One controller is is calculated with the help of clock synchronization;
applied for achieving heading regulation, and the second controller is • Time Difference of Arrival (TDOA) - the difference between the
applied for achieving the distance to the tracking target. times that a signal is received at two transceivers with a known
In this paper, Section 2 presents related works, Section 3 describes distance between them; and
acoustic positioning techniques, Section 4 describes the target platforms • Phase shift — by measuring the phase shift of the propagated
that were used and the communication structure, Sections 5 and 6 wave between closely placed receivers, the direction of the wave
present approaches to the model and control of the ASV, respec- can be calculated.
tively, Sections 7 and 8 show the simulation and experimental results,
respectively. There are several different implementations of acoustic positioning
systems, which differ from each other mainly by the distance between
2. Related work the transponders, also known as baseline, and also based on the fre-
quency typically used and the accuracy that is achievable (Vickery,
There are several ways to track underwater acoustic sources: from 1998). A summary of the more popular methods can be seen in Table 1.
surface vehicles, underwater vehicles, and from underwater sensor The long baseline (LBL) method involves measuring the range to several
networks (Pearson et al., 2014). Among these methods, tracking from (three or more) spaced beacons with known coordinates and solving the
a surface vessel is the most flexible in terms of simplicity and ease in relevant system of equations, where AUV coordinates are unknown (Ke-
monitoring and offers a low cost of operation (Majid and Arshad, 2016). bkal and Mashoshin, 2017). The Ultra-Short Baseline (USBL) consists of
For example, Webster et al. (2009) and Eustice et al. (2007) employ at least three acoustic sensors for two-dimensional positioning and at
a single beacon, one-way-travel-time acoustic approach. However, this least four acoustic sensors for three-dimensional positioning (Alcocer
approach requires a complex system, highly accurate synchronization et al.; Vickery, 1998). These sensors are placed close with each other
between the clocks of the different platforms, and knowledge of the to form an array. The position of the source can be estimated from its
AUV’s position. Tracking a diver based on an acoustic signal is another direction with respect to the origin of the sensor array.
means to approximate the position using an ASV (Miskovic et al., The Single Beacon Navigation (SBN) uses a tightly coupled filter
2015). However, this approach requires a more expensive and complex which allows the AUV to be able to estimate its position using only the
system, such as USBL. A similar principle was applied to track a fish, range measurement of a single beacon (Kebkal and Mashoshin, 2017).
as reported in Eiler et al. (2013). The beacon can be a stationary one in a known position or a moving
This paper extends the previous research reported in Braginsky beacon that can transmit its estimated position to the AUV as reference.
et al. (2016), which presented the preliminary results of a tracking Due to the simplicity of the method, the SBN can be employed
algorithm. In this work, additional simulation and experimental results with an ASV as a moving beacon that can follow the AUV in its
are presented. Also, a more detailed description of the ASV model and mission (Braginsky et al., 2016). This method can also be used for
system is given. cooperative navigation of several AUVs. Although the AUVs do not
have any knowledge of their absolute positions, this method can keep
3. Acoustic positioning techniques the relative error small and thus reduce the final position estimation
error (Bahr et al., 2009).
An acoustic positioning system is strongly similar to the popular The SBN method does not offer a closed set of equations as the
Global Navigation Satellite System (GNSS). Like the GNSS, the acoustic trilateration, and for that reason, implementation requires optimiza-
positioning method relies on the distance between a navigating vehicle, tion (Penas, 2009; Eustice et al., 2007). Therefore, its accuracy is
namely an AUV, and some reference points in the navigation frame. strongly dependent on the algorithm that is used and the trajectory
With GNSS, these reference points are the satellites. The satellite’s of the vehicles. Under optimal conditions, this method can achieve an
position is known with respect to the earth and the distance is measured accuracy of about 1 m (Kebkal and Mashoshin, 2017).

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4. Target platforms

In this section, the target platforms – an ASV and an AUV – will

be described. Both systems have to fulfill similar requirements such as
path planning, communication, guidance, and navigation, with some
differences based on the specific medium that each vehicle is designed
for. Consequently, a general approach was used when designing the
systems’ hardware and software, thus allowing for lower costs and
simpler systems.

4.1. ASV

The ASV was developed at the Laboratory for Autonomous Robotics

(LAR), Ben-Gurion University of the Negev, with the objective of im-
proving the AUV’s capabilities such as positioning and communica- Fig. 2. Autonomous Surface Vehicle on the Red Sea, Eilat.
tion (Arrichiello et al., 2010; Aguiary et al., 2009; Aguiar et al.,
2009; Bahr et al., 2009). The ASV is based on a regular ocean kayak
manufactured by Ocean Kayak (Fig. 2) and with a 4-m-long hull. The That is, all nodes operate in a promiscuous mode, that is, capable of
ASV’s hardware and sensors are depicted in the block diagram in Fig. 3. receiving all transmissions from all other nodes. The range between two
The main computer is an ARM-based Micro-Controller Unit (MCU), nodes can be up to 6 km, but by the use of repeat mode, a distance of
which is responsible for guidance, navigation, and communication. The 20 km can be achieved (according to the manufacturer).
ASV can be deployed with various kinds of payload sensors for specific In above water segment is formed by 2.4 GHz wireless network
experiment needs. Thrusters produced by Torqeedo (2019) are used for equipment. The nVIP2400 wireless modem, produced by Microhard
propulsion. The range between the ASV and the AUV is measured by (2019), is employed on the platforms. The wireless modem has the
a DRI-267 system, which is capable of measuring distance up to 1000 capability of building a mesh network similar to the acoustic modem.
m and bearing to the tracked source. The DRI-267 is connected to the
MCU via a serial communication channel.
5. Model of the autonomous surface vehicle
4.2. AUV
To exploit the physical properties of the models, the equations of
The HydroCamel II AUV (Fig. 4) was also developed at LAR (Bra- motion are represented in a vectorial setting. It is often beneficial to use
ginsky and Guterman, 2014). physical system properties to reduce the number of coefficients needed
It is a torpedo-shaped AUV with a depth rating of 300 m. Its seven for control. This is the primary motivation for developing a vectorial
thrusters enable the vehicle to have 6◦ of freedom (DOF), which allows representation of the equations of motion. The following representation
it to hover in place and to perform ‘‘tight’’ maneuvers. It is equipped of three DOF models will be used in this work (Fossen, 2011):
with various types of sensors for navigation and surveying, alongside
𝐌𝑅𝐵 𝝂̇ + 𝐂𝑅𝐵 (𝝂)𝝂 + 𝐌𝐴 𝝂̇ + 𝐂𝐀 (𝝂)𝝂 + 𝐃(𝝂)𝝂 = 𝝉 𝐑𝐁 (1)
different kinds of computer hardware. A block diagram of the system
can be seen in Fig. 5. where
The AUV employs an Inertial Navigation System (INS) based on a
Micro-Electro-Mechanical Systems (MEMS) inertial measurement unit 𝝉 𝑅𝐵 = 𝝉 𝑤𝑖𝑛𝑑 + 𝝉 𝑤𝑎𝑣𝑒 + 𝝉 (2)
(IMU) and an Extended Kalman Filter (EKF) for data fusion (Baruch ]𝑇
The vector 𝝉 = [𝐹𝑡ℎ𝑟𝑢𝑠𝑡 , 0, 𝑀𝑡ℎ𝑟𝑢𝑠𝑡 represents the propulsion forces
et al., 2016). The AUV navigation performance was presented in detail and moments discussed in Section 5.2. External interference from wind
in previous work (Baruch et al., 2017). and wave are described as 𝜏𝑤𝑖𝑛𝑑 and 𝜏𝑤𝑎𝑣𝑒 respectively. The influence
of wave-induced forces can be simulated by separating the 1st (wave
4.3. Platforms communications
frequency motion) and 2nd (wave shift forces) order effects (Love et al.,
2004; Fossen, 1994). The waves’ effect influence can be estimated
The communication architecture in this system has two primary
using IMU measurements (Fossen and Perez, 2009), and winds’ effect
roles: to transfer data from point to point and to create a network
influence can be measured by an anemometer. The anemometer is a
between the surface and underwater platforms. To meet this require-
device used for measuring wind speed and direction.
ment, each communication channel (acoustic and RF) must be able
to communicate point to point and to create ad hoc networks. When
underwater vehicles are on the surface, they use RF to communicate 5.1. Rigid-body and hydrodynamic forces
with other surface vehicles, such as an ASV or a support ship. However,
when the AUV is underwater, RF communication is not available, due The state vectors are chosen where 𝝂 = [𝑢, 𝑣, 𝑟]𝑇 and 𝜼 = [𝑥, 𝑦, 𝜓]𝑇 .
to the high attenuation of electromagnetic waves in water. Due to This implies that the dynamics associated with the heave, roll, and pitch
these limitations, each platform must be equipped with two different motions are neglected; that is, w = p = q = 0. For the horizontal motion
communication channels in order to establish a network between all of a vessel, the kinematic equations of motion reduce from the general
the platforms, regardless of whether the AUV is on the surface or six DOF to one principal rotation about the Z-axis:
underwater. In Fig. 6 the communication system architecture with RF
⎡𝑐𝑜𝑠(𝜓) −𝑠𝑖𝑛(𝜓) 0⎤
and acoustic interface is illustrated. The same architecture is used on 𝑹𝑏𝑖 (𝜓) = ⎢ 𝑠𝑖𝑛(𝜓) 𝑐𝑜𝑠(𝜓) 0⎥ (3)
both the platforms presented in this work: the HydroCamel (AUV) and ⎢ ⎥
⎣ 0 0 1⎦
the Kayak (ASV).
The architecture is built primarily from off-the-shelf hardware, with where 𝑅𝑏𝑖 is the rotation matrix from inertial to body frame defined by
the underwater segment constructed from a set of Benthos ATM-903 the Euler angle 𝜓.
acoustic modems (Benthos, 2019). The acoustic network has a simple In general, any movement of the vehicle involves three DOF. It is
mesh topology, with each node transmitting to every other node. convenient to define two coordinate frames, as shown in Fig. 7. It is also

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B. Braginsky et al. Ocean Engineering 197 (2020) 106868

Fig. 3. Autonomous Surface Vehicle block diagram.

common to assume that the craft has homogeneous mass distribution

and xz-plane symmetry such that

𝐼𝑥𝑦 = 𝐼𝑦𝑧 = 0 (4)

⎡𝑚 0 0⎤
𝑴 𝑅𝐵 = ⎢ 0 𝑚 0⎥. (5)
⎢ ⎥
⎣0 0 𝐼𝑧 ⎦
Notice that surge is decoupled from sway and yaw in 𝑀𝑅𝐵 due to
symmetry considerations of the system inertia matrix. It is assumed that
the added mass matrix is computed in CO:
⎡0 0 −𝑚𝑣⎤
𝑪 𝑅𝐵 (𝝂) = ⎢ 0 0 𝑚𝑢 ⎥ (6)
⎢ ⎥
⎣𝑚𝑣 −𝑚𝑢 0 ⎦

𝑴 𝐴 = 𝑴 𝑇𝐴 = −𝑑𝑖𝑎𝑔{𝑋𝑢̇ , 𝑌𝑣̇ , 𝑁𝑟̇ } (7)

Fig. 4. The HydroCamel AUV.

⎡ 0 0 𝑌𝑣̇ 𝑣 + 𝑌𝑟̇ 𝑟⎤
𝑪 𝐴 (𝝂) = ⎢ 0 0 −𝑋𝑢̇ 𝑢 ⎥ (8)
⎢ ⎥
⎣−(𝑌𝑣̇ 𝑣 + 𝑌𝑟̇ 𝑟) 𝑋𝑢̇ 𝑢 0 ⎦
5.2. Propulsion model
and
𝑫(𝝂) = 𝑫 + 𝑫 𝑛 (𝝂) (9) Depending on the forces provided by the thrusters (Fig. 8), the
Linear potential damping and skin friction 𝑫 are ignored since applied force in the body–referenced frame is:
the non-linear quadratic terms 𝑫 𝑛 (𝝂) dominate at higher speeds. This 𝑭 𝑡ℎ𝑟𝑢𝑠𝑡 = 𝐹1 + 𝐹2 (12)
is a good assumption for maneuvering, while station-keeping models
should include a nonzero 𝑫 (Fossen, 2011): A moment is induced in the yaw direction due to the thrust:
⎡−𝑋𝑢 0 0 ⎤
𝑴 𝑡ℎ𝑟𝑢𝑠𝑡 = 𝑦𝑟 (𝐹1 − 𝐹2 ) (13)
𝑫=⎢ 0 −𝑌𝑣 −𝑌𝑟 ⎥ (10)
⎢ ⎥
⎣ 0 −𝑁𝑣 −𝑁𝑟 ⎦ where 𝑦𝑟 is the distance from the motors to the body center of mass,
For a marine craft operating in waves, linear damping will always and the difference in the thrust produced by the two thrusters will
be present due to potential damping and linear skin friction (Faltinsen apply moment (according Eq. (13)) on the platform that will change
and Sortland, 1987): the heading.
Eqs. (12)–(13) can therefore be rewritten as follow:
⎡−𝑋|𝑢|𝑢 |𝑢| 0 0 ⎤
𝑫(𝝂) = ⎢ 0 −𝑌|𝑣|𝑣 |𝑣| − 𝑌|𝑟|𝑣 |𝑟| −𝑌|𝑣|𝑟 |𝑣| − 𝑌|𝑟|𝑟 |𝑟| ⎥ (11) 𝐹1 =
1
𝐹 −
1
𝑀 (14)
⎢ ⎥ 2 𝑡ℎ𝑟𝑢𝑠𝑡 2𝑦𝑟 𝑡ℎ𝑟𝑢𝑠𝑡
⎣ 0 −𝑁|𝑣|𝑣 |𝑣| − 𝑁|𝑟|𝑣 |𝑟| −𝑁|𝑣|𝑟 |𝑣| − 𝑁|𝑟|𝑟 |𝑟|⎦
The parameters 𝑴 𝐴 , 𝑪 𝐴 , 𝐷, and 𝑫(𝝂) were estimated using the
least squares techniques presented in Martin and Whitcomb (2014). The 1 1
𝐹2 = 𝐹 + 𝑀 . (15)
definitions of the model parameters can be found in Appendix A. 2 𝑡ℎ𝑟𝑢𝑠𝑡 2𝑦𝑟 𝑡ℎ𝑟𝑢𝑠𝑡

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B. Braginsky et al. Ocean Engineering 197 (2020) 106868

Fig. 5. Electronics block diagram of the system.

Fig. 6. Communication system structure.

6. Suggested algorithm

6.1. AUV tracking approach

Below, an approach using an ASV to track an AUV is presented. The

usual technique is to use a support vessel on the surface to track the
AUV. However, reliable communication is difficult to establish due to
the physical properties of the water, especially when transmitting over
great distances.
Instead, a tracking algorithm using data from the DRI-267 ranger
system is used: the range and direction (angle) derived are used as input
for the attitude and position controllers, respectively (Fig. 9).
Fig. 10 shows the ASV propulsion system equipped with a DRI-267
ranger system. The detected distance can be from 1 to 1000 m, and the
direction is presented in nine discrete bearing ranges, as described in
Table 2.
The ranger-supplied information can be combined with the known
AUV depth to estimate the AUV’s position. The relative position be-
Fig. 7. ASV body frame and the motor thrust forces.
tween the ASV and the AUV can be calculated using the following
equation:

𝑥 = (𝑟𝑛2 − 𝑑 2 )1∕2 𝑐𝑜𝑠(𝛼) where 𝑟𝑛 is the range and 𝛼 is the bearing to the AUV (Table 2), both
𝑦 = (𝑟𝑛2 − 𝑑 2 )1∕2 𝑠𝑖𝑛(𝛼), (16) measured by the ranger, and 𝑑 is the depth of the AUV, as presented in

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Table 2
Bearing indicator.
Bearing output Bearing range 𝛼 𝛼𝑒𝑟𝑟𝑜𝑟
−4 <−20 [deg] −25 [deg] N/A
−3 −20 to −8 [deg] −14 [deg] ±6
−2 −8 to −3 [deg] −5.5 [deg] ±2.5
−1 −3 to −1 [deg] −2 [deg] ±1
0 ±1 [deg] 0 [deg] ±1
1 1 to 3 [deg] 2 [deg] ±1
2 3 to 8 [deg] 5.5 [deg] ±2.5
3 8 to 20 [deg] 14 [deg] ±6
4 >20 [deg] 25 [deg] N/A

Fig. 10. ASV equipped with ranger system.

Fig. 8. ASV propulsion system.

Fig. 11. The position (𝑥 and 𝑦) is calculated using Eq. (16) in the body 𝑦𝑒𝑟𝑟𝑜𝑟 = ((𝑟𝑛 + 𝑟𝑛𝑒𝑟𝑟𝑜𝑟 )2 − (𝑑 + 𝑑𝑒𝑟𝑟𝑜𝑟 )2 )1∕2 𝑠𝑖𝑛(𝛼 + 𝛼𝑒𝑟𝑟𝑜𝑟 ) − 𝑦𝑡𝑟𝑢𝑒 (17)
frame of the ASV, and it can be easily transformed into the inertial
where 𝑥𝑡𝑟𝑢𝑒 and 𝑦𝑡𝑟𝑢𝑒 can be calculated using Eq. (16) with true values
frame. The position error is a function of the bearing angle, range,
of 𝑟𝑛, 𝑑 and 𝛼. From sensors data-sheet follow that 𝑟𝑛𝑒𝑟𝑟𝑜𝑟 ≤ 1 m and
and depth. Range and depth can be measured very accurately with a
resolution of within one meter (according to the DRI and Keller X35 𝑑𝑒𝑟𝑟𝑜𝑟 ≤ 0.1 m, when 𝛼𝑒𝑟𝑟𝑜𝑟 depend on bearing output (Table 2) and an
depth sensor data sheets (Keller, 2019)), however, the bearing angle ASV heading uncertainty which is typically ±1◦ (Sokolović et al., 2015).
must be taken into account as one of the critical components of error. Consequently, the AUV position is highly depend on the range (𝑟𝑛) and
As we can see in Table 2, the bearing angle measurement is much more 𝛼𝑒𝑟𝑟𝑜𝑟 . For example at a distance of 100 m and given a bearing output
accurate for small angles, that is angles between 1◦ and 3◦ , where the 0 (𝛼𝑒𝑟𝑟𝑜𝑟 = ±1◦ ) and the ASV heading uncertainty of ±1◦ , the relative
maximum error can be 2◦ ; for indicator 3, for example, the bearing to position error between the ASV and the AUV will be 𝑦𝑒𝑟𝑟𝑜𝑟 ≃ 3.5 m and
the AUV is between 8◦ and 20◦ , and the possible error has increased to 𝑥𝑒𝑟𝑟𝑜𝑟 ≃ 0.1 m. Additionally, to the relative position error, the ASV GPS
12◦ . accuracy (typically 1.5 m (Groves, 2013)) will affect the AUV position
accuracy. However, if the bearing output increases to 3 (error of ±6◦ )
6.1.1. AUV position uncertainty based on a ranger the possible error increases to 11 m. From this example, we thus learn
Relative position error between the ASV and the AUV can been
that, for this application, it is very critical to be able to track with
calculated using Eq. (17).
the smallest bearing error possible so as to have a minimum possible
𝑥𝑒𝑟𝑟𝑜𝑟 = ((𝑟𝑛 + 𝑟𝑛𝑒𝑟𝑟𝑜𝑟 )2 − (𝑑 + 𝑑𝑒𝑟𝑟𝑜𝑟 )2 )1∕2 𝑐𝑜𝑠(𝛼 + 𝛼𝑒𝑟𝑟𝑜𝑟 ) − 𝑥𝑡𝑟𝑢𝑒 position error.

Fig. 9. ASV tracking algorithm diagram. (a) based on Eq. (1), (b) and (c) based on Eqs. (19) and (22) respectively, and (d) based on Eqs. (14)–(15).

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Fig. 11. Tracking example: (a) Top view, (b) Side view.

6.2. Distance and heading controllers Table 3

Simulation 1 initial conditions.
Trial 𝑥0,𝐴𝑆𝑉 𝑦0,𝐴𝑆𝑉 𝑥0,𝐴𝑈 𝑉 𝑦0,𝐴𝑈 𝑉
6.2.1. Distance controller
Two assumptions were made for the position controller: first, that a (red line) −100 0 0 0
b (yellow line) −100 50 0 0
the ASV can move faster than the AUV, so it can close the gap between c (purple line) −100 −50 0 0
them, and second, that the ASV cannot move backwards. This means
that when the distance between the platforms is too close, the ASV
will slow down to minimal speed or stop the thrusters. The second
assumption is that the AUV is generally moving at a constant speed Substituting Eqs. (21) and (22) into Eq. (23), the derivative of the
for better performance of the Side Scan Sonar (SSS). Given these resulting closed-loop system, namely, 𝑉̇ = 𝐾𝜓 𝜓̇ + (𝐼𝑧 + 𝑁𝑟̇ )𝑟𝑟,̇ satisfies:
assumptions, we have used a linear ASV forward model, so that Eq. (1)
𝑉̇ = 𝐾𝜓𝑟 + 𝑟(−𝐾𝜓 − 𝐵𝑟) = −𝐵𝑟2 ⩽ 0 (24)
can be rewritten as follows:
when 𝐵 is positive. Invoking LaSalle’s invariance principle (Khalil,
(𝑚 − 𝑋𝑢̇ )𝑢̇ − 𝑋𝑢 𝑢 = 𝐹𝑡ℎ𝑟𝑢𝑠𝑡 (18)
1996) and considering the null solution 𝑟 = 0 that is the solution
and a proportional–integral (PI) distance controller in the following of Eq. (21), is asymptotically stable if 𝑉̇ does not vanish identically
form was chosen: along any solution of Eq. (21) other than the null solution.
Thus, the nonlinear heading controller is able to deal with speed
𝐹𝑡ℎ𝑟𝑢𝑠𝑡 = 𝐾𝑝 𝑑𝐸 + 𝐾𝑖 𝑑𝐸 𝑑𝑡 (19) changes of the ASV and with external interference such as winds and
∫
sea waves within the limits of the thrusters.
where 𝑑𝐸 = 𝑟𝑛𝑡𝑎𝑟𝑔𝑒𝑡 − 𝑟𝑛 is the range error to the AUV, as received from
ranger.
7. Simulation results

6.2.2. Heading controller

To evaluate the performance and behavior of the system using the
The objective of the heading controller is to automatically steer the
derived controllers, simulations were run based on the model presented
vehicle in a given desired direction (yaw). To this end, the control
in Section 5. Tracking capability was tested in three different scenarios
algorithm accepts the reference signal 𝜓 as input (for example be
– different initial conditions, different target ranges, and using a rect-
the bearing output from DRI-267). For the heading controller design,
angle trajectory, as illustrated in Figs. 12–14. The simulation takes into
it is assumed that all state variables are measured. In this part, we
account the nonlinear response of the ranger (Table 2).
concentrate on the third element of the vector 𝝂 (𝑟 is the rotation
In the first scenario , the AUV is moving in a straight line. The initial
speed). We will define the rotation subsystem as follows:
position of the AUV is assumed to be (0, 0) and the initial position of
𝜓̇ = 𝑟 (20) the ASV is in three different positions (see Table 3). The robustness of
the tracking algorithm was tested by changing the initial position of the
1 ASV in each simulation. The target range in these three simulations was
𝑟̇ = (𝑀𝑡ℎ𝑟𝑢𝑠𝑡 + 𝜏𝑤𝑎𝑣𝑒 + 𝜏𝑤𝑖𝑛𝑑 − (𝑋𝑢̇ 𝑢𝑣 − 𝑌𝑣̇ 𝑣𝑢 − 𝑌𝑟̇ 𝑟𝑢 − 𝑁|𝑣|𝑣 |𝑣|𝑣
𝐼𝑧 + 𝑁𝑟̇ set to 100 m and AUV speed was 1.1 m/s. The range and bearing of the
−𝑁|𝑟|𝑣 |𝑟|𝑣 − 𝑁|𝑣|𝑟 |𝑣|𝑟 − 𝑁|𝑟|𝑟 |𝑟|𝑟 − 𝑁𝑣 𝑣 − 𝑁𝑟 𝑟)) (21) ASV to the AUV are computed based on the simulated positions of the
AUV.
The following attitude controller is defined: Fig. 12 shows that for most of the time, the distance error was less
𝑀𝑡ℎ𝑟𝑢𝑠𝑡 = −(𝐾𝜓 + 𝐵𝑟 + 𝜏𝑤𝑎𝑣𝑒 + 𝜏𝑤𝑖𝑛𝑑 − (𝑋𝑢̇ 𝑢𝑣 − 𝑌𝑣̇ 𝑣𝑢 − 𝑌𝑟̇ 𝑟𝑢 − 𝑁|𝑣|𝑣 |𝑣|𝑣 than 5 m. The error occurs due to the bearing measurement, which can
vary between −1 and 1◦ , and which, at a distance of 100 m, means that
−𝑁|𝑟|𝑣 |𝑟|𝑣 − 𝑁|𝑣|𝑟 |𝑣|𝑟 − 𝑁|𝑟|𝑟 |𝑟|𝑟 − 𝑁𝑣 𝑣 − 𝑁𝑟 𝑟)) (22) the AUV position error will be about ±2 m (Eq. (16)).
where 𝐾 and 𝐵 are arbitrarily selected constant scalars. For proving In the second scenario, the AUV is following a sine trajectory as
stability using the Lyapunov approach for the non-linear heading con- presented in Fig. 13(a). The initial positions are assumed to be (0, 0)
troller described in Eq. (22), the following Lyapunov candidate function and (−100, 50) for the AUV and ASV respectively, and the AUV speed
is proposed: was 1 m/s. The target range varies from 10 to 100 m.
According to Fig. 13(b), more than 90% of the time, the error was
1
𝑉 (𝜔𝑏 , 𝜂) = (𝐾𝜓 2 + (𝐼𝑧 + 𝑁𝑟̇ )𝑟2 ) (23) less than one meter from the defined target.
2

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B. Braginsky et al. Ocean Engineering 197 (2020) 106868

Fig. 12. Simulation 1 results of tracking with different initial conditions. (a) Trajectories, the stars indicate start positions of the vehicles. (b) Normalized histogram.

Fig. 13. Simulation 2 results of tracking with sine trajectory, with three different target ranges. (a) Sine trajectory, the stars indicate start positions of the vehicles. (b) Normalized
histogram.

The results of the third scenario, tracking an AUV survey mission, Interuniversity Institute for Marine Science in Eilat (IUI) (IUI, 2019).
are shown in Fig. 14(a). The initial position of the AUV is assumed to A start command was simultaneously sent to both systems, whereupon
be (0, 10) and the initial position of the ASV was (−25, 25). The target the AUV began diving and the ASV began searching for the AUV by
distance between the AUV and the ASV was 10 m, and AUV speed was 1 revolving. Once the ASV locked on the AUV, the tracking algorithm, as
m/s. Fig. 14(b) illustrates that the error was less than one meter from described in Section 6.1, began working.
the tracked platform for over 90% of the time, with error occurring For the sake of clarity, tracking and position results will be pre-
mainly during the turns. The relatively high error bars (greater than 5 sented separately (Sections 8.1 and 8.3, respectively). The combined
m) reflect the initial stage of the tracking. tracking distance of the twelve trials was approximately 5 km.

7.1. Comparison between tracking using a ranger vs USBL

8.1. AUV tracking by an ASV
To compare the performance of the tracking approach, two simula-
tions were completed. The first based on a ranger system and the second The experimental results of four trials with different ranges and
on a USBL. The USBL system was simulated (instead of ranger) with different AUV depths/altitude and set points which summarize all
resolution of 0.25◦ . experiments are shown in Figs. 17 and 18. During the experiments,
The tracking capability was tested in two different scenarios – (a) the AUV maintained either constant altitude (Figs. 17(a) and 18(a)) or
the AUV is moving in a straight line, and (b) the AUV is following a constant depth (Figs. 17(b)–17(d) and Figs. 18(b)–18(d)). Each tracking
sine trajectory, as illustrated in Figs. 15 and 16. From Figs. 15(a) and experiment was divided into three different stages:
16(a) clearly can be seen that in both scenarios tracking performance I. diving maneuver;
were similar.
II. cruise maneuver;
III. ascent maneuver.
8. Experimental results
Fig. 18 illustrated the ranger output and heading controller input.
Following the simulations, the tracking algorithm was tested ex- As can been seen from Fig. 17, regardless of range and AUV
perimentally on the ASV described in Section 4.1. The experiments depth/altitude, the ASV performance was satisfied as expected from
took place on the Israeli coast of the Red Sea. Several trials were simulation. More detailed comparison between the simulation and the
performed using different AUV-ASV ranges and AUV depths/altitude. experimental result are presented in the next section. The average
Before starting a series of experiments or after any changes in the tracking range error for all the trials was about one meter (Fig. 19(a)).
ASV or AUV electronics magnetometer calibration was performed. At The normalized histogram of the bearing indicator received (from
the beginning of each experiment, the AUV was on the surface at a the DRI-267) for all the trials is shown in Fig. 19(b). It can be observed
distance of about 10 m from the ASV. As well, external effects influence that most of the time, the bearing angle was between ±3◦ (refer again
(𝜏𝑤𝑖𝑛𝑑 and 𝜏𝑤𝑎𝑣𝑒 ) were updated using meteorological data from the to Table 2) .

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B. Braginsky et al. Ocean Engineering 197 (2020) 106868

Fig. 14. Simulation 3 tracking results with survey rectangle trajectory. (a) Survey rectangle trajectory. The stars indicate start positions of the vehicles. (b) Normalized histogram.

Fig. 15. Simulation 1 results of tracking using ranger vs USBL. (a) Trajectories, the stars indicate start positions of the vehicles. (b) Bearing.

Fig. 16. Simulation 2 results of tracking with sine trajectory, using ranger vs USBL. (a) Sine trajectory, the stars indicate start positions of the vehicles. (b) Bearing.

8.2. Comparison between the simulated model and experimental data 8.3. AUV position estimation using tracking data

A comparison between the simulated model and experimental data The experimental results of using two surface platforms is presented
in this section. In this case, the ASV was supported with a ship equipped
can be seen in Fig. 20. The simulation was performed using initial
with an acoustic modem. By using the acoustic modem, the AUV was
conditions similar to those of the experiment. The previously show the
able to measure its distance from the ship. Again, the AUV’s mission
AUV’s trajectory is divided into three operational stages. The ASV main-
can be divided into three main stages, as presented in Fig. 21.
tain the target range closely during stage II while following a similar
The distance and azimuth to the AUV as measured by the ASV
trajectory to the simulated model during stages I and III (Fig. 20(a)). A can be used for the AUV position estimation. For the sake of brevity,
constant positive bias relative to the target range is observed during only a subset of the results are presented here. The combined tracking
stage II. Further analysis revealed that the bias is related to four distance of the trials was about 2 km. The experimental results of
factors: ranger inaccuracy, error in the determination of the sound two trials with different range, depth, and altitude set points are
velocity, the receiver turn-around time of the transponder and the presented in Figs. 21 and 22. The AUV position was estimated in post-
influence of winds and waves during the sea experiment. The closeness processing using the data collected from the AUV, the ASV, and the
between simulation and experimental data can be further observed by supported ship. The data was synchronized using the GPS clock. As
comparing the statistically bearing changes (Fig. 20(b)). It might be can be seen from these figures, the estimated position error of the AUV
observed that bearing was closely maintained during the experiment. upon surfacing and getting a GPS fix (region III in Fig. 21) is about 7

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B. Braginsky et al. Ocean Engineering 197 (2020) 106868

Fig. 17. Tracking algorithm range performance. Blue line is actual range to AUV, red line is target range to AUV, and magenta is AUV depth. Stages: (I) diving, (II) cruise, (III)
ascent. (a) Range 75 [m], AUV altitude 20 [m]. (b) Range 30 [m], AUV depth 10 [m]. (c) Range 55 [m], AUV depth 55 [m]. (d) Range 100 [m], AUV depth 50 [m]. (For
interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 18. Ranger output and heading controller input (see Table 2). (a) Range 75 [m], AUV altitude 20 [m]. (b) Range 30 [m], AUV depth 10 [m]. (c) Range 55 [m], AUV depth
55 [m]. (d) Range 100 [m], AUV depth 50 [m].

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B. Braginsky et al. Ocean Engineering 197 (2020) 106868

Fig. 19. Normalized histogram of tracking range error and bearing indicator for all trials. (a) Range error. (b) Bearing indicator.

Fig. 20. Comparison between the simulated model and experimental data. (a) Tracking algorithm range performance. Experimental range to AUV (blue), Target range to AUV
(red) , simulation range to AUV (magenta). (b) Normalized histogram of the tracking algorithm’s bearing indicator. Experimental bearing (blue). Simulation bearing (magenta).
(For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 21. AUV position 1st trial: (I) Diving, (II) Cruise, (III) Ascent. +: position calculated using a ranger, * position calculated using acoustic range measured from a supporting
ship and an ASV to the AUV, blue line is INS with DVL, violet line is INS with DVL and ranger, red line GPS fix position. (a) AUV east position. (b) AUV north position.

m. The position estimation is based on a loosely coupled, GPS aided 9. Conclusions

Strapdown Inertial Navigation System (SINS) (Farrell, 2008). In this
case, the ranger system measurements were processed by an outlier The ASV was developed mainly as a vehicle to serve as a support
filter (median absolute deviation) (Verboven and Hubert, 2005) and platform for, and cooperate with, an AUV, and to this purpose, it was
then used as pseudo ‘‘GPS’’ input for SINS. The algorithm equations fitted with an acoustic ranger. Real experiments successfully demon-
presented in detail in Appendix B. Due to the lack of a Doppler Velocity strated the ASV’s ability to autonomously track an AUV and serve as
Log (DVL) bottom locking, during diving, the AUV navigation error was a repeater. The tracking algorithm is based on a non-linear controller
about 50 m (blue line). In both trials, where the travel distance was 700 which allows to keep the heading of the ASV despite the effect of the
m in the first and 1200 m in the second, the ranger navigation error sea waves. This controller keeps the AUV in a tight area of a few degrees
was less than ten meters. during the tracking.

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B. Braginsky et al. Ocean Engineering 197 (2020) 106868

Fig. 22. AUV position 2nd trial : (I) Diving, (II) Cruise and (III) Ascent. +: position calculated using a ranger, * position calculated using acoustic range measured from a supporting
ship and an ASV to the AUV, blue line is INS with DVL, violet line is INS with DVL and ranger, red line GPS fix position. (a) AUV east position. (b) AUV north position.

The navigation error using the ranger system does not depend In this paper, the state vector that was used for the error state
on travel distance, as it does when using dead reckoning navigation. estimation is:
The proposed approach provides the same accuracy of USBL based [ ]𝑇
tracking systems at lower cost. Furthermore, the experiments showed 𝑥 = 𝛿𝒑𝑇 , 𝛿𝒗𝑇 , 𝛿𝛹 𝑇 , 𝛿𝒇 𝑇 , 𝛿𝝎𝑇 (B.1)
that these tracking capabilities could significantly improve accuracy in where 𝛿𝑝, 𝛿𝑣, 𝛿𝛹 are the position, velocity and orientation errors respec-
positioning the AUV. tively, 𝛿𝒇 , 𝛿𝝎 are the accelerometer and gyroscope errors.
The change in time of the state can be written as:
Declaration of competing interest
⎡ 0 𝐼3 0 0 0 ⎤
The authors declare that they have no known competing finan- ⎢ 0 0 [𝑓 𝑛𝑐 ]𝑥
𝑛
𝑅𝑏𝑐 0 ⎥
⎢ 𝑛 ⎥
cial interests or personal relationships that could have appeared to 𝑥̇ = ⎢ 0 0 0 0 −𝑅𝑏𝑐 ⎥𝑥 (B.2)
influence the work reported in this paper. ⎢ 0 0 0 0 0 ⎥
⎢ ⎥
⎣ 0 0 0 0 0 ⎦
Appendix A. ASV parameters description 𝑛
where 𝑅𝑏𝑐 is the rotation matrix from the body frame to the cal-
culated navigation frame, 𝑓 𝑛𝑐 is the specific force measurement ro-
Parameter Value Units Description tated to the calculated navigation frame and the operator [𝛼]× ≡
m 127 kg Mass of vehicle ⎡ 0 −𝛼3 𝛼2 ⎤
⎢ 𝛼 0 −𝛼 ⎥. The rotation from the body to the true navi-
𝜌 1027 kg/m3 Density of the surrounding fluid ⎢ 3 1
⎥
𝐼𝑧 33.3 kg m2 Inertial properties with respect to 𝑧 ⎣ −𝛼2 𝛼1 0 ⎦ ( )
𝑛
𝑋𝑢̇ 65.1 kg Added mass
gation frame is given by 𝛼𝑏 = 𝑅𝑏𝑛 𝑅𝑛𝑐 𝛼𝑛 = 𝑅𝑏𝑛 𝐼3 − [𝛿𝛹 ]𝑥 𝛼𝑛 . The
𝑐 𝑐
𝑌𝑣̇ 137.6 kg Added mass
measurement vector that is used for the update is:
𝑁𝑟̇ −30.85 kg Added mass 𝑦 = [𝜙𝑎 , 𝜃𝑎 , 𝜓𝑎 , 𝐷𝑃 𝑆 , 𝑣𝐷𝑉 𝐿 , 𝑃𝑅𝑎𝑛𝑔𝑒𝑟 ] (B.3)
𝑌𝑟̇ 25.5 kg m Added mass
𝑋𝑢 −5 kg/s Lift force from translation where 𝜙𝑎 , 𝜃𝑎 are the roll and pitch measurements of the inclinometer
𝑌𝑣 −835 kg/s Lift force from translation (accelerometer), 𝜓𝑚 is the heading as measured by the magnetometer,
𝑌𝑟 660 kg m/(rad s) Lift force from rotation 𝐷𝑃 𝑆 is the depth from the pressure sensor, 𝑣𝐷𝑉 𝐿 is the vehicle velocity
𝑁𝑣 −9.8 kg m/s Lift moment from translation with respect to the sea-floor from the DVL and the 𝑃𝑅𝑎𝑛𝑔𝑒𝑟 is the AUV’s
𝑁𝑟 −4.53 kg m2 /(rad s) Lift force from rotation horizontal position as calculated from the ranger system. This state
𝑋|𝑢|𝑢 −2 kg/m Axial drag model is used with the Extended Kalman Filter algorithm to estimate
𝑌|𝑣|𝑣 −1242 kg/m Axial drag and minimize the Inertial Navigation errors.
𝑌|𝑟|𝑣 14.2 kg/m Axial drag
𝑌|𝑟|𝑟 −2359 kg m/rad2 Cross flow drag Appendix C. Experiment of the autonomous tracking
𝑌|𝑣|𝑟 275.4 kg/m Axial drag
𝑁|𝑣|𝑟 19.9 kg/m Cross flow drag Supplementary material related to this article can be found online
𝑁|𝑣|𝑣 −3.7 kg/m Axial drag at https://doi.org/10.1016/j.oceaneng.2019.106868.
𝑁|𝑟|𝑣 53.1 kg/m Axial drag
𝑁|𝑟|𝑟 25.8 kg m/rad2 Cross flow drag
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