Longitudinal Motion Control of Underactuated Cruising AUVs for

Acoustic Bottom Survey

Kangsoo Kim

National Maritime Research Institute, National Institute of Maritime, Port and Aviation Technology,

6-38-1 Shinkawa, Mitaka, Tokyo 181-0004, Japan

Keywords: Longitudinal Motion Control, Acoustic Bottom Survey, Cruising AUV, Underactuated, Depth Control,

Bottom Following.

Abstract: Longitudinal motion control approaches for underactuated cruising AUVs primarily tasked with acoustic

bottom surveys are addressed. For controlling the longitudinal motion of a cruising AUV, we implemented

waypoint-based depth control and terrain following approaches during simulated acoustic bottom survey

missions. Simulation results revealed that the distinct motion control approaches significantly influence the

pitch motion of the vehicle, thereby directly impacting the quality of the acoustic bottom survey results. The

safety issue of a cruising AUV, particularly regarding the occurrence of bottom collisions during its near-

bottom survey missions is also investigated in this research. Concerning the safety issue, we found that while

traversing the same trackline, the likelihood of an AUV encountering a bottom collision varies considerably,

based on the specific motion control approach being utilized.

1 INTRODUCTION

Conducting high-definition bottom surveys is a

pivotal task encompassing a diverse range of ocean

development endeavours, with particular significance

in the exploration of submerged natural resources like

marine minerals, offshore oil, and gas. Preceding the

essential bottom samplings in the conclusive phase of

surveys targeting these resources, a high-definition

bottom mapping or imaging is imperative. In the

realm of underwater exploration of such purposes, the

Autonomous Underwater Vehicle (AUV) assumes a

vital role. It facilitates the acquisition of bottom

survey data with considerably higher definition

compared to what can be obtained through surface

vessels (Honsho et al., 2015; 2016). In regard to

acoustic bottom surveys, nowadays, bottom mapping

sonars like Multi-Beam Echo Sounder (MBES) or

Interferometry Sonar (IFS) have achieved widespread

utilization in AUV-based high-definition seabed

surveys (Ferrini et al., 2007; Kim et al., 2023). In the

context of acoustic bottom mapping, it is widely

recognized that the angular motion of a mapping

sonar typically has a significant impact on the

accuracy of mapping results. More specifically, it is

https://orcid.org/0000-0003-1496-4145

well known that excessive pitch or roll motion

significantly degrades the quality of acoustic bottom

mapping (Cobra et al., 1992; Kim et al., 2023).

Based on their behavioural characteristics, AUVs

are typically categorized into two groups: cruising or

flight-class AUVs, and hovering AUVs (Lea et al.,

1999; Houts et al., 2012). While a hovering AUV has

the capability to remain stationary and manoeuvre

around a specific operational point, the majority of

cruising AUVs lack this ability. This arises from the

fact that the majority of cruising AUVs are

underactuated, which means they possess fewer

actuators than the degrees of freedom (DOF) they

need to control (Spong, 1998; Tedrake, 2009).

Underactuation results in certain degrees of freedom

becoming uncontrollable, thereby limiting the path-

following capability of underactuated systems.

Hence, it is easy to envision that a cruising AUV

inherently faces challenges when it comes to evading

imminent collisions with nearby obstacles (Pedbody,

2008; Kim et al. 2023). In terms of the vehicle

dynamics, the underactuation presents itself as the

coupled vehicle motion. Within the framework of the

longitudinal dynamics of a cruising AUV, for

example, heave and pitch motions are strongly

754

Kim, K.

Longitudinal Motion Control of Underactuated Cruising AUVs for Acoustic Bottom Survey.

DOI: 10.5220/0012257200003543

In Proceedings of the 20th International Conference on Informatics in Control, Automation and Robotics (ICINCO 2023) - Volume 1, pages 754-762

ISBN: 978-989-758-670-5; ISSN: 2184-2809

coupled. Consequently, whenever a cruising AUV

alters its vertical position, a concurrent pitch motion

invariably accompanies. In case a cruising AUV flies

over a flat and uniform seafloor without a specific

objective, it does not need to alter its vertical position

with respect to the surface, that is, its depth. In

general, however, similar to terrestrial landscapes,

there are various complex bathymetric features

consisting of submarine valleys and mountains on the

seafloor as well. This implies that a cruising AUV

engaged in its bottom survey mission must

consistently adjust its vertical position, leading to

continuous changes in its pitch motion. It is readily

foreseeable that as an output of a closed-loop control

system, the pitch motion response of a cruising AUV

is directly influenced by the approach taken to control

the longitudinal motion of it. And in general, it can be

asserted that the most suitable longitudinal motion

control for AUV-based acoustic bottom survey is

achieved by minimal alterations in pitch motion. On

the flip side, the longitudinal motion control of an

AUV significantly influences vehicle safety, as it

shapes the vertical flight trajectory that directly

impacts the likelihood of the AUV encountering a

bottom collision. Therefore, it is apparent that

determining an approach for the longitudinal motion

control of a cruising AUV during an acoustic bottom

survey has to take into account both safety concerns

and the minimization of pitch motion. In this

research, we conducted a simulation-based

investigation to analyse the characteristics of some

waypoint-based longitudinal motion control

approaches. Based on the investigation results, we

found that the probability of an AUV encountering a

bottom collision varies significantly while traversing

the same trackline, depending on the particular

motion control approach being employed.

2 LONGITUDINAL MOTION

CONTROL

The longitudinal motion control of a cruising AUV

involves motion adjustments within the vertical

plane, in order to ensure precise vertical motion of it.

In the majority of cases, the controlled variable for the

longitudinal motion control of an AUV is either the

depth beneath the surface or the altitude above the

seabed (Caccia et al., 2003). It is noted that the motion

control of an AUV achieved through seabed-based

altitude control using a fixed reference is referred to

as terrain following (Hérissé et. al, 2010; McPhail et.

al, 2010) or bottom following (Bennet et al., 1995;

Caccia et. al, 1999). Therefore, while conducting a

terrain-following flight, an underwater vehicle is

managed to consistently maintain a specific altitude

above the along-track bottom surface. On the other

hand, depth control uses the depth beneath the surface

as a reference for position control within the vertical

plane.

2.1 Waypoint-Based Navigation

The navigation systems employed in the majority of

present-day AUVs for commercial, civilian, and

military applications predominantly depend on

predetermined nominal tracklines, which are

composed of waypoints defined within the earth-

fixed frame (Figure 1).

Figure 1: Waypoints and corresponding nominal tracklines

established for an AUV mission.

In Figure 1, each waypoint is labelled with a number

that corresponds to the assigned reference depth. That

is, during the mission as depicted in Figure 1, the

longitudinal motion of an AUV is controlled to track

the reference depths in a sequential manner. It is

noted here that, in the context of waypoint-based

navigation, when a vehicle approaches the vicinity of

the current target waypoint within a predefined

acceptable range, the target waypoint is updated to the

subsequent one (Medagoda and Gibbens, 2010).

Therefore, in our waypoint-based AUV navigation

implemented by depth control, no sooner has the

vehicle reached (n-1)-th waypoint, i.e., wp_

n-1

, then

the reference depth of (n)-th waypoint is activated,

deactivating that of current (n-1)-th waypoint

simultaneously (Figure 2a). This waypoint activation

rule is also extended to the longitudinal motion

control of other control outputs. In case of altitude

control, a reference altitude is assigned to a waypoint,

making an AUV engage in terrain-following flight

until it reaches that waypoint. In Figure 2b, a terrain-

Longitudinal Motion Control of Underactuated Cruising AUVs for Acoustic Bottom Survey

755

following flight of an AUV implemented on the basis

of the waypoint-based navigation is depicted.

Figure 2a: Waypoint-based AUV navigation implemented

by depth control.

Figure 2b: Waypoint-based AUV navigation implemented

by altitude control.

In Figure 2a, d

r_n

represents the reference depth

assigned to the (n)-th waypoint, while in Figure 2b, h

represents the reference altitude assigned to all

waypoints for the terrain-following flight of an AUV.

Altitude control operates by utilizing the altitude

error, which is defined as the disparity between a

vehicle's current altitude and the designated reference

altitude.

It is worth noting that by substituting the altitude

error with its corresponding depth error, a depth

controller can effectively facilitate altitude control as

well (McPhail et al., 2010; Kim and Ura, 2015). In

such cases, we see that within the along-track interval

spanning from the (n-1)-th to the (n)-th waypoint,

altitude control is executed through the use of the

depth error, as shown in (1).

= -e

= h - h

(1)

In (1), e

and e

respectively denote the depth error

and altitude error, while h denotes the current vehicle

altitude.

2.2 Underactuation and Pitch Motion

As previously mentioned, cruising AUVs inherently

exhibit underactuation. Owing to the emphasis on

highly efficient cruising performance, cruising AUVs

feature a slender body shape. Like turning and pull-

ups, cruising AUVs alter their course by changing

their orientation, effectively changing their direction

of movement through manoeuvrers. This appears in

the form of the coupling in vehicle motion, that is, the

surge-heave-pitch coupling in longitudinal dynamics,

and sway-roll-yaw coupling in lateral dynamics of the

vehicle motion. It is well known that within the

framework of the longitudinal dynamics of a cruising

AUV, heave-pitch coupling is particularly strong

(McRuer et al., 1973; Kim and Ura, 2010). Hence, as

depicted in Figure 2, whenever an underactuated

vehicle adjusts its vertical position, corresponding

changes in its pitch attitude invariably occur. Here

comes the importance of selecting longitudinal

motion control in acoustic bottom survey mission

using a cruising AUV. As previously stated, the pitch

motion directly influences the quality of the acoustic

bottom survey.

2.3 Disruption in Acoustic Bottom

Survey

As previously noted, contemporary AUV-based

acoustic bottom surveys extensively utilize advanced

bottom mapping sonars like MBES or IFS. Using a

wide acoustic fan-shaped pulse, a bottom mapping

sonar necessitates precise tracking of its angular

movement to ascertain the transmission and reception

angles for each individual beam. Hence, the absence

of the proper attitude compensation for the platform

carrying the sonar prevents accurate echo sounding

through a bottom mapping system. In contemporary

bottom mapping sonar systems, real-time attitude

data sourced from navigation devices like an Inertial

Navigation System (INS) or an Attitude Heading

Reference System (AHRS) are commonly employed

for this purpose. However, there exists a limitation on

the attitude that can be compensated for in echo

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sounding. Figure 3 shows a result of acoustic bottom

mapping obtained by a near-bottom survey using a

cruising AUV. For the bottom mapping, a MBES

system working at 400 kHz was used.

Figure 3: A result of acoustic bottom mapping with

highlighted excessive along-track pitch rates.

As seen in the figure, the resulting bottom bathymetry

exhibits pronounced undulations in the along-track

direction, which are scarcely representative of real-

world bathymetric features. In Figure 3, along-track

pitch rates exceeding ±4 deg., a magnitude too

substantial to be adequately compensated for by a

typical bottom mapping sonar (Teledyne Reason,

2012), are overlaid onto the bottom bathymetry map.

As seen in the figure, the pronounced undulations

exhibit a strong correlation with the highlighted

along-track points, showing the prominent impact of

excessive pitch rates on the bottom mapping.

3 HARDWARE SYSTEM AND

GNC ARCHITECTURE

3.1 Hardware System

While the AUV navigation strategy outlined in this

paper holds a general-purpose nature, its initial

implementation was conducted on the hardware

system of our cruising AUV, referred to as NMRI C-

AUV#04. As the latest model of our cruising AUVs,

NMRI C-AUV#04 was designed and developed by

National Maritime Research Institute (NMRI) of

Japan. With the aim of achieving a highly-efficient

near-bottom survey over challenging steep terrains,

the NMRI C-AUV#04 prioritized the core features

encompassing exceptional high-manoeuvrability and

high-speed capability. As a result, accompanied by an

adjustable pitch range of ±80 deg., the NMRI C-

AUV#04 attains the maximum velocity of 3.3 m/s.

Figure 4 depicts the overall layout of the NMRI C-

AUV#04. And in Table 1, principal dimensions and

main specifications of the vehicle are listed.

Figure 4: Overall layout of NMRI C-AUV#04.

Table 1: Principal dimensions and vehicle specifications of

NMRI C-AUV#04.

Principal dimensions

Length overall 3.9 m

Diameter 0.65 m

Main specifications

Mass 545 kg

Speed (designed / max.) 1.8 / 3.3 m/s

Depth rating 2000 m

Controllable pitch

±80 deg.

Endurance 19 hrs. @ 1.8 m/s

3.2 GNC Architecture

Within our vehicle system, it is worth noting that we

utilize a Guidance, Navigation, and Control (GNC)

architecture that rests upon a hierarchical control

structure encompassing two distinct control levels.

Namely, this encompasses high-level control for

guidance and navigation, alongside low-level control

dedicated solely to tracking, as illustrated in Figure 5.

Figure 5: GNC architecture composed of two-level

hierarchical control.

Longitudinal Motion Control of Underactuated Cruising AUVs for Acoustic Bottom Survey

757

Generally, in the longitudinal dynamics of a cruising

AUV, akin to aircraft, the primary outputs encompass

surge, heave, and pitch. On the lateral axis, the

counterparts consist of sway, roll, and yaw (McRuer

et al., 1973). Following the prevalent model of

bifurcated vehicle dynamics commonly applied in

flight control, our GNC system incorporates two

distinct feedback controls at the lower level: one for

depth (altitude) to manage longitudinal dynamics, and

the other for heading to govern lateral dynamics.

Figure 6 shows the schematic of the depth control

implemented in our vehicle system (Kim and Ura,

2009). As depicted in the figure, our depth control

consists of dual feedback loops. While the outer loop

governs depth control, it utilizes the depth error to

derive a proportional pitch reference, within which

the nested pitch-to-elevator control operates. Hence,

throughout our depth control process, the pitch

control operates implicitly and continuously.

Figure 6: Schematic of the depth (altitude) control

architecture of a cruising AUV.

4 SIMULATIONS

4.1 Conditions for Simulations

Figure 7 shows a 2D top view of the waypoints and

trackline superimposed onto the bathymetric map,

employed in our simulations.

Figure 7: Top view of the terrain, waypoints, and trackline

employed in simulations.

The digital bathymetric map data has been

sourced from the bottom bathymetry database

situated in Suruga Bay, located in Shizuoka

Prefecture, Japan. Running southward, the trackline

crosses the site's steepest terrain, where the maximum

along-track slope angle exceeds 40 degrees.

In this research, we have affirmed the suitability

of longitudinal motion control approaches for

acoustic bottom surveys by conducting simulations

utilizing the mathematical model of the GNC system,

in conjunction with the previously mentioned terrain

data, waypoints, and trackline. The GNC system

model comprises waypoint-based guidance, a low-

level motion controller implemented through

Proportional-Integral-Derivative (PID)

compensation, and the vehicle dynamic model, as

illustrated in Figure 6. Among these components, the

dynamic model of NMRI C-AUV#04 has been

derived through a system identification (SI) approach

(Kim et al., 2023). In the array of models used to

depict motion responses to actuator inputs, the pitch

to elevator deflection transfer function is shown in

(2).

0.0480.546s2.681ss

0.173s-q

+++

(2)

In (2), q is the pitch rate of the vehicle in deg./s, while

is the elevator deflection in degree. As depicted in

Figure 8, (2) accurately reproduces the vehicle's

actual pitch response, resulting in a normalized root-

mean-squared error (NRMSE) fitness of over 96%.

Figure 8: Estimated and actual pitch responses of NMRI C-

AUV#04.

The state-space pitch dynamics of NMRI C-AUV#4

actually used in our time-domain simulation is shown

in (3). Converted from the pitch to elevator deflection

transfer function (2), (3) is a canonical form, the state



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758

variables in which are directly related to the pitch

response of the vehicle.

uBxAx

qqqq



(3a)

uDxCy

qqqq

(3b)

In (3), A

, B

, C

, D

are the state matrix, input matrix,

output matrix, and feedforward matrix of the pitch

dynamics of NMRI C-AUV#4 given by (4).













0.00.250.0

0.00.01.0

0.192-0.546-2.681-

(4a)













0.0

0.5

(4b)

In (3), x

∈ R

denotes the state vector. And as

inferred from (2), the output vector y

corresponds to

the pitch rate q, and the input vector u represents the

elevator deflection, denoted as

. It is important to

mention here that in this paper, we consistently

employ degree units for angular displacement and

rate throughout.

4.2 Depth-Controlled Bottom Survey

Flight

At first, we performed a simulation in which NMRI

C-AUV#4 executes a depth-controlled bottom survey

flight by following the waypoints shown in Figure 7.

It is worth emphasizing that in this flight, the target

altitude is set to be 80 m, with a minimum allowable

altitude of 60 m. As a result, the along-track bottom

section, elevated by 80 m, serves as the target altitude

envelope. Figure 9 shows the 2D vehicle trajectory

resulting from the simulation. 3D view of the same

result is shown in Figure 10. As noted in the figures,

depth control lets the vehicle successfully follow the

waypoints.

Figure 9: 2D view of simulated depth-controlled bottom

survey flight.

Figure 10: 3D view of simulated depth-controlled bottom

survey flight.

Figure 11 depicts a comparison between the reference

pitch and the simulated pitch response throughout the

flight. The figure highlights excellent tracking

performance in pitch control, a crucial factor in

maintaining depth control performance. However, the

substantial pitch amplitude, nearly reaching 48

degrees, is anticipated to adversely affect the results

of the acoustic bottom mapping.

Figure 11: Pitch response during simulated depth-

controlled bottom survey flight.

Simulated pitch rates are also shown in Figure 12. As

seen in the figure, even the maximum peak value of

pitch rates is below 5 deg./s. Moreover, the majority

of pitch rates remain confined within the range of ±1

deg./s, a sufficiently small range to ensure stable

bottom mapping (Teledyne Reason, 2012). Therefore,

the pitch rate is thought to have limited adverse

impact on the acoustic bottom survey.

Longitudinal Motion Control of Underactuated Cruising AUVs for Acoustic Bottom Survey

759

Figure 12: Pitch rate during simulated depth-controlled

bottom survey flight.

In addition to the quality of acoustic bottom survey,

safety concerns also play a crucial role in the

evaluation of near-bottom flight for a cruising AUV.

As previously discussed, the inherent underactuation

of a cruising AUV poses a significantly greater risk

of bottom collision when compared to fully-actuated

underwater vehicles like hovering AUVs. Figure 13

depicts along-track vehicle altitudes that directly

relate to the safety concerns associated with potential

bottom collisions. As also noted in Figure 9, vehicle

altitudes are consistently confined within a narrow

range around the reference altitude of 80 m, ensuring

they remain safely above the minimum allowable

altitude of 60 m.

Figure 13: Vehicle altitude during simulated depth-

controlled bottom survey flight.

4.3 Terrain-Following Bottom Survey

Flight

Following the depth-controlled bottom survey flight,

we then have simulated terrain-following flight. With

the exception of the controlled output in longitudinal

motion control of the vehicle, all simulation

conditions remain identical to those employed in the

previously depicted depth-controlled bottom survey

flight. Figure 14 shows the 2D vehicle trajectory

derived from the simulation. 3D view of the same

result is depicted in Figure 15.

Figure 14: 2D view of simulated terrain-following bottom

survey flight.

Figure 15: 3D view of simulated terrain-following bottom

survey flight.

It is found that, overall, the flight trajectory exhibits a

closer resemblance to the reference altitude envelope

compared to that of the depth-controlled flight. And

it is worth noting that while we are currently using the

term reference altitude, we previously referred to it as

target altitude for the depth-controlled flight. In depth

control, the controlled output is the depth, not the

altitude, which is why we employed the term target

rather than reference.

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In Figure 14, it is evident that while the flight

trajectory closely resembles the reference altitude

envelope, there are more or less discrepancies in their

vertical positions. Moreover, in some tracks vertical

positions of the vehicle fall below the minimum

allowable altitude. This indicates significant safety

concerns arising from the increased risk of potential

collisions with the seafloor. A comparison between

the reference pitch and the simulated pitch response

throughout the flight is shown in Figure 16.

Figure 16: Pitch response during simulated terrain-

following bottom survey flight.

Apparently, the pitch response obtained from the

terrain-following flight is totally different from that

of the depth-controlled flight. As observed in the

figure, the reference pitch undergoes pronounced

fluctuations throughout the flight. This is not

particularly surprising, however, when considering

the schematic of our altitude control architecture. As

explained in 2.1 and 3.2, the pitch reference is derived

through the PID compensation of the depth error,

thus, for altitude control, the altitude error

counterpart. Hence, during terrain-following flights,

even minor alterations in the bottom elevation exert

an influence on the reference pitch. It is worth noting

here that in this simulation, the reference pitch is set

to be restricted within the range of ±40 deg., as seen

in Figure 16. Figure 17 shows simulated pitch rates.

Despite the presence of high-frequency fluctuations,

the magnitude of the pitch rate remains within a

sufficiently narrow range. As seen in the figure, the

majority of pitch rates are limited within the range of

±0.5 deg./s, which is half the range compared to that

of the depth-controlled flight. Thus, in bottom-

following flight, the pitch rate is unlikely to

detrimentally impact acoustic bottom mapping.

Figure 17: Pitch rate during simulated terrain-following

bottom survey flight.

Along-track vehicle altitudes are shown in Figure 18.

As previously mentioned and evident from Figures 14

and 18, in certain intervals, vertical positions of the

vehicle fall below the minimum allowable altitude.

Moreover, as observable in the figures, the majority

of vehicle altitudes are below 80 m, the reference

altitude for terrain-following flight. Thus, it can be

said that from a safety perspective, the terrain-

following flight result is not satisfactory.

Figure 18: Vehicle altitude during simulated terrain-

following bottom survey flight.

5 CONCLUSIONS

In order to clarify the impact of longitudinal motion

control approaches on acoustic bottom surveys, we

have conducted simulations of bottom survey flights.

Longitudinal Motion Control of Underactuated Cruising AUVs for Acoustic Bottom Survey

761

The simulation results indicate that the depth-

controlled bottom survey flight follows a trajectory at

moderate altitudes well within an acceptable range.

However, concerns arise regarding the potentially

harmful impact on acoustic bottom mapping due to

the pitch responses including some large amplitudes.

On the other hand, while the magnitude of the pitch

response is on a similar scale to that of depth control,

the magnitude of the pitch rate is notably reduced by

employing the terrain-following control approach.

However, safety issues may arise during a terrain-

following bottom survey flight. As a result of

unsatisfactory bottom-following flight, including

vertical vehicle positions below their allowable lower

limit, the risk of potential collisions with the seabed

can significantly increase. In conclusion, it is

essential to exercise caution when selecting a type of

longitudinal motion control. This decision should be

made after careful consideration of various factors,

such as the mission objectives, seafloor topography,

target or reference altitudes, and vehicle dynamics,

among others.

ACKNOWLEDGEMENTS

This work was supported by JSPS KAKENHI Grant

Number 21H01555.

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