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1 23
Peer-to-Peer Networking and
Applications
ISSN 1936-6442
Peer-to-Peer Netw. Appl.
DOI 10.1007/s12083-020-01006-0
A precision adjustable trajectory planning
scheme for UAV-based data collection in
IoTs
Zuyan Wang, Jun Tao, Yang Gao, Yifan
Xu, Weice Sun & Xiaoyan Li
1 23
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Peer-to-Peer Networking and Applications
https://doi.org/10.1007/s12083-020-01006-0
A precision adjustable trajectory planning scheme for UAV-based
data collection in IoTs
Zuyan Wang1,2,3,4 ·Jun Tao1,2,3,4 ·Yang Gao1,2,3,4 ·Yifan Xu1,2,3,4 ·Weice Sun1,2,3,4 ·Xiaoyan Li1,2,3,4
Received: 6 March 2020 / Accepted: 26 September 2020
©Springer Science+Business Media, LLC, part of Springer Nature 2020
Abstract
With the increasing popularity of the IoTs (Internet of Things), the efficient data collection with Unmanned Aerial Vehicles
(UAVs) is demanded by numerous applications. The technical challenge, which restricts the deployment of the UAVs, is the
high latency of the data collection. In this paper, we focus on the problem of trajectory planning, specifically, determination
of how the UAVs traverse through the sensing field and the scheduling of the communication tasks with the IoT nodes. We
first ignore the energy consumpti on of IoT nodes but relax it eventually. Therefore, the trajectory planning problem can
be formulated as a special case of the traveling salesman problem with neighborhoods (TSP-N). We propose a Precision
Adjustable Trajectory Planning (PATP) scheme, which can calculate the k-communication area based on the stratified grid
approach and shorten the traveling trajectory of the UAV by reducing the data collection sites, to enable a tradeoff between
execution time and calculation precision. We then take the realistic energy consumption of wireless communications into
account, which is one of the key questions in researches of IoTs, to extend the network lifetime with the On-Demand PATP
(OD-PATP) scheme. The simulation results show that the PATP scheme can obtain a 15% reduction in number of visiting
point at least and the trajectory length obtained by the OD-PATP scheme can be shortened about 45%.
Keywords Trajectory planning ·Data collection in IoTs ·UAV ·Stratified grid ·Energy consumptions
1 Introduction
IoTs, Internet of Things, are networks composed of
distributed micro-devices embedded with various sensing
abilities, which are utilized to serve data collection from
the environment [1]. Typically, numerous IoT nodes are
recruited simultaneously to conduct the large-scale sensing
tasks and generate large amount of sensory data, which can
be directly forwarded to a static sink by wireless multi-
hop transmissions [2]. However, due to the data aggregation
toward the sink, the IoT nodes that distribute near the sink
have to forward a heavier volumes of traffic to the sink [3–
5], and these nodes would deplete the energy much faster
than others, which leads to unbalance energy consumption
and causes the energy hole phenomenon around the sink [6].
Another approach, which utilizes the UAVs, Unmanned
Aerial Vehicles [7], with controlled mobility moving to
Zuyan Wang
zywang92@seu.edu.cn
Extended author information available on the last page of the article.
the IoT nodes to serve data collection in IoTs, has been
attracting increasing research attentions, i.e., water-saving
irrigation [7], disaster relief [8], hard-to-reach areas mon-
itoring [9] and multi-mode communication platform [10].
The whole procedure of UAV-based data collection was pro-
posed by [11]. Wu et al. [12] experimentally demonstrated
that data can be efficiently transmitted between UAVs and
ground user equipment. By adopting the UAVs to assist the
data collection in IoTs, not only the loads of nodes can be
reduced (and thus their energy consumptions) [13], but also
the communications and networking become possible in the
hard-to-reach areas.
Unfortunately, two major design restrictions hinder
the applicability of UAV-based data collection in IoTs.
First, much research effort on the trajectory planning for
data collection exists in the literature, where the UAVs
periodically collect data from all IoT nodes according
to a pre-optimized path with minimizing the energy
consumption of the UAVs or IoT sensors [14,15].
However, heterogeneous IoT nodes with different sensing
demands may leave a big performance gap towards the
trajectory panning schemes. Second, in most traditional
static IoTs, it is a potential problem that the IoT nodes
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with a large volume of sensory data would deplete their
energy much faster than those with less to-be-transmission
data. Some perspectives have also been discussed such
as maximum energy consumption minimization [16,17],
compressed sensing [18], UAV-based wireless charging [19]
and energy-efficient UAV routing [20]. However, how to
prolong the network lifetime is still an unresolved issue in
IoTs.
On the other end of the spectrum, Precision Adjustable
Data Collection (PATP)—IoT nodes send data collection
requests, which can be retrieved by the UAVs, to the sink
when they have enough data to report. The UAVs can adjust
the precision of the trajectory according to different task
demands and node state, i.e., the amount of data, the buffer
consumption and the remained energy of the node.
In this paper, we focus on how to tackle the problem
of UAV’s trajectory planning for efficient data collection
in IoTs with adjustable precision. It is known that the
trajectory planning problem can be modeled as a TSP-N
(Traveling Salesman Problem with Neighborhoods) [21],
which is NP-hard. We tackle this problem from a new angle.
The main contributions of this paper are threefold.
– We propose a PATP scheme, which tessellates the
sensing field into equal-size grids and construct a table
to record the relationship between the grids and the IoT
nodes. We select the k-communication area based on
the grid table and the isomorphic property. Furthermore,
we adopt the stratified grids approach to achieve the
balance between the precision of the trajectory and
the computation amount through limiting the iteration
times. A TSP model with analytically evaluation is
formulated to plan the trajectory for the UAVs based
on the tessellating sensing field and the isomorphic
property.
– If the UAV flies closer to the IoT nodes with large
amount of sensory data, the energy consumption
of the IoT nodes can be more reduced. However,
this uplink transmission manner will increase the
trajectory length significantly. To characterize this
tradeoff, we take the realistic energy consumption
of wireless communication into account and adopt
an energy consumption model where both the free
space and the multipath fading channel depend on
the distance between the UAV and the IoT node.
Accordingly, the basic scheme can be extended to On-
Demand PATP (OD-PATP) scheme, which can achieve
tradeoffs between UAV trajectory and transmission
energy.
– We verify the accuracy of the proposed schemes by
comparing with the analytical model, analysis the
efficiency of the proposed schemes in data collection
and prove that their performance outperforms other
traditional approaches in terms of tour length, delay
time and overflow probability through simulation.
The rest of the paper is organized as following: The work
related to exploring mobility for data collection is reviewed
in Section 2. In Section 3, we introduce the notation used
in this paper and describe the network model. Section 4
models the considered problem, presents the proposed PATP
scheme and illustrates the superiority of our scheme. We
take the energy consumption of the IoT nodes into account,
and present the OD-PATP scheme to obtain the tradeoff
between network lifetime and data collection latency in
Section 5. Further discussion is given in Section 6. Finally,
we conclude this paper in Section 7.
2 Related work
Observing that the typical problems in traditional data col-
lection approaches, i.e., the unbalanced energy consumption
and/or the high latency, many efforts have been made to
explore the data collection with the UAVs. For example,
[23] investigated a line-model UAV-based data collection
for the energy-constrained ground sensors, which consists
of two scenarios, i.e., Flying and Hovering, to minimize the
flight duration. For efficient data collection, the optimal col-
lection trajectories are constructed for the distributed ground
sensors [14,22]. In [24], the discrete optimal transport the-
ory was utilized to minimize the collection cost and the opti-
mal flight trajectories for the UAVs in time-varying mobile
IoTs. For large scale WSNs (Wireless Sensor Networks), the
task of data collection is difficult to be completed by using
the ground mobile elements. Authors in [25] analyzed that
the performance of UAVs in IoTs depends on a lot of fac-
tors, i.e., the flight time, altitude and speed. To improve the
efficiency of the UAV-based data collection, they proposed
the possibility of combining the clustering algorithm and the
mobility of UAVs. A water filling structure, called Staircase,
was proposed in [26], which maximized the throughout for
UAV-enabled mobile relaying systems. Say et al. [27] pro-
posed a Priority-based data gathering framework with UAVs
in WSNs for maximizing the network throughput and life-
time simultaneously. An efficient algorithm was studied in
[28], which made a trade-off between the optimal trajectory
and the energy efficiency based on state-space approxima-
tion and the sequential convex optimization methods.
Since the location information of sensors was delivered
to the UAVs, the design of the trajectory can be modeled
as the classic TSP-N problem, which is NP-hard. A
trajectory initialization was proposed in [10] based on the
TSP solution, in which the UAVs act as an aerial MEs
(Mobile Elements) to serve the ground users according
to the actual activities, i.e., uploading, downloading or
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relaying. An optimization approach, multi-rate Combine-
Skip-Substitute scheme, which outperformed the known
heuristic algorithms for MEs, was proposed in [3]. A
Combine-TSP-Reduce approach was proposed to determine
the visiting sites and address the TSP problem[5]. In our
previous work [29], we proposed the SAS scheme, which
can actively skip sites while sweeping the sensing field and
optimally selecting the proper locations to start and finish
the data collection, to reduce the data collection latency by
combining the collection sites of nearby sensors. Specially,
to address the TSP and combine the hierarchical routing, a
hybrid data collection approach, including the node density-
based cluster head selection, local geographic routing
with void avoidance and low-complexity path planning
algorithm, was investigated in [30].
Noticing the difficulty in improving network energy
efficiency, [31]and[15] proposed the data collection
methods to ensure efficient utilization with a fairness
constraint. In UAV-enabled IoT system, the communication-
related energy can be ignored due to its smaller value
when compared with the consumption caused by the
UAV’s movement [32]. Ebrahimi et al. [18] investigated the
problem of energy-efficient data collection in dense WSNs
through jointly optimizing node clustering, forwarding tree
construction and cluster head selection, and UAV trajectory
planning. In [33], the authors proposed an efficient iterative
algorithm, which includes the block coordinate descent
method and the Dinkelbach method, to jointly optimize the
UAV’s trajectory, transmit power, and user scheduling under
the constraints of the UAV’s mobility. To reduce the energy
consumption of IoT devices, [34] proposed a clustering
compressive data collection scheme, based on which the
total amount of data transmission over the network can be
reduced effectively, to collect and reconstruct the sensed
data in large-scale IoT. In order to prolong the lifetime of
the network, [16] proposed a differential evolution method
to minimize the maximum energy consumption of all IoT
devices.
Most of these existing efforts focus on designing the
optimal trajectory to minimize the travel distance, the
collection latency and the energy consumption. However,
due to heterogeneous IoTs environment, i.e., rural, urban,
or dense forest, it is difficult to calculate the trajectories
in practice. Furthermore, They neglected the fact that
the network lifetime is limited by the on-board energy
supply of IoT nodes. Therefore, we explore the precision
adjustable data collection in this paper. Aiming at achieving
the optimal trajectory, we start with the assumption
of a negligible energy consumption, and then take
the energy consumption into account. Our analytical
framework can reduce collection latency, prolong network
lifetime and provide detailed insights into the collection
process.
3 Preliminaries
In this paper, we consider the network scenario, where a
UAV provides data collection services for the IoT nodes
deployed on R2with a constant travel speed [3]. Let each
IoT node, which can monitor its surrounding environment,
generate data at a fixed rate and store the sensory data in its
buffer, has its location information available, e.g., via GPS
or other localization techniques, and the UAV is also aware
of such information [34]. The main notations are defined as
follows:
–S={s1,s
2,···,s
n}:ThesetofnIoT nodes.
–s0: The sink of the network, where the UAV uploads the
collected data, with corresponding location p0.
–T: The set of all possible tours/trajectories that start and
end at s0on p0.
–A={a1,a
2,···,a
m}: The set of communication areas
formed by nIoT nodes in the sensing field.
–F(aj): The set of IoT nodes that construct the
communication area aj.
–P={p1,p
2,···,p
m}: The set of the UAV’s
collection sites obtained by our PATP scheme, m≤m.
–T∗: The optimal tour required to directly visit all IoT
nodes with length |T∗|in R2.
–TPATP : The trajectory obtained by our approach
with length |TPATP |, which connects location p0and
collection site pj,j=1,2,3,···,m
.
–rL: The maximal communication distance projected on
the sensing field.
–h: The flight altitude of UAV.
The data collection process for each sensor node is
initiated by the UAV, and the IoT node will upload its
data to the UAV with a fixed transmission power upon
the arrival of requests, which leads to a fixed transmission
range (or neighborhood). The center of the transmission
region locates at the IoT nodes [35]. For convenience, the
trajectory of the UAVs can be projected onto the sensing
field. Therefore, the UAV seems to adopt the unit disk
model to communicate with the IoT nodes in the sensing
field. Because the typical data transmission speed is much
faster when compared with the travel speed of the UAVs,
we assume that the time required by the sensory data
transferring is negligible [36].
4 Precision adjustable trajectory planning
4.1 Problem formulation
Due to the Doppler shift [3], the movement of the UAV
will establish an unstable wireless channel between the UAV
and IoT nodes, which seriously affects the transmission
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rate and reliability. We assume that the UAV potentially
collects data from the IoT nodes over the geographical
locations, i.e., collection sites, which are denoted by C=
{c1,c
2,···,c
n}. The UAV will fly along a trajectory T
with length |T|, which is a sequence of n+1 locations
starting and ending at p0, i.e., T=(p0,c
1,c
2,···,c
n,p
0),
in this sensing field. Then we have |T|=dist(p0,c
1)+
dist(cn,p
0)+n
i=2dist(ci−1,c
i). Furthermore, with the
assumption of the negligible communication time and a
constant travel speed of the UAV, our objective is to find the
optimal collection site set Cfrom the neighborhood of IoT
nodes to construct Twith the minimized |T|. Therefore, the
trajectory planning problem can be formulated as:
min |T|(1)
s.t. F(T ) ≤n, T ∈T,(2)
0≤|T|≤Tmax ,T∈T,(3)
dist(si,T)≤rL,∀si∈S,(4)
where Tis the traveling trajectory that visits all IoT nodes
only once in each round, |T|is the trajectory length, F(T )
is the number of visiting points in T,Tmax is the maximum
flight distance of UAVs and dist(si,T) is the Euclidean
distance from IoT node sito trajectory T. Problem (1)isa
variant of the TSP-N problem, which is difficult to be solved
in polynomial time due to its NP-hardness [37].
In next subsections, we propose an efficient heuristic
scheme to solve Problem (1) approximately and demon-
strate the performance of the proposed scheme based on
theoretical analysis and simulation. Inspired by the fact
that the communication region of nearby nodes maybe
overlapping with each other,
our strategy follows three phases: First, it establishes a
area table to store the coverage level and the nodes relation,
based on which the visiting areas of the UAV can be
determined. Next, it utilizes the selected grid stratification
algorithm to approximate the measures of the visiting
areas. Finally, it plans a trajectory by TSP algorithm and
further optimizes the length of the calculated trajectory by
substituting some collection sites in the trajectory.
4.2 Scheduling principle of the UAVs
Due to the possible overlapping of the communication range
between adjacent nodes, it is difficult to obtain the optimal
results of the trajectory planning with the polynomial
time complexity [3]. On the contrary, it also provides
opportunities to optimize the collection tour, because we
can obtain a shorter length of the tour by letting the
UAVs collect associated data together at any location in
communication area, where the overlapping occurs, instead
of visiting multiple sensors [5]. In general, the overlapping
communication area is formed by a group of sensors, i.e.,
area a1is covered by {s1}and a4is covered by {s1,s
2,s
3}
(see Fig. 1). The remaining area in the plane is a15,which
is covered by ∅. Inspired by this observation, we make
the following definition and construct the area table, which
consists of the Identity Document (ID), the relationship and
the coverage level as shown in Fig. 1. Consequently, the
entry in the table can be represented as aj,k,F(aj).
Definition 1 (k-Communication Area): Let Sbe the subset
of Sand |S|=k. The area, where any sites can
connect all IoT nodes in Ssimultaneously, is defined as k-
Communication Area, and kdenotes the coverage level. As
showninFig.1,a4is a 3-communication area.
The coverage level kof the area ajrefers to the number of
IoT nodes that a UAV can communicate with if it moves to
aj. When calculating the communication areas, a node may
belong to multiple areas, i.e., both a4and a8contain s3as
showninFig.1. However, based on the constraint that each
IoT node is served by the UAV only once in each round, the
scheduling of the UAV is that it collects the sensory data at
which communication area and from which IoT nodes. Thus
the first issue that we need to address is how the UAV carry
out the data collection. Essentially, the scheduling problem
is a special case of the Set Cover problem, which is a
classical problem in combinatorial mathematics. Denote the
set of communication areas in R2as A={a1,a
2,···,a
m}.
Our goal is now to find a minimum set A⊆Asuch that
each IoT node si∈Sis contained by one area in A.
Theorem 1 For any set of communication areas Ain R2
and m=|A|, we have m≤n2−n+2,wherenis the
number of IoT nodes.
Proof The above theorem follows from [38].
Algorithm 1 Greedy area selection.
Require: Aand S
Ensure: A
Initialization:A←∅
Construct Awith S;
while
aj∈A
F(aj)= Sdo
Find the communication area ajwith the maximal level
from Aaccording to the area table, and add it to A;
Update Aand the corresponding area table;
end whilereturn A;
In this paper, we propose a “Greedy Area Selection”
algorithm to solve the set cover problem. The core of the
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Fig. 1 Communication areas
and corresponding table
algorithm is the following simple heuristic: It starts with
A=∅, always selects the ajwith the maximal level kand
output a set A={a1,a
2,···,a
m}that cover all IoT nodes
in S. It is clear that m≤m. The pseudocode of the greedy
area selection algorithm is given in Algorithm 1. For the
example shown in Fig. 1, the proposed algorithm fist finds
a4because its level is maximal when compared with other
communication areas and F(a4)={s1,s
2,s
3}. Then the
area table is updated by removing the selected IoT nodes,
which appear in the selected areas, from the remaining table
entry. Second, it selects a13 with the greedy principle due
to F(a13)={s5,s
6}and update the area table. Finally,
because F(a7)=F(a8)=F(a10)=F(a11 )={s4},a7,
a8,a
10 and a11 will combine to make a large one, which is
represented by a7. Thus A={a4,a
7,a
13}is the the res-
ultant visiting areas because F(a4)∪F(a7)∪F(a13)=S.
4.3 Estimating the shape of
k
-communication area
Based on the Section 4.2, we can obtain the visiting areas
by solving a set cover problem. However, the intersection
and the continuity of the communication areas make it very
difficult to calculate its shape directly. We adopt a spatial
separation approach, which tessellates the placement area of
IoT nodes into many small subareas. Let Qbe a minimum
axis-parallel square with side-length Q, which intersects
every communication disk of the IoTs node and the sink.
We construct a subdivision of Qinto many uniform grids
with side-length δasshowninFig.2a. This way, there are
2number of girds denoted by ga,b,∀a, b ∈{1,2,···,},
which locates in the ath row and the bth column and =
Q
δ.
For a grid ga,b,wherega,b =[(a −1)δ, aδ]×[(b −
1)δ, bδ ],letH(ga,b)be the the sentinel points of ga,b (see
Fig. 2a). Specifically,
H(ga,b)=(a −1/2)δ, (b −1/2)δ,∀a, b ∈{1,2,···,}.(5)
Note that the sentinel point H(ga,b)may belong to
only the grid ga,b. Therefore, H(ga,b)can represent the
region of ga,b. More formally, the distance between a grid
ga,b and a IoTs node siis defined as dist(si,g
a,b)
dist(si,H(ga,b)).
Lemma 1 Set δ=Q
8nγ where γis an arbitrarily
positive parameter (γ > 0). For any optimal trajectory
T∗constructed by nIoT nodes with length |T∗|,theerror
caused by using H(ga,b)to represent ga,b is not exceeding
√2|T∗|
16γ.
Proof By Lemma 2.2 in [21], which verifies the relation
between the tour T∗and its minimum axis-parallel square
Q,wehave
2Q≤|T∗|.(6)
As shown in Fig. 2b, by triangle inequality, we have
dist(pj,H(ga,b))−dist (pj,p
j+1)<dist(pj+1,H(ga,b)),
(7)
and
dist(pj+2,H(ga,b))−dist(pj+1,p
j+2)<dist(p
j+1,H(ga,b)).(8)
By (7)and(8), the error caused by using H(ga,b)to
substitute pj+1is less than 2dist(pj+1,H(ga,b)).The
maximum distance from any point in ga,b to its sentinel
point H(ga,b)is smaller than or equal to √2
2δ. Thus, we have
2dist(pj+1,H(ga,b)) ≤√2δ.(9)
Assume that there are total ncollection sites in T∗, the total
maximum error is less than √2nδ. With (6), we have
√2nδ =√2Q
8γ≤√2|T∗|
16γ. (10)
This completed the proof.
We utilize binary variable xi
a,b to denote whether ga,b
can connect to sior not with transmission range constraints.
Thus we have
xi
a,b =1dist(si,ga,b)
rL=0
0 otherwise ,∀a, b ∈{1,2,···,}.
(11)
For example, if x1
1,2=1 denotes that the site g1,2locates
in the transmission range of s1; Otherwise x1
1,2=0.
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Fig. 2 Process of the PATP
scheme
Furthermore, we compute the grid weight to describe the
relationship between the IoT nodes siand the grid ga,b.
wa,b =
n
i=1
xi
a,b,∀a, b ∈{1,2,···,}. (12)
Inspired by the fact that a grid may be similar to
its neighbors in terms of the relationship, we define the
Isomorphic Grids, which can be exploited to conduct the
grids selection for the communication area calculation.
Definition 2 (Isomorphic Grids): Assuming ga1,b1and
ga2,b2are two grids in the the tessellating sensing field.
When
wa1,b1=wa2,b2and for all xi
a1,b1=xi
a2,b2,∀i∈
{1,2,···,n}, we think that ga1,b1is isomorphic to ga2,b2.
Then we can calculate the grid-based visiting area
P={P1,P
2,···,P
m},wherePjincludes the grid
with the optimal weight and its isomorphic grids. The
area calculation works as follows: It first selects the grid,
which can contain the node set F(a1)(a1in A),and
corresponding isomorphic grids as P1. Later, it finds out the
gird that can cover the node in F(a2). The given operation
will repeat iteratively until a
mis computed.
Though the obtained Pcan represent the visiting areas
approximately, the coarse-grained grids set will affect the
performance of trajectory planning, especially in a dense
network. The stratified grid approach is used to estimate
the arbitrary geometric graphs on the plane [37]. Aiming
at increasing the precision of grid-based visiting area, we
utilize the stratified grid algorithm in a different way, which
we refer as Selected Grid κ-stratification,asshownin
Algorithm 2. Stratify(P) is the function to divide each
grids in Pinto once four congruent axis-aligned squares.
P−κ
jkeeps the κ-stratification grids set of Pj,wherePj∈P
and κis a system parameter to control the depth of the grid
stratification. Apparently, κis used to determine when to
terminate the grid stratification. The output girds set Pis
exploited to substitute the coarse-grained grids set Pfor
the trajectory calculation in the following section. Figure 2c
shows an example of 2-stratification, where the shadow is
the overlapping area of three IoT nodes, i.e., s1∼3, the grids
enclosed by the black line represent 2-stratification result.
Algorithm 2 Selected grid stratification.
Require: Pand κ
Ensure: P
for all Pj∈P(j =1,···,m
)do
P−0
j←− Pj;
for all k∈[1,κ]do
P−k
j←− Stratify(P−(k−1)
j,k);
Remove the non-isomorphic stratified grids in P−k
j;
end for
Pj←− P−κ
j;
end forreturn P;
The accuracy of calculating the visiting areas is closely
related to the control parameter κand γ. It is obvious that
the bigger κand γcan result in a more precise solution with
the higher computation cost. Thus κand γis the precision
adjustable parameters in our proposed PATP scheme.
4.4 Trajectory planning for UAVs
After calculating the stratified grids set P, we can obtain a
set of grid-based communication areas that must be visited
as shown in Fig. 3. Based on these areas, we use the TSP
algorithm to plan the traveling path. The TSP algorithm
requires input of points instead of areas. Let H(Pj)be all
the sentinel points in Pj. This way, we calculate pj,which
is the cluster center of H(Pj), as the representative point.
In other words, Problem (1) can be reformulated as finding
the optimal visiting sequence of these representative points,
which is a special case of the TSP problem. The reason
why we choose the cluster center of H(Pj)rather than an
arbitrary point in the area as the representative point for
traveling-trajectory planning is to avoid the impact of using
a point located at an extreme location. Then we utilize the
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Concorde TSP Solver [39] based on cutting-plane method,
which can obtain the optimal solution by iteratively solving
linear programming relaxations, to calculate the visiting
sequence.
Suppose that the visiting sequence is denoted as π=
{p0,p
1,p
2,···,p
m,p
0}. We connect the respective points
in order so as to construct the initial closed tour T.Note
that p0is the location of the sink. Because each visiting
area has a countless number of points that can be selected as
the representative point of the area, it is possible to further
reduce the length of the calculated trajectory by finding a
better collection site in the Pjto substitute pj.Thenwe
again greedily select a vertex from Pj, which is isomorphic
to the current collection site pj, but now based on the
minimal distance to previous collection site. The details are
given in Algorithm 3.
The substitute algorithm works as follows: For each
pj∈π, it first constructs the line pj−1pj+1that connect
site pj−1and pj+1and check whether Pjintersects with
pj−1pj+1. If yes, the point on the segment of pj−1pj+1
inside Pjcan be selected as the new visiting point p
j.
Otherwise, it substitutes pjby find a point nearest to
pj−1among the vertex of grid in Pj, which in the sub
is not located within the convergence area. As shown in
Fig. 3, the visiting sequence is {p0,p
1,p
2,p
3,p
4,p
5,p
0}
(see Fig. 3a). p1is not covered by p0p2(see Fig. 3b).
We will find a point p
jby comparing the least distance
to p0. Similarly, we can substitute p2,p3,p4by p
2,p
3,
p
4(see Fig. 3b-e). p5intersects with p4p0. Thus, we select
a point on p4p0, while it lies inside P5, to substitute
p5(see Fig. 3f). Finally, the traveling path is updated to
{p0,p
1,p
2,p
3,p
4,p
5,p
0}.
Algorithm 3 Trajectory optimization.
Require: P
Ensure: trajectory TPATP
Initialization:TPATP ←∅and π←∅
for all Pj∈P(j =1,···,m
)do
pj←the cluster center H(Pj);
Append pjinto π;
end for
Obtain the visiting sequence πbased on Concorde;
π←π;
for all j=1,···,m
do
if pj−1pj+1intersects with Pjthen
pj←p
j, where p
jis a point in pj−1pj+1∪Pj;
else
Obtain the corresponding grid set of pjin πas P;
p
j←arg min{dist(p
j,p
j−1)}, where p
jis a grid
vertex in P;
pj←p
j;
end if
end for
TPATP ←π;return TPATP
4.5 Performance analysis
4.5.1 Upper bound of the trajectory length
The proposed PATP scheme, which forms uniform grid
inside the sensing field, computes the minimum length
of the trajectory over this grid and returns this length
as an approximate solution to Problem (1). The core of
performance analysis is based on bounding the detour,
i.e., [3]and[21]. Following these similar researches, we
Fig. 3 Example of the trajectory
optimization. (a) Trajectory
planned by
TSP. (b∼f) Execution of
algorithm 3
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further investigate this problem in these grids and derive
upper bound of our TSP-N tour in the following:
Theorem 2 |TPATP |≤(1+ε)|T∗|+√2Q
8γ(n +2
n−1),
where εis the approximation factor of the TSP algorithm.
Proof In our scheme, the upper bound of TPATP relates to
the size of the original grid, that is, recursively stratified grid
only increases the calculation accuracy based on the original
grid size δ. Following the similar argument as the proof of
Lemma 1, the optimal trajectory T∗that visits all IoT nodes
can be modified to be a trajectory T∗with length |T∗|that
visits P={P1,P
2,···,P
m}.
Since T∗visits some point in P, for each communication
area, we can simply add to T∗a detour that goes from the
collection sites to a grid point and back to the sites. So each
of the detour is of length at most √2δ.Wehavemnumber
of collection sites such that the total detour length is √2mδ.
Utilizing Lemma 1, we have
|TPATP |≤(1+ε)(|T∗|+√2mδ) =(1+ε)(|T∗|+√2Qm
8nγ ).
(13)
With Theorem 1, we have
m≤m≤n2−n+2,(14)
Therefore, we have the following relations as
(1+ε)(|T∗|+√2Qm
8nγ )≤(1+ε)|T∗|+√2Q
8γ(n+2
n−1).
(15)
This completed the proof.
4.5.2 Lower bound of the trajectory length
Suppose the optimal TSP tour is known in the an
N-by-Ngrid of congruent squares with N2sentinel
points. According to [40], we know an lower bound of
( 6
log N/log log N), which represents progress toward
proving the conjectured lower bound (log N) [41].
If we treat the ×grid after the PATP scheme as a new
instance, we have
|TPATP|≥( 6
log / log log )|T∗|,(16)
where ( 6
log / log log ) ≥1 is the competitive ratio.
The lower bound found can be obtained if none overlapping
occurs, i.e. the distances between IoT nodes are much longer
than the radio range.
4.5.3 Time complexity
Here, we analyze the time complexity of the proposed PATP
algorithm. There are a total of nIoT nodes in the sensing
field. To construct the grid tessellation, it takes O(n2)to
compute the grid table.
Assuming that there are mcommunication areas with
our approach. For moverlapping areas, we take O(m2)
to construct isomorphic grid set. The grid stratification
is similar to the quadtree decomposition. Thus, the
time complexity for the stratification is O(|P|log κ) =
O(2log κ),where|P|denote the number of girds in P
and log κis the depth of the quadtree. To determine a
trajectory, the time complexity varies by the TSP algorithm.
For example, the brute-force search algorithm takes O(n!)
and the dynamic programming algorithm takes O(n22n).
We assume that the time complexity of obtaining a desired
TSP tour is Ctsp. Finally, we take O(m)to adjust the
trajectory. According to Theorem 1, Lemma 1 and (14),
we have O(m2)=Om( Q
δ)2=Oc2n4. Treating κ
and cas fixed input parameter, the complexity of the PATP
scheme is O(n4)+Ctsp.
4.6 Performance evaluation
In this subsection, numerical results are provided to evaluate
the performance of the proposed PATP scheme. We consider
a sparse square sensing field with size 500 ×500m2,and
the sink is located at the coordinate (0,0). Moreover, the
velocity of UAVs is set to 50 Km/h.
We assume that the data generation rate and storage
capacity of a IoT node are 128 Kbps and 16MB, respec-
tively. Like previous studies of this kind of problem, we
compare our solution |TPATP|with the optimal solution
|T∗|in this paper. To find the optimal solution T∗, we need
to run the Concorde TSP Solver [39] to obtain the optimal
solution of the TSP instance. Note that, all statistical results
of our scheme are obtained by Monte Carlo method.
4.6.1 Trajectory length
It is known that TSP problem is an NP-hard problem [37].
To examine if a reduced number of visiting points can
lead to a shorter length of the trajectory, we evaluate the per-
formance of the TSP scheme and the PATP scheme. Table 1
shows the comparison of the optimal trajectory T∗and our
trajectory TPATP. The radio range projected on the plane is
set to 30m. As can be seen, if we use the TSP scheme to visit
200 nodes, which are uniformly distributed in the sensing
field, the length of trajectory will be 5209m. After the exe-
cution of the PATP scheme, the number of collection sites is
57. The length of the trajectory for the TSP scheme can be
shortened to 3538m. We confirm that the smaller number
of collection sites the shorter the length of the trajectory.
We evaluate our analysis on the trajectory length with
varying number of IoT nodes (from 100 to 200) and radio
range (from 10m to 50m), respectively. With the increased
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Tab le 1 How the number of collection site affects the trajectory
Number of IoT nodes 50 100 150 200
Trajectory length |T∗|3203m4216m4832m5209m
Number of collection sites (obtained by PATP) 36 55 63 57
Trajectory length |TPATP|2711m3314m3673m3538m
Rate of reduction in length of trajectory 15.4% 21.4% 24.0% 32.1%
Rate of reduction in number of nodes 28.0% 45.0% 58.0% 71.5%
number of nodes, the evaluation results on the trajectory
length using the PATP scheme are plotted in Fig. 4a. As can
be seen, the PATP scheme outperforms the TSP, COM and
CSS schemes [3]. We can observe that our scheme performs
effectively even when the node density becomes high and
the TSP algorithm creates the longest traveling paths.
As shown in Fig. 4b, when the radio range rLvaries
from 10 to 50, the length of the traveling paths computed
by the PATP scheme also shorter than other schemes. This
is because COM and CSS schemes combine the visiting
sites on the planned traveling paths and our algorithm focus
on reduction the number of the sites at first. In addition,
our simulation in Concorde are finished in 4 seconds. This
verifies the time-efficiency of the PATP scheme.
4.6.2 Delay time
Next, we statistically verify the proposed PATP scheme by
validating the delay time. Figure 5a shows the delay time
when the communication range is 30m and the number
of IoT nodes varies from 100 to 200. Figure 5bshows
the evaluation results of the approximation on the average
waiting time with varying rL. From these two figure we
can observe that different control parameters such as δ
and κaffect the simulation results. Another observation is
that the improvement ratio of the proposed PATP scheme
becomes larger with the decrease in the initial grid size
δ. It can more effectively reduce the collection delay time
with the decrease in δ. More iterations in the selected grid
κ-stratification algorithm will increase the accuracy of the
data collection. This verifies the potential scalability of our
precision adjustable scheme and the feasibility of using an
UAV to collection data in large-scale IoTs.
4.6.3 Overflow probability
Sensory data may be lost, which is not desirable for
data integrity sensitive applications, if the sum of the
amount of data it collects from the environment exceeds
its transmission throughput. We explore the overflow
probability of IoT nodes before being served. As shown
in Fig. 6a, the TSP has the highest overflow probability
compared to the other schemes and the PATP scheme
outperforms the traditionally scheme significantly. One
possible reason is that finding an optimal solution requires
huge computational effort and time, particularly when the
number of visiting points is large. Our scheme, which
reduces the number of visiting sites effectively, can lead
to a shorter length of the trajectory exactly. Fig. 6bshows
the comparison of input parameters. This figure verifies our
Fig. 4 Evaluation results on the trajectory length
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100 120 140 160 180 200
Number of Nodes
180
200
220
240
260
280
300
320
340
Delay Time(s)
10 15 20 25 30 35 40 45 50
Communication Distance(m)
160
180
200
220
240
260
280
300
320
340
Delay Time(s)
Fig. 5 Evaluation results on the delay time
conclusion again and indicates that the grid size and iterative
number has influence on the PATP scheme. We believe
this observation will motivate more research efforts in this
direction.
5 On-demand PATP scheme
In the previous section, we did not consider the energy
consumption of the IoT nodes and proposed a trajectory
planning scheme for the UAVs based on the unit disk
communication model in R2, which is adopted by most
existing work, i.e., [3]and[5]. However, due to the existence
of practical budget constraints on the IoT node’s battery
capacity, how to extend the network lifetime is one of the
key questions in researches of IoTs [16,18,32].
Therefore, the unit disk communication model is not
appropriate for the data collection in IoT when considering
the realistic energy consumption. In this section, we take the
realistic energy consumption of wireless communications
into account and extend the basic scheme to the On-demand
PATP (OD-PATP) scheme.
5.1 Problem formulation
It is known that wireless signals suffer from path loss,
fading, shadowing, interference, and other impairments [3].
Theoretically, if the flying altitude of a UAV is high enough,
100 120 140 160 180 200
Number of Nodes
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Overflow Probability
TSP
COM
CSS
PATP
10 15 20 25 30 35 40 45 50
Communication Distance(m)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Overflow Probability
Fig. 6 Evaluation results on the overflow probability
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it has a high probability of LoS communication channel
between the UAV and IoTs nodes in rural environment. We
assume that the UAV flies with a constant altitude h,which
is the minimum altitude required for safety. Therefore, the
uploading channel is established as LoS. The collection
site of the UAV not only impacts its communication with
IoT nodes, but also has great impact on the lifetime of
the communicating IoT nodes. However, the IoT nodes
with large volumes of data to be transferred would deplete
their energy much faster than the other IoT nodes. This
unbalance energy consumption will introduce the energy
hole phenomenon. Therefore, the question to be solved in
this section is that how to obtain a data collection trajectory
for the UAVs while balancing the traffic load of the IoT
nodes and guaranteeing a low energy consumption.
Denote rias the radio range of sidetermined by the IoTs
based on the to-be-transferred data volume of si. Each node
adopts multihop wireless communications to send a HELLO
message, which contains its unique identification and ratio
range to the sink, when it has enough sensory data to
report. Since the data volume of the HELLO message is not
excessively large, this only leads to a small additional cost.
Thus the trajectory planning problem can be reformulated
as:
min |T|(17)
s.t. C(T ) ≤n, T ∈T,(18)
0≤ri≤rL,∀si∈S,(19)
dist(si,T)≤ri,∀si∈S,(20)
ET(si)≤Emax ,∀si∈S,(21)
The constraint (18) guarantees that the number of collection
sites is less than or equal to the number of IoT nodes. The
constraint (19) guarantees that the transmission distance
determined by the IoT node is no more than the maximum
rL. The constraint (20) guarantees that the UAV can
visit all IoT nodes in the system when traveling along
the collection tour. The constraint (21) guarantees that
the energy consumption of IoT node does not exceed a
maximum value.
5.2 Transmitting power control
The IoT system is a composite of various heterogeneous
devices, which means different kinds of data sources
normally have different data transmission requirements and
abilities. An example is given in [7], where the aerial UAVs
collect the environment information from a large number of
distributed temperature and humidity nodes to achieve the
precision agriculture. When a large number of IoT nodes
are densely deployed in an area, the load balancing and
efficient data uploading should be taken into account. For
the IoT node, it has incentive to reduce its transmission
power when the volume of collected data is large, because
transmitting these data to the UAV will consume a lot of
energy. For the UAV, it moves closer to the IoT node with
large amount of sensory data instead of at the edge of the
communication area, because a shorter collection distance
can ensure a higher data rate. According to these principles,
in this paper, we propose a simple power control method for
the IoT nodes. Before proposing the method, the following
assumptions are made:
– The memory buffer size equipped for each IoT nodes in
the system is B.
–Foranysi∈S,ithasI(s
i)bit sensory data to be
collected by the UAV.
– The IoT node can adopt different modulation and cod-
ing schemes, resulting in Ldifferent communication
range (r1,r
2,···,r
L),wherer1and rLis the mini-
mum and the maximum radio range of the IoT node,
respectively.
– The gaps between any two communication distance
levels are equal.
For the IoT node siwith the memory buffer B, it can
determine the applied radio range to the UAV by using the
following formula:
rl(si),l(s
i)=B−I(s
i)
B·L,∀si∈S,(22)
where · is the ceil operator to obtain the nearest integer
and l(si)∈{1,2,··· ,L}is the level as shown in Fig. 7a.
As mentioned before, the IoT nodes’ information can be
transmitted to the sink through a multihop transmission
approach, which only leads to a small additional time cost
and energy consumption.
Up to now, the only uncertainty is the transmission
energy consumption of the IoT nodes siwith the radio range
rl(si). An energy dissipation model, where both the free
space and the multipath fading channel are considered, is
given in [42]. Since the threshold D0is 87m, we assume that
r2
L+h2<D
2
0. Therefore, the energy consumption when the
IoT node sisends 1 bit data with transmission range rl(si)is
denoted as
ET(si)=Eelec +εfree(r2
l(si)+h2), ∀si∈S,(23)
where Eelec =50nJ /bi t and εfree =10pJ/bit/m2.
We extend the basic UAV’s scheduling method to make it
fit the Problem (17). Based on (22), we can obtain ndisks,
whose sizes may be different, and let ˜
A={a1,a
2,···,a
m}
be the set of communication areas constructed by these disk
as shown in Fig. 7b. We utilize a binary variable ϒ(si,a
j)to
denote whether IoT node siis belong to the communication
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Fig. 7 On-demand
communication model
area aj. For example, the variable ϒ(si,a
j)is 1 if node the
siis belong to the area aj; otherwise it is 0. Thus we have
ϒ(si,a
j)=1 node|siis belong to aj
0 otherwise . (24)
According to the additivity of data, the total amount of
data collected by the UAV when it visits the area ajis
I(a
j)=
si∈S
I(s
i)ϒ(si,a
j), aj∈˜
A. (25)
In general, the earlier a area with a large amount of
data is collected, the higher the effectiveness on that area
is. According to this principle, OD-PATP scheme work as
following: It first finds the communication area, whose level
and data volume is maximal at same time. Then repeat this
until the resultant set can cover all the node. Finally, it
will return the minimum set of areas and utilize Algorithm
2 and Algorithm 3 to create a visiting trajectory for the
UAVs. The pseudocode of the OD-PATP scheme is shown
in Algorithm 4.
By inspecting (22), we note that the aim of the power
control is to decrease the radio range between to the IoT
node with a large amount of sensory data, as the energy
consumption in Friis frees-pace model is of the super-linear
relationship to the communication distance. Although it can
decrease the energy consumption of the IoT nodes, the
shorter communication distance between the UAV and IoT
node reduce the flexibility to optimize the traveling tour
when compared with the maximum range rL. Therefore,
the trade-off between the UAV’s scheduling and energy
consumption by applying the power control scheme is to be
studied in the following subsection.
5.3 Performance evaluation
In this section, we evaluate the energy consumption
proposed OD-PATP scheme.
Algorithm 4 On-demand trajectory planning.
Require: ˜
A
Ensure: TOD−PAT P
Initialization:˜
A←,∅temp ←0
while
aj∈A
F(aj)= Sdo
for all aj∈˜
Ado
Calculate I(a
j)based on (25);
end for
Find the ajwith the maximal level from Aaccording to the
area table, and annotate its level by k1;
temp ←j;
for all au∈S/ajdo
k2←the level of au;
if I(a
u)>I(a
j)and k1=k2then
temp ←u;
end if
end for
Add atemp to ˜
A;
Update ˜
Aand the corresponding area table;
end while
Invoke Algorithm 2 and Algorithm 3 to obtain TOD−PATP ;
return TOD−PATP ;
5.3.1 Energy consumption
To validate the performance of the proposed scheme, we
first investigate the energy consumption with different
radio range of the IoT nodes. According to (22)and(23),
the energy consumptions for data transmission can be
computed. The sensing field is changed to be 200 ×200,
300 ×300, and 500 ×500 square meters, respectively.
As shown in Fig. 7a, the distance between the IoT node
and the UAV is a random variable which is uniformly
distributed in [0,r
L]. According to the distance-dependent
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energy consumption model [42], the average energy needed
to deliver 1 bytes sensory data to the UAV is
¯
ET(si,r
L)=rL
x=0
1
rL
ET(si,x)dx=Eelec+εfree(rL2
3+h2).
(26)
Since the analytical model assumes that the IoT nodes are
uniform distribution in R2, the energy consumption of the
same nodes is uniformly distributed as well. Thus, we have
¯
Etotal =
si∈S¯
ET(si,r
L)I (si), (27)
where ¯
Etotal is mean of the total energy consumptions of
the IoT system.
As mentioned before, the closer the UAV to the IoT node,
the lower the energy consumption for the data transmission.
Hence, we first specify total energy consumption by
adjusting their maximal communication distance. Figure 8
shows the simulation and analytical results of the total
energy consumption using the OD-PATP scheme with
radio range 20m, 25m, 30m, 35m, 40m, 45m and 50m,
respectively. For each sensing field, the total number of
randomly deployed sensors is set to 200.
The Ground-to-Air channel follows the free-space path
loss [26,42], where the received signal power depends
on the transmission distance between two communication
parties. According to (26), we can know that the analytical
result about total energy consumption is in a monotone
increasing situation with the growing rL. The red dotted
line in Fig. 8 proves this conclusion. In contrast, smaller
communication distance can reduce energy consumption.
Our scheme utilizes this observation. The IoT nodes can
adaptively adjust their uploading power according to their
20 25 30 35 40 45 50
Comunication Distance (m)
500
1000
1500
2000
2500
3000
3500
4000
Total Energy Consumption (J)
Area size: 200×200
Area size: 300×300
Area size: 500×500
Analytical result
Fig. 8 Evaluation results with varying rL
transmission requirement. As can be seen, our scheme
consumes more energy than the analytical result when rL
varies from 20 to 30. This is because a combination of
communication strategy is also adopted, which will lead
to extra energy consumption due to the larger transmission
distance from collection sites to IoT nodes. The total energy
consumption of our scheme is monotonically decreasing
with respect to the increasing rL. The reason is that the extra
energy consumption caused by the combination strategy can
be offset by the adaptive power allocation with the increase
of rL. In addition, our simulation results outperform the
analytical results when the radio range is rL=30 and the
sensing field size is 500 ×500.
To investigate the total energy consumption, we vary the
total numbers of the IoT nodes. The communication range
of the IoT node is set to 30m. As shown in Fig. 9,the
total energy consumption is monotonically decreasing when
increasing the number of sensor nodes. When the size of the
sensing area increases, the density of IoT node deployment
will decrease. This illustrates that our OD-PATP scheme can
obtain a better performances when the nodes density is low.
This also indicates the advantage of using an UAV in large-
scale IoTs. In summary, The parameter rLcan be used to
address the trade-off between the energy consumption and
the data collection latency.
5.3.2 Comparison with other data collection schemes
Based on the above simulation results, the radio range of the
IoT nodes are fixed at 30 (in meters), the sensing filed is set
to 500 ×500 square meters. The Emax is set to 20. Table 2
shows the comparison of different schemes in rate of energy
consumption.
100 120 140 160
Number of Nodes
800
1000
1200
1400
1600
1800
2000
Total Energy Comsumption (J)
Area size: 200×200
Area size: 300×300
Area size: 500×500
Analytical result
Fig. 9 Evaluation results with varying n
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Tab le 2 Comparison of different schemes in rate of energy consumption
Number of IoT nodes 50 60 70 80 90 100
TSP scheme 42.5% 41.9% 41.6% 41.2% 41.0% 41.9%
OD-PATP scheme 45.1% 45.3% 45.1% 46.2% 45.1% 44.8%
PATP scheme 53.0% 53.7% 54.6% 54.5% 56.5% 56.5%
As can be seen, if we use the Concorde Solver [39],
which calculates the optimal TSP trajectory, to visit 100
IoT nodes distributed in the sensing field, the rate of
energy consumption will be 41.9%. The total rate of energy
consumption computed by the PATP scheme and the OD-
PATP are 56.5% and 44.8%, respectively. It is clear that our
schemes cost more energy when compared with the TSP
scheme. This is because our algorithm sacrifices some of
the energy efficiency to get a shorter trajectory.
As shown in Fig. 10a and b, the OD-PATP scheme
outperforms the traditional algorithms in terms of the tour
length noticeably, in which TSP represents the optimal
solution obtained by the Concorde Solver, COM and CSS
are the tour length obtained by these two combination
algorithm, respectively.
From this figures we can see that the TSP algorithm
creates the obviously longer paths length than others. This
is because the TSP algorithm requires the UAV to visit
each IoT node. Another observation from Fig. 10aandb
is that the tour length with the OD-PATP scheme can be
further shortened by about 50 −60 percent when compared
with the TSP scheme. For instance, given 100 IoT nodes,
the length of the trajectory planning by OD-PATP can
reduce about 45%. Given 400 IoT nodes, the length of the
trajectory planning by OD-PATP can reduce about 42.6%.
In summary, the improvement ratio of the OD-PATP scheme
over the TSP scheme becomes smaller when increasing the
number of IoT nodes.
6 Future discussion
Although the proposed schemes are efficient, there are still
existing problems that should be studied in our future work.
6.1 Dense networks
The proposed schemes can help to improve the performance
of data collection in dense IoT networks. Considering the
average number of neighbors as:
¯
N=πnr2
L
R2,(28)
where rLis the communication range, nis the number
of IoT nodes and Ris the deployment area size. If the
average number of neighbors is greater than a threshold,
i.e., ¯
N>3, we can partition the sensing filed into
clusters. In the intra-cluster moving phase, the UAVs will
conduct the trajectory with the proposed schemes, and
collect sensory data from IoT nodes within this cluster.
In the inter-cluster moving phase, the UAVs will move
along a deterministic trajectory, i.e., circle-like, square-like,
arc-like and track-like trajectory, to visit these clusters. In
addition, the shape of the trajectories between clusters can
be adjusted according to the network topology in practice.
Another approach to data collection in dense IoT networks
utilizes the multi-UAVs corporation for load balancing and
efficient data uploading. We did not consider the multi-UAV
Fig. 10 Evaluation results on
the OD-PATP scheme
100 150 200 250 300 350 400
Number of Nodes
2
3
4
5
6
7
Tour Length (Km)
TSP
COM
CSS
PATP
OD-PATP
100 110 120 130 140 150
Number of Nodes
2.5
3
3.5
4
4.5
Tour Length (Km)
TSP
COM
CSS
PATP
OD-PATP
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deployment explicitly in this paper, but our future work
will focus more on extending the proposed schemes to the
situations.
6.2 Time-varying mobile networks
The proposed schemes described above are based on a
static network topology. However, the network environment
continuous change with the normal running [24]. The
proposed schemes can also apply to a time-varying network
scenario. For example, in UAV-assisted VANETs, smart
cars are mobile and have a line of sight towards a specific
UAV with an environment-dependent probability. Due to
the mobility of IoT nodes in VANETs, we will take
the probabilistic performance of proposed schemes into
consider and try to find the design optimization of the
proposed scheme. One suitable expression for the LoS
probability is given by [43]:
PLoS =1
1+ψexp(−β[θ−ψ]). (29)
In such time-varying IoT scenarios, the proposed schemes
can be extended to the case of a variable velocity. When the
UAVs enter the sensing field to collect data, normally they
just construct the trajectory with our scheme, adjust velocity
according to the data rate constraints, slow down when they
are close to the IoT node.
6.3 Energy consumption of rotary-wing UAVs
The limited on-board battery of the UAV can not support a
long redundant flight. Therefore, it is imperative to consider
the energy consumption of the UAV when planning trajec-
tory. In general, the UAV energy consumption is evaluated
with respect to three realistic cost functions—the commu-
nication related energy (Pcom), the propulsion energy (Ppro)
and the hovering energy (Phov). The communication related
energy consumption can be ignored due to its smaller value
when compared with the consumption caused by the UAV’s
movement [44]. As discussed in [45], for a rotary-wing UAV
with speed v, the propulsion power consumption can be
modeled as
Ppro =P0(1
v+3v
Utip2
)+P1v−4+1
4V0−1
2V01/2
+1
2d0ρsAv2,(30)
where P0and P1represent the blade profile power and
induced power in hovering status, respectively. Utip is the tip
speed of the rotor blade. V0is the mean rotor induced velo-
city in hover. d0and sare the fuselage drag ratio and rotor
solidity, respectively. ρand Aare the air density and rotor
disc area, respectively. The hovering energy Phov can also be
obtained by substituting v=0into(30). It is observed that
the energy consumption is quite complicated. This paper
does not go into a lot of detail about the UAV’s energy
optimization but our future work will focus on this respect.
7 Conclusion
In this paper, we have analytically investigated the trajectory
planning for the UAVs in IoTs. A simple yet efficient
trajectory planning strategy, PATP, has been proposed to
achieve the balance between the collection precision and
the computation load. We further proposed an OD-PATP
scheme, which takes the realistic energy consumption
and the different sensing demands of the IoT nodes into
account. The proposed schemes shed light on the impact
of different parameters on the trajectory planning, and
the corresponding analytical results serve as guidelines in
the design of more sophisticated data collection solutions.
We have theoretically evaluated the performance of the
proposed schemes from the trajectory length and the time
complexity. Our results have shown that the proposed
schemes outperform the traditional algorithms, i.e., TSP,
COM, CSS. Our future work will focus on applying the
proposed schemes to more complex network, i.e., the Multi-
UAVs task scheduling, the varying-time network scenario
and the UAV energy optimization.
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Publisher’s note Springer Nature remains neutral with regard to
jurisdictional claims in published maps and institutional affiliations.
Zuyan Wang is currently
working toward his Doc-
tor’s degree at the School of
Cyber Science & Engineering,
Southeast University, Nanjing
China. His research interests
include Wireless Rechargeable
Sensor Networks (WRSNs),
secure communication and their
applications in the Internet of
Things(IoTs).
Author's personal copy
Peer-to-Peer Netw. Appl.
Jun Tao received the B.S. and
M.S. degrees in computer sci-
ence from the Department of
Computer Science and Engi-
neering, Northeast University,
in 1998 and 2001, respec-
tively, and the Ph.D. degree
in computer science from the
Department of Computer Sci-
ence and Engineering, South-
east University, in 2005, where
he is currently a Full Profes-
sor and a Supervisor of Ph.D.
candidates in cyber science
and engineering. His research
interests include social net-
working, D2D, and information security
Affiliations
Zuyan Wang1,2,3,4 ·Jun Tao1,2,3,4 ·Yang Ga o 1,2,3,4 ·Yifan Xu1,2,3,4 ·Weice Sun1,2,3,4 ·Xiaoyan Li1,2,3,4
Jun Tao
juntao@seu.edu.cn
Yang Gao
yanggao@seu.edu.cn
Yifan X u
xyf@seu.edu.cn
Wei c e Sun
sunweice@seu.edu.cn
Xiaoyan Li
220171697@seu.edu.cn
1School of Cyber Science and Engineering, Southeast University,
Nanjing 211189, Jiangsu, China
2Key Lab of CNII, MOE, Southeast University, Nanjing 211189,
Jiangsu, China
3Purple Mountain Laboratories for Network and Communication
Security, Nanjing 211111, Jiangsu, China
4Key Laboratory of Computer Network Technology of Jiangsu
Province, Nanjing 210096, Jiangsu, China
Author's personal copy
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