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Sensors and Materials, Vol. 35, No. 2 (2023) 411–422
MYU Tokyo
S & M 3177

Trajectory Planning Strategies and Simulation
for Autonomous-surface-vehicle–Remotely-operated-vehicle(ASV–ROV) Cooperative System
Akihiro Morinaga* and Ikuo Yamamoto
Nagasaki University, 1-14 Bunkyo, Nagasaki City 852-8521, Japan(Received January 6, 2023; accepted February 6, 2023)

Keywords: underwater robot, ROV, ASV, path planning, feedback control

With the increase in the number of offshore power generation facilities and aquaculture
ponds, demand for remotely operated vehicles (ROVs) to inspect underwater structures andconduct ecological surveys is increasing. Because ROVs are connected to a ground station on thewater by a tether cable to enable the transmission of operating commands and images
underwater, where radio communication is difficult, they can only operate within the range ofthe tether cable. To expand the operational range of ROVs, an autonomous surface vehicle(ASV)–ROV cooperative system, in which a tether cable is connected to an ASV and radio
waves are used for remote operation from the autonomous vessel, is attracting attention. In a
cooperative system, the tether cable must be managed on the ASV side, and the position andcable length of the ASV must be controlled to prevent the cable from pulling against or tangling
with the ROV, which moves around underwater under the command of a human controller. We
propose a method of controlling the position and cable length of the ASV using the informationon the position of the ROV obtained from an underwater positioning device for an ASV–ROV
cooperative system that we are also developing. In addition, we confirmed through simulations
that the ASV and cable length follow target values even when the ROV moves along acomplicated path.

1.

Introduction

In recent years, demand for underwater robots has been increasing for the purpose ofunderwater infrastructure inspection and environmental surveys. With the increase in thenumber of wind farms and aquaculture ponds, remotely operate vehicles (ROVs) are being
actively used instead of divers to perform underwater monitoring.(1,2) Because radio
communication is difficult underwater, the underwater vehicle is connected to a base station
above the water by a tether cable that transmits operational commands and underwater images.
The cable also serves as a lifeline for the ROV, allowing the ROV to be retrieved by hand if itmalfunctions.
*Corresponding author: e-mail: a-morinaga@nagasaki-u.ac.jp

https://doi.org/10.18494/SAM4302

ISSN 0914-4935 © MYU K.K.
https://myukk.org/

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However, the use of tether cables also has disadvantages in ROV operation. If the cable lengthis smaller than the distance between the ROV and the base station, the ROV will be pulled by thecable, making it impossible for it to achieve the movement intended by the operator. In addition,
as the ROV moves around in the water, the cable can become entangled in the ROV’s fuselage,
surrounding reefs, or hull, causing fatal problems that in some cases make the ROV
unrecoverable. The effect of the cable on the ROV cannot be ignored and has been evaluatedthrough simulations and experiments.(3,4) To prevent the cable from interfering with the ROV’s
motion due to these problems, the length and direction of the cable feed must be adjusted
appropriately according to the ROV’s position and attitude. For large ROVs, such as those usedin deep water, the base station is located on a larger workboat, making it difficult to unroll thecable from the vessel or manually manage the cable, so a tether management system (TMS), in
which a cable drum is thrown into the sea, is used. In the case of commercially available small
ROVs, the tether cable is connected to a cable drum on board or on land, and a person manages
the length and direction of the cable depending on the position and attitude of the ROV. Cable
management requires experience. In addition, the range that an ROV can search is limited to the
distance that the cable can reach from the base station, which means that the operator must go
offshore or along the coast by getting on a boat or by other means.
In recent years, to expand the range of activities of ROVs, attention has been focused on acooperative system between ROVs and autonomous surface vehicles (ASVs),(5–11) in which anautonomous vessel and an ROV are connected by a tether cable. The autonomous vessel relays
between the ROV and the base station to enable underwater observations by ROVs in areas far
from the base station.
We have developed an ASV–ROV for surveying marine debris on remote islands. With thissystem, litter washed ashore can be photographed by a camera on the ASV, and underwater andseabed litter can be photographed by the ROV, enabling efficient surveys in areas where it isdifficult for people to enter by land. Various ASV–ROV coordination systems have also been
proposed; a simple small vessel with thrusters attached to a floating body has been combinedwith an ROV to survey shallow water areas,(6) and in this system, the small vessel is pulled by
the ROV’s motion and follows it. Because the cable is attached to the ASV side via a spring, noparticular control of the cable is required. Anglerfish, which is an ASV-controlling ROV, hasbeen developed, and a method of determining the cable length from the estimated position of the
ROV has been proposed for a coordinated system between the ROV and the ASV, but it does notindicate the appropriate position on the ASV side. To analyze the motion of the cooperative
system, it is necessary to model the cables.(12–15) Hong et al.(13) modeled the behavior of a tether
cable in the sea using the lumped-mass method and showed the effect of the tether cable on the
ROV in a simulation. However, these cable models are simplified models, and it is difficult toaccurately estimate the shape of the cable in real time using the models. A method of considering
the cable as a catenary curve for control has been proposed, but the cable between the ASV andthe ROV has a catenary shape only in special cases.
We propose herein a method of controlling the position of the ASV and the cable length using
the position information for the ROV obtained from the underwater positioning system for the
ASV–ROV coordination system that we are developing. Instead of estimating and controllingSensors and Materials, Vol. 35, No. 2 (2023)

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the shape of the cable drifting in the sea, the ideal positional relationship between the ASV andthe ROV and the cable length were determined, and the ASV and cable length were controlledusing these as target values. We confirm that the ASV and cable length follow the complicatedmovement of the ROV in simulations using a kinematic model.

2.

Specification of the ASV and ROV Cooperative System

This section describes the system shown in Fig. 1, in which the ASV and ROV cooperate. The
system consists of an ROV that searches underwater, an ASV that carries a base station for the
ROV and can itself navigate independently or be piloted remotely, and a cable drum that uses a
motor to feed and unwind the tether cable.
2.1

ASV

The ASV in this system has two main thrusters for moving and four rhombus-shaped
thrusters for fine fixed-point holding, and is capable of omni-directional turning movements.
The body is 1400 mm × 1100 mm × 650 mm in size, and its weight is approximately 30 kg,
which allows for operation by two people. It is also equipped with a global navigation satellite
system (GNSS), enabling it to maintain a fixed point at sea and to navigate automatically by
specifying coordinates. The ASV can be remotely operated from land, and the images from thecameras mounted on the ASV can be transmitted to an operator on land in real time via wirelesscommunication. In addition, a basket for storing the ROV is installed between the left and rightfloats of the ASV, and the height of the basket can be adjusted so that the ROV does not act as a
drag when the ASV is sailing.
2.2

ROV

The ROV connected to the ASV is small, measuring 470 mm × 450 mm × 200 mm andweighing less than 10 kg. The ROV is equipped with Pixhawk and RaspberryPi as controllers,and an XInput controller is generally used to control the ROV through QGroundControl.

(a)Fig. 1.

(b)(Color online) (a) Concept of an ASV–ROV cooperative system and (b) actual vehicles.

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However, this system must be operated remotely via wireless communication, and the XInput
controller cannot be connected directly to the PC on the ASV. For this reason, Futaba’s R3008SB
is connected to the microcontroller (Arduino Pro Micro) to enable wireless communication andto receive radio signals from the land side as pulse width modulation (PWM) signals, and themicrocontroller is used as the XInput controller to convert the radio signals so they may berecognized by QGroundControl. The QGroundControl is connected to the microcontroller.
2.3

Cable drum

The tether cable extending from the ROV is connected to the cable drum mounted on the
ASV as shown in Fig. 2. From this cable drum, the cable is converted to an Ethernet cablethrough a slip ring and connected to the base station. The cable drum is rotated by a DC motor toautomate the feeding and unwinding of the cable, which is usually performed by a person. Whenthe drum is rotated passively, the electromagnetic clutch is turned OFF. A rotary encoder is
attached to the rotation shaft of the cable drum, and the length of the deployed cable can becalculated from the rotation angle of the drum.
2.4

System configuration

To link ROVs and ASVs, relative location information is needed. Therefore, this system
incorporates Shallow Compass 50, which is an acoustic positioning device. This device fixes atransponder that transmits sound waves to the ROV and the antenna that receives sound waves
on the ASV, and by combining them with the depth information from the ROV, the relative
position can be obtained.

(a)Fig. 2.

(b)(Color online) (a) ASV and ROV in the cooperative system, and (b) the cable drum.

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The system configuration, including the ROV, ASV, and acoustic positioning device, isshown diagrammatically in Fig. 3. In this system, the ROV is operated by the operator, and theASV moves autonomously according to the position and heading of the ROV. The ASV
determines its movement from the relative position and azimuth of the ROV, as well as the cable
length. The relative position of the ROV to the ASV is determined by an acoustic positioning
system, which has a sampling rate of approximately 1 Hz.

3.

Autonomous Control of ASV and Cable Length

3.1

Mathematical models

The coordinates shown in Fig. 4 are used to mathematically describe the positions of the ASV
and ROV and the cable length. The term Σb is the reference coordinate, and Σa and Σr are
coordinates fixed on the ASV and ROV, respectively. Both are assumed to be right-handed
systems with the x-axis in the forward direction of the vehicle. For simplicity, the roll and pitch

Fig. 3.

Fig. 4.

(Color online) Configuration of cooperative system.

(Color online) Coordinates and position vectors.

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Sensors and Materials, Vol. 35, No. 2 (2023)of the ASV and ROV are always assumed to be zero, and the vertical motion of the ASV isignored. The position vector of the ASV is ra = [xa, ya, 0]; the position vector of the ROV,
rr = [xr, yr, zr]; and the orientations of the ASV and ROV are θa and θr, respectively. The term l isthe cable length, not considering the part of the cable that is wrapped around the drum; therefore,l ≥ |ra − rr| and is zero when ra = rr.
The ASV can obtain thrust in three degrees of freedom (forward, backward, left, right, andturn) using six thrusters. Therefore, after setting the velocity of the three degrees of freedom as[ux, uy, uθ], the kinematics of the ASV can be expressed as xa  cos θ a y  =  sin θa a θ a   0

− sin θ acos θ a00   ua 
0   va  .
1  ωa (1)

The ROV is equipped with eight thrusters and is assumed to be capable of arbitrary velocities
for four DOF directions. Let the velocity of the ROV be [vx, vy, vz, vθ], then the kinematics of the
ROV can be expressed as xr  cos θ r y   sin θr r =  zr   0 θ r   0− sin θ rcos θ r
0
0

0
0
1
0

0   vx 
0  v y .
0   vz  
1   vθ (2)

If the drum rotation speed multiplied by the radius is ul, the variation of the cable length overtime is l = ul . Each of the velocities is constrained by the limitations of the thrust and the drum
rotation speed. That is, |ux| ≤ ux,max, and the same is true for the other seven velocities.
3.2

Strategy of control ASV and cable length

While the ROV is exploring in the sea, the ASV is required to adjust its position andorientation, the viewpoint from which the cable is unrolled, and the cable length to prevent thetether cable from tangling with the ROV or pulling the ROV and interfering with its motion. In
addition, the cable length must be adjusted by controlling the cable drum. However, it is difficult
to calculate under what conditions the cable may become entangled in the ROV and under what
conditions tension may be generated against the ROV because a complete estimation of the
shape of a cable deployed in the sea requires calculating the deformation of a flexible body under
the influence of tidal currents, which is itself a very large problem. Furthermore, it is impracticalto compute the shape of the cable, because it must be computed in real time for use in the controlof the ASV.
We took advantage of the ability to freely move the cable steering position using the ASV asa base station and the plan for the ASV trajectory and control with the following policy.

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First, as shown in Fig. 4, we assumed that if the ASV is always positioned directly behind andoriented with respect to the ROV, the cables will not become entangled. In other words, for the
position of the ROV, rr = [xr, yr, θr], the target position of the ASV, rr = [xt, yt, θt], is determinedasxr − d cos θ r x=tyr − d sin θ r , y=tθt = θ r

(3)

where d is the horizontal distance between the ROV and the ASV and is determined by the depthof the ROV, d = azr, a > 0.
Next, the target cable length lt is determined by multiplying the distance between the ROV
and the ASV by a constant plus a value proportional to the error in orientation between the ROV
and the ASV.

{}lt =β + γ (θ rk − θ a ) rr − ra ,(4)

where β > 0 and γ > 0 are coefficients for lengthening the cable according to the differences inlinear distance and orientation. If the ASV and cable length always follow the target values in
Eqs. (3) and (4), the cable is expected to approximate a catenary shape with the endpoints at the
ASV and ROV as shown in Fig. 5. If the parameters β and γ in Eq. (4) are large, the cable
becomes longer, and the shape changes owing to currents and the movement of the vehicles,
increasing the likelihood of entanglement. On the other hand, if β and γ are small, l < |rr − ra|,which may adversely affect the motion of the ROV. Therefore, it is desirable to assume as small avalue as possible, adjusting it according to the motion of the ROV and the environmental
conditions.

(a)Fig. 5.

(b)(Color online) (a) Waypoint of ASV set behind the ROV and (b) setting the cable length.

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3.3

Sensors and Materials, Vol. 35, No. 2 (2023)

Motion planning and control

Herein, we describe a method of controlling the ASV and cable length on the basis of theobserved state variables with respect to the target values in Eqs. (3) and (4). The simplest method
is to introduce feedback control using the values in Eqs. (3) and (4) as target values. If the valuesof each variable can be obtained by sensors at a high sampling rate and a large feedback gain canbe taken, it is always possible to follow the target values. However, the maximum sampling rateof the underwater positioning device used to obtain the ROV’s position is about 1 Hz. In
addition, the speed of the ASV and the rotational speed of the cable drum have limitations, so
the target value cannot be tracked if the ROV suddenly changes its orientation.
Therefore, the target position of the ASV, which is calculated from the position of the ROV
obtained at regular intervals, is set as a waypoint, and trajectory tracking control is introduced inwhich trajectories with straight lines connect the waypoints obtained at each time. The positionof the ROV obtained at time tk is rrk , and the waypoints rwk set at this time may be expressed as xrk − d cos θ rk =
rwk  yrk − d sin θ rk  .


θ rk



(5)

As time passes, waypoints are generated in sequence rw0 , ..., rwk from t0 = 0 to tk = kT. The
ASV is always feedback-controlled with the waypoint with the smallest upper index as the target
value. When the error between the current target value and the ASV becomes smaller than thekallowable error, that is, when rw − ra ( t ) < e is satisfied, the next numbered waypoint is changed
to the new target. The behavior of ASVs and waypoints in this sequence is shown in Fig. 6. To
control the cable length, the target cable length is calculated from Eq. (4) for the position data of
the ROV rrk with the largest index k, and feedback control is applied.

4.

Simulation

The behavior of the ASV and the cable length when the ASV and cable length control method
proposed in Sect. 3 is applied was verified in a simulation versus the kinematic model in Eqs. (1)and (2). In an actual operation, the ROV moves on the basis of the speed command given by theoperator. The actual speed is different from the commanded value because the ROV is affectedby tidal currents and tether cable tension. For simplicity, we assume that the speed of the ROV
can achieve a given speed command value by a sufficiently large thruster thrust, unaffected bycurrents or cable tension, and that its motion follows the kinematic equation [Eq. (2)]. The target
values for the ASV and cable length were determined by assuming that the position of the ROV
had a true value every second. A proportional (P)-controller was applied with respect to thetarget values. In addition, the upper limit of the speed of the ASV was ux,max = uy,max = 3 m/s,uθ,max = 3 rad/s, and the tolerance for determining that the ASV had reached the waypoint was
set at e = 0.01.

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(a)

419

(b)

(c)

Fig. 6. (Color online) ASV control flow: (a) waypoints are set every time ROV positioning data is obtained, (b)waypoints are set one after another, but the oldest waypoint is the target, and (c) when the target waypoint is passed,
the next waypoint is reset as the target of the ASV.

In this simulation, the velocity input of the ROV was set as shown in Fig. 7, with a constanttranslational velocity input every 5 s and a feedback input given at the target angle. The resulting
motion of the ROV is shown by the red line in Fig. 8. The trajectory and time variations of the
ASV and cable length when the control method described in previous section was applied areshown in Figs. 8–11. The solid blue line in Fig. 8 shows the trajectory of the ASV, and the circle
marks the waypoints determined by the position of the ROV every second. The arrow indicatesthe forward direction of the ASV. When the error between the ASV and the target waypoint rwk isless than tolerance, the target waypoint was switched to rwk +1. The dashed lines in Figs. 9 and 10
respectively indicate the target position and orientation at each time. The P-controller wasapplied to the cable length using the value in Eq. (3) as the target value, and the cable length
always changed to a larger value relative to the linear distance between the ROV and the ASV
shown by the red line in Fig. 11. Thus, when the proposed method was applied, the ASV always
moved behind the ROV, even when the ROV performed complex motions, and the cable length
could be varied to assume a value greater than the linear distance between the ROV and theASV.
In this simulation, the controller of the ASV for the waypoints was a simple proportional
control. This controller did not consider that the target value changed discontinuously as the
waypoints were updated, nor did it consider input saturation. As a result, as seen in Fig. 8, thetarget value was moved away from the target value on the way from waypoint 7 to waypoint 8,
and, as seen in Fig. 11, the change in cable length oscillated. Considering the operation of motorsthat rotate thrusters and cable drums in actual ASVs, the control controller must be improved.
Furthermore, the shape and tension of the cable were not considered in this simulation, so it is420

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Fig. 7.

(Color online) Velocity of ROV over time.

Fig. 8. (Color online) Trajectories of ASV and ROV on an x–y plane. Small circles and arrows on the blue
trajectory line denote the position and heading of waypoints, respectively.

not possible to check whether the cable became tangled. It is conceivable that an equation of
motion for the cable could be established and verified by simulation, but it is difficult to calculate
the correct shape of the cable with existing models. Furthermore, because it is difficult tomathematically define whether cables became entangled, we plan to test the effectiveness of the
proposed method, including cables, through experiments with actual machines. It is also
necessary to verify the method of determining the parameters included in Eq. (4).

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Fig. 9. (Color online) Position of ASV over time. Dashed lines denote the position of the target waypoint at eachtime, which corresponds to each circle in Fig. 8.

Fig. 10. (Color online) Orientation of ASV over time and orientation of waypoints at each time.

Fig. 11. (Color online) Cable length and distance between ASV and ROV over time.

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5.

Sensors and Materials, Vol. 35, No. 2 (2023)

Conclusions

We proposed a method of controlling the position of an ASV and the cable length using theposition information from an ROV obtained from the underwater positioning system for an
ASV–ROV coordination system. Instead of estimating and controlling the shape of the cable
drifting in the sea, the ideal positional relationship between the ASV and ROV and the cable
length were determined and the ASV and cable length can follow target values. In addition, theeffectiveness of the proposed method was confirmed by simulations on a kinematic model. In
the future, the proposed method will be implemented on actual vehicles and verified throughexperiments.

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