1 Environment-Aware AUV Trajectory Design and Resource Management for Multi-Tier Underwater

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Environment-Aware AUV Trajectory Design and
Resource Management for Multi-Tier Underwater
Computing
Xiangwang Hou, Student Member, IEEE, Jingjing Wang, Senior Member, IEEE, Tong Bai, Member, IEEE,
Yansha Deng, Member, IEEE, Yong Ren, Senior Member, IEEE, Lajos Hanzo, Life Fellow, IEEE
Abstract—The Internet of underwater things (IoUT) is envi-
sioned to be an essential part of maritime activities. Given the
IoUT devices’ wide-area distribution and constrained transmit
power, autonomous underwater vehicles (AUVs) have been widely
adopted for collecting and forwarding the data sensed by IoUT
devices to the surface-stations. In order to accommodate the
diverse requirements of IoUT applications, it is imperative to
conceive a multi-tier underwater computing (MTUC) framework
by carefully harnessing both the computing and the communica-
tions as well as the storage resources of both the surface-station
and of the AUVs as well as of the IoUT devices. Furthermore,
to meet the stringent energy constraints of the IoUT devices
and to reduce the operating cost of the MTUC framework, a
joint environment-aware AUV trajectory design and resource
management problem is formulated, which is a high-dimensional
NP-hard problem. To tackle this challenge, we first transform
the problem into a Markov decision process (MDP) and solve it
with the aid of the asynchronous advantage actor-critic (A3C)
algorithm. Our simulation results demonstrate the superiority of
our scheme.
Index Terms—Multi-tier computing, Internet of underwater
things (IoUT), autonomous underwater vehicles (AUV), trajec-
tory optimization, resource allocation, asynchronous advantage
This work of Jingjing Wang was supported in part by the National
Natural Science Foundation of China under grant No. 62071268 and grant
No. 6222101, in part by the Young Elite Scientist Sponsorship Program
by the China Association for Science and Technology under Grant No.
2020QNRC001, and in part by the Fundamental Research Funds for the
Central Universities. T. Bai was supported in part by the National Natural
Science Foundation of China under Grant 62101015. Y. Deng was partially
supported by Engineering and Physical Sciences Research Council (EPSRC),
U.K., under Grant EP/W004348/1. Y. Ren was supported in part by the Na-
tional Natural Science Foundation of China under grant No. 62127801, in part
by the National Key R &D Program of China under Grant 2020YFD0901000,
and in part by the project ‘The Verification Platform of Multi-tier Coverage
Communication Network for Oceans (LZC0020)’ of Peng Cheng Laboratory.
Moreover, L. Hanzo would like to acknowledge the financial support of the
Engineering and Physical Sciences Research Council projects EP/W016605/1
and EP/P003990/1 (COALESCE) as well as of the European Research Coun-
cil’s Advanced Fellow Grant QuantCom (Grant No. 789028). (Corresponding
author: Jingjing Wang.)
X. Hou is with the Department of Electronic Engineering, Tsinghua
University, Beijing, 100084, China. (E-mail: xiangwanghou@163.com.)
J. Wang and T. Bai are with the School of Cyber Science and Technology,
Beihang University, Beijing 100191, China. (E-mail: drwangjj@buaa.edu.cn,
tongbai@buaa.edu.cn.)
Y. Deng is with the Department of Engineering, King’s College London,
London WC2R 2LS, U.K. (E-mail: yansha.deng@kcl.ac.uk.)
Y. Ren is with the Department of Electronic Engineering, Tsinghua Univer-
sity, Beijing, 100084, China, and also with the Network and Communication
Research Center, Peng Cheng Laboratory, Shenzhen, 518055, China (E-mail:
reny@tsinghua.edu.cn.)
L. Hanzo is with the School of Electronics and Computer Sci-
ence, University of Southampton, Southampton, SO17 1BJ, UK. (E-mail:
lh@ecs.soton.ac.uk.)
actor-critic (A3C).
I. INTRODUCTION
As an extension of the Internet of things (IoT) in underwater
environments, the Internet of underwater things (IoUT) is envi-
sioned to be a crucial enabler for supporting diverse maritime
activities [1]. More explicitly, the IoUT aims for constructing
a “smart ocean” by connecting various underwater devices,
e.g. sensors, robots, cameras, to monitor and reconstruct
underwater objects and environments [2]. In contrast to the
terrestrial IoT systems, radio frequency (RF)-based techniques
are unsuitable for the IoUT, owing to the severe absorption
of electromagnetic waves in underwater environments. As a
remedy, underwater acoustic communications (UAC) [3], [4]
are widely adopted, but it still remains unrealistic for energy-
limited IoUT devices to directly transmit their collected data
to a surface-station through long-distance propagation, because
ten-times higher transmit power is required compared to RF-
based communications. To cope with this issue, autonomous
underwater vehicles (AUV) have been widely adopted for data
collection in underwater environments [5], [6].
The seminal AUV-aided data collection techniques have
routinely been based on a fixed AUV trajectory, such as an
ellipse [7]. In this case, the IoUT devices distant from the
AUV’s trajectory have to aggregate their data at the IoUT
devices in the close proximity of the AUV’s trajectory for
delivering it to AUVs. This inevitably leads to redundant com-
munications and to potentially excessive energy requirements,
especially at the data aggregation nodes. Hence, to overcome
this impediment, recent studies opted for optimizing the AUV
trajectory for actively collecting data from the IoUT devices
[8]–[10]. However, only the specific locations of the IoUT
devices are considered in these research contributions, while
ignoring the impact of hostile environmental factors, such as
dynamically fluctuating water velocity, vortex, etc., which may
lead to excessive propulsion energy consumption and even
disable the AUV.
Apart from the data collector node mentioned above, AUVs
may also play the role of an intermediate node for data relay-
ing. However, the requirement of ocean exploration activities
is not limited to communications. Besides sensors, a large
number of advanced devices have been harnessed, such as
diverse underwater robots. Consequently, a large variety of
computing and storage tasks has to be processed in a time-
sensitive manner. For example, when considering robots, their
arXiv:2210.14619v1 [cs.DC] 26 Oct 2022
2
tasks have to be completed in time for adjusting the next
mission. Although these devices are indeed equipped both with
computing and storage capabilities, it is challenging to handle
all the tasks locally, given their limited battery lives. Hence, it
is beneficial to establish a multi-tier computing [11] framework
by integrating both the computing and the communications as
well as storage resources of surface-stations and of AUVs, as
well as of the devices for providing on-demand computing
services.
Both AUV-centric [12]–[15] and IoUT-centric [10], [16],
[17] designs were considered in the open literature conceived
either for latency-minimization or for energy-minimization.
However, both types of designs have their limitations. As a
remedy, we propose a system-level framework for maximizing
the benefits of an intrinsically amalgamated hierarchical net-
work comprised of IoUT devices, AUVs, and surface-stations.
Note that it is not a simple conglomerate of its constituent
components. For example, a rechargeable AUV and an IoUT
device anchored underwater may consume the same energy
but they have entirely different effects on the whole system,
which deserves specific investigation.
Against this background, we design a multi-tier underwa-
ter computing (MTUC) framework intrinsically amalgamating
both the computing and communications as well as storage re-
sources of surface-stations and AUVs as well as IoUT devices
for providing on-demand services for IoUT applications. Our
new contributions are summarized as follows:
•To the best of our knowledge, this is the first attempt to
integrate the surface-stations, AUVs, and IoUT devices to
form an MTUC framework for providing on-demand un-
derwater computing services instead of simply collecting
the sensory data for satisfying the diverse requirements
of advanced IoUT applications.
•Considering the limitations of both the AUV-centric
and IoUT-centric designs, we conceive a system-level
optimization model for maximizing the profits gleaned
from the perspective of economics by integrating our
environment-aware trajectory design, communication re-
source allocation, computation offloading and data
caching.
•Since the problem formulated is NP-hard and high-
dimensional, conventional methods cannot deal with it
well. Hence, we transform it into a Markov decision
process (MDP) and employ an asynchronous advantage
actor-critic (A3C) algorithm [18] for solving it.
•Our simulation results show that the proposed scheme is
capable of improving the system’s profit by relying on
environment-aware trajectory design and always exhibits
better convergence speed and scalability in the face of an
escalating problem dimension than other state-of-the-art
schemes.
The remainder of the paper is organized as follows. Section
II reviews the related state-of-the-art. In Section III, we
describe the system model and formulate an optimization prob-
lem for maximizing the system’s profit. Section IV introduces
how we transform the optimization problem to an MDP and
utilize A3C to solve it. In Section V, a range of experiments
is carried out to show the efficiency of the proposed scheme.
Section VI concludes the paper.
II. RELATED WORK
AUV-aided data collection has been extensively studied in
recent years. Early efforts were focused on the collaborative
transmissions of IoUT devices, while the trajectory of the AUV
was usually assumed to be fixed [7], [19], [20]. As the first
attempt to introduce AUV to relay the data of IoUT devices,
Yoon et al. [7] proposed a new underwater routing scheme,
where the sensing devices send their data to an aggregation
device either directly or via a multi-hop transmission, and
then the aggregation device transmits the data aggregated to
the AUV when it passes by. For reducing the number of
communication hops, the sensing devices intelligently select
the next hop according to the aggregation device’s preference.
With the objective of minimizing the energy consumption of
the IoUT devices, Chen et al. [19] conceived a novel routing
protocol relying on the selective awake-sleep mechanism of
IoUT devices and accurate estimation of the AUV’s coverage
range. Khan et al. [20] investigated an energy-efficient AUV-
assisted clustering scheme, comprised of a fixed time-slot-
based intra-cluster communication mechanism with a wake-up
sleep cycle and a sectoring mechanism, which is capable of
reducing the processing latency, while avoiding excessive en-
ergy consumption. However, the previous contributions relying
on data aggregation among IoUT devices impose an excessive
burden on the aggregation devices selected.
For enhancing the battery lives, AUVs may be intelligently
configured to cruise and collect the data of all the IoUT de-
vices. The trajectory design of AUVs will be revealed to have
a significant impact on the performance of the IoUT system,
including both IoUT devices and the AUV. Hence, a series of
treatises were dedicated to the AUV’s trajectory design, where
some of them aim for reducing the operating cost of the AUV
in terms of cruising distance or energy consumption [21]–[23].
Others focused on whether the IoUT devices’ requirements are
satisfied [10], [16], [17]. Specifically, considering the unreli-
able communications between the IoUT devices and AUVs,
Hollinger et al. [21] formulated a communication-limited data
collection problem as a special traveling salesperson problem
(TSP) and presented both an AUV path planning method as
well as a communication protocol to solve it. The efficiency of
the proposed strategy was validated both under a deterministic
access and a random access scenario. To reduce the cruising
distance of the AUV, Ma et al. [22] designed a spanning
tree covering algorithm for solving the path planning problem
formulated. Faigl et al. [23] proposed employing a self-
organizing map and an unsupervised learning technique to find
a short path for the AUV considering the priority of the IoUT
devices, which have a low computational complexity. This
regime may also be readily extended to multi-AUV scenarios.
With the emergence of advanced IoUT applications, such as
mission-critical IoUTs [24], extremely stringent IoUT device
requirements have to be considered. Hence, meeting these
requirements of the IoUT applications with limited resources
has drawn significant research attention. Bearing in mind that
3
…
AUV1
DG1
Surface
station
DG2
11
W
12
W
1
1
N
Task set
21
W
22
W
2
2
N
W
Task set
…
DGk
1
k
W
2
k
W
k
kN
W
Task set
…
DGK
AUVj
AUV1
AUVj
K
KN
W
Cached results
12
W
22
W
k
kN
W
1
K
W
2
K
W
K
KN
W
Task set
1
K
W
5
K
W
2
k
W
21
W
1
1
N
W
2
2
N
W
IoUT device
UAC link
Vortex
Trajectory
Fig. 1. The architecture of MTUC.
the value of the sensed data rapidly decays in time, the
authors proposed a heuristic adaptive greedy AUV path-finding
algorithm to find an optimal path having the maximal data
value delivered to the aggregation devices [10]. Liu et al.
[17] presented a hybrid data collection scheme, taking both
the timeliness and energy efficiency requirements of IoUT
devices into consideration. To guarantee the freshness of the
collected data, Fang et al. [16] introduced the concept of age
of information and designed a two-stage algorithm for the joint
optimization of the resource allocation and trajectory planning
of AUV-aided IoUTs. At the time of writing, however, there
is no recommendation in the open literature for optimizing
the amalgamated system’s performance relying on integrating
both the surface-station, AUVs, as well as the IoUT devices.
It is beneficial to construct a system-level optimization frame-
work for balancing the operating cost and meeting the IoUT
devices’ requirements. However there are some pioneering
works on system-level optimization in terrestrial networks.
Wang et al. [25] conceived a revenue-maximizing framework
for cellular networks by jointly considering the computation
offloading, resource allocation and content caching. Focusing
on accuracy-aware machine learning (ML) tasks in the Internet
of Industrial Things, Fan et al. [26] constructed a long-
term average system cost optimization framework by jointly
considering the resources of sensors, edge server and cloud
server, as well as the inference accuracy of the ML tasks.
However, when the application scenario changes from cellular
networks to AUV-aided underwater networks, the research
mentioned above is no longer applicable. Hence the system
considered deserves further study. Therefore, in this paper,
a max-profit problem, integrating environment-aware trajec-
tory design, communication resource allocation, computation
offloading and data caching, is conceived for filling this
knowledge gap.
III. SYSTEM MODEL AND PROBLEM
FORMULATION
A. Network Model
Fig. 1 shows our MTUC architecture, where multiple AUVs
communicating with surface-stations perpetually cruising to
provide computing service for a set of IoUT devices distributed
in several device groups (DGs). Each AUV starts from the
point of origin sight below the surface-station, and supports
the assigned DGs in turn. We assume that there is a single
surface-station, MAUVs, and KDGs. The MAUVs are
denoted by the set AU V ={AUV1, AUV 2, . . . , AUV M},
while the KDGs are represented by the set DG =
{DG1, DG2, . . . , DGK}. Let us assume that there are a total
of NkIoUT devices located in DGk, which are represented
by a set N Dk={nk1, nk2, . . . , nkNk}. For brevity, let
M={1,2, . . . , M}represent the subscript of the AUVs,
while K={1,2, . . . , K}the subscript of the DGs, and Nk=
{1,2, . . . , Nk}as the subscript of the IoUT devices located in
DGk. Let furthermore PSS = (0,0, H),PA
j=xA
j, yA
j, d0,
PDG
k=xDG
k, yDG
k, zDG
kand PS
ki =xS
ki, yS
ki, h0repre-
sent the three-dimensional (3D) Euclidean coordinates of the
surface-station, AUV k,DGk, and IoUT device nkilocated in
DGk, respectively.
We assume that each IoUT device has a task that has to
be solved. The task generated by IoUT device nkican be
represented by the twin tuple Wki,{Zki, αki}, where Zki
represents the size of the input data (in bit), while αkiis the
computational complexity (in cycles/bit) indicating how many
CPU cycles are required to process 1 bit of the data [11]. Let
O={oki, k ∈K, i ∈Nk}denote the offloading strategy
vector. If task Wkiis offloaded to the surface-station via an
AUV, we have oki= 1, and oki= 0 otherwise. Let r={0≤
rki≤1, k ∈K, i ∈Nk}denote the bandwidth allocation
vector to represent the specific proportion of the bandwidth
resources allocated to the device nki. The caching strategy
vector is denoted by H={hki, k ∈K, i ∈Nk}. We have
hki= 1, if the surface-station has cached the data of the task
Wkiand hki= 0 otherwise. For convenience, the notations
are summarized in Table I.
B. Communication Model
UAC has complex propagation characteristics, where both
the multi-path effects, Doppler effects and environmental noise
influence the quality of the link. For simplicity, we consider
a shallow-water acoustic propagation environment assumed to
be both spatially and temporally homogenous.
1) Noise model: The environmental noise in the ocean
may be caused by bubbles, shipping activity, surface wind
fields, etc. According to [27], [28], the power spectral density
(p.s.d) of the four main types of noise in dB per Hz at the
communication frequency fcan be characterized by
10 log Nϑ(f) = 17 −30 log f, (1)
10 log Ns(f) = 40+20 s−1
2+26 log f−60 log(f+0.03),
(2)
10 log Nw(f) = 50+7.5w1
2+20 log f−40 log(f+0.4),(3)
10 log Nth(f) = −15 + 20 log f, (4)
where Nϑ(f), Ns(f), Nw(f)and Nth(f)represent the tur-
bulence noise, the shipping noise, the waves noise, and the
thermal noise, respectively. Furthermore, s∈[0,1] is the
4
TABLE I
NOTATIONS
Notation Meaning
MNumber of AUV
KNumber of device group
fCommunication frequency
sShipping activity factor
wWind speed
HDepth of water
VViscosity of the fluid
h0Height of the IoUT device from the seabed
d0Height of the AUV from the seabed
r0Radius of the vortex
Ω0Strength of the vortex
CdDragging coefficient
CaCross-sectional area
ksSpreading factor
ρLDensity of seawater
Zki Size of input data
fki CPU cycles per second
BLBandwidth between AUV and device
BHBandwidth between AUV and surface-station
PA
tr Transmitted power of AUV
PD
tr Transmitted power of IoUT device
ζConversion efficiency of electricity
ηOverall efficiency of electronic circuitry
Γb,ΓsCoefficient factors related to the channel gain
ωkiUnit revenue of reducing time of IoUT device
λkiUnit revenue of saving energy consumption of IoUT device
%Unit cost to the surface-station
χUnit cost to the AUV
shipping activity factor, while wrepresents the wind velocity
(m/s). Hence the combined noise N(f)can be represented as
N(f) = Nϑ(f) + Ns(f) + Nw(f) + Nth(f).(5)
There is a two-phase transmission protocol, if the IoUT
devices offload their data to the surface-station, including the
IoUT devices to AUV, and AUV to the surface-station phases,
which can be modeled as follows:
2) The first phase transmission: IoUT device →AUV: The
UAC channel is the superposition of the direct line-of-sight
(LOS) path and a collection of non-line-of-sight (NLOS) paths,
where the NLOS paths are typically reflected by underwater
surfaces, the seabed and the water-air surface. Fig. 2(a) depicts
the geometry of the UAC between IoUT devices and the
AUV, where mu= (xm
u, ym
u, H), u ∈ {1,2, . . . , α}and
nu= (xn
u, yn
u,0) , u ∈ {1,2, . . . , β}are the reflection points
at the sea surface and the seabed, respectively, while His the
depth of water. Hence, the Euclidean distance of the LOS path
is calculated as
lL=
PS
ki −PA
j
2,(6)
while the distance of the acoustic signal reflected from point
muand point nuof the NLOS propagation can be expressed
as
lm(mu) =
PA
j−mu
2+
PS
ki −mu
2,(7)
and
ln(nu) =
PA
j−nu
2+
PS
ki −nu
2,(8)
respectively. Since NLOS paths have lost much of their energy
after multiple reflections, we only have to pay attention to a
Surface
station
AUVj
1
m
2
m
m
1
n
2
n
n
IoUT
device
LoS channel
NLoS
channels
NLoS
channels
(a) The first phase transmission.
Surface
station
AUVj
1
n
2
n
n
IoUT
device
NLoS
channels
LoS channel
(b) The second phase transmission.
Fig. 2. Multi-path effect.
finite number of significant paths [27]. Furthermore, obtaining
the lower bound of the signal-to-noise ratio (SNR) is more
beneficial by finding the minimum NLOS path lengths. We
can easily to calculate the shortest NLOS path lengths lm(m?)
and ln(n?)reflected from the top and bottom surfaces as
lm(m?) = qxA
j−xS
ki2+yA
j−yS
ki2+ (2H−h0−d0)2,
(9)
and
ln(n?) = qxA
j−xS
ki2+yA
j−yS
ki2+ (h0+d0)2,(10)
respectively.
Let A(l, f )be the attenuation at frequency fover the
distance l, which is given by
A(l, f ) = lksa(f)l,(11)
where ksrepresents the spreading factor, and a(f)is the
absorption coefficient, which can be expressed empirically in
dB per km with fin KHz as follows [29]
10 log a(f) = 0.11f2
1 + f2+44f2
4100 + f2+ 2.75 ·10−4f2+ 0.003.
(12)
摘要：

1Environment-AwareAUVTrajectoryDesignandResourceManagementforMulti-TierUnderwaterComputingXiangwangHou,StudentMember,IEEE,JingjingWang,SeniorMember,IEEE,TongBai,Member,IEEE,YanshaDeng,Member,IEEE,YongRen,SeniorMember,IEEE,LajosHanzo,LifeFellow,IEEEAbstract—TheInternetofunderwaterthings(IoUT)isenvi-s...

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